Transcripts!In this file we present the combined transcripts of all the lesson videos, for your reference.!!Lesson 1: Sirius B!!V1.1 BRIAN: So Paul, in this series of lectures we're going to be talking about the part of the universe that I really like-- the deep, dirty, secret underworld of black holes, neutron stars, supernovae. The violent universe. This is really what I love about astronomy and cosmology. !!PAUL: Yeah. And to my mind, this whole story really starts in the 19th century with the discovery of something very strange and very massive-- of orbiting the star Sirius B. So we're going to start off with that story now. !!The story starts, actually, hundreds of thousands of years before. People were trying for a very long time to measure the parallax of stars.The idea is, as the Earth goes around the Sun-- as Copernicus told us it is-- our point of view varies. And so the star should appear to wobble backwards and forwards. !!BRIAN: This is the old thing where I always go like this with my thumb. And I blink eyes. And my thumb moves relative to the background. !!PAUL: Yup. And no one had ever discovered this. The stars just did not appear to move. As the Earth went round the Sun, the stars did not seem to move to extreme precision with regard to each other. In fact, the Inquisition used that as an argument against Galileo. They said look, if the Earth really is going around the Sun, the stars should appear to move. And they don't. !!BRIAN: Right. And even the Greeks used this to try to figure out how far away things were, unsuccessfully. !!PAUL: It has been used successfully to work out how far away the moon was, and the Sun was, and things like that. But of the stars-- we couldn't measure it. And people had been trying for a very long time. There'd been lots of false claims of discovery. But the telescopes at the time just weren't good enough. !!And that's where a German by the name of Utzschneider comes in. He-- back then, in the early 19th century, the British had a monopoly on high quality optics. All the best telescopes and surveying instruments came out of the workshops mostly in London. And the Germans weren't very happy with this. There was huge demand across Europe, mainly for military surveying purposes, for precision optics. !!And so it turned out that Utzschneider had been called to a collapse of a house. And this guy had been rescued from the ruins after several days. You see nowadays, there are earthquakes. And they find someone gone, and there's huge media coverage. He was the equivalent of that when this house collapsed. !!And Utzschneider and the Prince of Bavaria decided to sponsor his education. And this guy is Fraunhofer, a very famous optical engineer and astronomer. We'll hear lots about him as time goes on. And he was given the job of setting up a company to rival the British and develop superb optical instruments. !!

And he set about doing a different approach. Previously it had been pretty much trial and error. Let's take this glass. Ooh, maybe this one fits. Just try lots of things. He decided, yeah, that's good. But we need to combine it with some actual real understanding of the physics of light. !!BRIAN: So Fraunhofer was the first person to really go through and be a serious optician. And that sort of caused a revolution in our ability to do astronomy. !!PAUL: Yes. And built brilliant telescopes. We haven't got one f his telescopes here at ANU. But we have got one very similar one. So let's go and have a look at that and talk about some of the innovations that he came up with. !!A common mistake people make when buying telescopes is they get a really powerful telescope, but put it on a really flimsy mount. Fraunhofer wasn't going to make as elementary a mistake like that, but many of the earlier telescopes did. For example, the great Melbourne telescope-- the biggest in Australia for many years-- was a very powerful telescope on a really shaky mount . They'd never get good data. !!This is a sort of mount Bessell invented: what's called a German mount. It's very sturdy. There's concrete. It has thick bits of metal and bars. Counterweights. We can use counterweights so you can push a telescope around with only a very small amount of force. !!There's this axis here, which points at the celestial pole-- in this case, the south celestial pole because we're in the Southern hemisphere. And so the telescope rotates around this axis. It can track anything across sky with just a single rotation. !!Then there's a declination axis-- this one here, which comes through there, which will now just point north or south in the sky. And everything is counterweighted. So there's a counterweight over there, so it's easy to move. !!In fact, as an even better trick, the telescopes were designed to automatically follow things as they move across the sky. Actually, of course, they're not moving. What's happening is the Earth is rotating. !!Here it's powered by clockwork. We wind up a weight here. We wind up a weight, which is in the middle of here. And as the weight falls, it drives a set of gears controlled by the spinning regulator, which will automatically rotate the telescope to cancel out the movement of the Earth, and keep you lined up on target. !!One innovation in Bessel's telescope was that the main lens was actually cut in half. And the two halves were put on sliders, which could move up or down with respect to each other. And you could measure with little screws precisely how much you moved them. This meant you got two images of whatever part of the sky you're looking at, rather than just one. !!Why would you possibly want to do this? Well, the idea was they were trying to look for parallax, the very slight wobble of stars. And the way they'd measure it is by reference to other stars in the field. And what you do you is you take the star you're interested in, and line it up with a second image of another star in the field. And then over the year, you could see by how much you'd need tweak the adjustment to keep it lined up And those tiny tweaks would tell you the amount of parallax. !!V1.2 BRIAN: All right. So we have a great set of telescopes, two telescopes that Fraunhofer made. And to get the most out of a good instrument, you need to have a great experimentalist. And it turned

out Fraunhofer gave-- his telescopes were used by two great early astronomers. And none more important than this astronomer, Bessel. !!And so, Bessel was not just an experimentalist. He was also a mathematician. There's a very famous set functions-- Bessel functions-- that he was involved with it. I won't say invented them. But he was involved with their tabulation and things. And so, he was able to get the most out of this telescope that he was given. !!PAUL: He used to say that every telescope had to be built twice. First of all, it was actually built when it was originally manufactured. But secondly, you had to-- when you observed with it-- understand every single piece of it, and all the things that could go wrong. So for example, whenever he got delivery of a new telescope, he wouldn't start taking data for possibly two years. He'd spend two years trying it out, measuring everything that could possibly go wrong, all the systematic errors. !!He worked very hard at these telescopes. In this telescope, for example, he had to work out exactly what angle corresponds to the shifting of the two halves of the front lens. He had to work out how the whole thing would bend, depending on gravity. As the temperature changed, the screw that controlled the two halves of the mirror would change because of expansion and contraction. He calibrated all that. !!In fact, he often spent a lot of his time going to look at other people's data, and recalibrating it. He was able to show, for example, one of his assistants always measured the stopwatch 2 seconds too late. Because he looked at how the timing of the different stars in different parts of the sky, and found on one side it was always 2 seconds off from the other side. So he actually spent a lot of his time going through other people's data from other astronomers, and analyzed in great detail what we now call data reduction, what we both spend a huge amount of our time doing. !!When you observe, you're only half-started. Most of the work is afterwards, trying to find all these possible systematic errors, and weeding them out, and fixing them. !!BRIAN: So this is exactly what a modern scientist of the day would use. He only spent two years working on his telescope. Our own SkyMapper-- we've had to work six years to get all its issues, and we're continuing. Part of my daily work is to go in and try to weed out all those systematic errors, in the same way that Bessel really started doing. But when you do it, then you get good quality data. !!And I can tell you that good quality data, no matter how smart you are as a mathematician, you always do better if you have good quality data. !!PAUL: And so, at long last, he measured parallax. He actually was able to see a star wiggling. He didn't trust his own--he published his own data. He wasn't the first to measure it, but he was the first person to measure it and be believed. Because he was so careful and precise. !!It's much like with your discovery of dark energy. There were plenty of other clues before, but you were the first-- actually the data was so good that people actually believed it. !!When he measured it, he thought, I'm not quite sure. So he then closed down the observatory, took the telescope to pieces, rebuilt it again, and then measured it again to make sure it was still that after everything had been rebuilt from scratch. !!BRIAN: That's being very dedicated. !!PAUL: And it was still there. And this is the level of dedication that made him famous. And he was really believed. And he was one of the great astronomers of the time, brought great prestige to Prussia back then. !

!So he'd found parallax. But what we're concerned with is another discovery he made a few years later. He was out looking for parallax around more stores. And he recognized-- this is a picture I took three nights ago. Here's Orion. And up there is the brightest in the sky-- Sirius. !!BRIAN: The dog star, yes? !!PAUL: The dog star. And he decided to try and look for a wobble in this. And he found a wobble. But not the wobble he expected. !!BRIAN: A much bigger wobble than he was expecting. !!PAUL: And of wobble not with a one-year period, as the Earth goes around the Sun, but a 50 year period. !!BRIAN: Right. And it was a very large wobble that was on order of 7 arc seconds, which would be-- we now know is an order of magnitude more than the parallax measurement of this star. And so you can see Sirius is moving in a nice ellipse. And the reason why stars move in ellipses is typically because they're in orbits around other stars. !!But in this case, the star isn't very bright. Sirius is very bright. And whatever it's orbiting-- not very bright. !!PAUL: Yes. Sirius weighs about twice the mass of the Sun. It's a luminous star. And clearly, you can tell there must be something maybe-- if it's over here, it must be over that way. As they go round, they're opposite each other the whole time. So there's something there. Must be quite a lot, because it's making Sirius move a lot. It couldn't be a planet. It's got to be much heavier than a planet. But we're not seeing it. !!BRIAN: So Paul, you should be able to use that orbital motion and calculate the star that we cannot see. !!PAUL: OK. Let's go and do that. !

V1.3 PAUL: OK. So what are the properties of this thing that's making Sirus go in a circle? So what do we know? Well, we have Sirus. We know it has a mass m1-- is about twice the mass of the sun. So that's about 4 by 10 to the 30 kilograms. !!And it's going in a circle. I do know the radius of the circle. It's about 7 astronomical units. An astronomical unit is the distance from the Earth to the sun. So an AU is about 1.5 by 10 to the 11 meters. !!Actually, the orbit is not a circle. It's an ellipse. But we're going to approximate it as a circle to make the maths a bit easier. The answer will come out pretty close to the right one. !!So what can make a star move in a circle? Presumably you've got Sirus, and there's a center of mass of the system. And then somewhere on the other side of that center of mass is our mystery object. !!And we've got m1 here, r1 there, r2 here, which may be larger than r1, as I've drawn here or maybe smaller-- we don't know. And we've got some unknown mass m2. !!

And what we want to work out is what the mass of the second object is. And we're probably going to have to find out how far out it is as well. !!So how can we do that? Well, there are two unknowns-- the mass of the second object, and how far out it is. So we're going to need two equations. !!The first equation comes from the definition of the center of mass. If you have any system, it always orbits around the center of mass, and the definition of center of mass is that m1 r1 equals m2 r2. !!So if this object is heavier, this distance will be smaller. If it's lighter, it'd like to be further away to balance out. So this is just like a scale, or a balance, or a seesaw, or something like that. If the weight is small, it must be far out to balance the big weight close in. !!So that tells us some idea of what the mass must be. If, for example, r1 and r2 are the same-- so they're orbiting around a point halfway between-- then the masses must be the same. If m2 is twice as far away, it must be half as massive. But by itself, that doesn't solve the problem. It simply tells us for a given r what the m is. But we don't know which actual combination is the right one. !!So what else can we do? Well, if Sirus is moving in a circle at some velocity v, for anything in fact to move in a circle with velocity v there has to be a centripetal force towards the middle. I'll call that force centripetal. !!Whenever anything moves in a circle, it's accelerating. While its speed may be the same, its velocity-- which is a vector-- is changing, because it's changing in direction. And that force is equal to mv squared over r. Or, in this case, that's m1 v1 squared over r1. So these are all properties of Sirus. !!So we can work out what that force is, because we know the mass of Sirus. What's its velocity? Well, we don't know the velocity, but we know that it goes in a complete orbit every 50 years. That's the orbital period. !!Now the period is going to be the distance for us to travel, which is a circumference of the circle, which is 2 pi r1 over the velocity it's traveling at. So the velocity is therefore just 2 pi r1 over the period. !!OK. So we can calculate this. But what's supplying that force? Something has to be supplying this force to make it go in a circle. That's innate centripetal force-- it's not a real force. You can't be hit by a centripetal force. It's just that force that you need to make something go in a circle. It has to be supplied by something else. If you're spinning a string around your head, it'll be the tension in the string. In this case, it must be gravity that's doing it. !!So this must be equal to the gravitational force. So we get the centripetal force that we need-- m1 v1 squared over r1 is equal to the gravitational force of the mystery object on Sirus. !!Now gravitational force is given by Newton's law of gravity. So it's G m1 m2 over the distance between them squared. Distance between them is r1 plus r2 all squared. !!So that's our second equation. We can cancel the mass of Sirus in this. And so once again we have an equation which relates the mass of the mystery object to how far out it is. !!So what do we do now? Well, we could combine these two equations-- substitute, say, this one into that one-- and solve for the answer. The trouble is that gives us a cubic equation, one that's either r cubed or mass cubed, which is a bit painful to solve. Perfectly solvable. You can plug it into a symbolic maths program and get the answer out, but it's long and messy and beyond the scope of this course. !

!However, we can estimate the answer by drawing a graph. Let's rearrange this to get the m2. So we get that m2 is v1 squared over r1 squared times r1. What I've done is I've multiplied top and bottom by r1 for reasons that will become clear in a moment. r1 plus r2 squared over G. !!But we know that the velocity is given by this. We know that v1 over r1 equals 2 pi over p. So we can substitute that into here. That's why I put the square on both sides. We can just square the entire thing. And so we find that m2 is 4 pi squared over g times the period squared, r1, r1 plus r2 squared. !!OK. So we have two equations. We have this equation, which can be rearranged as m2 equals m1 r1 over r2. So it's an equation for m2 as a function of r1. And we have another equation for m2 as a function of r1. !!So we can plot a graph. So if you plot the value of m2 against an assumed value of r2. So let's have this in astronomical units. So we'll go 5, 10, 15, 20, 25. And over here we'll have the mass in units of 10 to the 30 kilograms. That's 10 to the 30, 2 by 10 to the 30, 3 by 10 to the 30, and 4. !!OK. So if you plot this equation, we'll see that as r2 goes up, the mass is larger. That make sense, because we're looking at this equation as telling us how big the mystery object must be to apply the necessary force. And if it's further away, it has to be more massive to apply the necessary force. !!So we can plug numbers into here. Remember to convert r from astronomical units into meters, convert period from years-- 50 years-- into seconds, to gravitational constant 6.67 by ten to the minus 11. !!And we get a graph of five astronomical units. You got a point, something like that. 10 astronomical units is something like this. 50 units up around here. 20, it's up around there. Some sort of curve like this. !!So the mystery object, if it's far away, would have to weigh two times the mass of the sun. If it's close in, it would be less than half the mass of the sun. !!Then we can take the other equation, this one here, and plot that. So if r2 is 5 astronomical units, then that gives us a mass way up here. If it's 10, it's down about there. Once again, just plugging the numbers in. 50 units, something around here. 20 is going something like that. !!So in this case, we're looking at the center of mass. So if the second object is far out, it has to be lighter. And so what you can see is the two curves meet somewhere like that. !!So the second object, whatever it is, must be somewhere between 10 and 15 astronomical units from the center of mass, and has a mass of about 2 by 10 to the 30 kilograms, which is about the mass of the sun. So we're talking about something about the mass of the sun orbiting Sirus. !

V1.4 BRIAN: All right Paul. So you've shown us that this missing star weighs about the same as our Sun. !!PAUL: Yes. We've got something dark going around, opposite in the orbit. And it's pretty heavy. !!BRIAN: And our Sun is pretty bright. So at the distance of Sirius, which is less than 10 light years, the Sun would be actually easily visible with our naked eyes. So, where is it? !!

PAUL: So we need something with the weight of the Sun, but much fainter. Now, obviously the thing is go and try and look much harder. It wasn't possible with Bessel's telescope-- brilliant thought it was. But, 50 years later-- the best time is every 50 years, when these things are at the furthest point apart. 50 year later, the crown of telescope engineering had passed from the Germans to the Americans. !!BRIAN: Right. And so Alvan Clark and sons were out testing an 18 and 1/2 inch refractor, the largest refractor of the day. And by accident, they were looking at Sirius, just to check out the lenses. And they saw the little companion. And they didn't really realize what was going on. But just down the road-- this was all happening in Massachusetts-- just down the road at Harvard College Observatory, using the great 15 inch refractor that's still on top of Harvard College Observatory-- and I've had the opportunity to actually use-- it was spotted again by an astronomer. And they immediately realized the significance of the find. That the star had been identified. But it was really faint. It was about 1,000 times fainter than Sirius. !!PAUL: Yeah, I mean, here's a modern Hubble Space Telescope image. So there's Sirius-- very, very bright. And there is what's called Sirius B. So this thing that weighs the mass of the Sun is 1,000 times fainter. So this is about 2 solar masses. That's about 1 solar mass, a factor of about 2 in mass, but a factor of 1,000 in brightness. !!BRIAN: And you know, one of the ironic things here in the story is that these little things you see here is part of an Airy function, that describes diffraction. And we mathematically write those down as Bessel functions. So Bessel came back in a way that probably he didn't expect. !!PAUL: Yeah. So what is it that is 1,000 times fainter than Sirius, but still weighs the mass of the Sun? Or, how do you make something faint? !!BRIAN: Well, the easiest way I know how to make things faint is to make it cool. Because things that are hot-- which, they glow. The hotter you make something, the more it glows. It actually comes up with a law, we call the Black Body law. And so it's a very high power. It's the 4th power of the temperature tells you how luminous something is. So we would expect this to be very cool. !!PAUL: Yes, that was the expectation. The idea was that this was a star, but a very cool one. Probably not that different in size from Sirius-- physical size-- much cooler. You have to bear in mind, looks like the star is about this big. That's not really the size of it. It's actually far smaller than a pixel, as is this one. All of this is just spreading out due to the immense amount of light. So both these things look like dots. !!BRIAN: Yep. !!PAUL: So, yep, a hot-- Sirius is about 10,000 degrees. And this one, to be so much fainter, must be a lot cooler. !!BRIAN: Yep. !!PAUL: That's what people thought, until a few decades later, you get more powerful telescope. Now we had the Hooker, a 100 inch reflecting telescope at Mt. Wilson in California, the biggest telescope in the world. !!BRIAN: Right and that's because the Clarks made the largest refractor at Yerkes a 40 inch. And that sort of made the lenses start sagging. And it didn't work very well. And so you could do better with a giant mirrored telescope. !!PAUL: And they'd measure the spectrum of Sirius B, this little thing. This image is not quite to scale. Actually both these things would be much smaller relative to their separation. !!

BRIAN: And it takes 50 years to do this. So it's a little easier to catch than it looks like on this diagram. !!PAUL: But when you look at it-- the spectrum-- they found that in fact, from being cool, it was hot. In fact, hotter than Sirius A. So we knew it was very blue color. And the spectral features that indicate heat. This is 1,000 times less luminous than Sirius A, but had a surface temperature of about 25,000 degrees, whereas Sirius was only 10,000 degrees. !!BRIAN: So that's against my initial reaction. Because as I told you earlier, that the luminosity of an object is its area-- this is a black body-- of things that are hot, glowing, like for example, a hot poker or something you get glowing red hot-- is the area, so 4 pi r squared, the surface area of the sphere, times the Stefan Boltzmann constant, times the temperature to the 4th power. And so that would mean that the area would have to be tiny in order to make this thing 1,000 times less luminous. !!PAUL: Yeah, it seems impossible. I mean, this would have to be so small, given it's so hot. Every square meter of the sun's putting out huge amounts of power. So to be as faint as it is, it would have to be absolutely microscopic. So let's go and work out how small it would have to be. !

V1.5 PAUL: OK. How small will Sirius B have to be to give such a low luminosity? Luminosity is 1 over 1,000 that of Sirius A. So that's Luminosity of B over A equals 1 over 1,000, despite its high temperature. !!Well, the luminosity of an object is proportional to its surface area, times temperature to the 4th power. That's the Stefan Boltzmann equation. But the area, the surface area of something, is just proportional to its radius squared. That's 4 pi r squared-- the surface area of a sphere. So now the luminosity is proportional to r squared, t to the 4th. !!So, Luminosity B over Luminosity A, which is equal to 1 over 1,000-- it's going to be equal to r, B squared, T, B to the 4th over r, A squared, T, A to the 4th. It's just using this. It's proportional to, not equals to. But the constant will be the same in both cases. So you can divide the two luminosities. The constant will cancel out. And you get the ratio of the radii, and the ratio of the temperatures. !!Now, what do we know here? Well, we know the two temperatures. We know the temperature of B is 25,000 Kelvin, whereas temperature of A is about 10,000 Kelvin. We know the radius of A, which is 1.2 by 10 to the 9 meters. !!So let's rearrange this. What we don't know is the radius of Sirius B. So let's rearrange it. So we have that r, B squared equals L B over L A, r, A squared, T, A to the 4th, all over T, B to the 4th. !!Take the square root. And we end up with r B equals R A, times the square root of the luminosity ratio, times the ratio of the temperatures squared. !!Now, we can substitute the numbers in. So we know our r A. We know the two temperatures. And we know the ratio of the luminosities. And this comes out as about 6 by 10 to the 6 meters, which is 6,000 kilometers. Which is actually not star-size. That's smaller than the Earth. Radius of the Earth is 6,400 kilometers. So we're talking about something with a mass of the Sun and a smaller size than the Earth. !

V1.6 BRIAN: That's absolutely amazing. You have something that weighs as much the sun, so 2 times 10 to the 30 kilograms. And the radius that you just calculated-- assuming it's a black body and

that's what stars are, to first order-- is only 5,800 kilometers. That's less than the radius of the earth. So you've got something the size of the sun, or the mass of the sun, crammed down in something the size of the earth. !!PAUL: You see, we've got the density. Just divide the mass by the volume. Volume of the sphere, 4/3 pi r cubed. And you come out by 2 by 10 to the 9 kilograms per cubic meter, 2 billion kilograms per cubic meter. !!BRIAN: Right. So that's a huge amount relative to water which is, for example, 1,000. !!PAUL: Yeah, you find out if you had a teaspoonful of the stuff, it would weigh 10 tons. !!BRIAN: Well, on earth, at least. That's under the earth's gravity. So the gravity on the surface of the star must be enormous. !!PAUL: Well you can calculate that as well. Let's say, for example, what's the force on a typical, let's say, roughly 100 kilogram person? You can use the usual Newton's law of gravity, and plug in the mass. Mass is the same as the mass of the sun, but the radius is much smaller. So the gravity-- and of course it depends on 1 over radius squared. So that means the gravity's going to be way higher than the earth. That's because the mass is much higher than the earth, with a tiny radius. But it turns out the force is about 400 million newtons on a typical person. !!BRIAN: Ooh, so that is a lot more than, for example-- that's as like, I would weigh-- well, I don't quite weigh 100 kilos yet, fortunately-- but that means I would weigh about 40,000 tons rather than what I would weigh here on earth. !!PAUL: Yeah, so about as much as any oil tanker or something like that. !!BRIAN: I don't think my bones and body would do very well if I weighed that amount. !!PAUL: Yeah, so this gives us a puzzle, because we've got something that's very hot, and absolutely incredible pressure, presumably, from all this gravity forcing down. Surely that means it's going to undergo nuclear fusion. I mean, we know that nuclear fusion-- like hydrogen, most of the universe is made of hydrogen. So our first guess must be that these are made of hydrogen, like every other star that we know about. And if you push hydrogen together with enough pressure and temperature, the hydrogen nuclei will fuse and generate energy. So presumably, this is a very good place to have nuclear fusion. !!BRIAN: So we should able to calculate pretty straightforwardly the pressure and the temperature type conditions and compare it to, for example, our sun. And see if we expect fusion to be going on. !!PAUL: OK. So let's do that. !

V1.7 PAUL: OK, so how do we work out the pressure in the middle of a star? I should warn you that this video we're going to be using some rather more advanced maths than we've used elsewhere in the series of courses, in particular calculus and integration. If you don't feel up to this, feel free to skip over this video and just go onto the next one. But if you're up for a challenge. let's go. !!So let's imagine we have a star, a sun or a white dwarf, or something, and it's got pressure in the middle. How can we work that out? Well, all the outer parts of the star are being sucked by the immense gravity of the star towards the middle. !!

Why don't they collapse in towards the middle? Well, there must be some force pushing out to hold them where they are. And that force is caused by a pressure gradient. What it means is the pressure in the middle must be bigger than the pressure out here. !!So let's zoom in-- surface of the star. And let's take a cylinder of gas somewhere in the interior of the star. Now it's got an area, A, on top and bottom. And a thickness which is quite small, so we'll call it Delta r, that being the calculus notation for a small amount of radius. !!And this cylinder is going to want to have a mass. The mass of the cylinder is going to be its volume, which is A, area, times the thickness, r, times the density, rho. We're going to assume unrealistically that the density is constant throughout the star in this calculation. In reality of course, density increases towards the middle, but this approximation will get us a rough answer. !!So we've got that-- that's the mass. So there's going to be a downward force, due to gravity acting on that mass. How much is the gravity? Well, there a clever trick. You may remember, in a previous course we did this with respect to dark matter. !!We could divide the star into two bits. We can divide it into all the bit that's further down than the cylinder, and all the bits that are further up. And it turns out that the net gravitational effect of all the bits that are further up cancels out, has no effect, so we can treat everything below it as if it were a point in the center, with the same mass. !!So what's the mass of everything down here? We'll call that Mr, the mass of everything up to radius r in the star-- this is the radius, r. And Mr is just going to be the volume below that, which is the volume of a sphere, which is 4/3 pi r cubed, times the density. !!So that's the mass. And that mass, acting from here, will apply gravitational force downwards. So that force is going to be combined-- Newton's Law of Gravity, G Mr M-- this mass here of this littler cylinder-- over r squared. !!OK, so we've got a gravitational force pulling downwards, but in steady state. Level of the gas doesn't shrink down. It might do that in the middle of a supernova explosion, but normally it's just sitting there. So there must be some equal and opposite force pushing it up. And what's that force? Well, the pressure here must be a little bit more than the pressure up there. !!What Is pressure? Pressure is just all the molecules zooming around, and banging into surfaces. So there must be more molecules, or they're moving faster, which means a bit hotter at the bottom. So as they all bounce off here, a bit less bouncing off there. !!So there's going to be a pressure gradient. So that's going to be a delta p, a change in pressure from the bottom to top, and that implies an upward force to balance out the gravitational force. So let's balance those things out. !!The pressure force is going to be a pressure-- is the force per unit area, so the total force in the pressure is going to be the area times delta p. So it's area times p at the bottom lines, area times p at the top. That's speaking of change in pressure. There's going to be no sideways pressure, because the effects on all sides will be equal and opposite. So it's only difference from the top to the bottom that matters. !!So that's the pressure force, and that equals G Mr M, over r squared, over here. Now we know what Mr is, so we can substitute that in and get G over r squared, times 4/3 pi r cubed, times the density. That's Mr. Now what's this M, that's given up here? So that's A delta r rho. !!So what we can see is that we have an area on both sides that cancels out. So we've got difference in pressure, and the difference in radius here. So we've got two small changes. We take

the ratio-- that's what you do in calculus. So you get dp by dr, and that comes out as 4/3 pi-- we've got r cubed over r squared, so it just comes out as r-- G, times the density squared. !!You have to be a bit careful about the sign here. This is how much the pressure increases at the bottom. If you're measuring how much the pressure decreases, there'd be a minus sign here. It all depends which way you define things. But let's leave it at that for the moment. !!So that's given us the pressure gradient. This is a small change in pressure over a small change in radius. What we could do in true calculus fashion is take that to the limit. So make them both go small, but preserve the ratios. That's dp by dr. !

V1.8 PAUL: In our last video, we calculated the pressure gradient-- dp by dr-- how rapidly the pressure needs to decrease as your distance from the center of a star goes up, so that it balances gravity. And we came up with this equation here. !!In the current video, we're going to now use this work out what the central pressure in a white dwarf is compared to central pressure in the Sun. !!So if we have d pressure by d r equals-- I'm going to use a minus, so that as r increases, pressure goes down. You could define it either way, but-- OK. So we've got d pressure by dr. !!What we now need to do is work out what the central pressure is. So we know the differential, and we want the actual value-- we're going to have to integrate. It's definite integral, but we'll fix it by knowing that the pressure at the surface of the star is 0. !!So the pressure in the center is going to be the integral from the surface. I'll call that a big R-- the radius of the star-- down to the center, of minus 4/3 pi G rho squared. Those are all constants, so they can go outside the integral. R, dr. So it's basically the integral of r, which is 1/2 r squared. !!So this comes out as minus 4/3 minus pi G rho squared, r squared, over 2, from R to 0. Which just comes out has 2/3 pi G rho squared, R squared. !!So this is our equation for the pressure in the center of a star, if that star has uniform density all the way through. Not very realistic. But it'll give us a good enough estimate for our current purposes. !!But now how do we compare this in the Sun to a white dwarf? Well what we can see is that the pressure in the center is proportional to the density squared, times the radius squared. !!Now naively, you'd think that because the Sun had a bigger radius than the white dwarf, that means the pressure were bigger. But also the Sun has a much lower density. If we assume that a white dwarf and a normal star have the same mass-- say 1 or so solar masses each-- then the mass is going to be proportional to the volume, which is proportional to R cubed, times the density. !!So if we fix the mass, that means density is proportional to 1 over R cubed. So if you have two stars with the same mass, but one is 10 times smaller, its density must be 1 over 10 cubed times bigger. !!So what this means is the central pressure is proportional to density squared. And density is proportional to 1 over R cubed. That's 1 over R to the 6th times R squared. So that's proportional to R to the minus 4th power. !!So what this means is, if you have a star of fixed mass, if you make it smaller, the pressure in the middle goes up enormously, to the 4th power. So what this is telling us is, the pressure in the

middle of a white dwarf must be absolutely vastly greater than the pressure in the middle of the Sun. !

V1.9 BRIAN: So we've seen that the pressure of temperature in the middle of these things vastly exceeds that in the Sun. And it's a puzzle. I mean, if it's really so dense and so hot in the middle, why isn't it undergoing huge amounts of nuclear fusion? You should see immense amounts of nuclear fusion. But if it was fusing much faster than the Sun, it should be much brighter than the Sun was. You know, this thing is 1,000 times fainter than the Sun. What's going on here? !!PAUL: So clearly, it's not fusing hydrogen. Because if it were, it wouldn't look like it appears. So you could imagine it maybe being made out of something else that doesn't fuse. So for example, iron wouldn't fuse. But we don't even need anything necessarily that extreme. If we make something, for example, it's much harder to fuse helium and harder still to fuse things like carbon and oxygen and sulphur and silicon. !!So maybe these white dwarfs are made out of something that's much harder to fuse, where even though the density and temperature is enormous, it's still not high enough to make those nuclear reactions occur. !!BRIAN: But that's a bit strange. I mean, the universe as we know, by and large, is made of 80% hydrogen and 20% helium. So we need these things to be something quite different. !!PAUL: That's right. So we need to look at how you might make such an object. And of course, we could assume that this object just decided to form. But it had to get really dense to begin with. And maybe one of the easiest places to look for dense objects is in the center of stars, which are of course dense on their own. !!BRIAN: We'll come back to that. But to my mind-- it's actually a secondary problem. I'm sure it's made of some weird stuff. The real puzzle to me though is, how something this dense and this heavy can support its own surface. Because you've got the surface layers. There's actually incredible density and gravity sucking them down. Why don't they collapse down? !!I mean, on Earth, we're sitting in these chairs. And gravity's trying to suck us down. But luckily the chairs have got good strong chemical bonds that stop us from collapsing through the floor. But if we weighed 40,000 tons, those chemical bonds wouldn't do the trick. You can calculate how strong chemical bonds could be. And there's no way any chemical bond we could conceivably think of could resist the incredible pressure of these things. !!PAUL: Right. So we need to go through and come up with some way for this little star, for Sirius B, to push against gravity. And it can't be the normal forces that we see here on Earth or even that we see on the Sun. I mean, those chemical forces are what keep the Sun from collapsing down. !!BRIAN: Yeah, and the Sun, what's helping it is the heat coming out from the middle. That's what stops it from collapsing down. But there is no heat coming from the middle of these things. If there was nuclear fusion, as we know, it would be far too bright. So it's not heat coming out that's causing it. It's not chemical bonds. So, what could possibly stop it from just collapsing all the way down to no size at all? !!PAUL: So it strikes me that we have a couple tricks up our sleeves through the wonders of quantum mechanics, where we can go through and see how quantum mechanics can provide this extra force that we don't necessarily see here in this room. !!BRIAN: So let's talk about some of the weirdnesses of quantum mechanics. !

Lesson 2: White Dwarfs!

V2.1 PAUL: To understand how the white dwarf, Sirius B, can not collapse despite this immense pressure, we're going to have to delve into the wonderful world of quantum mechanics. And once again, this started in the early 19th century when people were first measuring good spectra. Fraunhofer himself was one of the pioneers in this, with the discovery that we you get a gas heated up, it gives a spectrum looking something like this. !!BRIAN: So this is essentially one of the-- it's a tube containing, in this case, copper and argon. And it's something we would put on a telescope. And when you put an electric charge to there, the thing glows like a giant neon sign. And when you take a spectrum of it, where we plot wavelengths versus intensity, you can see that all of the light coming out of this tube of copper and argon isn't just a black body rather you have discrete colors. !!So you have, for example, very bright places where there's a lot of coming out and then essentially nothing. And there are literally, in this case, hundreds of these spectral lines, as we like to call it, emerging from copper and argon. And it turns out, if we made a gas of hydrogen or something else, you get a different set of lines depending on what it's made out. !!PAUL: So this is really weird. Why, when you have a gas, does it emit light-- or absorbed depending on the conditions-- at particular wavelengths, not everywhere. Now, by the early 20th century, the standard model of an atom was something like this. You got the protons and neutrons in the middle and electrons orbiting around the outside. And then people were thinking it was like a solar system, only smaller. !!This is grossly not to scale. To scale, this is 100,000 times smaller than the orbits out here. You wouldn't even see it. But in some situation like this, it seemed to make sense. We knew our solar system had things sucked into orbits by the gravity. So we do the same thing here. You've got the positive charge in the middle, the negative charge on the outside so things would orbit. !!But the trouble is what if you get a charge that's moving in a circle. Moving in a circle requires centripetal acceleration. Acceleration means radiate, so it radiates energy and spiraling very, very quickly to the middle. !!BRIAN: Yeah, that's right because you get, every time an electron accelerates, it's going to put out some light. And in this case, you're going to have a bunch of orbits that can be in random orientations, and so you expect to get almost any color of light depending on the conditions of the orbit. And of course, it's not going to be stable. Eventually, you're going to end up with the electrons down in the center. !!PAUL: Also, the electrons could have any energy they like. There's no particular suborbits are allowed and some aren't. The solar system, we think, could orbit stably at any distance from the sun. So it could be any energy, so any wavelength. !!BRIAN: And yet we know that this-- whatever we think is going on-- you're going to get discrete little places where you have these energy coming out. So it's like they can only do certain things. So that's a funny situation. !!PAUL: It's really puzzlesome. Why does the stuff only put out particular wavelength? What's forbidding it from having a wavelength halfway between two of the lines or 25% in between? Well, people's thinking about this, and there is an analogy on Earth. There's a situation on Earth where you can get a spectrum which only has particular wavelengths on other ones, and that's actually musical instruments, discovered all the way back in prehistoric times. !

!So if we take a guitar and pluck the string, you hit a particular note. And I recorded that note, and here's what it sounds-- here's what its waveform looks like. So what you're seeing is air pressure varying. !!BRIAN: Well, it's quite a regular pattern. It's not a beautiful sine wave, but the pattern repeats. You can see this little thing here. And so you have a real distinct pattern when pluck a guitar string. !!PAUL: Yeah. When you pluck it, you hear a particular note. La. Not so much like sh if it was across all spectrum. It was a particular note. What you can actually do is a spectral analysis of this. This can be broken up into multiple sine waves by a mathematical operation called a Fourier transform. !!And here's what you get. So this is frequency and how much power is at that frequency. And what you can see is just below 100 Hertz, there's a lot of power. And then it just doubled that just below 200 Hertz, and a whole series of integer ratios to this. !!BRIAN: So you have 100, 200, 300, 400, 500, et cetera. !!PAUL: And a bunch of other ratios like 2 to3, 4 to 5. These are the harmonics which is what gives the guitar, or any other instrument, it's particular characteristic sound. But this is just what we like. We've got a spectrum which is low in the most part, but with a whole bunch of narrow spikes. There's a huge load of power here, but not halfway between this. So seems to work. !!BRIAN: OK. So let's think about why this occurs. Let's just look at what one of these strings is going on. !!PAUL: OK so here's a string. It's locked at both ends. And when you pluck it-- !!BRIAN: Boing! !!PAUL: --it could vibrate like this. So it's got a fixed point, what's called a node at both ends. And the antinode in the middle where it vibrates as much as possible. Right. And that will give you the fundamental note, the first, but then you can also do something like this. !!BRIAN: So that would be going twice as fast. !!PAUL: Yes, and that will give you the second spike. And you could also have third, fourth, fifth we wiggles. And so these are giving you the spike, the spike, the spike. In all cases, you have to have an integer number of wiggles from one end to the other because it sticks to both ends !!BRIAN: All right. So that is a way to get discrete things out of a musical instrument. But that means that we need to have some sort of discrete set of orbits or something for the electron inside of an atom. !!PAUL: Yeah. And for a musical instrument, you need two things. You need a wave, in this case, sound waves. And you need to block it in. So in the case of the guitar string with waves locked at both ends, in the case of a woodwind or something, it will be sound waves up and down a column of air, once again, with a barrier or some change at both ends. !!So in principle you could do this in three dimensions as well. So for example, if you had a wave trapped in a spherical cell, like if you make an electron a wave, which is weird. But if a particle is a wave, and you could look inside of an atom, it wouldn't be simple as one dimension, but you get actually patterns like these. !!BRIAN: So these are patterns in three dimensions. And you can see like this pattern is nice and circular, but then you get these clover leaf patterns and quite intricate looking flower patterns. !

!PAUL: Yeah. So these are the waves bouncing back and forth in different ways in three dimensions. And once again, you're getting standing waves just like you do from sound. So if the electron was a wave, we need a wave, remember, to make it work. We need to lock it in place. The atom will lock it in place. !!So we get a-- if it was a wave and we could lock it in place, then you would get a series of discrete, possible standing waves, which would give us a spectrum we like. But particles-- electrons are waves? That's a bit weird. !!BRIAN: Well, I think we're going to have to understand the basics of quantum mechanics then, Paul, because electrons do appear to act like waves, don't they? !!PAUL: Mhm. !

V2.2 PAUL: So we've got this really strange result, the fact that you get discrete energy levels, particular wavelengths. And the only way we can think of to produce it is if electrons are actually not particles, but waves. And waves trapped in a box, in this case, the box being the atom. !!BRIAN: Yeah. And that's not very obvious. Because when we look at electrons, and one of the places we see electrons are, for example, on an old style TV set, which is a giant cathode ray tube where electrons come and hit the screen and illuminate things. And there you're really seeing individual particles hitting. Nothing like a wave at all. !!PAUL: Yes. And then through a photomultiplier tube, you fire electrons. And you can see flash, flash, flash, flash, as each individual electron arrives. It sounds like a particle, then it travels here and there, and there. Not spread out. And waves by their very nature are spread out. !!BRIAN: Right. So this sort of lends itself to a new interpretation, which is that the electrons themselves are some sort of probability descriptions. So the wave is telling you where they might be at any given time. And when you measure them, suddenly know right where they are on that little wave. !!PAUL: This is a really strange idea. The basic idea is that these are probability waves. So you get the waves. As long as you don't look at them, they are waves, and they do all the interference and diffraction and standing waves that we need to get these discrete energy levels. But as soon as we look at it, the amplitude of the wave, actually squared, tells you the probability that a particle is there. So you take the waves and you say, well, it's going to probably be here or probably be there. !!BRIAN: And there are these places where there's almost zero probability of they're being, and that's sort of what pins the electron in to a little place. It can't actually be there. !!PAUL: The classic experiment that shows this is what's called the two slit experiment. You fire a beam of electrons at a board which has two slits in it. And you might think the electron either goes to one slit and land over there, or goes through the other slit and lands over there. So you see two stripes of little flashes along there. !!But in fact, as long as you don't look, what you actually see is a series of interference waves all the way along here. So it looks like the particles-- even when there's only one electron in the system at a time, as long as it's got two electrons interfering with each other, you can have it so there's only one electron in the whole experiment at the time. And it still seems to go through both slits and give an interference pattern, which is totally weird. !!

Let's go over this two slit experiment in a bit more detail. So let's start off with an electron gun over here and a phosphorescent screen over here. Electron gun is firing out electrons in a range of directions. Now what would we see here. !!What we'll see, is when each electron hits the screen, you get a little flash. There will be a flash there, then a flash here, then a flash there. More flashes in the middle, fewer towards the outside. Now, because each electron produces a flash, it looks like the electrons are just single particles. !!They may-- the electron is here, or here. It's not spread out in some way, because you're definitely seeing definite flashes. But overall, you know the flashes are more likely in the middle and less likely at the outside. So you get some sort of probability, bigger in the middle and smaller as you go away. !!Now what would happen if you put a slit-- a mask in front, with two slits. So there's one slit over here and then another slit over there. Now what you would expect? Common sense would tell you, is that an electron that hits there won't get through, electron that hits over there won't get through, electron that hits there won't get through. The only ones that are going to get through are the electrons that go through one of the slits. !!So what you'll see is a bunch of flashes over here. Electrons that wedge through the top slit, and a bunch of flashes down there from electrons that went down the bottom slit. And all the other electrons are just going to bounce off or get absorbed by the screen. That's common sense. !!What do you actually see? What you actually see is the most flashes occur about here. And you also get flashes appearing there, and there, and there, and there. So you've got a series of waves of flashes. So you get flashes here, here, here, here, here, here, here, et cetera, but not in between. !!No flashes halfway between there, halfway there, halfway there, halfway there, halfway there, halfway there. Which is weird, right? How can an electron fired out from here get through these slits and go there. And if it does go there, why isn't it going just next door, over here? Why is it here but not there? !!Now this all makes sense if, instead of electrons, we were talking about a wave, like radio waves. If we were looking at radio waves, you can imagine them spreading out from here. And then as they go through this aperture, they start diffracting out so you get waves coming out from that aperture, and the same from here. !!Now, if you are exactly halfway between, the waves travel the same distance here as there, which means all the peaks of the waves are going to line up. So you get good, strong constructive interference. But if you go a bit to the side, like over there, the waves from this bit have a bit shorter distance to go. The waves from this one have a bit of a longer distance to go. Which means that the peaks from one will line up with the troughs of the other, so they'll cancel out and get nothing. !!So this pattern-- signal, no signal, signal, no signal-- makes sense if electrons are waves, but it doesn't make sense if they're particles. But that's the puzzle. What we see at the screen is a flash, like I was saying, right there, right there. Not some sort of wavy thing. But how can particles behave like waves? !!And that's where the idea of the probability wave comes in. That they are waves, as long as you're not looking at them. And so they do all the interference things. And so the amplitude of the wave will be strong here, and low there, and strong there, and low there, and strong there and low there, and so on and so forth. Just like you'd get for radio waves. !!But then as soon as you actually observe, it collapses the wave function, and you get a definite spot in a different place. But the probability is given by the amplitude of this. This is a high

amplitude, this is a high probability of getting a flash there. Low amplitude there, so low probably of getting a flash there. Pretty weird. !!BRIAN: So Schrodinger came up with a sort of an analogy, which he called-- well, we now call Schrodinger's cat. So you can imagine, if you have a cat, so I do have a cat. My cat's name is Rodney. !!And you put him in a box. And in the box you put a very sensitive vial of poisonous gas that may break with some probability. And you don't know if that event has occurred until you open the box to see of Rodney is alive or dead. !!PAUL: So according to quantum mechanics, until you open the box, what's inside is not an alive cat or a dead cat, but actually one over root2 dead Rodney and 1 plus 1 over root2 alive Rodney. Two waves interfering with each other. !!BRIAN: Right. So there's a probability he's dead or alive. And you can figure out that probability, because what you do is you have more than one Rodney, and do the experiment a billion times, you realize that 52% of the time Rodney is dead, and 48% of the time he's alive. !!PAUL: Yeah. And this whole business about when don't know it, it's behaving like a wave, I mean, that sounds ridiculous. The short of it really is a live or a dead cat. But like in the two slit experiment, the fact that you don't know where particle is allows it to go through both, interfere with each other. So you could get some sort of strange interference effect between alive and dead Rodney which would give quite different results. !!BRIAN: Right. And when you open the box, then you know, and you know what's going on. You've collapsed the probability down to a value. !!PAUL: Now, a lot of people, myself included, don't like this very much. I mean, why should it matter whether someone's watching? Electrons do one thing all by themselves in the privacy of their own room, while no one's watching. !!But as soon as you look, suddenly everything collapses. What is it about us that makes it collapse? Is it something about the human brain or something? !!It just doesn't-- for example, can Rodney observe itself? It's very uncomfortable. But it actually seems to be how quantum mechanics works, and you just have to live with the discomfort of it. !!BRIAN: Yes. I have to admit, I do not find it easy to deal with either. But it is a way that describes the universe that we live in. !!PAUL: So quantum mechanics is weird. It's telling us that things are behaving like a wave when no one's watching and like a particle when we watch. And it turns out that is one of the crucial clues to explaining white dwarfs. Now let's go back and talk about the other two crucial clues quantum mechanics gives us to explain how a white dwarf can survive this immense pressure. !

V2.3 PAUL: So quantum mechanics is seriously weird. These things behave like waves when you're not looking, get privacy away all by themselves. And as soon as you look up, suddenly, it's a particle. But how's it going to help us with white dwarfs? Let's get back to the matter of physics now. The idea is that quantum mechanics, it can help us allow this white dwarf, Sirius B, to withstand this immense pressure. How is that going to work? !!

BRIAN: Well, I think it really comes down to quantum mechanics is even weirder than what we've already told you, because there are some other rules that are very counterintuitive So when you look at, for example, a hydrogen atom, these are the different places, the little energy levels that an electron can be around a hydrogen atom. !!But there's a rule that chemists have figured out four atoms heavier than hydrogen that have multiple electronics is that the electrons do not like to be in the same state at the same time. This is known as the Pauli exclusion principle. And so for example, if this were for example the ground state of iron, you might expect all of it's 26 electrons to pile down right next-- in the lowest energy state. !!But it's not allowed to do that. Indeed, it's only one atom in each state. And so they end up having to distribute themselves through all the different levels. And that turns out to give you a set of rules that means that you can't push things together very closely. !!PAUL: Yeah, so if our exclusion principle says that particles called fermions, which includes quarks. And hence, neutrons and protons and electrons can only have one energy state. It actually goes right down to some fundamental symmetry in their nature. But other particles, it can pile up in the same energy state like protons, for example. !!But the fermions owns can't, which, as every chemist knows, tells you start filling up the energy levels from the bottom and so and so up. It's interesting to think if electrons have not obeyed that rule, then everything would be in the ground state, and everything would be chemically like hydrogen. And so it wouldn't be possible to have life. Hydrogen can't do anything like carbon. !!BRIAN: But it would be so much easier to calculate. !!PAUL: Chemistry would be so easy. !!BRIAN: Yes, that's right. !!PAUL: But luckily, for the instance of life, there is this Pauli exclusion principle, and things can't all sit in the lowest energy state. Then, there is a second clue. It's called the Heisenberg Uncertainty Principle. Now p here is momentum. !!What it's telling us in x's position, what it's telling us is if you have an uncertainty in the position and an uncertainty when you're meant to multiply them together, it must be more than h bar on 2. H bar is Planck's constant divided by 2 pi. So what this is telling you is when you confine an atom to a very small space, cementing becomes highly uncertain. !!BRIAN: Right so if I can go through and say, the uncertainty in the position is tiny, then I'd end up not knowing much at all about it's momentum and usually velocity, but mass. !!PAUL: This is a generic thing about waves. If you think about it, if you've got a wave and you compress it into a small space, it must have a very short wavelength. Or short wavelength means lots of energy, so it's going to be moving like crazy. !!In some sense, this is actually what drives diffraction in telescopes we talked about in a previous course. If you have a wave going through a narrow aperture in a telescope, it bends out a lot. It's got quite a lot of momentum. If you have a wide aperture, it bends out less. !!So these are the two clues that are going to allow us to work out why white dwarfs like Sirius B can survive the Heisenberg Uncertainty Principle and the Pauli exclusion principle. So let's look at that. !

V2.4

PAUL: So how can quantum mechanics help explain a white dwarf? Well, let's think about the problem. We've got this small star with absolutely, incredibly intense gravity but no nuclear fusion going on. !!Now, let's zoom in on the surface. Here's a little surface layer. That weighs a lot, so there's very strong gravitational pull down towards the center. !!Because it's not falling in, it's just sitting there, there must be an equal and opposite force outwards to balance the gravity downwards. And remember because these things are so dense and so small that gravity is very intense, so it must be a very strong force outwards to balance the gravity. !!What is this force? Well, it's caused by pressure. But what is pressure? Well, pressure is just a cumulative effect of being hit by atoms and molecules. !!So what's happening here is the inside edge, and you got lots of atoms, electrons, protons, whatever. They're flying in, and they bounce off the insides in very large numbers. !!You don't get sore by getting hit by one atom. Ow! That atom hurt me. Oh, no. It doesn't matter. But there are so many billions upon trillions of atoms hitting that their cumulative effect can be quite strong, and that's what pressure is. !!So the idea would be that in a normal star, the pressure inside is very high, so vast numbers of atoms are bouncing off the inside of the surface layers. And their impacts apply enough net force to balance the downward gravity pull. But there's a problem. These items must be moving really fast to supply enough force, which means their temperature is high. But if they're very hot, the heat will leak out. The heat will radiate out into space somehow. It might be conducted through there and then radiated out into space. !!So they will get cooler and therefore slower. And it they're slower, there will be fewer impacts. The impact will have less oomph behind them, and so the pressure will go down. So no longer balanced, gravity and the star will shrink. As it shrinks, it compresses what is inside. It makes it hotter again. Once again that heat will radiate out, and so the whole star will shrink smaller and smaller and smaller until it's no size at all. !!So that doesn't work. What we need is something that stops these moving particles from slowing down below a certain speed, like a minimum possible speed. And that's what quantum mechanics, in the form of degeneracy pressure, gives us. What's the idea? Well, here we've got our star just shrinking, and it's got a whole bunch of electrons in it. !!Now, from the Pauli exclusion principle, we know that the electrons cannot all be-- no two electrons can be in the same state. So one way to think about that would be to divide a white dwarf into little cubes. And we'll put one electron in each cube. Now, the electrons could move back and forth inside the cube, but they can't trespass into another cube because that would be overlapping in a state with another electron. !!But now let's look at one of these cubes, and apply what we know about quantum mechanics. The electron, remember, it behaves like a probability wave. So let's, for the moment, just to imagine it's going to be a wave along one dimension. It could be, like a guitar string, in the ground state, which is something like this. Or, it could be in the first excited state. Or, it could be in the second excited state and so on. !!But it's always going to have an integer number of waves across the length. Now of any wave, whether it be a light wave or electron, the shorter the wavelengths, the more the energy. So the lowest energy will be this blue state. And the green and yellow lines have more energy, and so a state like this would be a very energetic state. !!

Normally, if you're on something like the Sun, most electrons are in states like this. They're in their little cube. They've got very wound up in terms of their wavelength, so that they have way more than the minimum energy. But what quantum mechanics tells us is the wavelength can get longer and longer and longer, but the longest it can be is when you only got onto wavelength covering the entire length of the box. !!And you can't be longer than that because then it would have to not be 0 at one end, so it wouldn't be a proper standing wave. And that is what the Uncertainty Principle encapsulates. It tells us delta p delta x is greater than h-bar over 2. So this is the momentum related to the energy, and what that's telling us is as the box becomes smaller, the longest wavelength you can have also becomes smaller, which means the momentum becomes larger. So there's a lower limit to the momentum corresponding to the size. !!I'm going to do a very approximate, very rough calculation to show how a white dwarf could work. The full calculation is too complicated for this course, but we can get the basic physics, a roughly right answer out by making some big approximations. !!So let's start off by thinking about electrons stuck in a box. This box could be 1 cubic meter of white dwarf material or 1 cubic meter of anything really. And let's assume we have a number of electrons per unit volume, so a number density of electrons of ne. So that's the number of electrons per unit volume. !!Now, all the electrons can't be in the same space because of the Pauli Exclusion Principle. They all have to have their own discrete identity, and they can't all sit in the same state. So each electron-- so we've got an electron there-- has to have its own unique volume. So assume each has a cube like this. As the electron is trapped in that volume, it's going to-- the size of this volume, the size of each side here, is the uncertainty in its position, delta x. !!And what is delta x? Well, each electron has a volume, delta x cubed, that being the volume of a square of each side delta x. And there are ne electrons in one unit volume. So what that is telling us is that delta x is equal to 1 over the cube root of ne. So that's ne to the minus a third. !!Now, if we have that uncertainty in its position, that means there's going to be uncertainty in momentum. So the uncertainty in momentum times uncertainty in the position is going to h-bar. That's Heisenberg uncertainty principle. So the uncertainty and the momentum is going to be h-bar over delta x. So that's going to be h-bar ne to the plus 1/3. !!So that tells us that the electrons are not still. They have momentum. There's an uncertainty in it. And that's going to be very roughly equal to momentum. Some are going to be going forward. Some are going to be going backwards. This is momentum in one direction. So roughly speaking, the uncertainty is going to be about the size of the momentum. So roughly speaking, again, not a very good approximation, but close enough for this work, the momentum is going to be about the size of the uncertainty. And it's given by this. !

V2.5 PAUL: So now, let's use our equation for the mentum to try and work out what pressure these electrons will exert. And once again, we're going to do this in a very approximate way. So once again, let's imagine we have a box. And there's one side of the box. Now, each electron-- let's assume that every electron is going either this way or that way or vertically or in and out. !!So 1/3 of the electrons are going back and forth this way, 1/3 are going up and down, and 1/3 are going front and back. This is an approximation. Of course, electron's going in all sorts of directions, but it's not going to be too bad. So that means the number of electrons going this way that might hit this wall is going to be 1/3 of the total. !

!So let's zoom in on that wall. So here is the wall. And we've got the number of electrons, 1/3 of the total, which are going either this way or that way. Now, what is pressure? Pressure is just the combined effect of the impact of all these things on the wall. So every time an electron bounces off the wall, it exerts a force on the wall. The wall exerts an equal and opposite force on the electron. !!So we want to do is work out the cumulative effect of all those tiny electrons bouncing off the wall because that will be the pressure, the force on square meter of wall. Now, one way we can work this out is that force is the rate of change of momentum. So if we can work out the mentum of all the electrons that are going to hit one square meter in a given time-- and they'll bounce off opposite-- that will tell us the total amount of momentum that changed in one second, and that will be the average force. !!OK, so how many electrons are going to hit this wall in a second? Well, this could be all the one going this way. The one's heading that way are not going hit the wall. And they've got to reach there within a second, which means they're-- we can draw an imaginary line around here where this is equal to velocity times the time, which is one second. !!And anything in there will have to be fast enough to hit the wall. The ones out there won't hit the wall. The second, they'll hit the wall, next second. So what's the volume here? It's going to be just the velocity times the area, which is 1. How many electrons there are going to be coming in? So it's going to be the pressure is going to be the number of electrons that are going left or right, which is 1/3 of the total. !!The rest are going up and down or in and out, so they are not going to hit this wall. But only half of these are going to be going the left direction, so we've got to have another half. Then times the number of electrons per unit volume times the volume, which is 1 by 1 by v. So that's v. !!But each momentum-- each electron that bounces off reverses, used to have a momentum, p. This way, after it bounces off, assuming it's elastic collision, it will have momentum the other way. So the change in momentum of each is going to be 2p. I should say this is a capital P. That's the pressure. This is a small p, which is the momentum. It's a bit confusing, I know, but we'll try and make it clear. !!So the pressure is the rate of change in momentum comes out as 1/3 the number density of electrons, typical velocity, and typical momentum. OK well, we know the momentum. We calculated it up here. What about the velocity? Well, if they're not going close to the speed of light, then the equation for momentum is just mass times velocity. If they are close to the speed of light, we'll come back to-- there's a gamma factor in here. !!But for the moment, let's assume the electrons are nowhere near the speed of light. So that means velocity is going to be the momentum divided by the mass of an electron. So if we plug that in, we find that the pressure-- I'll write it out in full so we don't get it confused with p for momentum-- is 1/3 number density of electrons, velocity, which is-- rearrange this. That's going to be p over typical mass of an electron times momentum. !!Momentum coming from over here. And if we substitute in our equation for the momentum, we get that pressure is equal to h-bar squared over 3 times the mass of an electron times the number density of electrons to the 5/3 power. OK. There's one extra complication we need to put in here, that we don't often know the number of electrons. What we know is the density of the material. So what is the number of electrons? !!The number of electrons in a given volume is going to be the density divided by the mass of a hydrogen atom. That will tell you how many electrons there were if it was entirely made of hydrogen. But it's not made of hydrogen. This is a carbon, oxygen thing. So we need something-- We need to correct it for the fact the atomic mass. We put an A on the bottom. !

!So if it was carbon, that would be the joint mass of carbon, so each carbon atom weighs 12 times the mass of hydrogen. So we're going to get 12 times its electrons. But also carbon has six electrons. Well, let's assume every single electron has been knocked out because it's so hot, they've all been ionized. So you got to put the atomic number at the top. !!So in this case, it's the density divided by the mass of hydrogen divided by the atomic mass, 12, multiplied by the number of electrons, 6. So this is going to be for carbon or oxygen. That's going to be about half the density divided by the mass of hydrogen. So we can plug that into there. The answer we get turns out to have all the right functional form but to be wrong by about a factor of 5. !!If you did a more careful calculation, you actually get a value of the constant, here, that's about 5 times bigger. So in fact, the true equation for the pressure in a situation like this is the rather unwieldy-- so our simple calculation got all the functional form right. It got the h-bar, the me, and all these things right. Just the constant comes out a bit different if you actually do the proper calculation of the electrons going in all directions. !!The most important difference, actually, is that in the real calculation not all electrons are going at the same speed. Some are going faster and slower. So this calculation came out pretty close. So that is the pressure you can get from quantum mechanics. !!V2.6 PAUL: As the final step in our calculation, let's work out if this pressure is actually sufficient to produce a white dwarf like Sirius B. So we've calculated the pressure we need. We've also calculated in the earlier video the pressure in the middle of a white dwarf, and we found that the pressure in the middle of a white dwarf of uniform density is 2/3 pi G density squared times the radius of the white dwarf squared. !!Now we also know that the density is just the mass of the white dwarf divided by the volume, which is for a sphere, 4/3 pi R white dwarf cubed. So what we can do is substitute this into here-- that gets us the pressure in the middle of a white dwarf-- and set it equal to the quantum mechanical pressure. And from that we could deduce what the radius of the white dwarf actually is, and I'll leave that as an exercise for you. It's fairly straightforward, though, a bit algebraically complicated. But what you get is the radius of a white dwarf is given by-- !!And there you have it. And if you plug numbers into this, you come up with an answer of about 3,000 kilometers, which is about half the real size, about 6,000 kilometers as we derived earlier. So considering all the approximations that have gone in here, that's a pretty good job. So you can see that using quantum mechanics, you actually can explain how white dwarfs can sustain themselves and from fundamental principles, which is pretty amazing, this linking of the very small to the very large. There are also a few more puzzling things that we'll come back to. For example, you can see that the radius of the white dwarf goes down as the mass goes up. If you make the mass bigger, it's in the bottom here, so the white dwarf actually gets smaller, and that's going to have really important consequences later. !

V2.7 BRIAN: So Paul, you've shown us that if you take the idea behind quantum mechanics, the Heisenberg Uncertainty Principle, and you combine that with the ideas behind gravity, that you can push things together with gravity, and the Heisenberg Uncertainty Principle ultimately ends up pushing things apart, you can explain something like these white dwarfs that we see. These really massive stars. !!

PAUL: Yeah, we've solved one of the problems, the problem of how you could make something that dense not collapse. How it can actually support itself against intense gravity. But there's still another problem, a nasty one. !!Which is, we need this lump to be not made of hydrogen. If it's hydrogen, it's got a nuclear fuse. Most everything in the universe is hydrogen. What isn't hydrogen is helium, which is almost as bad. How could we get something that isn't hydrogen and helium, a dense lump of the stuff, when that's not what most of the universe is made out of. !!BRIAN: Well, I have an idea. If we look at our sun, our sun is made out of primarily hydrogen and helium. But of course it's being powered by the conversion of hydrogen to helium. And then we believe, eventually, helium to things like carbon and oxygen. !!So one could imagine that if we looked at a star like our sun, not now, but later on, after it's burned through most of its nuclear fuel, in the center you should have a reservoir of a bunch of stuff which is like carbon and oxygen, or maybe helium, depending on exactly how the nuclear processes work. So that's a good place to look. !!PAUL: OK. So in the middle of a star, you're going to accumulate just what we want, a large, dense pile of heavier elements. But the trouble is, that's only ever going to be the core of the star. In our own sun, it's only about the central half a percent that's actually doing nuclear fusion. !!Most of the rest is just this is incredibly thick blanket of hydrogen, which is just there to press down on that central half a percent to make it dense enough to undergo nuclear fusion. Even when a star like our sun comes into its life. It's still only going to be a little bit in the middle of those turning to this type of stuff. You've still got this huge shell of hydrogen around the outside. How are you going to get rid of that? !!BRIAN: Well, I think the best thing to do is to go out and have a look around the universe. When we look out at the universe, we see that all stars are not exactly like our sun. Some of the objects are much, much bigger than our sun. Not in terms of mass, but in terms of size. !!And we call these red giant stars. And indeed, we believe our sun, in the future, is going to turn into a red giant. Because it turns out that the nuclear reactor in the center of our sun changes over time. Right now it's burning hydrogen into helium. But in the future, that's going to exhaust that supply of hydrogen, and it's going to start wanting to burn the hydrogen in a shell outside of the core into helium. !!And when it does that, it's going to become much more energetic. And that's going to cause the outer part of the star to puff up to a size much, much bigger than today, almost all the way out to where the earth is. And so that red giant star, of course, doesn't solve our problem. But that big puffy star, that gas is only barely attached now to the core. Because the gravity is so much weaker. !!PAUL: Yes. If you look at images of red giants, or red super giants, you see they're actually rather fuzzy edged. It's very hard to get a picture of these things. But all pictures you can get using clever optics and similar techniques show that, in fact, it's not like our own sun, with a nice sharp edge. It's a very fuzzy edge. A lot of stuff is actually being blown out of these things. !!BRIAN: That's right. Because they're not very stable. And as I said, the thing that makes our sun round is the fact that there's just so much gravity. I mean, it's much-- the gravity's really pulling things together and making that giant sphere. !!Here things get extended, and this is one of the few stars where you can actually see the star and how big it is. And this leads us naturally to a time when, for example, the star itself runs completely out of its ability to fuse its hydrogen and helium into heavier elements. And then what's going to happen? !

!The center of the star is going to be overcome by gravity. And it's going to want to come together until it is-- reaches that magical point where that quantum mechanical pressure pushes back and stops it. But there's going to be a lot of energy in that process. !!You have this weakly attached envelope of stuff, and it's likely to get blown off a little bit into something you might see like this. A planetary nebula. Possibly my favorite object in the cosmos. !!And you can see right in the center, you've got a white dwarf, a really tiny star that's mass that we've been talking about. And then you've got all this junk that has sort have been blown off. Not really violently, but kind of gently, to form this amazing neon sign in the sky. !!PAUL: Yes. And there's a lot of beautiful pictures of these things. Here are some taken by the Hubble Space Telescope. !!BRIAN: That's one of my favorites. !!PAUL: This is lovely, yes. What's lighting this all up is the ultraviolet light from the white dwarf in the middle. The core in the middle is, as you said, very small, very dense, and very hot. Because it's just come out of the middle of a star. !!And so it's emitting ultraviolet light, which is coming out and zapping the gas around it, knocking the electrons up the energy levels. As they fall back down again, they emit all these lines we see. So they're absolutely beautiful things. !!But we're seeing that, in fact, most of the mass of what was in the middle here, the star may be much like our own sun, and it's lost most of its mass. Most of the mass has been blown out in these cataclysmic last few days, weeks, months, years, leaving just behind the core. so maybe we can, in this method, get rid of all this huge blanket of hydrogen, and give us a core. !!BRIAN: So yes, these things litter the sky. But they don't last very long, so it's quite interesting. They're not rare in the sky. And for astronomical objects, these planetary nebula really only have lifetimes of order 100,000 years or so. So they are short-lived. And that tells you that it's not an unusual phenomenon. Almost every star that's born is going to end up producing one of these at some point, to explain how many that we see across the sky. !!PAUL: But then after their 100,000 years or so is over, the nebula has faded away, you're still going to be left with a white dwarf. It's not got any power source anymore, it's not actually generating any energy. But it's got a lot of heat inside it, because it started off at a very, very high temperature. !!And it will just slowly cool down as it radiates the heat. So it might start off at a very high temperature. As time goes on, it'll get a little bit cooler, a little bit cooler, a little bit cooler. So it might start off as a very blue colored dwarf, and then become a bit more white, and eventually might end up sort of yellow, or even red as it cools down. Though probably the universe isn't old enough for them to have reached that stage yet. !!BRIAN: It's sort of a cooling ember, a rock that you heat up in a fire and then you know that if you grab that rock, very soon afterwards, you're going to burn your hand, because it's still hot. And so-- but it cools over time. And because things that are hot glow, you can see these things. And they literally litter the sky, these white dwarfs, and it's a beautiful process that makes them. !!PAUL: So, pretty amazing things. This white dwarf, the whole mass of a sun in the size-- it's only the size of a planet. The incredible density, the incredible gravity, the combination of quantum mechanics and gravity. They're amazing things. !!

But they're not really all that violent. And this is a course on the violent universe. Or are they? Well, that's what we're going to talk about next time. !!Lesson 3: Dwarf Novae!!V3.1 PAUL: So the first clue that white dwarf stars could actually be violent came in the 19th century from this guy, John Russell Hind, who was actually a lacemaker from the midlands of England and worked on the Naval Almanac. And he was surveying part of the conservation of Gemini when he saw a star that he was pretty sure hadn't been there when he'd last looked at it a little while ago. It seemed to be a new star that had appeared, and it went away again. !!So maybe something exploded, something appeared, became very bright, and went away. But then, a few weeks later, another astronomer reported it was back again. If you plot brightness against time, here's some data from the amateur astronomers who monitor these things and do a fantastic job. What you can see is normally it's pretty faint, but it's still there. You can see when it's not exploding. !!You've got a rather faint star. Every now and then, it gets about 100 times brighter. So this is in magnitude scale, so it goes to a ninth magnitude from 14. That's 5 magnitude, which is a factor of 100 in brightness. !!BRIAN: So 100, so you could imagine if our Sun got 100 times brighter, we would notice it here on Earth. That's a huge change, so that's a major event on these things. !!PAUL: Yeah. But a puzzling thing is normally that sounds like an explosion. Getting 100 times brighter, that sounds like something pretty cataclysmic. You imagine a bomb goes off gets 100 times brighter. You wouldn't normally expect it to do it again. Normally, bombs don't explode twice, the same bomb. !!BRIAN: And this is doing it every month or so. And it's doing it more than once. It happens, and it keeps on doing this. !!PAUL: It's been doing it since the middle of the 19th century every month or so. And there's no regular pattern. It's not as if it does it every second Tuesday or every 40 days or something. !!BRIAN: So it's not like the Old Faithful Geyser, and it comes on every-- !!PAUL: It's the Old Unfaithful Geyser, if you like it. It does it whenever it feels like it. There doesn't seem to be a pattern to it, but it's roughly on monthly time scales. !!BRIAN: So I always say that, if you see something like this and you want to understand it better, what you really want to look at is the spectrum. Remember the spectrum tells us a lot more about the physical situation of what's going on. !!PAUL: Yes. So indeed a spectra obtained of these things pretty soon-- Now if you remember what a spectrum is is we take the light from-- just looks like a dot, just looks like a star. We can't see any details, just far, far, far, the smallest pixel of our best detector. But we can take the light from that pixel and put it through a prism, or a diffraction grating, and break that into its component wavelengths. !!So down here we're plotting the wavelengths in nanometers. This is from the ultraviolet out to the near infrared. Since this is visible light, this is what the eye perceives as green. This is what the

eye perceives as blue. This is what the eye perceives as red. And up here, we're plotting the amount of power at each of these wavelengths. !!And this blue curve down here is what? The spectrum of one of these objects, looks like. But actually many of these things, and they became called dwarf novae. The first one, U Geminorum, was the one Hind discovered. Since then, dozens more have been found. And you can see at most wavelengths, it doesn't emit much light. !!But there are these big spikes at this wavelength, 656.3 nanometers and 486.1 nanometers, and other lower things down here, there's a huge amount of light. !!BRIAN: And so those numbers ring a bell to Paul and me, and maybe even to you right now, because those are the places where hydrogen likes to emit light as it makes a transition from level 3 to level 2, in this case, level 4 to 2, 5 to 2, 6 to 2. So that's an interesting clue that these things-- there's obviously hydrogen at play. And for some reason, it's being up and making these transitions, so it's easy to identify. !!PAUL: And you've also got a bit of light in between these spikes. And this light-- what we call the continuum, like the flat bit at the bottom, seems to increase as you go to short wavelengths. So it's very, very blue. And that's a second clue. But much stranger, indeed, is what the spectrum looks like when it's at flare. So this is what it's like in between these explosions. So it's actually exploding. It looks quite different. What do you make of that Brian? !!BRIAN: Well, let's see. So it's still hydrogen, so we see the same transitions. But for some physical reason, instead of the material going from 3 to 2, in this case, it's going from 2 to 3 in this case. It's actually taking light from what would appear to be that continuum. And the hydrogen is sucking up light from the continuum where, here, it seems to be emitting light from the continuum. !!So there's a physical process at play here, which will hopefully help us understand what's going on. !!PAUL: OK. So in the next clip, we'll talk about what could actually make spectra go up as opposed to go down. !

V3.2 PAUL: So if you remember, in the earlier parts of this course, we've talked about how electrons can't have any energy they like around an atom, because they're basically probability waves, like waves on a guitar string. They can have one oscillation, two oscillations, three oscillations, when they're confined, which correspond to different energy levels. And as we've just said, when an electron jumps down from the high energy to low energy, it will emit a photon, whose energy is equal to the difference between the electron energy levels. So it comes at a particular wavelength. So-- !!BRIAN: So imagine we have a bunch of gas full of hydrogen. And for some reason, we're able to excite the hydrogen. That is, we can inject energy into that hydrogen, so that some of the electrons go up to level three, then just due to the laws of probability of an atom, they're going to go down to two. !!And when they do, they'll emit a photon at that H-alpha, as we like to call it, the red wavelength. And so, every time that happens, you're going to get emission. And so if you have a bunch of gas, you would expect to see emission at all of the energy levels that are excited within the atom. !!PAUL: Yeah. So how are you going to heat up gas, or excite gas to bring the electrons up to high levels? !!

BRIAN: Well, in the case of a neon sign, you go through and plug it in, and put a lot of energy into it. But you could imagine a star might do it by giving ultraviolet photons. Or you could heat the gas up, and then the collisions of the objects to each-- the atoms into each other, would knock the electrons up into new levels. !!PAUL: OK. So if you ever get gas on you, you either zap it with ultraviolet, or flood it through with particles, like in a neon sign, or you heat it up. That will excite the electrons, and as they jump back down the levels, they will produce a whole bunch of emission lines. !!BRIAN: And we have to be clear, that we describe this in what we call the optically thin regime. That's where none of the atoms talk to the other atoms, and so the light being emitted here just keeps going and never sees another atom. !!PAUL: OK. So this is one situation. It might explain what's happening in our mysterious object when it's at low state. You seem to have a cloud of gas that's somehow being heated up or zapped or something. But this, as I said, is optically thin. !!When the light electrons jump down, they emit a photon, and it just goes straight out. But in practice, if you have a very thick gas cloud, that's not going to happen. Because in addition to the photon being emitted, it can also be absorbed. If an electron jumps from level three to two and produces an H-alpha photon, that's just the same energy if it's another hydrogen atom to bump it back up from level two to level three again and absorb it. !!BRIAN: And so then you wouldn't see anything, right? You'd go through and you'd produce something, yee haw, but then you'd run into another atom, and yee huh. And you'd end up with nothing. !!PAUL: So what you can think about is how far, on average, a photon is going to get before it gets absorbed. And that will depend on the density of the gas. If the gas is a very low density, it maybe can escape clean out the other side and were in optically thin case. !!If, on the other hand, the gas is denser, or just bigger, then it's going to be optically thick. So let's say, for example, this is a typical distance a photon can get before it hits another hydrogen atom and is absorbed. The only emission we're going to see from our cloud is from this front region. !!If an atom there jumps-- electron jumps down from three to two, the photon can get out. If it does it from here, it will get sort of as far as there, maybe get absorbed again. So already this-- !!BRIAN: So we sort of call this as the optical depth. That means it's sort of where the average photon comes from. That's the depth within the stuff that it can escape. !!PAUL: It's not going to be an absolutely sharp line. It's a random process, so there will be some photons from here that don't escape, and some from there that do. But it's the ones well inside this mostly will escape, and then the probability of escape will go down, until by the time you're way over here, the probability is very, very low. !!BRIAN: And there's a very good analogy that we have a normal life, which is on a foggy day, it's sort of how far you can see before things completely get obliterated. And this line sort of represents just the last little thing you can see. That's how far through the fog you can see. !!PAUL: But of course this optical depth, how far you can see, is actually going to depend on the wave you're actually looking at. Because bear in mind, all the laws of physics are reversible. They go both ways around. !!

So let's say you take this wavelength, the wavelength of say, the H-alpha line, or any other line. This is say-- there's a transition. Lots of electrons are going to be in the state to make that transition. So it's going to radiate an awful lot. !!So if you get a given, say cubic volume of gas, it's going to emit a lot of that wavelength. But because there are a lot of electrons in those states, it's also going to absorb a lot of those wavelengths. So, this wavelength, dropped to a depth that's going to be very short. !!So we're only going to see the radiation coming from a very small region at the front. But let's say you've got a different wavelength, like this one down here, where there aren't any particular transitions that match it. In that case, the gas doesn't emit very much. Only very little about per unit volume. But on the other hand, it's not going to absorb very much. So you get a very large region of the gas cloud which is transparent. !!BRIAN: Right. So that means that if you're looking at something in hydrogen, that at that specific red wavelength of the hydrogen alpha transition, that three to two transition, you can only see a little bit. And then you move off that transition, you can see a long ways in the material. So it's sort of what you see depends on exactly the color you are looking at. And that's actually quite an interesting way to diagnose what's going on. !!PAUL: Yeah, so you wouldn't actually expect to see a spectrum like this. You've got two effects going the opposite way. On one hand, at this wavelength, it's emitting like crazy. But you're only going to see a tiny bit on this place. It's only emitting pathetically. !!But you're seeing a huge amount. So you'd expect the two to kind of cancel out. And in fact, you can do the calculation. You can assume the radiation is in equilibrium with the matter. !!This is a calculation done by Planck in the late 19th century. And it turns out, in this case, you completely lose all these emission lines. You actually get a very smooth spectrum, what's called a black body curve. !!BRIAN: And that smooth spectrum, it turns out, depends on the temperature of the material. How fast the atoms, or the material, is moving around, effectively. !!PAUL: It only depends on that. It doesn't matter anymore what the thing is made out of, because all the emission lines are canceled out. If you've got an emission line, yes, you emit more of that wavelength, but you can only see less of it, and so that cancels out. So in some sense, it's great. You learn the temperature, and it's very simple, but you lose all the richness and information about what the composition is. !!BRIAN: And you can see that if you have something hot, so something, for example, substantially hotter than our sun, it's going to emit a lot of blue light, or even ultraviolet light. !!PAUL: This one's peeking down around in the near ultraviolet, about 350 nanometers. !!BRIAN: So that's so blue, you can't even see the light with your eye. And something cooler than our sun, for example 4,000 degrees Kelvin, produces a lot of red light. And indeed, a lot of light you can't also see with your eye. And our eyes are magically trained through evolution to be very sensitive to about the temperature of the sun, where the sun puts out most of its light. !!PAUL: So you can write down an equation for this. We'll show you this in the reference notes. It's a fairly complicated equation. You can take two simple derivatives of that equation. !!One of them is to work out what wavelength things peak at. This is called the Wien Displacement Law. So what this means is, if you have a particular temperature, you can work out what

wavelength a black body curve should peak, or go the other way around. If you know what wavelength it's peak at, you work out what the temperature is. !!The second thing you can derive from that is one we've seen before many times in different courses in the series, which is the Stefan-Boltzmann Equation. You can add up the total amount of power radiated per unit area, and it depends only on the area and the temperature. And I guess the temperature is our fourth power. !!BRIAN: So hot things are really bright when it comes to how much energy they put out. !!PAUL: So that's given us a flat continuum spectrum, and it's given us a spectrum with emission lines, how about a spectrum with absorption lines, how are we going to get one of those? !!BRIAN: Well, this is kind of an interesting idea. So imagine, for some reason, that I have one of those black bodies, and it's shining through gas. So then I'm going to be putting photons in all sorts of energies. And some of those energies are going to line up with the wavelength of hydrogen in that three to two transition, four to two transition, which means that that light would be taken out of the black body or the continuum, as we say, and you would get absorption at those specific wavelengths. !!PAUL: So what you need is an optically thick thing, which is emitting sort of like a black body in the background. And then in front some optically thin gas. And this could actually often be the same gas. Now this, for example, in the case of our sun, this will be the deep regions of the sun, and this would be the cool surface regions of the sun. !!BRIAN: That's right. And so that's a very good way to get absorption lines. And it sort of tells you that you have a thin layer of stuff that's relatively-- it turns out cool, relative to the stuff in the background. !!PAUL: OK. So that's how you get emission lines, continuum and absorption lines. In the next video, we'll go and apply this to what we've learned about this strange exploding star. !

V3.3 BRIAN: All right, Paul. So let's put what we have seen in the spectrum of this object together with what we just learned. So we know in this case when the object is faint and not an outburst that we have a mission. So that means we sort of have a bunch of diffuse hydrogen that's emitting. We know that there's a lot of blue light here. So maybe there's something hot going on as well. I don't know. !!And then when we have it in outburst it means that we have some things happen where we have an opaque emitting black body or something with a bunch of cool diffuse stuff on top of it also made out of hydrogen. !!PAUL: Yep. So here's my toy model. So we start off with see through gas. !!BRIAN: All right. There's not a lot of boxes in the sky, Paul. !!PAUL: We've no idea what shape it is so I just chose a box completely arbitrarily. We have a blob of see through gas of some description. And that's what it's like it's not flaring. But then when it's exploding, flaring, we've got an opaque blob or shape or something. !!BRIAN: Right. !!PAUL: With gas around it. !

!BRIAN: So if you go back to this one, that means that the hydrogen here will be excited for some reason. Something's exciting it. !!PAUL: Little bit of energy in there. !!BRIAN: And wherever it emits, it's nice and diffuse. So that light just gets out. And then when we see an emission, we have all this light coming out from essentially something that's opaque. So it's emitting as a black body. A big bright thing looks like not dissimilar to our sun. And then there's this stuff around it, this diffuse hydrogen-- maybe the same stuff-- that absorbs the light. Because the light comes out here, excites the hydrogen, and that takes the light out at those hydrogen wavelengths. !!PAUL: OK. So that's the first clue, but it turns out there's another clue you can get from the spectrum if you look really closely at it. This black line here is the real spectrum of one of these objects, dwarf novae, and you can see it down at the blue end, its got a continuum that slops up plus a whole bunch of hydrogen emission lines. That's what we've already talked about. !!What do you make of that stuff down the red? !!BRIAN: Well this red bit looks to me to be like a star that's very cool. What we would call an M star. And you actually see lines here from funny molecules that just simply can't be there at warm temperatures. !!PAUL: You see all these big dips and troughs up here in the black spectrum. And that's what you actually expect from titanium dioxide typically. So titanium dioxide molecules. And to have molecules it has to be cool. !!BRIAN: Right. !!PAUL: I think temperature was very hot like you're expecting over here then the molecules would be blown apart. You wouldn't be getting them. So this definitely looks like a cool red star. !!BRIAN: And a cool red star actually has to be pretty big. Because remember, as you make an object cool, the amount of energy it puts out drops as the temperature to the fourth power. So you're going to have a lot of area there in this red star. So a big red star actually. !!PAUL: Yeah. So we've got to add something to our model. We now have our gas. This is ought to be thin gas because it's not when it's flaring and you've got a big red bruiser of a star in there as well. So we've got two things, gas cloud and star. We can't separate them in our images from the earth. This is all just inside the same dot. Bare in mind this is all [INAUDIBLE] more than one pixel from any conceivable telescope on Earth. !!BRIAN: So Paul, when we have two things in space, they normally orbit each other. So that might be a signature we can look at in that spectrum. We could look at those spectral lines. And using the Doppler shift-- remember the Doppler shift we talked about in the first course, is whenever you have something that emits waves, whether it be sound waves or light waves, that if you're moving relative to the speed of sound or the speed of light, you essentially compress the waves in the direction of motion or stretch the waves against the direction of motion. !!And we can use that stretching, in this case that color shift or a wave length shift, to measure the velocity very accurately. So what do we see in this? !!PAUL: Yeah, so, if the, for example, the gas is moving towards us the wavelengths would shift slightly to shorter wave lengths, moving away it would shift slightly to the red. And likewise, all

these titanium dioxide absorption bands also should shift slightly one side or the other, depending whether the red is a dwarf star. !!And you can plot that. And here is the velocity and kilometers per second and the filled circles are the absorption from the red star and the round hollow circles are the emission from the lines. And you can see they're doing different things. !!So the absorption starts off moving away from us and then comes towards us. Whereas the reverse is happening for the emission. The emission starts coming towards us then goes away from us. You've got the red star, starts going away while the gas comes towards us and then the other way around. So they're alternating. !!BRIAN: And it's interesting that the stuff from the diffuse material seems to be moving as fast as the big red star. So there's like lots of mass because we know the stars got to be pretty big. So that means that gas has got a lot of mass as well. So that's interesting. !!PAUL: Yeah. So I'm presuming our model is going to look something like this. That we're looking at gas cloud and the red star orbiting around their common center of mass. So the red stars now going away from us and the gas is coming towards us. Then it swaps around. And this is happening, it's happening very fast. !!The times scale is only a few hours for this to go around. These are going around at some enormous speed. Hooning, as we would say in Australia. !!BRIAN: Right. So there's got to be a lot of mass involved and they got to be very close to each other. !!PAUL: And you have to bear in mind, you might expect the gas cloud because you know it's very diffuse. More or less the star would sit still and the gas cloud could go round it. But the fact they're actually going around the middle indicates that this gas cloud must weigh about as much as a star. In many cases, it's actually considered even more than the star. So we'd actually talking about, this sounds like a very strange diffuse gas cloud. We know it's see through. !!BRIAN: So it sounds to me like we're going to need some more clues to sort this out. !

V3.4 PAUL: One clue comes from the speeds of the motion we see. We know we have a red star and this mysterious gas cloud. And we know from the Doppler effect, they're going around each other at a speed about 20 kilometers per second. We also know that they're both going at about the same speed, but one's coming towards us. The other is going away and vice versa. !!Now this tells us quite a lot. For a start, if they're both going at the same speed, they must be both going around a point that's halfway in between, which means they are still about the same mass. We can look up the mass of the red star by normal models of stellar evolution, and it's about the mass of the Sun. !!So you got m is about the mass of the Sun. The Sun is written as m with an o dot below it, a zero with a little dot in the middle. So this cloud must also have about the mass of a Sun, 2 by 10 to the 30 kilograms roughly speaking. But how far apart are they? We can also work that out. !!Now, because they're moving in circles at a high speed, there must be a centripetal force towards the middle of the circle to allow them to keep going in the speed. But if anything goes in the circle, there must always be a force towards the middle to hold it there, and that force is given by mv squared over r. !

!Let's call this here, r, the radius of the circles in their orbits. The distance between them is actually 2r. So for each object, we've got the mass, which was the mass of the Sun times v squared over r must equal the centripetal force. Now, what's causing this centripetal force? Well, it must be gravity between the two. So that's given by Newton's normal law of gravitation. So g, mass of the first object, mass of the second object, over the distance between them, which is 2r squared. !!So that's balancing centripetal force against gravity. What can we do here? Well, we can cancel out one of the masses. We can cancel out one of the r's over there. And we end up with v squared equals g m Sun over 4 r. Now, we know everything here apart from r, how far apart they are. Separating that off to this side of the equation, you end up with r equals g m Sun over 4v squared. Plug-in the velocity of 120 kilometres per second, and that comes out as about 2 by 10 to the 9 meters. !!Now, that's a very interesting number. The radius of the Sun is about 6 by 10 to the 8 meters, so it's only about 3 times the radius of the Sun. And red stars are bigger than the Sun, so that's telling us that the star and this gas cloud are actually very close together. If you are sitting on the surface of the gas cloud, the star will cover half the sky almost. !!So this is not some distant binary. It's not as if you got a star and a gas cloud a long way away. These are really up and almost touching. That's a really important clue. !

V3.5 BRIAN: So Paul, we've seen that we think we have a bunch of gas orbiting a big red star. Now, I would think that if we looked at several of these objects, sometimes that gas would go in front of the star, and we would see an effect. So if we looked at the light, over time, of a lot of these objects, we should occasionally see like a transit or an eclipse that will help us figure out what's going with that box of gas. !!PAUL: Yes. So just like in the exoplanet course in the series, we talked about how a planet goes in front of the star or the star goes in front of the planet, and you block out the light. And this can tell you a huge amount, and we can do the same thing here. When the gas goes in front, you wouldn't expect to see anything because remember this gas is transparent, so the light from the star is just going to go straight through it. !!But when the star goes in front of the gas, which would block out the light-- and of course, must of the light is coming from the gas. The gas is brighter than the actual star. And indeed you see in about 30% of the time, you do see these sort of eclipses. So this is the lights, and then this is a point when the star goes in front of the gas cloud. !!BRIAN: Yeah. So we have a lot going on here. For some reason, the object is brighter, and then the gas goes in front, blocks it out. But it's funny. It goes through, and there's a little step here, which you can barely see. But then there's this big glitch on this side, so it's almost like the box of gas has two parts to it. It's like there's a bit that's denser than the other bit. !!PAUL: Yeah. It turns out if you look at the shape in great detail, it turns out there are actually three parts to this gas. There's a spread out, diffuse part, and then there are too narrow bright parts. And when the first narrow, bright part goes in, you get this very sharp drop in brightness when it goes behind the limb of the star, And then here, a short time afterwards, a second one goes behind. And then a bit later, the first one comes out and the second one comes out. !!BRIAN: OK. So it's a very complicated structure. What happens if we zoom in? !!

PAUL: So here's the idea of what we've got going on here. We've got the gas cloud and the two bright things inside it, one in the middle and one a bit off center. And you see now one then the other goes behind. Then, one then the other comes out, giving you this double step up and the double step down. !!BRIAN: Right. OK. So a very funny system. Hopefully, this is all going to make sense eventually. But I guess maybe we need a little bit more information. !!PAUL: Yep. There's more information in these light curves. These light curves were obtained using photoelectric photometers because they're new technology which allow you to measure the brightness on an absolute linear scale, very precise and on very short time scale. So when you apply it, in this case, to U Geminorum, the very first of these things discovered, let's see what's going on here. !!BRIAN: So it's flickering. And so this is only flickering every 10 or 15 seconds or so. And so it's flickering up and down. !!PAUL: No particular pattern - it is jumping around in brightness on very short time scales. !!BRIAN: Right. And then that flickering, when that thing goes behind the red star, disappears. So we know what's flickering. We know it's the bright thing that's going around the red star. !!PAUL: And also, the fact that it's flickering tells us it's very, very small. We knew it was small anyway because it cuts out. The white drops very abruptly, so it must be a small thing that was going behind. If it was a big thing, it would take a while for it to move behind the limb of the star and cut out. But also, if it can flicker on 15 seconds or so, that means the sound crossing time must be no more than 15 seconds, which means we're talking about something much smaller than a typical star. So a small, variable thing in one of the bright spots. !!So I guess our model is now getting something like this. We're now getting what's probably the off-center of the two sports that's doing most it is randomly flickering like crazy. !!BRIAN: OK. Interesting. So let's talk a little bit about this bit. So there's something funny going on where the object, as it goes around, it's flickering is brighter and then it fades away depending on exactly where in the orbit the object is. !!PAUL: Yeah. You normally expect the light to be perfectly flat, except to where it was going into the eclipse because it's just looking at the gas cloud, and the gas cloud should look the same from every angle. But it seems that we're actually seeing more light in the gas cloud, not really on the reverse side, but a little bit off the reverse side. It's like this gas cloud, or particularly the bright spot within it, are beaming their lights in a backward direction, not quite aimed towards the red star, but not far off. It's like torch. !!So if you imagine, for example, that your head was the red star and this is our bright spot, it's shining. And when it's on the far side, the light is shining towards us, so we can see it. When it's around the near side, shining away from us, apart from seeing Brian's face illuminated, we can't see very much. !!But it's not pointing straight towards him, so it's pointing at a bit of an angle because you see it's off-set to one side. So you've got a torch going something like that around the red star. !!BRIAN: So you need to put a torch on your next diagram. !!PAUL: Yes. !!BRIAN: Well, at least a version of a torch. !

!PAUL: Yeah. What it's like is the thing that's flickering is like a glowing surface painted on something opaque. So what I've done is I've put a black slab, and I've painted a flickering white thing on the surface. So when the black slab-- now, we can't see it. We just see the black slab. When it's on the far side we can start to see the flickering, but we see it more in this case after rather then before the eclipse. !!So it probably needs to be angled the other way to make it work the way we actually see. So this flickering thing is only visible from some directions. It's like something has been painted on the surface. !!BRIAN: All right. I'm not sure if I'm any of the wiser at this point, but I guess what we're going to need to do is put together even some more information to get a better picture. And I'm afraid this is the way science often works is you get a bunch of complicated things that you've got to build up in a story, but you don't really know what's happening till you get all the pieces of the puzzle together. !

V3.6 PAUL: So considering these things are just a dot, you can't actually see any of what's going on. All we've measured is a spectrum of the change of brightness. We've learned an incredible amount. We're developing a really complicated, messy picture with multiple spots, one of them flickering, viewable from certain angles, gas clouds that's opaque and then transparent depending on what's going on, a red star spinning round something very massive. !!But what's going on here? I mean, to me, the real clue that really clenched it was this one. If you look really close in at the spectrum of most of these things, the lines, hydrogen emission lines don't turn out to be single but turn out to be double. !!BRIAN: Double? So double emission lines, that means that there's material moving at two speeds, some going this way and some going that way. And that's the Doppler shift for that material separating it. And that's-- I could think of a couple ways to have that. For example, if I shoot material out in a jet two directions, like one towards the screen and one away from the screen, then that would do that. !!PAUL: Yeah. But let's say you did have your that's gas cloud that we'll say is squirting one towards the red star, one away from it, then as it moved around, when it's face on, we'd see one going towards. When it was a sideways-- when they'd both be going sideways, we wouldn't see the two lines. When it was edge-on, we'd see the lines combine and then come out again. !!BRIAN: So we have a prediction. If there are jets coming out that we should see a split, and then they should come together, and then they should split again depending on when we look at the data. !!PAUL: That's assuming that it was aimed towards the star. Here's what we actually see. Here's the phase, which is telling you where in the orbit it is. And there's the spectrum of these hydrogen lines. !!BRIAN: Hm, so we always see the two lines, so they don't seem to be moving. But they do change a bit in brightness. So sometimes, we see, for example here, the stuff moving towards us is not as bright. And here, it's brighter, so the stuff is brighter than the stuff moving away. So let's think through what that might mean. !!PAUL: So if you want to get two lines, no matter which direction you look at it from, the best way to do that would be have something like a spinning shell or a spinning ring or like a hula hoop or something that's rotating because then there's going to be the bit coming towards you and the bit

going away from you and the bit going sideways, which would be that little lower bit of emission in the middle. But it doesn't matter which angle you look at it from. You're always going to see some bit coming towards and away from any angle. !!BRIAN: And then the idea would be-- that would mean that you would always see the split. But the fact that it goes brighter and fainter on the two sides would mean that part of the hula hoop gets obscured and then the other part gets obscured depending on what angle we looked at. So what would that look like? !!PAUL: So here's our model. We've got the blue arrows showing gas moving around. And as you see, as it goes behind, first of all, the light coming towards us is obscured then the light going away. Then, they reveal one after another. So you obscure one side than the other, and you reveal one side than the other. !!BRIAN: But the fact you can always see both means you wouldn't completely obscure it. That is that diffused gas is so big, you can always see part of it behind the star. !!PAUL: Yeah. So it looks like we've got some almost spinning disk of gas going around maybe the central white dot, and quite where this other one directional flickering white dot is off-center somewhere. I'm not quite sure where that fits in. So let's see if we can make some sense of this. !!So this is looking really complicated. I mean we've got a cloud of gas that's sometimes transparent and sometimes opaque. And we've got-- the scatter cloud is very tenuous, but weighs an awful lot and has some blue light coming out. So there's something causing opaque in there as well. We've got a spot in the middle of the gas cloud and another spot off to the side that flickers, but only shines backwards. I mean should we give up at this point. !!BRIAN: Well, it seems like it, but this is the way science always works. So we need to think a little bit more through on the physics, and that's going to be our guide, I think. So the first thing that strikes me is that we've got this diffuse gas, but there's a huge amount of mass there. So something is very massive that's not emitting much light. !!PAUL: And that sounds just like the white dwarfs we've only just been talking about. We know there's a bright thing emitting blue light in the middle of this, and that would be about the right mass. We're talking about something that weighs about the mass of the Sun, and small, and dense. So yeah, I think we probably have a white dwarf in the middle of this. That's probably a good working hypothesis. !!BRIAN: So if we start with that hypothesis, and we know we've got this big red star, then one could imagine figuring out, if we need a big, bright amount of material, that we could start thinking about if material from the red star goes to the white dwarf, how much energy is involved and whether that starts making sense. So maybe we need to follow that physical process. !!PAUL: Yeah. We need two things. We need an energy source to make all this gas really hot and flickering, and we also need a supply of gas. I mean that won't come out from a white dwarf, so the red star is the obvious place to supply the gas. We know red stars, when they come to the end of their life-- it's what red stars are. it's the end of a life-- blow the winds out. We were talking about these planetary nebulae. !!So maybe that's supplying the gas, and as the gas falls down this enormous gravitational potential onto the white dwarf, it's got quite a lot of energy. So maybe we can kill two birds with one stone. !!BRIAN: And we need to go through and remember that just because you have two stars next to each other, the heavier stars isn't just a vacuum cleaner. The Sun is not cleaning material, you and me, off the Earth right now. So there's some physics we need to think through about exactly what it takes to scoop material off a star, only a special situation. !

!PAUL: So let's do the calculation of how gas would actually flow if you had a massive star orbiting another massive star this close in. !

V3.7 PAUL: So what happens when a star in a binary system starts splitting up? To calculate this, we'll have to use the concept of potential energy. Now gravitational potential energy is minus G m over r when you have a single object. To plot this, we can plot the gravitational potential energy versus position. And we'll get something that looks a bit like this, gravitational potential energy would be zero. Come all the way out, and then we'll draw, become very negative, and then we'll come back out and go back to zero. !!And that's what the gravitational potential energy looks like around an isolated star. What's happening? Well, let's say the star is quite a small one. It will, its gaseous surface will sit at a particular height in here. As the star starts swelling up and it turns into red giant, surface areas require more energy and they will move up and up and so the star at some later stage fill this and get bigger. The principle star can get so big then it comes right up to the top and actually maybe start spilling over like that. And it's like filling up a bath. !!The shape of the star will just reflect the shape of the bath, with the level steadily rising as the star swells up. That's a single star. What happens to a double star? In this case, if you do a plot of this gravitational potential energy versus position you get two of these terms, one centered on the red star, one centered on the white dwarf. So what you get is a front curve that looks something like this. Might be 0 at some distance, and then it drops down for the red star. Then it comes up. And then it comes down for the white dwarf star. Then it goes back out again into 0. !!So now what happens when a star swells up? It might move up and up and up and up here. This time, if the energy goes up over a certain level, the material will stop spilling down into the potential [? well of ?] the white dwarf. In principle, it could fill up to both levels and give you sort of double lump star, but in practice, the matter falls down to the surface of the white dwarf gets very heavily compressed down there so it doesn't actually fill up the white dwarfs part of the gravitational potential. !!This is called the gravitational potential energy surface. We're just doing a cut through it. It's really a three dimensional thing. There is one more complication which is that in practice the two stars are orbiting around each other. So we have to allow for centrifugal force, which actually turns out makes this curve down a bit outwards. That means once stuff gets to some distance, it gets flung out by the rotation's centrifugal force. Centrifugal force doesn't really exist, it's just an artifact of the fact that we're measuring things in a rotating frame of reference. And we'll come back to that frame of reference later. !!So this is what's called the Roche surface. It's a surface of potential energy set by gravity and centrifugal force, and that tells us how the shapes of things change as they expand. It's really a three dimensional surface, and we'll see a plot of that now. !!So what does this potential energy distribution looks like? Here is a three dimensional rendering of the potential energy, so the higher, redder colors are where the energy is higher and the blue is where it's lower. And you've got the two stars here and the whole surface. !!BRIAN: That's very pretty. I kind of like doing it as a contour better so I can see in more detail what's going. !!PAUL: OK, so let's have a look at a contour part of the same-- !!

BRIAN: That's much better. !!PAUL: --thing !!BRIAN: So here, this is sort of like a topographic map, and so these are essentially how deep the holes are that you just saw. And these are these little potential places where you can see there's like these little plateaus. And these plateaus, when you have two things orbiting themselves, are very useful. For example, putting spacecraft there, because they don't like to move when you put them-- we call these the Langrangian points. !!But it also shows that if you look, there's sort of a saddle-- if you think of these being two holsters-- a saddle point where if you make things too big, material is going to leak from here to there-- !!PAUL: Yeah. !!BRIAN: --across the gravitational potential. !!PAUL: So this is the bigger potential. Well, it's presumably where the white dwarf is, and this is presumably where the red star is that we just talked about. Maybe it swells up at the end of its life. And the gas is going to leak out. And where's it going to leak? It's going to leak across the saddle and come down here. !!BRIAN: Yeah. So imagine that as the star starts using up its fuel and it gets bigger and bigger, well, if it's just within its own little well, nothing happens. But what happens when it leaks out through here? It gets bigger than that. Then it's going to want to fall down there. !!PAUL: And it's not going to fall straight. Remember, this whole thing is rotating around. It's got angular momentum, so it'll spiral in in some complicated pattern and probably end up forming a ring or spinning disk. !!BRIAN: And that's because we have to conserve angular momentum. And just like the ice skater who starts spinning when they bring their leg in, they spin up, this stuff is going to be doing the same thing. !!PAUL: So at last we can put all the pieces together and come up with something that both makes theoretical sense and kind of fits the data. !!BRIAN: That actually looks like something I can almost relate to, Paul. !!PAUL: Yes, we've got the red star which is expanded because it's come to the end of its life until it's filled with what we call the Roche lobe, this potential thing. And the gas is spilling over. !!BRIAN: And so that's the little bridge between the two potential well holes. !!PAUL: And as it falls in, it gets deflected to the side because of conservation of angular momentum, until eventually it crashes into a spinning disk. And where it crashes into it, we're getting a hotspot, because suddenly you get this column of gas falling down. It's gaining gravitational potential energy as it falls down the potential well. It smashes in, and hits here. And it smashes into something, and it's only see that emission from the far side. It's giving us our opaque flashlight. !!BRIAN: And presumably the material isn't just coming in nice and gently, evenly, it's coming in in bits and pieces so you get a flickering of the material. And that material, that disk of material, is made up of many, many, years worth of stuff coming in and spinning up. And so it's sort of a residual from what's happened in the past. !!

PAUL: OK, so let's see if we can work out what the physics of this actual disk is. !!V3.8 PROFESSOR: OK. Let's see if we can work out what the physics is of this accretion disk. Now what we have is a red star and a white dwarf. The white dwarf was originally a star, it came to the end of its life, had a planet nebula, left a what dwarf behind, and now the smaller star has also come to the end its life later. !!And matter starts falling, and then it starts expanding, and matter falls through the Roche saddle and then comes in towards the star. It doesn't fall directly because all things are rotating, so it'll end up doing a fall, and then loop round, and then smash into itself here. Maybe it'll it get through a bit and bounce around. So you're gonna get a whole bunch of smashing around going and eventually you'll end up with a disk, or not a disk, a ring with a more particular width of gas around it, around the white dwarf. And as more and more matter falls in, this doughnut or disk will get more and more massive. !!Now what's going to happen in that disk? Remember all parts of the disk are going to be spinning around, so its centrifugal force balances gravity as usual for an orbit, but the inner part of this ring, is closer to the white dwarf so gravity is stronger. So it would have to rotate faster, so the inner bit is going faster than then outer bit. That means if you've got gas going very fast in the inner part of the ring and gas going slower on the outer part of the ring, you're going to get friction between the two, fluid friction, which is called viscosity. What that's going to do is it's going to slow down the fastest gas and speed up the slowest gas. So as the inner gas gets slower that means it will actually spiral in, and as the outer gas get faster it will go out. !!So what you're going to start off with is a white dwarf and a ring, but as time goes on the ring that's inside of the ring is going to move in, and in, and the outside is going to go out and out. Until eventually you end up not with a ring but with a disk. At some point the center will touch the surface of the white dwarf. At that point, we will have the-- also the hot spots are going to be moving outwards. So you're going to have a hot spot here as the gas comes in and then a disk going all the way from there down to the center. And that's what our accretion disk looks like. !!Now one thing we could ask this accretion disc is how bright it will be? Why would it be shining? We can see the thing it must be very bright, but what's happening, of course, is that things are falling as they fall they must get rid of the potential energy. So we know that gravitational potential energy, that's given by minus g, mass in the middle, the white dwarf, the mass of the object that's falling in over r. So you plot the radius here against u, and we get the curve we've seen before looking like this. So the material starts quite a long way out of the hot spot and then moves in until it reaches the surface of the star down there. So this here is the change in gravitational potential energy, and that's the amount of energy liberated by each kilogram of matter as it falls in. !!So what have we got here? We've got the energy per unit mass falling in is equal to the g m white dwarf, mass of the thing that's falling in. We've got 1 over the radius of the white dwarf, that's the end state, take away 1 over the radius of the whole disk, the initial state. !!Now this is going to be about 10 to the 9 meters because we know that's roughly how far apart these things are going to be, roughly, this is a very approximate calculation we're doing here. Just to get the rough orders of magnitude of the different sizes. This is going to be 1 over, say, 5,000 kilometers, that being the radius of the white dwarf. So in practice we can ignore that it's 1,000 times smaller than this. This is the energy. What we really want is the power. So that's per unit time, so the power is just going to be g m white dwarf and the mass per unit time, which is really m dot. So that's not just the mass of one of them falling. It's how much mass force in per second, all over r, the white dwarf. !

!So that's how much power we'd expect. It depends on something we don't know, which is the rate at which mass is falling through the hot spots and spiraling in through the disk, but of course we can turn this upside down. If we measure the power, which is the luminosity of the white dwarf of the accretion disc around the white dwarf. We know everything else here, we could work out m dot. So we get that m dot equals the power observed, times the radius of the white dwarf over g, times the mass of the white dwarf. So we get one side of the mass of the white dwarf. We know observationally that the powers of white dwarfs dd is about-- luminosity is about 10 to the 27 watts. So if we plug the numbers in we end up with a rate at which mass is falling in of 3 by 10 to the 13 kilograms per second. !!So that's an interesting number. So that's pretty big, that's 30 trillion kilograms a second, 30 2 billion tons a second, but you compare that to the mass of the star, mass of the star is 10 to the 30 kilograms. So that means you can run for-- of order 10 to the 17 seconds, which is like over a billion years at this rate. So that's a lot of mass falling in. The red star's not going to run out of mass anytime soon, it's actually a very, very small fraction of the red star's mass. So these things can keep going for a very long time just a billion years at this right, far longer than the red star lights will remain a red star. So these things can last long, that's good to know because we know these variables have been-- or individual ones of them have been seen for at least 200 years. !!But there's another thing we can work out-- what is the temperature of one of these things? Now what we've got is a disk, which has an area of roughly pi r d squared . Of course there's the middle of the disk which isn't radiating, but that's very small compared to the outer disk, that's a rough size. All the mass is hitting the outside and working its way in, as it works in it has to get rid of its energy. Remember it's moving from here to here, so every time it goes in it has to get rid of more and more energy. It can't just leave all the energy till the end, it has to get rid of it gradually as it goes in. How's it doing that? Well the inner fast moving parts here are rubbing against the outer slow moving parts and that friction generates heat, as friction normally does, and that causes everything to glow. !!So let's say the whole thing is heated up by this friction of some temperature T. The amount of energy radiated, given by the Stefan-Boltzmann equation, the power radiated equals area, Stefan-Boltzmann constant, t to the fourth power. And that must be equal to the luminosity, which is given by this equation up here. So that equals g m white dwarf m dot over the radius of the white dwarf. So if we plug-in the area here, we end up calculating that the temperature is equal to the fourth root of g m white dwarf m dot, the rate at which matter is falling in, over pi r d squared r white dwarf. !!Now I should emphasize that this is a very rough calculation. We're assuming, for example, that all parts of the disk are the same temperature, and as you know we did a number approximations further up. But it gives us a rough order, 4 10 to the-- 3 by 10 to the 13 kilograms per second falling in giving a radius of the disk of about 10 to the 9 meters, and the mass of the white dwarf of solid mass. That comes out to as about 9,000 Kelvin. Pretty hot, so it's going to look quite blue, but in fact that's an underestimate of the true temperature of what we're going to see. !!You have to bear in mind that the gas is starting here and as the stars move in, the slope of this graph is quite gentle. As it gets closer and closer, the slope gets steeper. So that means the amount of energy liberated in the outer parts of the disk per unit radius is less than the amount of energy liberated in the inner parts. So most energy has to come out in the inner parts, compared to the outer parts. !!So we have to get rid of more energy from here, but also the inner parts have a much smaller area. So if they've got to get rid of more energy in a smaller area, how do they do that? Well the only was is to get the hotter. So what you're actually going to see is the inner parts of the disk have got to be extremely hot, much more than our average temperature, whereas the outer bits are going to be much cooler. !

!So the spectrum you're going to get, if you plot the flux against the wavelength. The inner parts are going to be extremely hot. So they're going to peak down here at very short wavelengths, and they're going to radiate a lot of power. Then as you go further out it won't be so hot anymore, and so it will radiate at less power, so it will radiate at less power at low temperatures so it peaks a bit further out. And then right to the outer parts of the disk it's going to radiate even less power and at much longer wavelengths because it's cooler. !!So if you add these all together, you're going to get a spectrum looks something like that, a smooth steady rise, and then a big peak well into the ultraviolet. And indeed that's exactly what you see for these things, it's a general feature of accretion disk that you get what's called a power-law spectrum like this. !!So it all seems to hang together, gas is falling in, viscosity makes the disk expand, it's stomping stuff on the surface. Some of the radiation actually may just come for the stuff falling on the service because it was probably moving pretty fast by the time it hits there. So it turns out actually about half the luminosity comes from the surface and not from the disk at all. !!The disk comes into equilibrium, as matter falls in, it generates power. And a rough calculation, very crude, indicates that we need mass inflow rates of a few by 10 to 13 kilograms per second, which means it's going from long time. Factoring that in we get an average temperature of about 9,000 Kelvin, but in practice that's an average that'll be much hotter in the middle and much cooler at the outside and the overall effect will give us a blue ultraviolet peaking spectrum just as we observe. !!V3.9 PAUL: So we've come up with a story about what happens when you get a binary star of which one component is a white dwarf. You get the star which is expanding, filling its Roche lobe, spilling gas via a hot spot onto an accretion disc and onto a white dwarf. Now that is indeed a true story for about 75% of these binary systems. But in this video, we're going to be talking about the other 25%, which are all together weirder. It's a great pleasure to have my colleague Dr. Lilia Ferrario from Maths here at ANU, who is an expert on the other 25%. So, the other 25%, what's different about them? !!DR. LILIA FERRARIO: They're different because, as you can see, what we have here is a very large accretion disk around this white object here, which is the white dwarf that is accreting matter. And here you will have a boundary layer. And the accretion disk coming all the way to the surface of the white dwarf. When we have that the white dwarf is magnetic, is highly magnetic, then the disk is not going to be able to reach the surface of the white dwarf. But it will be disrupted by the magnetic field. !!PAUL: See this is how I'd picture a magnetic field of a white dwarf. So are white dwarfs typically magnetic? !!DR. LILIA FERRARIO: No. Actually, magnetic white dwarfs are quite rare. We are talking about 8% to 10% of white dwarfs are highly magnetic. And when I say highly magnetic, I mean with a field of about 10 to the sixth Gauss, 1 megagauss and-- !!PAUL: Do we know what's different about those white dwarfs as opposed to the others? !!DR. LILIA FERRARIO: Well, why they are magnetic. This is a good question. There are actually quite a lot of papers now in the literature which try to explain exactly this point, why only a subset of white dwarfs are magnetic. Because if it is something that happens during the evolution of a star,

then you would expect that, well, they would all end up being magnetic. so why only this small subset? Something must be happening. !!So there are two theories that people are considering quite seriously. One is the fossil field theory. So they say, OK, stars are born from the interstellar medium. And some part of the interstellar mediums are more magnetic than others. So that when stars are born in these parts, in the magnetic parts of the interstellar medium, then these stars become highly magnetic. And they explain why there are some main sequence stars that are highly magmatic. !!PAUL: So this theory, it would all be from how the stars are born. !!DR. LILIA FERRARIO: Exactly, yes. !!PAUL: So nature rather than nurture. Some stars are born in [INAUDIBLE] fields. And they keep it all the way through their main sequence of life. And even when they die and turn into white dwarfs they've still got the magnetic fields. And other ones don't. !!DR. LILIA FERRARIO: Others ones not. So that would explain it. It also would explain why the magnetic field flux, the highest magnetic field fluxes are the same in all these types of objects from main sequence all the way to white dwarfs and neutron stars. But this theory has had some problems because it's not clear how a magnetic field could survive through stellar evolution, particularly in an intermediate mass star where yes, the evolution is-- !!PAUL: Diagnosing convection and lots of stuff. !!DR. LILIA FERRARIO: --extremely-- that's right. It is very complicated. So it's gone a bit out of favor. !!And the other possibility that people have been discussing is that of stellar merges. So when you have two stars merging in a binary system, then the differential rotation created in the envelope of the merging object creates these very strong magnetic fields. !!PAUL: So in that case, these magnetic white dwarf binaries might have been a triple star system originally. And two of them merged to be a magnetic white dwarf. And the other one's then feeding gas onto that. Oh, I though it was complicated enough as it was. !!DR. LILIA FERRARIO: No. Things can always be more complicated in astronomy as you know. !!PAUL: As in the rest of life. OK so, what difference does this make? Here's an artist's impression of a magnetic white dwarf. !!DR. LILIA FERRARIO: Of a magnetic white dwarf, yes. This is an intermediate polar in fact. And, well, what we can see is that the accretion disk does not come all the way to the surface of the star. So what we have is the formation of the two accretion curtains. They are called accretion curtains. And one accretion curtain is hitting the white dwarf at the north pole. And then we've got this other accretion curtain which is hitting the other magnetic pole. !!PAUL: This is a bit like maybe the aurora of the Earth. So charged particles are funneled down the magnetic field lines. Only the magnetic field here is much, much, much stronger. !!DR. LILIA FERRARIO: It's much, much stronger, yes. Here in the immediate polars, we talk about the magnetic field of about between say 1 Megagauss, 10 to the 6 Gauss to about 10, 15. !!PAUL: By comparison, what's the magnetic field of the Earth? !!DR. LILIA FERRARIO: Half a Gauss. !

!PAUL: Yes. So about a million times stronger than that of the Earth. !!DR. LILIA FERRARIO: Yes. It's a very serious magnetic field, yes. So yes, everything else is like we-- !!PAUL: Yes. So you still have the stream, and the hot spot, and the disk. The disk gets horribly traumatized when it comes close by this magnetic field. !!DR. LILIA FERRARIO: Yes. But otherwise everything is-- if when we observe these systems, we still see there are lines that are formed in the disk, in the hot spot. But then we also see the signatures of these curtains. So you can see that we don't have a Keplerian motion anymore. But we have the inflow of material onto the white dwarf's surfaces. And they are very strong x-ray sources. !!PAUL: Now there are some of these sources of magnetic fields as strong as steel. So what happens there? !!DR. LILIA FERRARIO: Yeah. Things get extremely weird at this point. So what happens is that here we have the basic stream coming from-- you are sitting on the Lagrangian point somewhere there. !!PAUL: So this is coming from the Roche overflow, falling to the other star. And instead of hitting a hot spot, it hits a magnetic field. !!DR. LILIA FERRARIO: Exactly. It hits the magnetic field. So you've got the very hot region at the base where the threading of the material occurs. And then the material starts streaming along what is called the funnel. And then what we have here is an accretion shock. So you have emission of very hard and soft x-rays and also cyclotron emission, which we are going to talk about in a second. And this is your highly magnetic white dwarf. !!PAUL: So Here's a view from a bit further out. !!DR. LILIA FERRARIO: Yes. So here you can see all the various components. So again you see your late type star. So your inner Lagrangian point would be somewhere here. Ballistic stream. But you can see that instead of having the material forming an accretion disc, you have a coupling region on the orbital plane. And then the material is lifted. It forms an accretion funnel. And it hits the white dwarf's surface. !!PAUL: OK. So how do these things look different. We talked about cyclotron radiation. So far for these white dwarfs, we talked about black body radiation, optically thick and optically thin. But here we're talking about something quite different. Do you want to talk us through what cyclotron radiation is? !!DR. LILIA FERRARIO: Well what happens is that what we have are charged particles. This is an electron. And these one's are your magnetic field lines. So the white dwarf will be somewhere off to the left. And what we have here is and electron that is spiralling along this magnetic field line. !!PAUL: Yeah, presumably an electron that is moving. It's has a moving charge, which is a current. And if you have a current, it is automatic for you get a sideways force. !!DR. LILIA FERRARIO: Yes. You get the sideways force, yes. !!PAUL: And so you got a particle moving in a sideways force, it will go in circles. So here it goes with the loop around here. !!

DR. LILIA FERRARIO: That is exactly correct. And it goes in circles, if emits radiation because any charged accelerated particle emits radiation. !!PAUL: Yes, just like a radio transmitter. You know in case you jiggle electrons up and down a pole, and they radiate a TV. And in this case, you're jiggling it round and round in circles and it generates the-- so what sort of frequencies are we talking about here? !!DR. LILIA FERRARIO: Well, here we talk about-- I mean, the emission occurs, for a typical AM Her would occur in the infrared. And then-- !!PAUL: So it's very high frequency compared to the terrestrial radio because it's accelerating really fast and the magnetic field is so strong. !!DR. LILIA FERRARIO: Yes but there will be harmonics that will be observed in the optical spectrum. !!PAUL: So spectrum's going to look a bit different. Do you want to talk us through this diagram? !!DR. LILIA FERRARIO: OK. Well, first of all, let me say that you don't see cyclotron harmonics in every spectrum of a magnetic system. So you have to have quite special circumstances because if the accretion rate is very, very high, then all the harmonic features will be washed out. !!PAUL: Smothered as all the stuff falls in somehow. !!DR. LILIA FERRARIO: Yes, so you don't see anything anymore. So we are in a situation a bit like your dwarf novae where what you really have is that the emission is really dominated by the accretion disk. In this case, in an AM Her type system, the accretion-- !!PAUL: AM Her the is the archetype of these sort of systems. !!DR. LILIA FERRARIO: --yeah, will we be dominated by the accretion funnel. So this is quite interesting. These are the very first cyclotron harmonics ever observed in an AM Herr type system. And as you say, AM Her was the prototype, the one that was the first observed in 1977. And somebody just, Santiago Tapia pointed the polarimeter to observe a cataclysmic variable and noticed it was highly-- !!PAUL: This is the type of spectrograph that measures the polarization. !!DR. LILIA FERRARIO: Yes, it was a highly polarized. And so these observations were made in the late '70s on the Angl0-Australian telescope. And as you can see, the spectrum has this-- !!PAUL: Wiggles. !!DR. LILIA FERRARIO: --cyclotron humps. !!PAUL: Each hum is caused by the frequency of the electrons spiraling around. !!DR. LILIA FERRARIO: Yes. !!PAUL: I would suspect them at the bottom. This is the faint-- !!DR. LILIA FERRARIO: Well, this is the faint side of the star. !!PAUL: So this is the side where the stuff is slamming into it. And that's the opposite side. !!

DR. LILIA FERRARIO: And this is the opposite side. So you can see in the opposite side, there is nothing. There are no wiggles. But on the side where the accretion shock is, then we have these cyclotron harmonic patterns. !!PAUL: We've go infrared spectrum here. !!DR. LILIA FERRARIO: And this is the infrared spectrum of another AM Her type system, which is called ST LMi. And these, as I said, it's in the infrared. So these one's are microns on the x-axis. And again, what we can see is this wiggle. We can see these cyclotron humps. And they can be modeled with a field strength of 12 Megagauss. !!PAUL: OK. So what do you find so fascinating about these systems? !!DR. LILIA FERRARIO: What I find fascinating-- physics is absolutely fascinating because it is something that cannot be reproduced in a terrestrial lab. I mean these kind of magnetic fields, well, we can't have them. We can't create them on Earth. And so it's a quite extreme type of physics that we are looking at, some that we can only observe in space. !!PAUL: Now most astronomers tend to avoid magnetic fields where ever possible-- oh oh, magnetic field-- because they're too complicated. I mean do you find them particularly complicated or what. !!DR. LILIA FERRARIO: Well, yes they are because obviously you do introduce a lot of complication. But you see in most cases, you can probably avoid having to introduce these magnetic fields. After all, as we know, some 90 odd percent of stars are nonmagnetic. So why bother with putting magnetic fields in? But when you start looking at these kind of objects, then you can't avoid magnetic fields. And you just have to try to fit the observations, to understand the observations as much as you can. And you have to understand the role that magnetic field play in these kind of objects. !!PAUL: Great. Well, thank you for coming in. !!DR. LILIA FERRARIO: My pleasure. !

V3.10 BRIAN: So we've learned a tremendous amount about these things we call cataclysmic variables in the sky. We seem to have a model where you've got a big, puffy, red star donating material to that very compact white dwarf. In that process, there's a lot of energy released, and that material spins up and creates what we call an accretion disk. So this is an interesting, and seems like a plausible, scenario we've pieced together. But I wouldn't say we've solved all the mysteries. !!PAUL: Yeah, but one puzzle is how we actually get the situation in the first place. We need to put a stars at the end of it's life when it's puffing up to become a red giant, very close to a white dwarf. And a white dwarf is, of course, a star that has all ready died. So how are we going to get these two so close to each other? !!BRIAN: Well, it's kind of interesting and maybe not realized by the average person that the average star in the universe is not born like our sun as a single star. It's born as a binary. And remember that star that was a white dwarf at some point had to puff up to become a very big red giant star as it was running out of its nuclear fuel in its core. !!And when a big star puffs up, there's going to likely be an interaction. Because the star, instead of being the size of the sun, is really going out the orbit of Mars or the Earth. So you have a great chance for, when those things happen, for there to be mass transfer and interactions that affect the entire system where you will-- for example, when those two stars are orbiting each other and one

puffs up, that will tend to cause a lot of friction, and cause the stars to become even closer in the future. And you could expect this not to be a rare event, but happening maybe 5 to 10 percent of all stars. !!And Dean, if you look at one of the closest stars in the sky, Sirius, Sirius has this as we know really nearby white dwarf. And that star almost certainly interacted with Sirius at some point in the past. So this type of event may well happen for one of the closest stars in sky, Sirius, in the future. !!PAUL: Yeah, so, it would have started off as two normal, perhaps, sun like stars. And then whichever one was more massive would die first and expand. And while it was very big, dynamical, friction would pull the things together. They might even actually orbit inside the atmosphere of each other at some point. So called common-envelope accretion. Then that one dies to a white dwarf and then at some later stage the one comes. !!So indeed, this could happen when Sirius A, at some point in the future, comes to the end of it's life and starts swelling up. We might get one of these dwarf variables right there very close to us. !!BRIAN: Yes. One question that still remains, though, the whole reason we're talking about these things is because they're cataclysmic variables. They were discovered because essentially a new star appeared. In our model we haven't really talked about what causes that cataclysm. !!PAUL: Yeah. In fact, that's probably one of the unsolved mysteries of the universe. No one is actually quite sure what causes these explosions. The current best guess is that you get the gas moving from the red star into the accretion disk via the hot spot, and probably the accretion disks gets denser and denser and denser. But there isn't enough to cause the stuff to spiral in. !!And at some point, it becomes so dense and so hot that something changes in the disk. Some sort of instability, maybe it becomes ionized and the magnetic field lines can cause the gas to spiral in. And then suddenly huge amounts of gas moves down towards the center, releasing its energy, producing a very bright, very dense phase for a little while until the disk had emptied itself out. !!Most of the gases end up on the white dwarf in the middle. And you have very thin disk and the whole process can start again. More and more gas will start-- !!BRIAN: So it's sort of like the straw that breaks the camel's back in some way. Where you have something preventing the material going on to the star, some physical process, and you're piling stuff, piling stuff up, you overwhelm that process. You sort of dump the stuff and then once that happens the thing builds back up and the whole process. !!PAUL: Yeah. That's our current best guess. Some people would still suggests that maybe it's actually something in the red star that's doing it. There's some instability there that will cause the flow to suddenly increase. But I think most people currently think it's probably instability in the accretion disk that's making it happen. !!BRIAN: What's quite remarkable about these objects is they're not rare. We see them quite-- all over the sky. We're discovering new ones all the time. Indeed, they're kind of the bane of my existence. Because with our sky mapper telescope we're out surveying the cosmos for objects even more violent than cataclysmic variables. And there are so many of these cataclysmic variables that come up that they sort of cause problems. They're almost like a cockroach in the transient universe because there's so many of them we just want to sweep to the side because we more or less understand what's going on with them. !!PAUL: Yes. It's kind of interesting because so far these seem like incredibly violent things. White dwarfs are amazing places way outside any imagination of, say, 19th century people. The incredible densities and pressures energies of these things. But in fact, they're just a tip of the iceberg of the violent universe. !

!And next time will come on to something which is actually considerably nastier and more violent. !!Lesson 4: Classical Novae and the Chandrasekhar Limit!

V4.1 PAUL: So we've come up with an explanation for dwarf novae explosions. We have white dwarf-- this incredible hellish, dense object. And we're dumping matter from a star into it, and this rather complicated system whereby the matter smashes into a disk producing a flickering hot spot and then builds up in the disk, and then dumps your stuff in the middle. I mean, surely it can't get much more violent than this, can it? !!BRIAN: Well, I think we must call them dwarf novae for a reason, Paul. Indeed, there's something that we call classical novae, or just novae, which are many orders of magnitude brighter. So for example, there's a very famous one called RS-Ophiuchi. And you can see, it's down here. And it gets 10,000 times brighter and then fades away. !!PAUL: Remember, the dwarf novae are only 100 times brighter, so in the scheme of violence, they're pretty pathetic compared to this. !!BRIAN: Yeah, the interesting thing about this is this object doesn't repeat every month. It repeats every 20 years or so, and some of them repeat after hundreds of years. !!PAUL: In fact, a definition of a classical nova is it doesn't repeat, of course. They probably do repeat. It's just that we haven't been observing long enough to see them repeat. So probably all-- there are differences between so-called recurrent novae and classical novae, but they're probably all the same thing. A current nova is one where we've seen at least two explosions. A classical nova is one where we've only seen one explosion so far. But they're by and large the same thing. And it's got this huge increase in brightness. !!BRIAN: They're quite interesting if you look at them after an explosion. So here's another one, and you can see after the explosion you're able to look at it. And you can see that there's this big shell that gets bigger and bigger over time, and it's sort of shooting material out. Two directions, sort of like, I don't know, well, I guess a gun if you manage not to have a stock when you shot off it goes out both directions. !!PAUL: Yeah, so that's a bit weird, in the classical novae, the explosion is caused by stuff going in. We're not seeing any blast wave come out. But here, we really are seeing a blast wave coming out, which is a bit different. !!BRIAN: Yeah, and we think this stuff is dust, so probably there's explosion stuff there but there's a ring of material around it you can't see. !!PAUL: Yes, that's making it a bit puzzling because the dwarf novae are caused by gravity, stuff falling in. And that's not really going to get our stuff going out, is it? !!BRIAN: Well, I guess that all depends on whether or not we can make enough energy, because the energy of whatever creates one of these things is the thing that'll eventually push material out. And presumably, if you make a big enough amount of energy you'll make a big enough bomb to make something that looks like what we see. !!PAUL: So, any clues about what's going on here? Well, there is-- this is a absolutely wonderful clue. Nova Persei 1901 went off in 1901, curiously enough. And you can see, it's blown a whole

shell of stuff out. It's now quite large and quite pretty. But there's a real clue here because if you look at the center now, you see a dwarf nova. !!BRIAN: Oh, that is an interesting clue, isn't it? !!PAUL: So it looks like the dwarf novae and the classical novae are actually kind of the same thing-- two different ways in which the same thing can explode. !!BRIAN: So that suggests that we have a white dwarf once again responsible for what's going on. !!PAUL: So it looks like we need to find another way to get an explosion out of a system like this. We've got a white dwarf again, presumably because it's acting like a dwarf nova gas is being dumped on the surface. How we can we get an explosion? The dwarf novae explosion we got from gravity, so matter would pile up in the disk, and then as a gravitational potential energy was released as it fell and you get an explosion. But that's far too small to produce these classical novae, unless we dump 100 times more matter down. So is there some other energy source we could use? !!BRIAN: Well Paul, if we think of the star in the sky we see every day, which is the sun, we think the sun was powered by gravity only for the very few minute-- well, not minutes-- but years of its lifetime. And since then, it's been powered by nuclear reactions of hydrogen and helium. !!PAUL: Well, that can't really work here. I mean, nuclear fusion releases huge amounts of energy when you turn hydrogen into heavier elements. But we've already said, the density here is so-- in the middle of a white dwarf- is so immense that if it was hydrogen there, it would've turned into a star. It wouldn't be a white dwarf. So it must be made of something that doesn't fuse as easily, probably carbon and oxygen left over from the star that formed it. And carbon and oxygen don't fuse very easily. It takes a lot of more pressure than we've got in the white dwarf to make them fuse. !!BRIAN: It is certainly true, but around this white dwarf in this model, we have a bunch of junk from that star. It's almost certainly going to be hydrogen, so clearly there's going to be hydrogen around. It's just a matter of making it-- configuring it-- in a way so that it can lead to some sort of nuclear reaction. !!PAUL: Yes, so presumably we've got this core of carbon and oxygen, which can't fuse in the pressure we've got here-- even in the hellish pressure of a white dwarf-- but we're going to be getting this layer of hydrogen building up on the surface. So something like hydrogen snow or something raining down steadily. Landing in a disc around the center but then presumably flowing around the surface of the white dwarf because a white dwarf's pretty hot. It's going to be pretty fluid. So you're going to get an ever thicker layer of hydrogen. !!So maybe we could get some fusion happening at the bottom of this layer, where there's pressure. But that doesn't seem to make sense to me because, I mean, this is a very thin layer of hydrogen. Look at the sun, you've got this huge great blanket of hydrogen, but the fusion is only happening in the central half a percent. The other 99.5% of the star is just an immense blanket to squash down that middle half a percent. How can a really thin layer, like on the surface here, do anything? !!BRIAN: Well, OK, Paul, remember, our white dwarf is incredibly massive and very compact, so it has a huge amount of gravity. So we go through and calculate, for example, the force on a little parcel of hydrogen. It's your normal equation of G, big M-- that's going to be the whole star-- little m, which is our little piece of hydrogen, and then the radius squared. But this radius is tiny instead of-- it's 100 times smaller, the white dwarf, than the sun. So that means that's going to be 100 squared or 10,000 times a smaller number, meaning the force is going to be 10,000 times bigger. !!

PAUL: And so, in any sort of star, you're balancing pressure against gravity. So in middle of a sun, the pressure in the middle has to balance the mass of that enormous blanket of hydrogen. And so, if the hydrogen's pressing down hard, there might seem more pressure in the middle. Here, what we're saying is that the gravity's going to be 10,000 times stronger at the surface. So a layer 10,000 times thinner will still have the same pressure at the bottom, roughly speaking. So that means you really can get away with just a very thin layer on the surface-- 1/10,000 of a thickness of the star-- and still have the same pressures that would start nuclear fusion. !!BRIAN: Right, so it's a great way to think about how to generate all that energy, but it's also a place where hydrogen is in a particularly interesting form that we need to talk about. !

V4.2 PAUL: So, we've got this layer of hydrogen on the surface and as it gets thicker and thicker, the pressure gets higher and higher at the bottom. So eventually, because of intense gravity of the pressure down here, it starts becoming comparable to that in the middle of the sun, at which put fusion will begin. That's not going to make an explosion, surely. !!In our own sun it's been fusing quite happily for several billion years without exploding. You might have thought that as all the gas rained down to form the sun in the beginning, there was a fusion, bang, the whole thing explode. Why doesn't the sun explode? !!BRIAN: Well, Paul, it's ultimately because the heat that's generated from the nuclear reactions, that temperature, also increases the pressure. So that central part of the star is going to want to expand a little bit when it gets hot and what does that counteracts gravity. And so rather than exploding, the whole thing puffs up a little bit, and then gravity pulls back a little bit, and you get this equilibrium where it's just able to burn at that rate where the thing doesn't explode and doesn't collapse. !!PAUL: So why doesn't that happen here? Why don't we get the fusion starts off that puffs up the bottom layer, therefore dropping the pressure and the fusion rate? And so it equilibrates and just burns slowly and happily like a star. !!BRIAN: Well, this is a very special place in the universe. This is the surface of a white dwarf, which we know is where they're the stars made up of a degenerate gas. That is where essentially the quantum mechanical nature of the electrons mean you sort of push them as close as you can. And-- !!PAUL: So it's the uncertainty principles supplying the pressure and not the temperature. !!BRIAN: That's right. And so that means that the temperature and the pressure, which are normally related like in the center of our son, are not related here. They're sort of independent of each other. !!PAUL: So as the temperature goes up because the fusion has started, it gets hotter, but that means there's no more pressure so it's not going to expand. !!BRIAN: That's right. And so that means when you make something really hot it's going to stay hot. It's actually going to be able to affect its neighbors, which we'll also get hot and want to burn. So you would expect, at about the speed of sound, the entire layer of hydrogen to burn as a giant bomb. !!PAUL: So presumably, a blob of gas falls through the accretion disk and lands on one place. And that's the straw that breaks the camel's back. It's kind of fun if you knew you had a white dwarf that was just nearly ready to go. And you could go and drop one feather on the surface and that would just push it over the crucial value. And then wham! It would light up in that place then a front would propagate around, you'd think very, very quickly. !

!So you'd get something like this. There's an explosion and moves around the surface. And then, bang, blows it all out. In fact, these things you'd expects to happen in a fraction a second. In fact, they take hours to peak in brightness and no one is quite sure why that's the case. There's some various theories about that. !!BRIAN: It's a bit of a mystery. !!PAUL: Maybe it just takes a while for the blast wave to move around. Or maybe it's generating power at lower level but it takes time to get up to the surface or something like that. !!BRIAN: Yes. Well, mysteries are good. !!PAUL: Yes, keep us in work. !!So what's actually happening here? You're getting all these fusion taking place at the bottom level here. It's pretty to see that to begin with. But down there it's going to generate lots of very highly radioactive isotopes. And also a lot of heat and the heats going to cause convection and carry up to the top. And so you get all those isotopes up to the top where they will decay and generate huge amounts of power. !!So you're now having something glow very intensely. There's a huge amount of radiation coming out. And it turns out the radiation actually apply pressure. If you get intense enough radiation, it can actually push things around. !!BRIAN: Right because the photons are going to interact with, for example, the electrons and push on them. The electrons almost look like targets, right? !!PAUL: OK, so let's see, maybe that's going to be what's actually going to push the speed over. There's a blast wave coming out. Maybe it's radiation pressure that can drive it. Let's do those calculations. !

V4.3 PAUL: Let's work out how much radiation we need to actually blow stuff off the surface of an object. Let's imagine we have a gas cloud, which because it's near an exploding star, is probably very hot, and so ionized. It will consist mostly of protons and electrons. And let's bombard it with some electromagnetic radiation. Now, some of the radiation go straight through, but some of the photons will get close to a charged particle. !!So, if you have an electromagnetic wave coming close to a charge particle, and an electromagnetic waves is an alternating electromagnetic field, which will cause the charged particle to alternate up and down. The one's that wiggle most, will be the ones with the smallest mass , ie, electrons. So by in large, it's electrons are going to interact with the photons. Because it's giggling up, and down it will radiate. !!So, what this means is that some of the radiation will go straight through, but a lot of it will make the electrons giggle, and will be radiated in different directions. So, it might come out all sorts of directions. Now, we could work out what fraction of the light is actually absorbed, because if you do this electromagnetic calculation, usually you could work out how close the photon has to get to an electron to actually interact with it. And it turns out that you can treat each electron as being a target with an area called, the Thomson Cross Section. So, Sigma-T which is, a whopping, 6.7 by 10 to the minus 29 square meters. !!

So, that, if you like, is how big a target every electron's going to be. And if the photon lands within that target area, it will get scattered off, or if it misses, and goes somewhere, over here, then it will continue straight through. So, that's telling us what fraction of the photons will actually bounce off. How is that related to force? Well, the photons that come in will have a certain amount of momentum. !!The photons that come out are in all directions, so they have randomized momentum that will average to 0. So, what you're doing is, you're cloud of gas is getting rid of momentum. The way you get rid of momentum is by applying a force. The momentum of the photons there must be a force of the gas on it , and that momentum will be transferred to the photons. So you're losing light momentum, and gaining acceleration of the particles. !!Now, we know that force is a rate of change of momentum, so if you work out the total flux of momentum that is going to test in a second, that will be equal, or opposite to force the gas cloud is applying to the photons. And so, it's going to be the same as the force the photons are applying to the gas cloud. So, how much momentum to the stream of photons hitting something? Well, according to relativity, the momentum of a stream of photons is equal to the energy of the stream of photons, divided by the speed of light. Now we want the amount of momentum hitting per second. !!So, that's go to equal to the amount of energy eating per second, divided by the speed of light. Energy per second per unit area is called flux, and we know how to calculate that. So, the flux of energy, that's the amount of energy per unit area, per unit time, is equal to the luminosity of the white dwarf or whatever, divided by 4 pi d squared. !!So, what's the force on one electron? It's just going to be this, times the Thompson cross section. And it's also, got to be divided by the speed of light, because momentum flux is energy divided by speed of light. So, the force of an electron, rather than the flux, it's now force. It's going to be this. Now, we can compare that to the gravity. If This force radiation is more than the gravity pulling something down, the gas will take off, and fly away. !!So what's the gravitational force? Electrons don't weigh much. There's not much gravitational force on that. Most of gravity is going to be applied to the protons. We're assuming this is Hydrogen, so just electrons, and protons. So, in principle, the radiation could blow the electrons away, and leave the protons behind. That won't work, in practice, because you'd have negative, and positive charges, which attract each other. So, the electrons are pushed afterwards, and they'll drag the protons along behind them, like a chain around their legs. So, the gravitational force, we need. !!So, force from gravity is given by the usual Newton's Law, so it's g, mass of the star, or white dwarf, times the mass of a proton, over the distance squared. Now, we can set these two equal to each other. And we can rearrange to find what the luminosity is that's needed to blow things off. The first thing to notice, is that both terms have a 1 over d squared in them. What this means is distance doesn't matter. !!So, if the radiation is strong enough to blow things away, it'll blow things away whether it's one meter away, or a million kilometers away. It seems a bit weird, but then, I guess, the amount of radiation goes down as d squared, and so does the gravitational force. They both go down by the same amount. So, when you're a long way out, the gravity force is very weak, the radiation is very weak , but they're still of equal size. So, the critical value is when these equal each other. Which gives you l equals 4 pi g m mpc, over the Thomson cross section. !!This is called, the Eddington luminosity, l, Eddington. After the British astronomer called Arthur Eddington, curiously enough. And this is telling you, if something has a luminosity more than that, it will be able to blow, at least, pure hydrogen off the surface by pure radiation pressure. And if you do the calculations for these classical novae, look at the luminosities, and the masses, it turns out, they are well above this, so in fact, radiation is probably what's driving the gas out. !

V4.4 PAUL: So we've seen that classical novae, the explosion of a thin layer of hydrogen around the surface of a white dwarf. The mass slowly builds up as more stuff gets dumped onto the surface, and eventually the pressure crosses that magic threshold, and the whole thing goes kaboom and explodes. !!BRIAN: And one of the interesting things about these objects is they're not all the same. Sometimes you get great big explosions that happen very rarely, and other times it'll be smaller explosions quite frequently. And we think this has a lot to do with how big the white dwarf is because you could imagine, if you've got a really heavy white dwarf, it's going to have a lot of gravity, which means that the hydrogen's going to want to blow up when there's not very much there. And so you'll get quite frequent, small explosions. But imagine a bigger white dwarf, or a lighter white dwarf, well that's one which has less gravity. And so you can build up a lot more on the surface before it goes kaboom. !!PAUL: And you might also have different sorts of things being dumped on the surface. For example, do you have more helium landing on the surface that might fuse a different-- you'd have to assume a higher pressure and temperature to actually fuse that? It would still happen eventually. !!BRIAN: Yeah, because there are these binaries. It turns out when you make these binaries with a white dwarf and other star, sometimes they do a very intimate dance with each other, exchange bodily fluids, and in the process end up converting a lot of it to helium. And so you might dump helium onto the white dwarf instead of hydrogen. And helium you have to get really hot and really dense before it's going to ignite. !!PAUL: And presumably it's not just going to be a single explosion. But if there's an explosion, blows stuf, there might be a thin layer left behind, because not to generate anymore. In that case, it could just burn for awhile like a normal star. !!BRIAN: Yes, and we also have the possibility that you can actually burn material rather than when it gets on the surface, that you actually burn it on the way in. So you have hydrogen coming from a star, burning as it reaches the surface of the star, and essentially being created as helium. And that allows you to essentially make the star grow heavier and heavier over time. !!PAUL: But if the white dwarf is growing heavier and heavier, I mean, we've known that the degeneracy pressure is wholly atop these electrons moving at relativistic speeds because of the uncertainty principle, but I wonder if there's a limit to that. I'm of course, not the first person to wonder about this. The famous Indian astrophysicist, Chandrasekhar, cycles was worrying about this in the 1930s. Let's see what his calculation came out as. !!OK, let's do the calculation. Can you really pile more and more matter onto the surface of a white dwarf without something nasty happening to it? Is there a limit to how hard this degeneracy pressure, this quantum mechanical electron pressure, can push back? Well from our calculation earlier, we derive the radius over white dwarf by balancing the downward force of gravity against the upward force of the degeneracy pressure. !!And this gets us some clue right away. You see it depends on the mass of the white dwarf to the one over 1/3 power. So one over the cube root of the white dwarf mass. So this means that as the white dwarf becomes more massive, the radius become smaller. Not very fast. You could increase this 8 times, this is only half in size. So this would seem to imply that white dwarfs can survive almost any amount of mass. As the mass gets bigger, the white dwarf gets smaller, but as the white dwarf gets smaller, its quantum mechanical pressure gets bigger and bigger. And so you just end up with very, very small very, very dense white dwarfs without limit to their mass. !!

So end of story. Well no, of course. And to explain why it's not the end of the story, of we're going to have to make a little detour into what makes a star stable. !

V4.5 PAUL: So what does it mean for something to be stable? Something is stable if whenever you move it away from its equilibrium, a force brings it back. So this book sitting on the table is stable, because if I try and perturb it bu, say, pushing the side up, there's a normal force that brings it back. No matter what I try to do to it, the force brings it back. If, on the other hand, I take a pen and balance it, I can balance it so the forces are in balance. It's an equilibrium. But if tilts, even slightly, one way or the other, the forces become more and more out balance. So it tips even more. So of course, it falls over. !!So is a white dwarf stable? Well consider this as a model of a white dwarf. A white dwarf is a ball of gas. This is a sphere of gas. Let's imagine that the surface of the balloon is like a surface layer on the white dwarf. If we push it in, it bounces back out again. What's happening is as we push it in, the volume inside the ball of gas decreases. As volume get smaller, pressure gets more. And so that pushes back out. Likewise, if I pull one side, it springs back in again. so a balloon is stable unless you puncture it. !!For a white dwarf, it's a bit different. For a white dwarf star, the same thing applies. You've got, say, a surface level of a white dwarf. And if it's pushed inwards, then the volume of the gas further in-- it shrinks. So it must push back. But on the other hand, you also have gravity on the white dwarf. If the surface layer gets closer to the middle gravity becomes stronger because of the inverse square law. So that will pull things further in. So is it stable or not? That will depend upon the balance between pressure force and the gravitational force and how they change as you squash on part of it. !!So you've got a simple model of a star, which is a sphere of uniform gas with a shell on the outskirts-- with radius R, let's say. And the question is, is the shell going to be stable? Now, this is a gross oversimplification because, of course, the density will steadily increase towards the middle. So calling everything in the middle just uniform is a bit silly. And you've also got gas on the outside, which we'll ignore for the moment. Though it turns out it works perfectly well if you put that in as well. !!But let's take the shell and push it in by a little tiny bit. As it's moved in, there's going to be less volume inside. As the volume goes down, the pressure will go up. And so the pressure will push back out with some change in the pressure. On the other hand, when you move close in, gravity's going to be stronger, because you're closer to the center of the whole mass system. !!So the question is how do those two effects differ? Now one thing we're going to have to figure out is how pressure changes as volume changes. If you've got an ideal gas, then it's just PV equals a constant-- [? NKT, ?] typically. So if pressure goes up, volume goes down, or vice versa. However, that's not always generally true. It may be true from ideal gas that's kept at the same temperature. !!But if the temperature changes when you compress it, then all bets are off, because this constant isn't so constant anymore. So, in general, what people tend to use is PV to some power gamma equals a constant. And if gamma equals 1, that's the ideal gas. But in other situations, for example, where the temperature is not fixed, then gamma may not be 1. !!OK, so if you've got that, how does the pressure force vary as you move something in? Well, the volume inside is going to be proportional to r cubed. The pressure is therefore going to be proportional to 1/V to the gamma, which is-- and V proportional to R cubed so it's 1/R to the 3 gamma. !!

So that tells us the pressure inside, the force is pressure times area-- the area of the inside of the show. So the area is just the area of a sphere, which is 4 pi R squared. So pressure force is going to be pressure times area. That's the definition of pressure. It's force per unit area. So it's going to be this times that. R squared-- I'm going to write that instead of one over R to 3 gamma, I'm going to write just R to the minus 3 gamma, which is the same thing. So it's going to be proportional to R to the 2 minus 3 gamma. OK, so that's telling us how the pressure force will vary as we our shell of star inwards. !!How about the gravitational force? Well the gravitational force is just my Newton's Law. G-- M over everything inside-- M of the shell over R squared. So it's just proportional to R the minus 2. So what we can see is we have a pressure force that goes as R to this power. And a gravity force that goes as R to that power. !!So if these two powers are identical, then if you push something in, sure the pressure will go up, but the gravity will go up just as much. So it will stay in balance. It will keep moving or keep moving out. If on the other hand, this increases faster than that, when you push something in, the pressure will increase by more than the gravitational force. So it will push the thing back out, it will be stable. If on the other hand, this varies more than that, then it's going to be unstable. If you push it in, the gravity will increase by more than the pressure. So accelerating faster and faster. !!So for stability-- the adjustability is going to be where this index equals that index. So minus 2 equals 2 minus 3 gamma. So let's rearrange that. So we'll move this over to this side. So we get 3 gamma equals 4. So gamma equals 4/3. And that is the criteria for stability. If gamma is greater than 4/3, then the star is stable, because the pressure will increase faster than the gravity when you push some shell inwards. !!If on the other hand, gamma is less than or equal to 4/3, it's unstable. If it were exactly equal, when you push it in, it will just keep on moving into the same speed, which is pretty disastrous. If it's less than that, it will accelerate, in which it's even more unstable. So that is the criteria for whether a star is stable or not. Whether if you perturb some layer of the star, it zooms all the way in and collapses or whether it bounces back and stays where it should be. !!V4.6 PAUL: OK. Now we know what makes a star stable is how the pressure and volume vary. Particular value gamma here, a constant. We can now apply this to white dwarfs and see are they really stable. !!Now, if you remember back when we were first deducing how a white dwarf could exist, we showed that if you have electrons bouncing back and forward in a box, the pressure they exert is proportional to the number of electrons times the typical velocity times the typical momentum. And normally momentum is written as p, but I'm going to write it as an m here, just so it's not confused with pressure. And we also know that the momentum is proportional to the number of electrons to the 1/3. !!If you have more electrons, that are all squashed into a -- That's a number per unit volume, I should say, not just a number. They have more electrons in a given volume. They're more squashed. Therefore, from the uncertainty principle, they must have more momentum. !!Now, in the original calculation, we then used the relationship, the momentum equals mass-- too many m's, [? they all ?] [? can't be ?] big m. The mass of an electron times the velocity. So we end up that velocity is proportional to 1, proportional to the momentum. !!

So the pressure is going to be proportional to the number times the momentum times the momentum, so that's momentum squared. Momentum is proportional to number to the-- number, n, to the 1/3. So that's going to be proportional to number times number to the 1/3 squared. So that's number to the 2/3. That's going to be proportional to the number density, the number of electrons per unit volume to the 3/3 plus 2/3, so 5/3. !!Now, how is this related to what we've talked about here? Well, the number, if you have a fixed number of electrons, then the number per unit volume is going to just be proportional to 1 over the volume. So what's this telling us is that for a white dwarf PV to the 5/3 is a constant. !!Just to go through that again, you've got n is proportional to 1 over V. So you got P proportional to 1 over V to the 5/3. So you've bring the V up there and you come up with this. !!Now if you remember, our criteria for stability was this index gamma be more than 4/3 and 5/3 is more than 4/3. So that's telling us that a white dwarf is stable. If you squash it, the pressure increases by more than the gravity pushes back out and it all stays where it is. Otherwise white dwarfs couldn't exist. OK. !!So what's the whole deal about these things not being able to survive at a large mass? Well, in doing this calculation, the crucial assumption we made is that momentum is equal to mass times velocity. Now, we used that to work out that velocities are proportional to the momentum. That is true if things are going much less than the speed of light, but if you calculate the speed, you find that in white dwarfs, especially as they get smaller and smaller, they actually get closer and closer to the speed of light. The electrons have to move closer to the speed of light. !!And in that case, well, they can't go-- the speed can't increase without limit if the momentum gets bigger and bigger and bigger. The momentum can get as big as you like since its got a gamma factor in relativity. But the velocity can't get bigger than the speed of light. So once you're close to the speed of light, instead of having V proportional to m, V is just going to be a constant. It's going to be roughly the speed of light. !!So let's fold that approximation in here. This is all a very approximate calculation, but hopefully, it gives us the key ideas. So in this case the pressure is going to be proportional to the number per unit volume times the speed of light, just as a constant, times the momentum. So we're just after the proportionality here, so that gives us momentum is proportional to n to the 1/3. So that's n times n to the 1/3. So that's proportional to n to the 4/3. !!Basically, what's happening here is once things are getting closer to the speed of light, the momentum can keep on increasing. So each time one of them bounces off the wall, it could still apply a pretty hefty force, then the force continues. But we also have to multiply by the number of electrons that hit per second. !!And that was just given by velocity times time because anything within that distance would hit the surface in one second. But as the velocity can't get more than the speed of light, that puts a natural limit. If this is more than the speed of light times 1 second away, it can't hit there in that second no matter how much momentum it's got. So that means that once your getting close to the speed of light, the pressure instead of going up strongly, it goes up more and more weakly as the number density goes down. !!So this is right on the edge of stability, which means it's unstable as we discussed. So that's telling us that when you get close to the speed of light, white dwarfs are no longer-- but, that is to say when the electron gets close to the speed of light, white dwarfs are no longer stable. And they can then collapse quite happily. !!Chandrasekhar did this calculation in a rather more sophisticated form and was able to show exactly what this mass is. He had to add up all the quantum mechanics properly and work out the

motions and the pressure and balance it all out. But it turned out that for a mass of the star that exceeds roughly 1.44 solar masses, if the mass of a white dwarf is bigger than that, then it's unstable. !!As the mass gets closer and closer to its limit, the white dwarf gets smaller and smaller and smaller and the electrons start moving faster and faster and faster to compensate. And when you're getting down to this sort of mass, with a very tiny size, the electrons are starting to move so close to the speed of light that instead of having P proportional to n the 5/3, you get to have it get into the speed of light limit and have it proportional to the 4/3, at which point it's unstable. And then if it keeps collapsing anymore, there's nothing to stop it because as it gets smaller and smaller, gravity increases every bit as fast as the pressure. So it would keep on shrinking and that is the Chandrasekhar limit. !!V4.7 BRIAN: So Paul has just shown us that if you take a degenerate ball of electrons, or a white dwarf star, there is a particular point where, if you add one extra piece of it, the star's gravity is going to be able to overcome the pressure of the electrons, the degeneracy pressure as we like to say, and the thing is going to want to run away and start shrinking to a black hole. !!Now, that is the calculation that Chandrasekhar did, in a slightly more sophisticated fashion, that ultimately won him a Nobel Prize. So you have just seen how to win a Nobel Prize, about 85 years after the fact-- after the event. Well done, Paul. !!PAUL: My pleasure. But how do we actually get a white dwarf to speak. It needs to be pushed over the limit, you add that last wafer thin mint to make it go bang. How do you actually get a white dwarf that large? !!BRIAN: So it turns out that most white dwarfs, like the white dwarf that our sun will eventually make, are going to weigh between 0.6 and 0.7 times the mass of our sun. Stars that are bigger, more massive than our sun, up to about maybe 7 or 8 times the mass of the sun, produce white dwarfs that are probably 1.2 times the mass of the sun. And that turns out not quite to be where we need to be-- !!PAUL: Where's the rest of the mass of the star gone, then, if you have a 7 solar mass star that turns into 1.2 solar mass white dwarf, where's it gone? !!BRIAN: So the center turns into the white dwarf, and it blows off all the rest into a nebula, which we typically call a planetary nebula. !!PAUL: Like the pretty pictures we saw earlier. !!BRIAN: Exactly. So we can get them back to 1.2, but that's not where we need to be. So it turns out there's a number of ways to make a white dwarf exceed what we call the Chandrasekhar mass of 1.4 times the mass of the sun. So one way to do it is we see through these classical novae. So as you take material on, or accrete the material, and it blows off, sometimes the explosions are such that you leave material behind so that the star is continually getting heavier as it accretes material. !!PAUL: So you might dump a certain amount of mass in this explosion, maybe 50% of it's blown off and 50% might stay behind. !!BRIAN: Exactly. !!

PAUL: And then more stuff accumulates. And then you get slowly adding action lay after extra layer. !!BRIAN: Yeah, and that turns out that's often not the case. Actually, the explosion sometimes makes the star less, but there are situations where it can make the story heavier. We talked about, earlier, the idea that material, as it comes on to the star, can be fusing on the way in and the deposited as helium. And it is possible, as you deposit helium, for that helium to, essentially, not be degenerate and burn on the surface-- convert to carbon and oxygen. And in that way make a star slowly rise up to that magic 1.4 solar mass mark. !!PAUL: So it's like a fusion burning star, but instead of the fusion being in the middle, the fusion's in a shell around the edge. But it's still burning gently because it's not in the generate level. So the pressure can regulate itself. !!BRIAN: And then finally, we can have a situation where imagine you have two white dwarfs together that are orbiting each other. Now, you might think they would orbit each other forever, but it turns out that they are releasing gravitational radiation. They're actually making space go through and do a little whoop, whoop. And that takes energy away. And over billions of years those stars, if they're close enough to start out with, will end up merging. When they merge, you get a catastrophic event where two, maybe 0.7 or 0.8 solar mass, stars merge into one big one. And so then you'll exceed that magic place and explode. !!PAUL: OK, so let's say this has happened. We've taken a white dwarf. We've added that last little teaspoon full of material. So the whole thing's gone over the limit. We've done it more catastrophically by colliding two of these things together. What's going to happen now? It's going to start shrinking. The mass is now over limit. So wouldn't it just keep on shrinking, without limit, 'til it gets down to 0 size? !!BRIAN: So obviously it would turn into a black hole before it reached 0 size. But it turns out that carbon-- well, many stars can burn carbon. If you add carbon and add a helium atom to it, or what we call an alpha particle, you can make oxygen and you can add the helium to oxygen and makes sequentially heavier elements. And so the density and the temperature inside one of these white dwarf stars is so high, that it's close to the ability to start burning carbon, but not quite. !!But when you squeeze it, that last little bit, when you go over that magical mark, you reach the point, very quickly, where you can burn carbon. And of course it's, again, degenerate. So temperature and pressure are kind of independent of each other. And once you start burning, the whole thing is going to burn as fast as it can go. !!PAUL: Yeah, so we talked earlier about the white dwarf's weren't doing fusion because they have a carbon oxygen, but that wasn't the density of a white dwarf. So we're now shrinking it down-- that can burn. You don't get as much energy out of carbon and oxygen and fusion as you do out of hydrogen, but you still get a fair amount if you confuse carbon oxygen all the way to the most stable element iron. So let's actually calculate how much energy you can get from one of these things. !

V4.8 PAUL: So to work out how much energy we can gout out if we make a white dwarf fuse carbon and oxygen by contracting, we need this diagram, one we've seen many times before in variants of this course. Brian, do you want to remind us what this diagram is showing? !!BRIAN: OK. To remind us how we're going to get energy out from E equals mc squared is, we're going to take one type of atom and transform it to another. And if that second atom weighs less, or

has a lower mass than the first atom, then there's a change in mass. And by E equals mc squared, we get nuclear energy out. !!PAUL: So for example, if you're turning hydrogen into, say, helium-- !!BRIAN: Yep. !!PAUL: --if you start off with one nucleon, you combine four of them to make helium-4. And the mass of the helium is not quite the same as four hydrogens. It's a slight difference. !!BRIAN: It's a little less. And that difference, which is about 7/10 of a percent, multiplied by c squared, which is a very big number-- it means you get a lot of energy out in, for example, a nuclear bomb where you do this reaction. !!So this diagram does it for all of the elements. And what we're plotting here is the mass of an atom, divided by the number of nucleons. So that's protons and neutrons. So that's the mass. And we're subtracting that mass from the mass of hydrogen. So we're looking at how much per nucleon it weighs less than hydrogen. And that tells you how much energy you're going to get out, !!PAUL: And so this diagram rises, which means if you combine small atoms like hydrogen, you get energy out. But then comes out as a plateau, about iron-56, which means that you can always get energy going towards iron. But then it starts sloping down the other side. Which means you can't get more energy by making things bigger than iron. In fact, you get the reverse. You take something really heavy like uranium, and shrink it-- so called fission. You get energy out. !!And if this curve was different, the universe would be a very different place. I mean, let's imagine the curve went up, but then kept on climbing. What difference would that make to the universe? !!BRIAN: Wow. If this kept on climbing, then you would not end up with iron being the thing we export from Australia around the world. Everything would sort of get to heavier and heavier elements. And we'd have a universe full of all sorts of heavy things. Probably the heaviest, stable stuff around. So, probably a lot of uranium is where you end up with. !!PAUL: Yeah. Well the principle if it kept on climbing, it means these things would be stable. And you could have elements way beyond. So you might have a lot more than 100 stable elements you've actually got. We might have thousands of elements. And most of the universe might be made up items with an atomic number and 3,000 or something, whatever that is. !!BRIAN: Yeah. So it would be a very different universe. But, if we're looking in the case of a white dwarf-- remember, a white dwarf is made out of carbon and oxygen, typically. So that's right here in this diagram. And so there's a bit of distance. This is a linear scale. So it's not nearly as big a difference from hydrogen to helium. But there is the potential when you burn carbon and oxygen to iron, to get energy out. !!PAUL: OK. So given this graph is so fundamental, I thought we'd probably better spend some time explaining where it comes from. So this is a quick lesson in basic nuclear physics. We're going to be talking about what's called the liquid drop model of a nucleus, which is remarkably good at very simple approximation. !!So if you think about the nucleus of an atom, it's about 10 to the minus 15 of a meter across. And it's got some protons and neutrons in it. But of course, there's a problem here. I mean, protons are positively charged. And two like charges repel each other. !!BRIAN: Right. !!

PAUL: So how's this going to work? You've got positive charges very close together. Why don't they just fling themselves apart? It's going to be incredibly strong repulsion between them. !!BRIAN: And those neutrons are neutral. So it's not like they're going to do any counteracting. They're just sort of sitting there, and don't worry about this electrostatic charge of the protons. !!PAUL: So we've got a real puzzle. How can these repelling things stick together? And presumably, we're going to need a new force. A force that stronger than electromagnetism. !!BRIAN: We should call it the strong force. !!PAUL: Ah! What an idea! !!BRIAN: Ah! !!PAUL: OK. And it's got to be an attractive force that sticks things together. !!BRIAN: Yep. !!PAUL: But if we have an attractive force that's stronger than electromagnetism, why isn't everything sucked in? !!BRIAN: Hmm. Yeah. So, yeah, if I have this big strong force-- well now, electromagnetism goes sort of as 1 over the distance squared. !!PAUL: Mm hmm. !!BRIAN: So what happens if it had a different power or worked differently on a different Scale !!PAUL: Yeah. So what we need is an attractive force that's stronger than electromagnetism. But it's got to be a very short-ranged force. And in fact, the way you do that-- any force in particle physics is created by virtual particles flying backwards and forwards. For electromagnetism, it's photons. They have no mass, which means they can travel for any distance they like-- a virtual particle. So that they're just spread out geometrically, which is why you get the inverse square law. !!This force, a strong force, is carried by the so-called Yukawa mesons. And they have actual mass. So these virtual particles, they appear out of nowhere because of quantum mechanics. But they can't go very far. So by the time they've gone from here to here, they've decayed. !!So the force will attract that proton to this one and this one. But it won't attract something over here. Its radius is only actually a bit smaller than 10 to the minus 15 of a meter. So that would make it work. !!BRIAN: OK. So you sort of have this balance where this group attracts itself. And that one attracts that self. And you have repulsion by all those things. And it's all in a nice, neat balance. !!PAUL: Yeah. It's a bit like they're sticky. When they're quite close to something else, they've covered in glue. And so, this explains how you can get energy from fusion. So let's say you had this helium nucleus, and you had another nucleon coming in. When it's a long, long way outside the range of the strong force, it'll just be repelled, if it's a proton. But once you get it close enough it's within the range of the force, it'll be sucked in. !!BRIAN: Yep. !!PAUL: And that bang, as it comes in, is what's going to be liberating the energy. !!

BRIAN: Right. OK. !!PAUL: So that's how you get fusion. But as you get something bigger and bigger and bigger-- !!BRIAN: That's a very big atom indeed. !!PAUL: I have no idea how many atoms it is. I didn't count when I made this up. But now let's imagine we want to add just one more proton. And you bring it in. Now you bring that proton in here. It's going to be attracted by the strong force, but only by these nucleons around here. The ones over there are going to be too far away to attract it via the strong force. But they're still going to repel it via electromagnetism. !!BRIAN: Right. And so we have all of these things adding up to a very strong electric repulsion of that new proton coming in. And even though it's 1 over r squared, there's so many of them, it ends up eventually being able to overcome that little tiny group of strong force from the neighboring nucleons. !!PAUL: Yep. So, the strong force is never going to get bigger. Because there's only a certain number of neighbors you can have-- one house on each side, if you like. Whereas the repulsion force depends on the entire atom, the entire suburb, if you like. And so as the suburb gets bigger and bigger, your number of neighbors isn't going to increase. But the number of people in the next street is going to get bigger and bigger. So eventually, the repulsion will break it apart. !!So if you try adding another proton, and another proton, and another proton, you end up with atoms that have become very unstable. And they're trying to stick together. But they're being pulled apart. And eventually, once you get out to the size of uranium, and so on, they just don't stay apart. And eventually, they fly apart. !!BRIAN: But presumably then, I could throw a neutron on, which is neutral and has the strong force, but doesn't get repulsed. So I should just make giant neutron atoms. !!PAUL: Yeah, that's a bit of a puzzle here. I mean, protons give you the trouble. But why don't you have an atom entirely made of neutrons? But hold on a minute. Back in the first course, we talked about the very early universe. We mentioned that neutrons are unstable. They have a half-life of just under 15 minutes. So after that time, they'd turn into a proton-electron neutrino. !!BRIAN: Mm. So they would just essentially decay on their own. !!PAUL: Yeah. So it's a bit puzzling. And in fact, to work at why you end up with a mix of neutrons and protons, we have to go back into a bit of quantum mechanics, which-- !!Let's imagine you've got a nucleus that's got a certain number of nucleons. So they could be either all neutrons or all protons, or some mixture of the two. Now, what's the best situation to have here? !!Well you've got to remember the two bits of quantum mechanics we talked about earlier. We've got the uncertainty principle. !!BRIAN: Yep. !!PAUL: Which says that these things are basically waves. And if you try and squash a wave, the wavelength has to be shorter, which means they've got more energy. So the more a particle you squeeze into a place, the more energy there needs to be. !!BRIAN: Right. !!PAUL: But you've got the second principle, which is the exclusion principle. !

!BRIAN: Two. !!PAUL: And the exclusion principle says that you can't have two identical particles in the same state. So now, let's apply them to these three cases. !!Now, here you've got a whole bunch of neutrons. And because the neutrons are identical, they can't all be in the same state. Their wave functions can't overlap. Which means you've got to squash a lot of them into a small space, it's going to have a very tightly wound up wavelength. And so there's going to be lot of energy. !!BRIAN: Right. !!PAUL: Ditto up here. Protons are identical to each other. So they can't all be in the same states, which means they've all got to have a little bit of the space to themselves. Which means they're going to be really squashed up and lots of energy. !!BRIAN: Right. !!PAUL: But, protons and neutrons are different from each other. So you can get a proton and neutron in the same space. Because they're not identical particles. So that means, if you get a 50-50 mixture of both, that actually means there's twice as much space for each particle. Because the protons can overlap with the neutrons. They just can't overlap with other protons. !!So that gives you twice as much space. So it's, roughly speaking, half the energy. !!BRIAN: OK. And so this is a lower energy state. !!PAUL: Yep. So if you've got something like this, it would much rather end up like that. Likewise, something like this will tend to go from that. So if you did get all neutrons, what would happen is they'll start decaying into protons until you get to a roughly 50-50 mix. The big ones actually tend to get more neutrons than protons to help bind it all together. But at that point, you're in the lowest energy state. !!And then for any more of these neutrons to decay, they'll have to get energy from somewhere. For just a neutron sitting by itself, it liberates energy when it decays to a proton. But in this case, it would still liberate a bit of energy. But it'd also have to gain a lot of energy, because everything had to be that much more squashed in. And once that gain of energy is bigger than the amount of energy it loses, it can no longer decay. Because it would need to get energy from somewhere. It would violate conservation of energy to decay. !!BRIAN: OK so atoms are this interesting balance between the strong force and the electrostatic force of repulsion. And then, this configuration-- the quantum mechanical configuration-- of essentially, the Pauli exclusion principle-- essentially adding another thing that keeps them from being in certain states. So it's a very complicated-- !!PAUL: And I've got a few more complications as well, of course. In reality, for example, the protons and neutrons will sit at energy levels. So you have to worry about the shells. And it's all these complications that keep nuclear physicists in business. !!BRIAN: Yes. !!PAUL: But this model gives you the basic picture and explains why we get this curve. We get 10 times the atoms with roughly the same number of neutrons and protons, and maybe a few more neutrons, when they get big, and explains why the curve goes up and comes down. !!

BRIAN: OK. !!PAUL: So now, let's actually use that knowledge to work out, if we did have a white dwarf's worth of carbon and oxygen, how much energy we get out converting it to iron-56. !!Lesson 5: Thermonuclear Supernovae!

V5.1 PAUL: So far, we've talked about two different ways of getting energy out of white dwarfs. The first is if you have your white dwarf and an accretion disk around it, as gas works its way in through the accretion disc closer and closer, it gives up gravitational potential energy. And that needs to dwarf novae. !!The second way is, you get a white dwarf and you pile a layer of hydrogen on the surface. And eventually, that layer of hydrogen becomes so thick that it undergoes nuclear fusion and blows up. And that gives you a classical nova. 100 times brighter than dwarf novae. !!But now we've come up with a third possibility-- the idea that you make the white dwarf so massive, that it starts to shrink. And as it shrinks and get smaller and smaller, eventually the density and pressure becomes so large that it can actually fuse carbon oxygen into iron. As we just talked about in nuclear physics, iron is the most stable element. It's got the perfect balance. And so, this will liberate energy. And the question is, how did the energy you get from this compare to the two things we've talked about over here? !!So let's work that out. The way we can work it out is look at the mass of carbon, oxygen-- which is what you're starting off with-- and iron. Now for carbon, the mass is typically 12.0107 atomic mass units. An atomic mass units is 1.67 by 10 to the minus 27 kilograms. !!Oxygen has very similar atomic mass. So it's 15.9994. So this is-- there are 12 nucleons, 6 protons and 6 neutrons here. Whereas there are 16 nucleons, 8 protons and 8 neutrons there. So this gives a mass per proton or neutron-- which is per nucleon-- of 1.00089 u per nucleon. And here, it's 0.99996 u per nucleon. So very similar. !!But if you look for iron, it's got a mass of 55.845 u, which comes out as 0.9972 u per nucleon. Now that may not sound like a very big difference, but it's telling you that about 0.3% of a difference in mass. If you take carbon and oxygen, and you get the right number of nucleons from them, and combine them to 56 to make iron, you'd think it would weigh 56 times as much as a single nucleon. !!But it actually weighs a little bit less than that. And that little bit less is caused by the binding energy. This little bit less-- the fact that that number is a little bit lower than those numbers-- is because the nucleons are stuck together with such strong binding energy. And energy equals mass, according to Einstein, according to the famous equation E equals mc squared. !!So, if we take one nucleon in the form of, say, carbon, and converted it into ions-- so that same nucleon ends up in iron-- we could look at how big the mass difference is. So let's just take carbon to iron. We could take oxygen to iron, and would get very similar answers. The change in the mass is 0.00366 atomic mass units. And that's just the difference between this and that. !!So every time you take one nucleon of carbon and somehow combine it so it's part of a nucleon inside iron, it weighs a little bit less. And that tells us that energy must be released. The energy's given by E equals mc squared. So the energy is equal to the mass, which is 0.00366 times the definition of an atomic mass unit from up here, 1.67 by 10 to the minus 27. So that gives you the mass, multiplied by the speed of light squared. So, 3 by 10 to the 8 meters per second squared. !!

And that comes out as 5.5 by 10 to the minus 13 joules per nucleon. So every time you take a nucleon-- a proton or neutron, and which is sitting inside a carbon nucleus-- and do some nuclear physics to get inside an iron nucleus, you get this much energy out. Doesn't sound like a lot. But of course, there are a lot of nucleons in a white dwarf. !!So how many nucleons do you have in a white dwarf? Well, what we can work out is the energy not per nucleon, but per kilogram. So energy per kilogram equals 5.5 by ten to the minus 13, divided by the mass of a nucleon. Because 1 over the mass of the nucleon is how many nucleons you have in a kilogram. So the mass of a nucleon is same atomic mass unity, roughly speaking. 1.67 times 10 to the minus 27. !!You can worry about whether it's this times the mass of that, but that's going to make very little difference here. Which comes out as about 3.3 by 10 to the 14 joules per kilogram, which is a lot. A small atomic bomb is maybe 10 to 11 or 10 the 12 joules, so this is a fairly medium-sized atomic bomb, as you'd imagine. Because atomic bombs work from the same principle-- nuclear fission or fusion. !!So that's how many we get per kilograms, how many kilograms in a white dwarf? Well, to make a white dwarf shrink down enough to fuse things, it's going to have about 1.5 solar masses. So that's 1.5 times the mass of the sun, which is 2 by 10 to the 30 kilograms. Multiply this by that. And you end up with an energy yield about 10 to the 45 joules. Whoa. That's a big number. That's a very big number. It is much bigger than classical novae, let alone dwarf novae, which are 100 times even wimpier. !!So, if you could get this to happen-- if you could get a white dwarf to shrink down and fuse carbon and oxygen all the way through the middle to form iron, you're talking about some sort of explosion that's much, much bigger than the explosions we've been talking about so far, which by themselves are pretty violent. We're talking about not really some nova, but something much worse. !

V5.2 !PAUL: So we've calculated that if you do get a white dwarf to collapse by putting too much mass on it, it'll fuse the carbon-oxygen up to something near the iron peak. And the amount of energy we're getting out is vastly more even these pretty spectacular novae we've been talking about. So we need some sort of explosion that's more than a nova. That's called a supernovae, for example. Is there actually any evidence for explosions even more violent than these classical novae? !!BRIAN: Well Paul, there were seen in ancient times some really bright things. Probably the brightest thing was seen in May, 1006-- actually the 1st of May, 1006; the Chinese were very good at keeping records. But this was also recorded across the Middle East and at St. Gallen in Switzerland. And this object was amazingly bright. It was about 100 times brighter than Venus, or roughly as bright as the moon when it's half lit, but in a point of light. !!PAUL: So that's vastly more than any of the classical novae we've ever seen. !!BRIAN: Yeah, so that would be a really bright thing. But of course, we know it's incredibly bright to look at. But you know, maybe it was just nearby. !!PAUL: That's the flux, not the luminosity. From the distance, we don't know how luminous it really was. !!BRIAN: But it wasn't the only one. In July of 1054 the Chinese recorded another guest star. And it is thought, in Chaco Canyon in the United States, that this petroglyph is related to that object.

Although it's rather difficult to connect that to that, it turns out, as you might imagine. So there's another one. !!And then, not much happened until almost 500 years later, when Tycho Brahe saw a guest star, or what-- he wouldn't have called it a guest star. He would have called it a new star-- in the constellation of Cassiopeia, recorded right here. And then just about 30 years later, his friend Kepler recorded another one of these stars. !!So, these things have been there. They seem to occur in groups. Well, it turns out that's probably just by accident. That's why you've got to be careful of patterns. But they only occur every couple hundred years on average, it would appear. !!And the most recent one that was seen in antiquity was in 1885, in August, when an astronomer in France was actually showing people the Andromeda galaxy-- or the nebula, as it was known back then. And they saw a new star in it. But they didn't know what this thing was. And remember, in 1885 we didn't know what a galaxy was. We just knew it was a nebula. !!So it was a real problem with these things. They were really bright, it would appear. But we didn't know if they were far or nearby. Maybe they were just nearby novae. !!PAUL: Mm hmm. !!BRIAN: And in 1923 on this plate taken on the 6th of October, none other than Edwin Hubble, he found a variable star that he knew how bright they would be in the Milky Way. And this one was many orders of magnitude fainter, indicating these nebulae or galaxies, as we know now, were very, very far away. And so S Andromedae, that object that occurred in 1885 in the Andromeda galaxy, must've been very bright indeed. !!PAUL: Yeah. And to be as bright as they appear to, but this case, billions of light years away-- I mean, that's got to be a phenomenal luminosity. !!BRIAN: Yeah, about 10 to the 44 watts. So a lot of 100 watt light bulbs worth. So, amazingly bright. !!PAUL: It's a ballpark about what we were calculating for the energy from collapsing a white dwarf. !!BRIAN: Yeah. Funny that, isn't it? !!PAUL: Yes. !!BRIAN: Hmm. So, one of the things you can go through and look at is these guest stars that occurred a long time ago. And what's there? It's probably a worthwhile forensic exercise. The problem is, those records in 1054 weren't really good. This is sort of the area they knew it occurred in. They knew it occurred roughly in the area of Taurus. And there's some interesting objects. !!There's the big giant star, Aldebaran, a big yellowish star in the sky. The Pleiades-- that's an interesting thing, a big grouping of stars. And then there's this thing that Messier found and confused with what he thought might be a comet, called M1. !!Now if you look at that, M1-- we call it the Crab Nebula now. And it's this remarkable ball of gas that's expanding at several thousand kilometers per second. It sort of looks like an explosion. !!PAUL: And if you take its current size and you extrapolate backwards at the speed of expansion, you can presumably estimate when it went off. !!

BRIAN: Yeah. Not only do you have the speed of expansion, you actually see this thing getting bigger in real time. If you run it back, it turns out it appears to have exploded whatever created it at about 1050 A.D. So, pretty well lined up to that 1054. !!PAUL: Hmm. OK. !!BRIAN: So, maybe these guest stars and this are related. Indeed, we are almost certain of that now. And they look like explosions, and very powerful explosions, indeed. !!So, when it was realized with the distance of galaxies that there were these super novae, none other than Fritz Zwicky, shown here, decided to go out and really try to understand these. The problem is, they're very rare. If you just wait for the next one to happen-- well, I've been waiting my entire life for a supernova to occur in the Milky Way. Fritz Zwicky was a smarter man than that. He said, I'm going to go out and look at a lot of galaxies. But to do that, I need a new type of telescope. !!I need a Schmidt telescope. Now, this Schmidt telescope isn't named after me or my relatives, but rather a German optician who designed a way to make a telescope that could look at a huge piece of sky at a time, and record the image onto a photographic plate. So he built this telescope from parts that he literally hand carried in from Germany, and started surveying the sky and finding dozens of these exploding stars we now call super novae. !!PAUL: So presumably, because a supernova only happens once every few hundred years per galaxy, you have to look at hundreds or thousands of galaxies at a time to find them routinely. So that's what this telescope allowed him to do. !!BRIAN: That's right. And he did it over several decades. Because even with this piece of equipment, he could only probably look at 10, 20, 30 galaxies at a time. But in the end, he had recorded some very interesting characteristics of these guys. They really came into two flavors. He actually found there were a few other ones that have individual representatives. But most of them he called Type I supernovae-- spectra that show no hydrogen. They seem to have no hydrogen whatsoever. !!And then Type II supernovae-- spectra dominated by hydrogen. So our two flavors. !!PAUL: Now these are the kind of things you'd expect because most of the universe is made of hydrogen. But these ones are very odd. It's very strange to imagine a place where there's no hydrogen. But of course, we know just such a place. A white dwarf star-- where the hydrogen's already been burnt off. And all we're left with is the carbon and oxygen. So, working hypothesis-- maybe these are the white dwarfs that have gotten too massive and started to collapse, and undergone nuclear fusion. !!Let's look in some detail about that and see if you can give us what we need. !

V5.3 PAUL: So, our idea is that we take this white dwarf, put too much mass on it-- we won't worry for the moment about why. We'll come back to that. And it shrinks. And that brings the density so high in the middle that you can fuse carbon and oxygen to form iron. We know that iron is the most stable element. It's at the top of curve. !!BRIAN: Yep. !!PAUL: So let's look in some detail about how this will work. !!

BRIAN: So let's think, if you try to burn carbon and oxygen, especially when its really dense. And presumably, when it burns it's going to be pretty hot. Let's just look at what happens within stars, or anything with nuclear binding energy. Most of us will see this. If you measure what the mass is, and divide it by how many nucleons, how many -- !!PAUL: Protons and neutrons. !!BRIAN: --protons and neutrons there are. And you plot that. Then you can go through, and you find that there's this maximum spot where iron is. Iron 56 is sort of the maximum of that. And so that means that, whenever I'm going to fuse two things together, I maximize my energy when I reach iron. !!PAUL: Yeah, so we've talked about this before. So we said, in other words, a star like the sun is taking hydrogen up to helium. And then maybe at some later stage, we'll bring it up to helium here. And that gives you a lot of energy. !!BRIAN: Yep. !!PAUL: There's rather less energy to be gained going from there to there, but there's still a reasonable amount. !!BRIAN: But if you overshoot this-- so imagine the star would overshoot that. Well, that takes energy away. And it's going to want to fission back. So the natural place for you to end up, when you burn something really fast with nuclear power, is up here, if you can get there. And it turns out, if you do detailed calculations of these things, that's exactly what happens. You end up burning to what we call the iron peak. !!Now, in detail, if you go through and do a full calculation-- and this is what the guys at the bomb labs are really good at doing-- and here we have a very high density and very high temperature. And for almost any sensible temperature, you end up making the stuff we call nickel-56. So that's nickel, rather than iron00 28 neutrons. 28 protons. !!Now it turns out that iron is two neutrons and protons different. So this is something that it turns out is radioactive and can end up eventually making iron. But it's the place that these nuclear reactions want to go. Because it turns out, it's neutral with its charge. And it turns out where the nuclear reactions like to take it. !!PAUL: So we've got this white dwarf. It's gone over the mass limit. And then presumably the center is going to start. And you're turning the carbon and oxygen to nickel-56. That's going to generate a lot of heat, presumably. !!BRIAN: It's going to generate a lot of heat. And of course, if we think about that-- let's just say we have this star. And we start burning stuff up to nickel-56 at its core. So like that. Then this is degenerate again. So if it's a degenerate gas, we know that temperature and pressure are once again sort of independent. So, unlike what we're used to here on earth. !!PAUL: So it can stop burning in the middle. And it gets very, very hot. But the pressure doesn't go up. So it doesn't cause anything to expand. It doesn't throw a blast wave out or anything. But that enormous heat will then presumably start fusion further out. !!BRIAN: Right. So you could imagine that what would happen is that you would sort of catch fire very quickly-- faster than the speed of sound. And that the whole thing would burn to iron almost like that. You end up with this huge ball of iron. !!PAUL: Or nickel-56. !!

BRIAN: Of nickel-56, in this case. In our case, because that turns into iron, it turns out nickel-56 is radioactive. And it turns in first to cobalt-56, which is also radioactive, and eventually to iron-56. And so, the half-life of this is about a little more than six days. And each time it does that, it lets out a lot of energy. So we measure things in-- MeV is sort of the-- !!PAUL: That's a megalectron volt. We talked about electron volts in the first course. !!BRIAN: And that's a little bit-- it's about 10 to the minus 13 joules per each one of those decays. And so that turns out to be a lot of energy. So when you create that big ball of nickel-56, you're actually creating a huge release of energy. And so, it's like you've suddenly released all this energy into this ball of gas. And what do you think that ball gas is going to do when you do that? !!PAUL: Well, I mean, normally if you put a lot of energy into a ball of gas, it'll get bigger. But this is degenerate. So it's not clear that actually happens. !!BRIAN: Well, it's not going to be very degenerate after it does all these nuclear reactions, it turns out. So the degeneracy-- the nuclear reactions that happen-- get rid of the degeneracy. So once again, temperature and pressure are related. And you suddenly have all this energy stored up in this ball of gas, which is no longer degenerate. !!PAUL: So what do you actually call this-- a fusion bomb? Or is it a fission bomb? Because you're getting lots of energy by going up the curve from carbon, oxygen, to nickel. !!BRIAN: Yep. !!PAUL: But then, a lot of the energy's coming as you'd then break nickel down to iron. So where's the energy coming from? Was it going from the first step or the last step? !!BRIAN: Well, the energy is created in what we call a thermonuclear detonation that creates the nickel-56. But then it's actually released-- the stuff that we actually end up seeing-- is released by this radioactive decay, as a fission process. !!PAUL: So first, when you get to the nickel-56, you see large amounts of energy. But that energy is stored in the form of these highly radioactive elements which then release it as they decay. !!BRIAN: That's correct. So it's an interesting process. And of course the cobalt-- also radioactive. Now, it has a half-life of 77 days, so more than 10 times longer than that. And it produces more energy for each of those decays. So you might think that this would be more energetic. But because it's happening slower, there's actually a bigger pulse of energy here. !!PAUL: So there's actually more energy there, but lower luminosity. Because that's sort of a more time. !!BRIAN: Right. So if you go out, and let's look at one of these Type I supernovae, and see how much energy they put out. This is what we call a bolometric light curve. We talked about them earlier. It tells you the total luminosity in astronomers' units-- ergs per second. So if you divide by 10 to the 7, then you're in watts, which is maybe a more sensible unit. And you can see that they produce a bit more than 10 to the 43 ergs-- or that's 10 to the 36 watts-- over a period of a couple weeks. So let's go through and figure out how much nickel-56 we need to create that light curve. !!V5.4

PAUL: OK. How much nickel-56 do we need to produce the light curve? We know if we plot the luminosity against time, we get the initial peak and then a slow decline. And this comes out as a peak of about 2 by 10 to the 36 watts. And that lasts for about two weeks. !!This is caused by the nickel turning into cobalt, which generates 1.7 megaelectron-volts for every atom. Whereas-- actually the bulk of the power is down here, which is going from cobalt to iron. But let's just look at the peak here for the purpose of this calculation. !!So the first we need to work out is the total energy liberated by the nickel to cobalt. So that energy is going to be equal to luminosity, 2 by 10 to the 36 watts. So a watt is a joule per second. So we need to multiply that by the number of seconds turned into actual energy from power. !!So we've got two weeks times 7 days in a week times 24 hours in a day times 60 minutes in an hour times 60 seconds in a minute, which comes out at about 2.4 by 10 to the 42 joules. OK. So that's the energy we're seeing liberated by the nickel going to cobalt. !!How many atoms of nickel 56 do need to do that? Well, each atom liberates 1.7 megaelectron-volts so the energy per atom equals 1.7 by 10 to the 6, 10 to the 6 is the megaelectron-volts, times electronvolt, which is 1.6 by 10 to the minus 19 joules. So that comes out as 2.7 by 10 to the 13-- to minus 13 joules. !!So how many atoms do we need? We can divide this by that and that will tell us the number of atoms, which is about 9 by 10 to the 54 atoms. But each atom weighs around 56 times the atomic mass unit. !!So you multiply this by that. You end up with about 10 to the 30 kilograms. There's your total mass. Mass of nickel-56, which is about half a solar mass. !!V5.5 PAUL FRANCIS: So we've got half a solar mass of nickel coming out. But we said earlier it was going to turn entirely into nickel. Does that means some of its turned into other materials? How do we find that out? !!BRIAN SCHMIDT: Well, let's take a look at the spectrum. !!PAUL FRANCIS: When in doubt, always look at a spectrum. !!BRIAN SCHMIDT: Yeah. A spectrum is where it codes all the information. !!PAUL FRANCIS: Hm. !!BRIAN SCHMIDT: Now, people are not going to know what this looks like too much without some help. So we're plotting blue light, red light, and how much stuff there is. And you will see these wiggles. And these wiggles are atomic transitions. The interesting thing is what atomic transitions they are. !!This feature, right in here, is silicon. This is also silicon. Note, that's not iron. This feature is calcium. !!PAUL FRANCIS: That's not iron either. !!BRIAN SCHMIDT: And that either. These are all things lighter. !!

Well, OK, what else do we have? We've got sulfur. That's lighter than iron. We've got oxygen. !!So is there any iron at all, you ask? Well, actually there is. There's a little bit of iron in this. But it's predominantly made, it turns out, of things other than iron. !!PAUL FRANCIS: There's another puzzle here. I mean as someone who spends far too much of my life looking at spectra, this is a really weird one. I mean we've talked earlier in the course about how you get emission lines when something is optically thin, things that stick up, and absorption lines, when things stick down, when you get a optically thick thing and something has been in front of it. And this seems to be sort of a hybrid of both. !!I mean look at this. It's going up and down. It's a sort of wiggle, up and then down, and sort of all these things. It seems to be a combination of emission and absorption lines. !!And they're also very broad. I mean normally lines are very narrow. They're at only one wavelength. But these things are spread over some immense range of wavelengths. !!BRIAN SCHMIDT: So let's think about how this spectrum is formed in a supernova. So I'm going to make a little schematic picture of a supernova. And so, like what we talked before, we're going to have that area that we say is optically thick. That's the opaque part. And then we're going to have a part around the outside, which is optically thin, which is translucent. !!PAUL FRANCIS: Yes. It's not like a star. It's almost like a solid surface. What's actually happening here is there's gas that's really dense. It gets less and less and less dense as you go out. And at some point, the density becomes low enough that the photons actually escape all the way to the Earth in one go. Whereas further in, they'd have to random walk their way out in some sense. !!BRIAN SCHMIDT: That's right. So, of course, if we're going to look at the light coming from that opaque part in the center, then, as we found out earlier, that you get a nice, what we call continuum from that. That's a featureless spectrum. That typically looks like a black body. !!PAUL FRANCIS: And it rises to the blue because this is extremely hot. !!BRIAN SCHMIDT: It's pretty hot. Yeah. OK. !!Now, of course, not all of those photons come directly to the Earth. Some of them are going to find an atom. So maybe, let's just say, a silicon atom, that has a transition, it turns out, at about 630 nanometers. And when it does that, it may be absorbed by that silicon atom and then reemitted, but not in the same direction. Typically, it'll go some other direction. And when it does that, that's taking a little bit of light out of that continuum. !!PAUL FRANCIS: Yes. That's a classical absorption. !!BRIAN SCHMIDT: Right. !!PAUL FRANCIS: I just like to get it in the sense of a star. And we've got it in our dwarf nebula when they were in flare. So that makes sense. But it's not like the spectrum of a supernova. !!BRIAN SCHMIDT: Right. But we have a difference here. Remember that this object we think had a whole bunch of energy in a ball of gas. So the whole thing is expanding. Its expanding quite rapidly, probably, given how much energy we've deposited in it. !!And when you take a big ball of gas, or a bomb, for that matter, and you look at it after the explosion, what do you see? The further away an object is from the explosion point, the faster it's moving, because that's how it got there. !!

PAUL FRANCIS: Yes. So these bits must have been going fast. They've gone so far out. Whereas, these bits must been going a bit slower. Despite it being a relative time, It's still pretty fast by most standards. !!OK. So that presumably means they're going to absorb at different wavelengths because of the Doppler effect. So this is going to absorb at a wavelength that's shifted to longer wavelengths, a redshift. And they're all going to be redshifted. But this is going to be much more redshifted because than the absorption from there. !!BRIAN SCHMIDT: Well, these are going to actually be blueshifted, Paul, because that's coming towards us. !!PAUL FRANCIS: Well, that's right. It's not going away, yeah. !!BRIAN SCHMIDT: So these would be redshifted. !!PAUL FRANCIS: So we're not going to see them in absorption. !!BRIAN SCHMIDT: You can't seen them because they're behind that opaque bit. So, you're right. You're going to get a different range of things. And, indeed, if we have this be the rest frame, we would expect these things to be scattered out, blueshifted towards us. !!But they're not all going to be at the same velocity because depending on exactly where they scatter, you're going to get different velocities. So the objects that scatter out way on the outside, they're going to have the highest velocities or the biggest blue Doppler shifts. !!PAUL FRANCIS: So you're saying the line would really be about here somewhere. So everything's blueshifted. And this is a very blueshifted. And then the gas that's maybe a bit closer in here is going to be a bit less blueshifted. So it might be down around over there, somewhere. !!BRIAN SCHMIDT: That's right. And so one of the interesting features is that the further you go out, the faster the material, so the more absorption, or the more Doppler shift. But if you go off the line of sight, then there's a geometric effect, essentially a cosine that comes in-- !!PAUL FRANCIS: Yeah. !!BRIAN SCHMIDT: --that gets rid of the Doppler shift effects. !!PAUL FRANCIS: So presumably you're going to light coming out here. And it's moving faster than the light there. !!BRIAN SCHMIDT: Yes. !!PAUL FRANCIS: But we only see the component of the motion on the line of sight, which is going to be less. So the two, I guess, sort of cancel out. !!BRIAN SCHMIDT: They do. They cancel out exactly. So that on these lines, everything has exactly the same Doppler shift. So depending on where you scatter on one of those lines, you line up to a different velocity here. !!PAUL FRANCIS: So you can read this as a scroll if you like. You would say here's how much absorption there in in-- so that's the fastest. That'll be over here. !!BRIAN SCHMIDT: Yup. !!

PAUL FRANCIS: And then going a bit further that way, you're going back to here, and here, and here. So you can actually tell how much absorption there is in each-- !!BRIAN SCHMIDT: That's right. So each bit winds up to a parallel part of the line. !!PAUL FRANCIS: It's parallel slabs across there. Neat. !!BRIAN SCHMIDT: That's right. OK, so that's part of the story. But, of course, the light comes not just straight through. Light can also come out, trying to head that direction to a different planet, but be deviated on its way, its path. !!And this light is, of course, going to be light that is emitted, again in those atomic transitions, but it adds to the continuum. So it gives us extra emission, more or less, rather than absorption. !!PAUL FRANCIS: Yes. So if you could point at just this part of the supernova, which, of course, we can't-- everything's much more than one pixel-- here we'd seen an emission. !!BRIAN SCHMIDT: That's correct. !!PAUL FRANCIS: There we'd see absorption. But, in fact, we're averaging over both of those things. !!BRIAN SCHMIDT: And since you're seeing things from coming back this way, where there's a redshift, or this way, which is a blueshift, you get a bit of everything, all centered around 0 velocity, in this case. And so when you add it all together, of course, against all those lines, you get something that more or less looks like what we describe in our supernova as a P Cygni profile, named after the star, P Cygni, which turns out to have a wind blowing out from it, where you get the same effect, albeit not at tens of thousands of kilometers per second, like we see in a supernova, but rather at hundreds of kilometers per second. !!PAUL FRANCIS: Let's go on up to the first spectrum, because they look like emission and absorption, and I was right. You're getting the emission lines from the bits out to the side and absorption from the stuff in the front. !!BRIAN SCHMIDT: Yup. And so we can go through and we can measure essentially how fast material is moving if we see this early on. But, of course, as the star-- or the supernova-- is expanding, it's becoming more dilute, right? Because you've got this big ball of gas getting bigger and bigger, which means that you can see further into it over time. !!PAUL FRANCIS: Yeah. It's kind of counterintuitive. You'd think if something gets bigger, it would appear bigger. But, of course, it's also getting more spread out, and therefore more transparent. So, in fact, as it gets bigger, it may actually appear smaller as you look at things closer and closer to the center. !!BRIAN SCHMIDT: It can be smaller or bigger. But it's certainly going to be material that's further in and moving at a slower velocity. !!PAUL FRANCIS: Yeah. So you're in a race between looking further in and the stuff moving out. !!BRIAN SCHMIDT: That's right. So if you look at it at one time and look at a little later, you're looking further in and so you'll see less velocity. And further still, less velocity. !!PAUL FRANCIS: The lines get narrower and narrower. !!BRIAN SCHMIDT: That's right. And so you can literally peel back the star as an onion and see what's going on, if you wait long enough, inside. !

!PAUL FRANCIS: Cool. !!BRIAN SCHMIDT: So that first spectrum I showed you was when the supernova was quite young and sort of at its maximum brightness, where you're looking, we think, on just the outer peel of the onion. So maybe we should look at it later on and see what's inside the star. !!PAUL FRANCIS: What do we see? I mean, nickle, lead. We can start seeing lines if we look right in the central regions. !!BRIAN SCHMIDT: Well, here, we are looking at 200 days. At this point, the object is so big that we can literally see right through the whole thing. And the spectrum has changed dramatically. And the calcium and the oxygen and everything's gone. And what do we see-- iron, iron, iron, nickel. And a little bit of nickle is around. !!PAUL FRANCIS: It's going away, presumably. !!BRIAN SCHMIDT: Yeah. There's not much left at 200 days. And cobalt, you just can't see in this part. You need to look in the infrared to see cobalt. !!And so the center part of the star is that iron that we expect, but the outer part isn't. So we need to change our story just a little bit. !!PAUL FRANCIS: OK. !!V5.6 PAUL: So Brian, we have two puzzles here, really. One is how you get a white dwarf to explode in the first place. How do you actually add enough mass to it to make it go bang? But then secondly, the remains should all be made of nickel-56. But we find all these other elements. What's going on there? !!BRIAN: Well, I think the secret is going to have to be looking and get the white dwarf so that it's no longer degenerate at the time of the explosion. Because if the whole thing's degenerate at the time of the explosion, the whole thing's going to turn into nickel-56. So we need to do something to it. And the best way to get rid of degeneracy is to somehow dump a bunch of heat into it, or stir it up, or do something that makes it not be that nice little quiescent ball of gas. !!PAUL: Yes, so you don't want a perfectly symmetrical, nice, spherical thing that's just resting there. And then you drop the last little feather on the top, and it all goes bang. We want it to be seriously traumatized even before the explosion goes off. !!BRIAN: Yeah, so it turns out, a number of ideas of how we might do this. So, maybe the most easily thought of is, you just take two white dwarfs. And instead of doing anything nice, you let gravitational radiation leave the system. Brings them closer and closer. And then at some point what happens is they merge. And when they merge, it makes a real mess. !!PAUL: Hmm. That's not pretty. !!BRIAN: And so, that mess-- that does not look like a nice degenerate ball of electrons. !!PAUL: There are presumably degenerate pieces, where the density's gone too high within it. !!BRIAN: Exactly. !

!PAUL: Some sort of mix of degenerate bits and not degenerate bits in some complicated spirally pattern. !!BRIAN: Right. And so if you can ignite that, if that ignites-- and there's a big question of whether or not it will in all cases-- then you would get a ball of stuff that's going to be a bit messy, but probably is not going to be all nickel-56. So that's one idea. !!PAUL: OK. !!BRIAN: You can also see, this is a good way to make a Type IA supernova. It's happening because these white dwarfs that will be made by two binary stars, sometimes, come together because of gravitational radiation. So it gives you essentially how often it happens-- not very often, but it can sort of explain what we see. !!Now, so that's one idea. Another idea has been in many respects the most popular, but it's a little more complicated. And essentially, it says that if you have a white dwarf, they start to simmer first before they reach that magical point of one-- !!PAUL: Because you're just gently dumping matter on the surface, in this scenario, are you? !!BRIAN: Right. And so-- !!PAUL: But before, it doesn't suddenly go bang at one point. It starts simmering. !!BRIAN: That's right. And the reason is that, imagine you have OK a white dwarf which is approaching the Chandrasekhar mass. At that point, every piece of material you put on, the whole thing gets a little smaller. Now, they're not all the same density. They actually have a density gradient such that the core is denser than the outside. !!PAUL: It would have to be to support the mass. !!BRIAN: Absolutely. That's right. And at some point, before you reach the magical 1.4 solar masses, you get to that density and temperature where carbon wants to start burning into oxygen. !!PAUL: Mm hmm. !!BRIAN: And so that will simmer. And when you simmer, then that's going to start liberating heat. The heat will bubble up, it turns out, in some cases. It will lift that degeneracy in the center. And so that will eventually, we think, run away. In the simulation, what happens is that the simmering starts. It starts happening faster and faster and faster until it runs away. And then suddenly it creates a detonation right there. And part of the star is already growing, so it doesn't completely burn to iron. It burns to oxygen and sulfur. And the inner bit, which has sort of been cooked more, that tends to burn-- give you the iron. !!PAUL: So it's kind of a slow start explosion. How long are talking about for the simmering? !!BRIAN: So the simmering is probably on order of decades to centuries. But then it's an exponential process. So it's one of those things that, each bit happens, and then when it runs away, it runs away in a period of about a second. So 1,000 years, maybe, in the making. And then, boom. When it does run away, it happens in that last-- that last exponential half-life is the one that rips the star apart. !!PAUL: But because it's been simmering for so long, a lot of the stuff is too far out. And degeneracy has already been lifted. So it doesn't all turn to nickel-56. !!

BRIAN: That's right. And then finally, a popular one recently is, we think sometimes that if you have two white dwarfs, one of them will be made of helium and be able to dump helium onto its partner. And helium, when it settles onto a white dwarf, can detonate itself on the surface of the white dwarf. And that's what you've just seen here, is you've seen material coming on from a white dwarf. !!PAUL: So helium's being dumped, and then you get a helium flash or something. !!BRIAN: You get a big helium flash. Now that helium flash is going to send pressure wave into the center of the star. And we think that sometimes-- actually quite frequently-- that pressure wave will again essentially compress the center of the white dwarf to a pressure and temperature such that carbon will detonate. And when that detonation-- because it's almost degenerate, the whole thing will start to burn. Again, because the thing has been disrupted, degeneracy has been lifted. The thing started expanding from the detonation. And again you'll turn the center into nickel-56, and the outer bits into lighter things. !!So those are three ideas. The question is, we don't know which one is right. And that's a bit of a problem. And so, you might think it's hopeless. But remember that Type IA supernovae-- we can actually see them. Because they've occurred in the last millennia, in our own galaxy, the Milky Way. !!So if we go out and look at them, here is the three easy-to-see remnants. This is SN 1006, seen by the Chinese. This is Tycho's Supernova, seen by Tycho Brahe. And finally, Kepler's Supernova remnant, seen by Kepler and Galileo. And so if you look in the center here, you see that's just a nice, spherical blob. !!PAUL: Hmm. !!BRIAN: There's no sign of really any mess or any. !!PAUL: Yeah, I mean you'd think if you were merging stars together, you'd have some horrible pattern. It would blast off in some directions and others. This looks like-- it's symmetrical. !!BRIAN: It's nice and neat. This one's surprisingly nice and neat, too. !!PAUL: Hmm. That one may be a bit more swirly. !!BRIAN: That one's a little more interesting. It turns out this one seems to have a band of, like, nitrogen and stuff that you might think came from another star. But two look kind of nice. And one's a little messy. !!PAUL: So which models do you think this would argue for? !!BRIAN: Well, it seems the simmering model seems to fit this pretty well. But there's a problem. And that problem is that, if you go through and you look at, for example, the center of the Tycho remnant, and you look at all the stars, we want to look for the star that was donating the material. !!PAUL: Yeah, presumably either the simmering model or the helium model, you've got another star there, which is dumping the gas on the surface to make this happen. And that other star won't be destroyed in the supernova explosion. You can destroy planets in a supernova explosion, but stars are just a bit too massive to be destroyed in that stuff. !!BRIAN: That's right. !!PAUL: So where is the star? !!BRIAN: Well. So, it turns out that when you go through and look at all the stars, you don't really see anything. What you expect to see is the following. Imagine you have a star donating material to the

white dwarf. Well, they're rotating. They're orbiting each other. And when that star explodes, well, the other star is going to go off at the orbital speed, rotating at the orbital speed. And that turns out to be several hundred kilometers per second. Should be easy to see. And yet, we don't seem to ever see it. !!PAUL: And you've spent a lot of time looking. !!BRIAN: And we have spent a lot of time looking. And much to my dismay, we haven't seen it. And there's another similar problem. Is that, that star when the explosion goes through that star, it's going to mess that star up. And when you heat a star up, it gets bright. And if we look, for example, at one of the nearest-- one of these exploding stars in 50 years-- you don't see anything. Indeed, if you go through and you new model what you expect to see when you blow something through a star, it makes things bright, almost as bright as the supernova itself. !!PAUL: So while the supernova is still rising in brightness while the radioactive elements start decaying, but for the very first case, you get a much greater brightness because of this hot, traumatized companion star. !!BRIAN: That's right. And so, this is what you would expect to see from that companion. And of course when we do look at it, we don't see anything at all. We see no sign of that. So we are missing sort of the smoking gun for the donor star. And so this leads us to, I guess, a number of possibilities and a bit of clues that we should sift through and think about. !!V5.7 BRIAN: So we've seen that Type IA supernovae may be the thing that happens when you exceed that magical Chandrasekhar limit, where the Heisenberg Uncertainty Principle and the pressure it provides is exceeded in the case of a white dwarf star. !!It fits the sort of places that these things should occur in galaxies. The objects don't have any hydrogen that you might expect from most stars. And they sort of provide the right amount of energy that you might expect. So, from that perspective it looks all pretty good. !!PAUL: But there is a problem, as we've just mentioned in the last video. How do you get these over-massive white dwarfs in the first place? We said one class of models involved a binary system, so another star is dumping gas on the surface. But in that case, where did this other star go? No one's found these other stars left lying around in the murder scene. !!And if it's not that, if it's a merging of white dwarfs or something like that, then how come these things are so beautifully symmetrical? !!BRIAN: Yeah. So this is one of the really big mysteries in my area of astrophysics right now, that if I have to admit confounds me even to this day. But we have some ideas. !!So one thing is that, imagine that you have one star donating material to the other. As the material falls onto the white dwarf, that white dwarf is going to spin up a bit. Now as it spins up, that centrifugal force actually removes some of the degeneracy and puffs the star up. !!PAUL: So it's more like a Frisbee than a sphere. !!BRIAN: Well, like a Frisbee. But it also means it's bigger. It means that it doesn't reach that central density necessary to ignite, as essentially as a big thermonuclear bomb. So imagine that you are dumping material, and you just run out of fuel. And you have this fast thing spinning that's maybe one and a half times the mass of the sun. Then it turns out, it will slow down over a billion years. !

!And when it slows down enough, then it will ignite-- a billion years after the material is donated, allowing that other star to fade away into a white dwarf. So it's essentially impossible to see. So, that's an idea. You might have a delay. And very tricky to go through and show that that's not true. Because it doesn't leave much behind. !!Another idea is that it really is a white dwarf white dwarf donating material. But the white dwarf is just feeding on this helium. And that helium detonates. And the whole thing explodes. Again, the little helium white dwarf donating material-- it's not very big. And you wouldn't see it easily. So that's another way to hide it. !!And of course, the white dwarf white dwarf mergers-- that's really hard physics. You gotta take two things, you know, with the mass of the sun, and mix them together in a period of a second, and blow them up. And the explosion itself will tend to regularize the messiness of the situation. Whether or not it can do it enough, I think is to be determined. !!And a lot of people, when they do that physics, don't even think the thing blows up at all. They think it might collapse down to something even smaller than a white dwarf, which we're going to talk about here in the future-- a neutron star. So, I think we have some ideas. But we don't have the answers yet. !!PAUL: And this is one of the most important questions in astrophysics, not only because these supernova are so damn interesting in their own right. But because they are the underpinnings of much of modern cosmology, through your own Nobel Prize work. Whatever these things are, it's their regularity, their standard candle nature that allows us to measure the existence of dark energy. So if we don't really understand what's going on in these things, that surely must cast a doubt on how useful they are. Would you ever really trust a standard candle if you didn't understand why it's standard? !!BRIAN: Well, at some point they are a useful tool, independent of how well we understand them. Because we can go out, and we can try them out all around the universe and make sure that they behave. If I have a whole bunch of light bulbs in a jar, and I don't know how well the 100 watts is calibrated on them. But I go and I put them all around me. And I see that when they're at the same distance, they're the same brightness. I sort of know that-- I don't know if they're 100 watts. But I know they're all the same. And I can use that over time. So it's not a loss. !!The problem is that if we want to use them to make ever increasingly better measurements, then the subtleties start to matter. And so, if you just want to discover that the universe is accelerating, you only need to know things, it turns out, to about 20%. But when you want to measure precisely, well then you maybe want to know things to 1%. And at that point, you really do need to know the details. And so we really do need to understand these things better, to make sure they're not changing back in time, if we want to make sure we have success in the future. !!PAUL: And how do you think we might go about coming to a better understanding of these things over the next decade or so. !!BRIAN: Well, I think there's some interesting work that we're doing. So some of the work that we're doing here at the ANU is, we're actually able to measure the masses of the things that explode. And one of the interesting features that we're finding is, it looks like a lot of them weigh less than the magical Chandrasekhar mass. And this is some work that one of the people who works with me, Richard Scalzo, has done. And it's still early days. We need to convince the rest the world that's true. So that would be a sort of a smoking gun. !!PAUL: Sort of a cat among the pigeons, I would think. !!

BRIAN: Right. Because there's only one way that we have that does that. And that's where you put the helium on the outside, and you detonate it. That's the only way to do that. But that work also shows that a lot of them are also at least 1.4 times the mass of the sun. So, maybe there's one or two ways of going. !!You know what I think maybe the best way to do is going to be, is at some point, one of these things is going to explode in our Milky Way, or one of the nearby Magellanic clouds again. And then we're just going to be able to see what happened. And I think, if I really had to bet how we're going to be absolutely sure, it's probably going to be that. !!PAUL: So, we've seen white dwarfs as part of the violent universe. It started off with the dwarf novae, the little baby explosions of these things due to the accretion disk. And then we've gone up to the classical novae, when they had a flash on the surface. Then we went all the way up even more in energy to the Type IA supernovae. So, these white dwarfs are pretty violent things. Is that it, then? Is the violent universe finished? Course over? !!BRIAN: well, you know, when we were out looking at the history, there was more than one way, it seemed, to blow a star up. Because there were stars that didn't have hydrogen. And there was that whole class of stars that did. And those don't seem to necessarily be a white dwarf exploding. So it seems an indication that there is more than one way to blow a star up. !!PAUL: So we're going to need something else violent, something even worse than white dwarfs. And that's the topic of the next video. !!Lesson 6: Core Collapse Supernovae!

V6.1 PAUL: So we've learnt about these incredibly explosions-- the supernovae. And we've got an explanation. It's a white dwarf that goes bang when too much mass somehow gets accumulated on it. So our problem solved? Well, I seem to remember you saying that actually there were two types of these things. I mean, we don't like this sort of complexity, but you remember some of them-- the Type Is, I think you called them-- had no hydrogen. And that would be a good match for these white dwarfs. But what about the Type IIs, which have lots of hydrogen? How could you get one of those? Do we actually need two types of massive explosion, not just one? !!BRIAN: Well, it would seem we need something to supply all that hydrogen since hydrogen's in short supply on these white dwarfs. And indeed, it is the case that we need something with a lot of hydrogen. And this was demonstrated because such a supernova, a Type II supernova, occurred in the nearby proximity of Milky Way, in the large Magellanic cloud, on my 20th birthday in 1987. !!And here we see an image of this part of the large Magellanic cloud, which is the nearby galaxy which orbits the Milky Way. It contains about 10 billion stars. And this is an image taken here in Australia before Supernova 1987A exploded. And you can see there's a little star there. And then, here in February 1987, we see something that's incredibly bright. Tens to hundreds of millions of times brighter than the star that apparently exploded. !!PAUL: So it looks like that's the star that went bang. !!BRIAN: It is. Now, with the benefit of the Hubble Space Telescope, where we can really zoom in and get above the effects of the atmosphere, we can see what's going on that part of the galaxy now. And so I'm going to zoom in on that little spot. And this is what it looks like with the Hubble Space Telescope. So a nice close-up picture. !!

And you can see that this thing is what we think is the supernova. And there are two other stars nearby that are quite bright, that turn out-- because of the blurring of the atmosphere-- those all combine to form one star. !!PAUL: So what's that one star we saw, just some of these two? !!BRIAN: No, it's the sum of this one, this one, and whatever exploded in the middle. !!PAUL: Aha. !!BRIAN: So if we go through and we look at that star, and we subtract off how bright these two things are, we're left with a brightness of a star. And the brightness of a star allows you to tell its mass. And this star apparently had a mass of about 15 times that of our sun. !!PAUL: So that's definitely saying this is not one of these exploding white dwarfs. I mean, a white dwarf would be much too faint. You imagine it might be the companion star that's feeding mass onto the white dwarf. But the companion star had to be less massive than the white dwarf star. Otherwise, it would have died first. And we need it to die afterwards. So the companion star may be one, may be two solar masses, if you push it. But there's no way it could be as big as this is. This is obviously something quite different. !!BRIAN: Yeah. So this is apparently something that is a different family of object. !!PAUL: So, how can you get a massive star like this to Explode !!BRIAN: Well, I think what we need to do is think back to sort of the life cycle of massive stars. So, a massive star course burns hydrogen into helium and helium into eventually carbon, just like our sun does. But small stars sort of run into a stumbling block. It's very difficult for them to burn things beyond carbon. Because they just can't get hot and dense enough. !!PAUL: Which is why these normal stars leave us a nice carbon-oxygen white dwarf behind. !!BRIAN: Absolutely. So, if you're a more massive star, when you run out of that nuclear fuel and gravity takes over, it's able to squeeze it harder. Squeeze it so you start adding heliums on to each successive nucleus. And eventually you end up burning silicon into iron and nickel. But of course, that's a process that turns out only lasts for a few weeks. Because it's happening so quickly. It's happening at very high temperatures and densities. But it's a different type of process than burning carbon into oxygen, for example. !!PAUL: this is going to be very final. I mean, if you've got carbon and oxygen, in principle you can still get wring more energy out of them somehow. But once you've got iron and nickel, there's no way you can get more energy out of that, is there? !!BRIAN: Yeah. That's right. Because remember, this diagram that we saw earlier on-- this is the binding energy per nucleon, per proton or neutron. And so what you see is that there is this maximum, which turns out to be right at iron. And that means that when you try to put things together beyond iron, it's going to take energy. And if you try to break iron apart, it takes energy. So you're at that maximum spot where you can't really do any more nuclear power. !!PAUL: So once you've got a large mass of iron and nickel in the middle here, and there's this sort of rapid, few weeks process-- what's going to happen then? I mean, it's going to be very massive. And it's not going to have any more source of fuel. So it'll shrink down. Do you think it might shrink down from a white dwarf, only this time an iron-nickel white dwarf. But this is a very massive star. We're talking 50 solar masses. !!

And as we saw earlier, there's an upper limit to how big a white dwarf can be set by the Chandrasekhar limit. If you're too massive, the electrons have to be going faster than the speed of light to be able to resist the pressure. So surely, that's it. Game over. It just keeps on shrinking, and shrinking, and shrinking till it forms a black hole. !!BRIAN: That would make sense. But we have to remember that you have these nucleons-- protons, neutrons all combined together to make iron. But in the 1930s, we had that understanding that neutrons themselves would behave like an electron, and have their own degeneracy pressure. !!PAUL: Yes. Of course back in the 1930s, Chadwick discovered the neutron for the first time. And certainly then realized, well hold on a minute. We've got electron degeneracy pressure. When you make something dense enough, the electrons start behaving quantum mechanically. But neutrons should do the same thing. But if you do compress them enough, they too, will start behaving like a quantum mechanical fluid, and maybe give it degeneracy pressure. !!And because they're more massive than electrons, it will happen at much higher densities. So let's do the calculation and see if this is at all feasible, and what would happen if you actually had a star supported not by electron degeneracy pressure, by neutron degeneracy pressure. !

V6.2 PAUL: So we know that we can have a white dwarf star supported by the electron degeneracy pressure. Can we have something analogous supported by neutron degeneracy pressure? Well, here's the equation for the radius of a white dwarf which we worked out by balancing the quantum mechanical pressure against gravity. !!And the same calculation should apply to something supported by neutrons. What's going to change? That's a constant, that term. And this is a constant, and that's a constant. So those are not going to change. This whole thing, here, is telling us how many electrons you get per atom. Which will be pretty much the same as the number of neutrons per atom. !!So we can ignore that. All that really matters are these two terms, over here, because they're going to change. This is the mass of the white dwarf. A neutron star will be more massive than a white dwarf. But not by a huge amount, maybe two solar masses rather than one solar mass. !!And so it's the 1/3 power. So that's not going to make a big effect. The crucial thing is going to be the fact that you've got the mass of the electron, here. And for neutron degeneracy pressure, we're going to have to replace that with a mass of the neutron. !!So by and large, we expect the radius of a degenerate object, something supported by degeneracy pressure, to be inversely proportional to the mass of whatever particle is doing the pressure. Now, neutrals have a mass 1,840 times that of an electron. So that's telling us the radius should be 1,840 times less. !!So instead of a typical white dwarf radius, which is maybe 6,000 kilometers, you divide that by 1,840, and end up with about 3 kilometers. In fact, it isn't more complicated than this. This is a good approximation. In fact, the radius comes out at about 10 kilometers. So we've got the right order of magnitude but out by a small factor. !!Nonetheless, that is absolutely tiny. Perhaps an analogy will help drive home just how small this is. Here is a view of Mount Stromlo. If we assume that a normal star, like our own sun, is the size of the entire mountain, then a white dwarf is the size of the dome of the 74 inch telescope over here. !!So if that dome is the size of a white dwarf, a neutron star on that scale is about the size of this pebble. !

!BRIAN: All right, Paul, so you've shown us that if neutron degeneracy is in action, we're going to end up with a tiny little star that is almost the mass of our sun. Or even more massive than our sun. So how much energy are we going to get making something big, for example, a big star, something very small. !!That strikes me as a good way to make a supernova. !!PAUL: Yup, so, in this case, presumably we're going to talk about gravitational potential energy that will start shrinking down. As it goes in, it will go faster, and faster, and faster. !!BRIAN: Yup. !!PAUL: And it'll form something that's too small for the-- much smaller than a pixel. But right in the middle, you're going to get the dense bulbs. [INAUDIBLE] the rest of the stuff is going to fall down out there, then bounce out somehow. !!BRIAN: Right. So let's go through and calculate how much energy we're going to get making a neutron star. And then let's think about what happens once that neutron star is made. Because that neutron degeneracy is going to stop the expansion. Then all that stuff coming in is going to want to pile in and bounce off. And we can figure out if this all makes sense. !!PAUL: So how much energy can we get out of the collapse of a star? Now, this is a rather complicated process. You've got a star and it runs out of fuel in the middle, so stuff starts falling in. A neutron star forms in the middle. More stuff rains down on top of the neutron star. !!Too complicated to solve for this problem. But let's make an approximation. Let's assume that the star collapses, leaving a shell of uncollapsed stuff, and a neutron star in the middle. So we'll assume the neutron star collapses really quickly. !!Let's say one solar mass. Leaving-- we'd say the whole star was about ten solar masses to begin with. So that leaves nine solar masses sitting out here. And that distance is about the size of our own sun, so about 700,000 kilometers. !!This is a gross approximation, but it won't give us too much of a wrong answer. We can now calculate how much [? energy ?] would liberate as the shell falls down the center. In reality, of course, some of the gas would not be falling from here, but falling from closer in. !!But on the other hand, the neutron star itself, had to liberate [INAUDIBLE] it formed. So this is probably not going to be too far off. Maybe a factor of three or four wrong, but should be within an order of magnitude of the correct figure. !!So we've got a shell weighing 9 solar masses, which is going to fall 600,000 kilometers to land on the surface of a neutron star of radius about 10 kilometers. How much energy is released in this process? Well, this is a straightforward gravitational potential energy problem. !!It's basically dropping something. We're dropping, like a ball, a certain distance. Gravitational potential energy is given by G mass of whatever is in the middle. So it's the neutron star. Mass of the shell over the distance between them. !!So in this case, the change in gravitational potential energy-- so the delta u, the change energy, is equal to at the difference between this at the beginning and this at the end, So that's going to be G, M neutron star, M shell, 1 over r of the neutron star, so 10 kilometers, minus [INAUDIBLE] emissions 1 over 700,000 kilometers. !!

Now you can see, this is going to be vastly smaller than that. So we can actually just neglect that. So what we find is the energy released-- just the change in potential energy-- is going to be, roughly speaking, G, M of the neutron star, mass of the shell, all over the final radius, which is 10 kilometers. !!So if you plug numbers into this, that's 6.67 by 10 to minus 11. That's G. Mass of the neutron star is going to be one solar mass. So that's 2 by 10 to the 30 kilograms. Times the mass the shell, that's 9 solar masses times 9 times 2 by 10 to the 30. One over 10 kilometers, so 10,000 meters. !!Which comes out as about 2 by 10 to the 47 joules. Now you have to remember the type 1A supernovae we were talking about last time, are only about 10 to 44 joules. So we're talking about an absolutely staggering amount of energy, here. 1,000 times more than the already staggering energy of a type 1 supernova. A huge amount of energy. !!V6.3 PAUL: So, we've seen that the amount of energy you can get out of a collapsing star is a staggering 10 to the 47 joules, or thereabouts. Bu there's a problem. !!Our idea was that the center of the star collapses to form a neutron star-- tastefully shown in purple there. And then you've got the rest of the star which collapses down. And this generates huge amounts of energy. And this then causes it to bounce back out again. !!But there's the trouble. If something drops in and bounces back out, it usually bounces back to at most the same height as where it came from. !!You see that here. When I drop the ball, it never bounces back higher than where it started from. In fact, with each bounce, it loses a bit of energy, and gets to a lower and lower height. !!So that wouldn't be a very impressive supernova. If you have the rest of the stuff in the star fall down, bounce out, fall down, bounce out, fall down, bounce out-- there'd be a lot of energy sure as it falls in. But energy's use up as it comes back out again. And then perhaps back as it goes in. And each time you lose more and more of it. You would get any blast wave thrown out. But we know that these supernovae produce things like the Crab Nebula. !!So how can get stuff blown out from something like this, a falling situation? Well, there is a way. Let me demonstrate. !!Instead of dropping one ball, let me drop two-- a small one on top of a big one. Look what happens. It goes much higher. What's going on here? !!Well, the basic idea is, let's say you've got something big. And you're bouncing something much smaller off it. And it comes in with some velocity, v. Then if it's an elastic collision, one in which energy is conserved-- so energy isn't wasted and you're making a noise or deforming the ball or heat or something like that-- that would also come out with the same velocity relative to the big thing. !!So that's all the physics we need. Let's see how it applies in this two-ball drop. So here we have a surface. Initial situation, let's separate the balls out to make it a bit clearer. I've got a big ball and a small ball. And they're both about to hit the surface Since they're both moving about the same speed, let's call it v. !!Now the first thing that's going to happen is the big ball will hit the surface. The big ball is much smaller than the earth it's hitting. So if it's an elastic collision, it will leave the earth at an upward

speed of v. So secondly, we're going to get the small ball, still moving downwards at speed v. And now we've got the big ball going upwards at speed v. !!So the next step is going to be the small ball hitting the big ball. So once again, the same rule applies. Let's assume the big ball is much bigger than the small ball. What is the speed with which the small ball approaches the big ball? Well, from the big ball's point of view-- it's moving up at speed v, the one's moving down at speed v-- so the relative speed is actually 2v. So from the big ball's point of view, the small ball is approaching it at speed 2v. And so afterwards, will leave it at speed 2v. !!So after this, the big ball is moving up at speed v. We're assuming it's much bigger than the small ball, so isn't much affected by the impact. Small ball came in at 2v, and it goes out at 2v. But that's 2v relative to 1v upwards. So that means relative to the ground, it's actually moving up at speed of 2 plus 1 equals 3v. !!So that's how you can get the ball to bounce very, very high. In the case of the small ball, infinitely smaller than the big one, and everything's perfectly elastic, it'll go up at about 3 times the speed. !!In principle, you could do even more complicated situations, like having an even smaller ball up here on top-- in that case, to have a third collision. So this one is now going down, still with speed v. It's now going to hit something with speed 3v upwards. So the rotor speed is going to be 4v, so it will then head up at 7v upwards. And in principles, have even small dots. !!So that's a possible explanation of how supernova can blow stuff out. The idea would be that you have your neutron star, and you have the heavy lower levels of the star come in and bounce out. And they're not going particularly fast. But then, a lighter higher level comes in. And it now, instead of bouncing off the stationary neutron star, bounces off the matter that's already moving out. So that means it'll go even faster. !!And then you might get an even lighter, further out layer of the star come in. And it's now bouncing off the extremely fast-moving stuff. And so it can go out at an enormous speed. So in principle, this could work it. It could give us extremely high output speed, which could produce something like the Crab Nebula we see. !!There's only one trouble. To get these very high speeds, you need ever-smaller balls, i.e., ever smaller amounts of mass. Most of the mass can't do this. Only a very tiny fraction-- like the highest ball-- can go out. So the amount of energy we're getting out has got to be much less than the total energy. !!So roughly speaking, it might only be a 0.1% or something like this. So instead of the 10 to the 47 joules we're talking about for the entire energy of collapse, we might only get a pathetic 10 to the 44 joules, or something like this. !

V6.4 BRIAN: All right, Paul. So you've shown us how much energy is liberated by the collapse to a neutron star. That is a lot of energy. !!PAUL: Yeah, but let's see. Does it actually match what we See I mean, "a lot" is a very vague term. Is it the right amount of "a lot"? !!BRIAN: Right. So it looks to us that you're going to get about 10 to the 47 joules of energy out. So that is a lot of joules. But the bouncing model-- where you bounce things off-- then it looks to seem plausible that you might get 10 to the 44 joules out, in the bounce. OK? So, let's go through and actually look at how bright a Type II supernova is, how much energy is in there. !

!So of course, a Type II supernova shines. So if you look at how bright, how many watts, or-- we astronomers still use ergs. There's 10 to the 7 ergs in a watt. And you can see that in this term there's about 10 to the 42 ergs, or 10 to the 35 watts that a supernova emits for about 100 days. So we can calculate from the luminosity the total amount of energy radiated. !!PAUL: OK. !!BRIAN: But, that's not the only place the supernova is going to have energy. Remember, they're big expanding balls of gas. !!PAUL: Yeah, some of it's going to come as radiation that we can see. But some of it's going to be accelerating the gas. So it's the kinetic energy of a gas, presumably. !!BRIAN: That's right. And so, we can go through and figure out how much kinetic energy there is as well, because we have spectra of these supernovae. And this is hydrogen and helium and hydrogen again. And we can measure the velocity over time. And it turns out these supernovae expanded roughly 3,000 kilometers per second. And there's about 10 solar masses of hydrogen that's expanding it that fast. So, we can calculate the kinetic energy. So let's go through and see how much energy is actually in a Type II supernova. !!PAUL: OK. Let's start off with the energy that comes out in the form of electromagnetic radiation, like radio waves, gamma rays, et cetera. Now we know we have a luminosity of about 10 to the 35 watts for about 100 days. So what's the total energy output? Well, luminosity is a power. So that's energy per unit time, which is why it's measured in watts. So we just need to multiply this by the number of seconds in 100 days. !!So we get 10 to the 35, times 10 days, times 24 hours in a day, times 60 minutes in an hour, times 60 seconds in a minute. And that comes out as about 10 to the 42 joules. Big, but a very tiny fraction of even the bounce energy, let alone the total energy. !!But now let's look at the stuff that's fired out. So we've got our supernova. And we've got some sort of shell of material flying out. And it's going at a velocity of about 3,000 kilometers a second. And the mass is about 10 solar masses. !!Now right away, bear in mind, that's a very large mass flowing out, which is quite different from our bounce calculation, which implied only a very small mass is coming out. So that right away is telling us there's something funny going on. Now we can work out the energy here. This is a kinetic energy. And the normal equation for kinetic is just half the mass times the velocity squared. So if you plug in this, so that's 2 by 10 to the 31 kilograms. And 3,000 kilometers a second, multiplied by 1,000, turn into meters per second-- we end up with about 10 to the 44 joules. !!BRIAN: All right, Paul. So let's recap the calculations just made. We have all this energy, 10 to the 54 ergs, or 10 to the 47 joules worth of energy making a neutron star. But the supernova we see really has several orders of magnitude less than that energy. About the same energy that you get out of the bounce. !!PAUL: So where's the rest going? I mean, there's this pesky law of conservation of energy. Presumably, the reason why the bounce is only a small fraction of the energy is because only a small amount of the matter is bouncing. So the rest of the energy must have something to do with the rest of the matter that's ending up in this ball of neutrons in the middle. But how-- the energy has to go somewhere. So where could it go? !!BRIAN: All right. So let's look at how you might form a neutron star, in detail. So, it turns out that as you're beginning to run out of nuclear power-- in the center of these massive stars it's very hot and

very dense. And there are gamma rays. Essentially the temperature is so high that the black body radiation peaks at gammas. OK? It's 10 to the 10 degrees. !!PAUL: That's pretty hot. !!BRIAN: Incredibly bright. Now it turns out that if you take an iron atom, and you shoot a really energetic gamma ray at it, the iron likes to fission. OK> And it takes that energy from the gamma ray. Because remember, it's going to lose energy in this thing. So it's actually going to take that energy out so if it can do this reaction. And this reaction's what happened. !!And so now you have lighter elements. And of course, gamma rays are going to hit them. And indeed, when you get these really hot temperatures that are really dense, things like iron get photo-disintegrated. All the gamma rays just split the atoms up, eventually all the way down to protons and electrons and neutrons. !!PAUL: That's kind of reverse in the whole process. We get the energy of the star by combining these things. And suddenly in a flash it's going all the way back down again. !!BRIAN: Right. !!PAUL: It must mop up a huge amount of energy. !!BRIAN: Yeah, it does. And so it's going to sap up all that energy that is-- or a lot of the energy of course-- that is being liberated by the potential energy chance, right? !!PAUL: So problem solved? The energy's just all gone away by reversing the nuclear fusion that it's spent the last million years doing? !!BRIAN: Well, it turns out, you only get a little bit. That's where-- some of the energy can be gotten rid of that way, but not all of it. So it turns out we need to look at that final reaction. You're going to end up with photo-disintegration making electrons and protons. And those can't be-- gamma rays don't break those apart. Those are pretty fundamental particles. In the case of an electron, completely fundamental. !!But when you get these really high densities, electrons and protons like to get together and make a neutron. And when they do that, they create a neutrino. !!PAUL: Aha. !!BRIAN: So the photo-disintegration is going to break all the iron apart into electrons, protons, and neutrons. And all the electrons and protons are going to get together to make a neutron and a neutrino. OK? !!PAUL: OK. !!BRIAN: And there's a lot of them. 1.4 solar masses of stuff is that many kilograms, 3 times 10 to the 30 kilograms. And a neutron only weighs 10 to the minus 27. So that's a couple times 10 to the 57 neutrons in a neutron star. !!PAUL: And the same number of neutrinos. !!BRIAN: And each one of those is a neutrino. !!PAUL: Now, astronomers of course, we're used to big numbers. But that's a big number even to an astronomer. !!

BRIAN: That's a very big number. And so, that's a lot of neutrinos. And if you remember, neutrinos are funny. Neutrinos weakly interact. They have tiny cross-sections. !!PAUL: They don't have any charge, so they don't interact via electromagnetism. They don't interact via the strong force. So they only interact via another third force, actually the weak force, which has its name. So it's pretty weak. !!BRIAN: Right. So they have-- if you were to call them a target-- they have a cross-section of about 10 to the minus 47 meters squared. So let's do a calculation and figure out what that means. !!V6.5 SPEAKER: let's look at how neutrinos interact with matter. Let's start off in our neutron star. The neutron star in the middle has put out an absolutely staggering number of neutrinos, about 10 to the 57 neutrinos. Can they get out? Well you've still got about 10 solar masses worth of material in some sort of shell, still falling in at the time the neutrino burst comes out. So the question is, can the neutrinos make it through this thick shell? !!This is a contest between two things. One is the stupendously high number of neutrinos. The other thing is the stupendously low cross-section. So let's imagine we have a neutrino. And it's trying to get through some matter. Now the matter is made of atoms. And if the neutrino comes within the cross-sectional area-- which as we remember is 10 to the minus 47 square meters. That's for each atom or molecule. If it goes within that area, then it will interact with it. If it misses that area, it will get through. !!So let's ask, what is the total cross-sectional area of all the infalling gas? So each atom has 10 to the minus 47 square meters. But there's a lot of atoms. How many atoms? !!Well, it's got a mass of around 10 solar masses. So that's 10 times the mass of the sun, 2 by 10 to the 30 kilograms. And it's mostly hydrogen. The mass of one hydrogen atom is about is 1.6 by 10 to the minus 27 kilograms. So number of atoms is going to be about the total mass. So that's 2 by 10 to the 31, from here, all over 1.6 by 10 to the minus 27. Which comes out as roughly 10 to the 58 atoms. !!So if each atom has a cross-sectional area of 10 the minus 47, the total cross-sectional area is just 10 to the 58, times 10 to the minus 47. Which is about 10 to the 11 square meters. So that's a pretty big cross-sectional area. !!What fraction of the neutrinos are thus going to be intercepted? Well, that's going to depend a bit about on how far out our shell of gas is? Of course, it's not really a shell. There'll be some gas very close and some gas further out. But let's guesstimate that at the moment, when the neutrinos rip loose, the bulk of the gases are something like 1,000 kilometers out. !!So if it's about 1,000 kilometers out, so let's approximate this being a shell that distance out, made of all these 10 to the 58 atoms. And each atom has its little cross-section. So there's a total cross-sectional area of 10 to the 11 square meters. But what's the total area of the shell? Area of a sphere is 4 pi r squared. So in this case, it's 4 pi times 1,000 kilometers. So that's 10 to the 6 meters, 1,000 kilometers times 1,000 turned into meters. 10 to the 6 squared. Which is roughly 10 to the 13 square meters. Which is about 100 times bigger than that. !!So what this is telling us is that if you could approximate all the infalling gases a shell, about 1,000 kilometers out, about 1% of the neutrinos will be intercepted. Which means that 1% energy will be dumped in the gas, which is not too far off the energy of the blast wave coming out. So that sounds

kind of plausible. It could actually be that the neutrinos are the source of the blast wave coming out, as they dump their energy in. !!Of course, this 1% figure was dependent on what radius we assumed. And in reality, that would be more complicated. You have to integrate over the overall amount of gas at that particular time. But it's at least looking plausible that a significant fraction of the neutrinos could be intercepted-- by no means all of them. But maybe 1% or 1 in 1,000, or something like that. And they could, therefore, dump a lot of energy. !!V6.6 PAUL: Now let's think about whether we could pick up these neutrinos on earth. Now let's imagine the nearest recent supernova, 1987A, was in the large Magellanic clouds, which are about 50 kiloparsecs from the earth. So let's have the earth down here. How many neutrinos will have reached us? !!So once again, we've got 10 to the 57 neutrinos coming out. They're now going to be spread over a sphere of radius 50 kiloparsecs. A kiloparsec is 1,000 parsecs. So it's 50 times 1,000, times a parsec, which is about 3.1 by 10 to 16 meters. So that comes out at about 1.6 by 10 to the 21 meters. !!So, how many neutrinos do you get per square meter of the earth from the supernova explosion? Well, you can simply take the 10 to 57, and spread that uniformly over the sphere. So divide it by the area of a sphere, which is 4 pi r squared. We've got r, so that comes out as approximately 3 by 10 to the 13 neutrinos per square meter. So that's 30 trillion neutrinos went through every given square meter of the earth when the supernova went off. !!30 trillion neutrinos. In one square meter. That's about the area of a human body. 30 trillion neutrinos went through your body, if you were alive in 1987, for everybody on earth at this time. I mean, wow. That's a lot of neutrinos. Why weren't we all fried, or murdered, or something like that? !!Well, once again, we have to bear in mind this extraordinarily small cross-sectional area. That is a lot of neutrinos, but would they actually interact with anything? !!Let's consider a human as a blob of water, because by and large, we are water. So let's, for example, take 1 cubic meter of water and fire our flux of [INAUDIBLE] 10 to the 13 neutrinos into it. Would they interact? Well, once again, we've got-- actually, here in this case, it's water molecules. How many water molecules? !!Well, one molecule of H2O has an atomic mass of about 16 for the oxygen, 2 for the two hydrogens. So that's about 18 times the atomic mass unit 1.67 by 10 to the minus 27 kilograms. So, one H2O molecule has a mass of about 3 by 10 to the minus 26 kilograms. !!So how many atoms are there in a cubic meter of water? Well, that's going to be about the mass of water, divided by the mass of each molecule, which comes out as about 3 by 10 to the 28 atoms. So, a lot of atoms in a cubic meter. !!But now let's look at our neutrinos coming in, at a flux of about 3 by 10 to the 13 neutrinos. What are the odds that these neutrinos will actually hit anything? Well, they've got 3 by 10 to the 28 chances they hit anything. But the chance of a given neutrino hitting a given atom is just the ratio of the total area to the cross-section of that atom. So the area is 1 square meter for a cubic meter of water. The cross-sectional area is 10 to the minus 47. So the probability of one neutrino hitting any given one atom is 10 to the minus 47. !!

But we've got 3 by 10 to 13 neutrinos. That's going to up the chance, so multiply by that. And we've also got 3 by 10 to the 28 atoms. So you factor these all together. You come up with approximately 10 to the minus 5. !!So, we've got this whopping 30 trillion neutrinos going through a cubic meter of water. But on average, the odds of even one of these neutrinos interacting with any atom is 10 to the minus 5-- 1 in 100,000. What this means is, a cubic meter is not enough. You need 100,000 cubic meters of water to have a decent of even one neutrino, anywhere in this huge amount of water, interacting with one atom. !!So yes, there were a staggering number of neutrinos that went through us when the supernova went off. But neutrinos really don't like interacting very much. You'd need 100,000 cubic meters of water, 100,000 tons of water to have even good odds of even one neutrino interacting with one atom. !!But there is a curious calculation we can do here. What are the odds that anybody actually saw one of these Neutrinos There are a lot of humans on earth. And humans have eyes. And eyes are mostly made of water. And if a neutrino went into your eyeball, the transparent stuff in there, and interacted with one of them water molecules, it would cause a little flash of light-- so-called Cherenkov radiation. !!Are there enough eyeballs on earth that anybody would have seen one of these flashes? Well, let's estimate that. How many people are there on earth? I don't know, about 10 billion. Let's call it 10 to the 10th. It's a very rough calculation. And how big is an eye? Let's assume it's a sphere of radius a centimeter. So the volume is 4/3 pi centimeter 0.01 meters cubed. And of course, you've got two eyes each. !!So that would give you the total number of cubic meters of all the people on earth, which comes out, it's about 10 to the 5 cubic meters. So, if you had 1 cubic meter, there's a 1 in 10 to the 5 chance for a flash. But there are about 10 to the 5 cubic meters of all the eyeballs of all the people on earth. So, odds are, one person would have seen a flash from a neutrino. !

V6.7 BRIAN: All right, Paul. That's pretty neat. So someone on earth probably got a little flash of light in their eye-- Cherenkov radiation, as we call it-- when one of the neutrinos from Supernova 1987A went through and interacted with their sclera-- with the stuff in their eye-- they saw a little flash of light. But-- !!PAUL: No one reported this. And probably good chance they're asleep. Or just one flash went off-- looking around, you wouldn't be noticed. So it would be nice to have a better way to actually measure these neutrinos. Maybe we don't need billions of eyeballs. Maybe we should just have one very large tank of water. !!BRIAN: Well, fortunately, it turns out that physicists had foreseen that they needed big tanks of water to look at neutrinos, specifically to understand why there weren't as many neutrinos coming out of the sun, as we expected. !!And so, there were some big tanks of water-- the largest of which is known as Super Kamiokande II in a mine in Japan. And it's this huge underground tank of water. And it's underground, so that nothing else can get through. So all the other particles and things of nature can't go through and interact. Only things that weakly interact. !!And in this big tank of water, there are these big photo multiplier tubes. They're very sensitive to light. And what you can't-- well, you can see how big these things are. I think, I have two people

here, as the water's being floated up. So these are giant balls, about that big. This thing is one of the biggest machines that we've made on earth. And so this is like all of humanity's eyeballs. !!And it was operating in 1987, on February 23rd, the day before the Supernova 1987A was discovered. And when they went through and looked at their results, they saw that there were 12 flashes of light in a very short period of about 15 seconds a day before the supernova was discovered. And that, we think, is the creation of the neutron star associated with Supernova 1987A. !!There was also a detector in South Dakota of the United States that also detected 8 events. So, confirmation. !!PAUL: Yeah, as an interesting aside, there's sort of bragging rights in astronomy about how many photons you need to publish a paper. And this, gravity waves would win. Because they've got thousands of papers an no detection of anything yet. But in this case, we've got 12 neutrinos, and another 8. And how many papers would you say have been published based on those? !!BRIAN: Oh, 100s, 100s. This is really the mainstay of my field, understanding how these neutron stars are formed, and how supernovae explode. !!Now, we have all these neutrinos. And as we've seen in our calculation, these neutrinos are able to interact inside the centers of these massive stars near the neutron star. So life is complicated. You need to actually do a big model to see what things look like. !!So let's look at what one of these calculations look like, where we've gravity coming in and neutrinos. And they interact and form this big ball of stuff that wobbles around, but doesn't seem to explode. !!PAUL: Hmm. I didn't see any explosion there. I saw a lot of violence and chaos and turbulence. But nothing went out. !!BRIAN: Yeah. So this turns out to be one of the hardest calculations we attempt as scientists, where you have to have all this material coming in, using general relativity. Things are very, very hot. And they're in states that we don't understand very well on earth, because we can't make things this hot on earth. And you have neutrinos whose properties aren't that well understood. Because-- !!PAUL: They're so hard to measure. !!BRIAN: --they go through everything, right? And so, when we put all this stuff together, we get something that almost explodes. Turns out, occasionally explodes, when you have a very small star that doesn't have much potential energy, compared to a great big star. That bounce does seem to get things far enough away that the neutrinos can take over. And the energy the neutrinos deposit is enough to blow those things up. But that's only a few stars out of many attempts that explode. So we seem to have a problem. !

V6.8 PAUL: So we seem to have a problem here. It's hard to make these things explode. And of course, when we're stuck in a situation like this-- it's such a nice model. Bouncing neutrinos and everything. It's a shame it doesn't seem to work. But maybe there's some way to make it work. Perhaps observations can help guide us as to what's going wrong here. !!BRIAN: Absolutely. Because we do know these things do explode. We see them. Now, one of the questions you might ask is, what exactly is Exploding and thanks to the Hubble Space Telescope

and some actual ground-based observations now, we can often see what explodes by pictures taken before the supernova exploded in nearby galaxies. !!One such example was here. Here is a supernova that exploded a couple years after it exploded. So we can see exactly where it's at. And then here's a picture taken of that same galaxy by the Hubble Space Telescope in the years preceding the supernova. And there's this little red tiny thing right there. That seems to have exploded. !!Now the nice thing is we can measure the mass of stars essentially by how bright they are. And it's a fairly straightforward process. And so, we have gone out and attempted to do that. And here's the work of Stephen Smartt, who has gone through, and he can measure the mass in many, many cases. These guys. And then there are cases where he can't measure the mass, because you look with the Hubble Space Telescope, and you just simply don't see anything. !!PAUL: So it gives you an upper limit. You know it can't be brighter than some things. So it can't be bigger than a certain mass. So we know it's going to be somewhere on that side of these boxes. !!BRIAN: So what do you conclude when you see this range of objects? Well, it looks like there's sort of a lower mass limit for Type II supernovae. We don't find anything smaller than this, which is about 8 and 1/2 times the mass of our sun. And that sort of makes sense. It's about the size we would expect from our calculations of when stars will start forming neutron stars. So that's great. !!But there's an interesting thing. It doesn't appear that there are any objects larger than about 16 and 1/2 times the mass of our sun. OK. So there seems to be like a limit of objects that turn into these Type II supernovae. !!PAUL: OK. So these are presumably giant stars. I mean, are there actually stars bigger than this? Is it just that there are no stars bigger than that to go bang? !!BRIAN: Yeah. So we can go out and, for example, look at stars in the Milky Way. And here's a diagram that shows essentially one of the supernovae and how massive it was. And then these little red dots are all red giant stars in the Milky Way, the stars we think that are going to explode and form Type II supernovae. And the range of 16 and 1/2 is in this area. That's the area that stars seem to explode. !!PAUL: So that's about half the red giants. !!BRIAN: Right. !!PAUL: But the other half are more massive. !!BRIAN: Right. So these objects-- we never seem to see turn into Type II supernovae. !!PAUL: So we seem to have two problems here. The first problem is that they don't explore at all, according to our theory. And the second problem is, only half of them seem to explode. So what can we do about this? !!BRIAN: Well, I think we need to go through and think about what happens to these objects. These objects don't appear as Type II supernovae. But they eventually die, right? So something has to happen to them. !!PAUL: OK. !!BRIAN: So, it might be that they simply disappear. !

V6.9 BRIAN SCHMIDT: So we have what I think is really quite a compelling story here. We have Type II supernovae. They have hydrogen in their spectra. And we see them directly associated with massive stars. !!We have a reason why a massive star's core might collapse down and form a neutron star. We see the neutrinos that you expect to happen in that process actually detected in the one case where we might detect it. And the amount of energy liberated seems to correspond to roughly the energy that a supernova has associated with it. So it seems about as good as it could be. !!PAUL FRANCIS: Well, apart from a couple of minor problems. I mean-- !!BRIAN SCHMIDT: Oh, you're so fussy, Paul. !!PAUL FRANCIS: Yes, I know. It's a good thing to be as a professional scientist. !!But one other thing, of course, is the trouble we have getting these explosions to actually happen in the theoretical models. And the other problem is that it seems like half the stars seem to not explode in the form of supernova, the more massive ones. So they've got to go somewhere when they die. What happens to them? !!BRIAN SCHMIDT: Well, let's talk about the models first because they are problematic. But they are such hard calculations. And I have someone in my group who works in this area right now. And the physics is really bleeding edge. !!We know they occur. And so I am confident, at some point, that the models really will explode. I have no doubt of that. I'm not confident yet we have all the physics in them. So, OK, it's a problem. But at least I can see where the solution is going to be. !!Now, the fact that half the stars that we expect to explode, seem not to be there, that's an interesting problem. One idea is that we can see how hard it is to explode these stars from the calculations. And it might well be that they simply don't explode above a certain mass. That the stars collapse down to a neutron star and material keeps on piling onto them and eventually that neutron star is going to become heavy enough that the Schwarzchild radius will be outside the neutron star. And we're actually going to have a black hole, rather than a neutron star. !!PAUL FRANCIS: And we'll talk about black holes in a couple of lessons. !!BRIAN SCHMIDT: That's right. And so those objects wouldn't be a supernova explosion at all. They would literally just disappear. So a star-- a big star-- literally disappearing. !!And an interesting star that is of the mass we're talking about is the star Betelgeuse, the big, red star in the constellation Orion. Could you imagine going out one day and it's just suddenly not there? How cool would that be? !![LAUGH] !!PAUL FRANCIS: In an odd, creepy sort of way. !!BRIAN SCHMIDT: Ah, yes. So that is a possibility. And we are out looking right now. There are groups looking for objects that disappear. !!The problem is you need to be able to see the individual stars in a galaxy. And it turns out you can't do that with a backyard telescope, which you can find the stars when they explode. Instead, you need to use the Hubble Space Telescope. That can individually identify stars. So there are projects

to go through and look at a galaxy and then come back several years later and see if anything has disappeared. !!PAUL FRANCIS: It's kind of like the reverse of a normal supernova. So there, you look for things that appear. Now, you are looking for things that are gone. !!BRIAN SCHMIDT: But the problem, of course, is there's only a few galaxies nearby enough. And you're only looking at tiny part of the galaxy a time, because the Hubble Space Telescope can't see the entire galaxy. It's too small. !!So it's not clear whether or not this will bear any fruit. If we do it long enough, it will. But the Hubble Space Telescope only has a few years left in it until it just gets old to work properly. !!But there's another problem which is much less exciting. It's dust. If there's anything in the world that I hate, it's dust. !!PAUL FRANCIS: Oh, I've always been quite fond of it myself. !!BRIAN SCHMIDT: Yeah. Well, it just messes up everything I do. !!It's been shown that in these red giant stars, before they explode, they have winds of particles coming out. And in those winds, dust can form, a long ways away from the star. And it turns out you can get dust. !!And what's dust do? It makes things appear fainter in optical light, where we're looking for these stars with the Hubble Space Telescope. !!PAUL FRANCIS: So the idea is that when we take a picture of a galaxy, and then a supernova goes off later, and we go back to that original image in the archive and try and work out what the star was, and we measure its luminosity, and from its luminosity we try and infer how bright it is. But if that star was partially obscured by dust, or even totally obscured by dust, then we'll either not see a star there or we'll think it its actually a lot less massive than it really is. !!So maybe some of these things we're thinking are like are eight or nine solar masses, are actually 20 solar masses. But it's hidden by enough dust to bring the light down. !!BRIAN SCHMIDT: Yeah. That is a real possibility right now we cannot discount, very frustratingly. But there is a way around it, which is that dust transmits, or doesn't scatter, as much infrared light. Now, the problem is is the Hubble Space Telescope is a pretty small telescope. It's not very good at taking detailed stellar images of nearby galaxies. !!But here at ANU, we have built a add-on instrument for the Gemini Telescope, along with the Gemini Observatory, which uses adaptive optics on an 8-meter telescope, over a big field of view, almost the same as Hubble's, so that we can take really precise images of nearby galaxies, down to the stellar level. And at some point, my hope is that a supernova will occur where one of those images are taken. And then we'd have an infrared view of it. And this nasty dust will, essentially, not cause us any problems. !!PAUL FRANCIS: You just go and image a whole bunch of galaxies near enough that you can pick the individual stars, at infrared wavelengths, so we can see every star irrespective of the amount of dust, and then do the calculation you just showed us again, when a supernova goes off there. But this time, we would always see a star. And they'll be more massive. And we'll start seeing if this theory is right, maybe some new 20-solar-mass star that exploded. !!

BRIAN SCHMIDT: So I think we're going to be able to resolve this problem. And we have sort of an explanation each way. It may be these things do explode or it may be they are just forming black holes. And that's one of the processes in the universe. !!So I always like it when I can see a way through how to answer questions. And that seems to be where we're at. !!PAUL FRANCIS: So where do you see this field is going? We've outlined two ways forward to try and solve the unsolved problems. What else is going to be new in the whole field of supernova research over the next few years, do you think? !!BRIAN SCHMIDT: So we have a bunch of telescopes around the world, which have these huge field of views that allow us to find more and more of these objects. So we're going to be able to statistically understand essentially what explodes and what it ends up turning into. And we're going to find some very rare objects. !!We haven't talked about it. But there are certain objects, we think, explode by different processes than making a neutron star. They become giant thermonuclear bombs, not quite like a Type I supernova, but a giant mass of star becoming a giant thermonuclear bomb. !!And you could imagine that instead of having a 1.4-solar-mass bomb, you had maybe a 100-solar-mass bomb. These are what we call pair-instability supernovae. Those would be really exciting and interesting explosions to look at, much more powerful than anything we normally see. !!We have a hint that those things are out there in the universe. And over the coming decade, we should see enough of the universe to find what we think are very rare objects, perhaps right at the dawning of time, right after the Big Bang. Because we think these big, massive stars, may have well been much more prevalent back 13 billion years ago. !!And, for example, the James Webb Space Telescope might well be able to find these things in the distant past of the universe, if they were frequent enough. They may be one of the parts of the first stars. !!PAUL FRANCIS: OK. So that concludes our section on supernovae. But if this theory is right, and supernovae produce neutron stars, we should be able to find a whole bunch of these neutron stars left over. That's what we're going to talk about next time. !!Lesson 7: Neutron Stars!

V7.1 PAUL: So, we've learnt that when a really massive star does, there's no longer anything that can hold up its center. It all collapses, forms a ball of neutrons. And in the process, the rest of the amount rains down and bounces off. There's a huge flood of neutrinos coming out of it. An immense explosion. This is going to leave this ball of neutrons behind, isn't it? !!BRIAN: Yeah. So the core of these stars collapse down. And you end up with the neutrons pushing on each other, rather than the electrons. But the densities are insane. They are literally as dense as the center, the nucleus, of an atom. So you get all sorts of funny effects. But the main thing is that you have literally a ball-- maybe oh, 5 or 6 kilometers across-- that has the mass 1.4 times our sun. So the gravity on the surface of one of these things would just be beyond anything you can imagine. Hundreds of thousands of times more than what we have on earth. !!If you were to stand on this, you would be ripped apart by the tidal forces and flattened, as flat as you can imagine. A micron thick. !

!PAUL: Absolutely. !!BRIAN: Yeah. So it's a very extreme environment. !!PAUL: Yes. And the material underneath is so dense, that if you could have a teaspoonful of neutron star material, it would have a mass equivalent to like a thousands of the Great Pyramid of Giza. That's the mass. The weight would be much, much, much, much more than that. Because of course, its gravity is so incredibly intense. !!BRIAN: One of the interesting things about neutron stars is, although they're very small and very extreme, you sort of expect most supernovae to produce one. And we have a lot of supernovae in the universe. One every second or so across the universe. And in our own Milky Way, we expect about every 100 years or so for there to be a supernova explosion, making a neutron star. !!PAUL: So our Milky Way galaxy is perhaps 10 billion years old. So about 10 to the 10 years old. So if you're producing a supernova explosion every 10 to the two years, that means there should be 10 to the 8 neutron stars. !!BRIAN: Yeah. 100 million neutron stars. So they're everywhere. !!PAUL: Yeah. So these are very common. And this was actually worked out, right back in the 1930s. But the problem is-- vast numbers of things all over the place-- but how could you see them? I mean, they're going to be so small. They're not going to shine. So back then, people thought, yes, it would be cool if we could see one of these neutron stars. There should be so many of them around there. But they're going to be really hard to spot. So people kind of gave up on the idea of actually observing these things. !!BRIAN: I think one could imagine having a chance encounter, though. For example, one comes zooming by the earth. And that wouldn't be very fun. !!PAUL: Yes. In fact, I set that as an exercise for my physics students. Throw a neutron star through the solar system and see what happens. And it's not very fun, as you say. !!BRIAN: Yes. !!PAUL: But indeed, you could easily imagine that these neutron stars would've been a purely theoretical construct. But then they were discovered much sooner than anyone would have thought, in a totally unexpected way. And that's what we're going to talk about next. !

V7.2 BRIAN: The first clues about how neutron stars might be visible came from a very unexpected source, that is from radio communications here on Earth at the beginning of the last century. You know when you listen to an AM radio, sometimes you can pick up radio signals from thousands of kilometers away. And that's because those radio waves are bouncing off the ionosphere, the part of the atmosphere that is ionized. !!PAUL: Yeah, but normally radio waves just go through here. They don't bounce. To make them bounce, you have to make it ionized, spit the electrons from the protons and the nuclei. !!But how are you going to do that for the atmosphere? I mean, the atmosphere, at least down here, is pretty neutral. But it became clear from about 1920s onwards that there was a layer somewhere up high-- you couldn't actually get up high enough to visit it back then-- that was ionized. And the amount of ionization depended on what was happening on the sun, particularly the sun spots. !

!When there are lots of sun spots, there's more ionized. So somehow, something from the sun was reaching out and making the upper layer of the Earth's atmosphere, stripping the electrons off. So how's that going to happen. !!BRIAN: Yeah. And the sun is only 5,500 degrees Celsius. So you need to have something that's a lot more energetic than that. !!And so if we recall the electromagnetic spectrum we have-- optical light here, infrared, microwaves, radio waves. And then the things that we need to ionize, like the nitrogen that's in our atmosphere, very energetic. We need X-rays or gamma rays. !!PAUL: Yes. A visible light photon won't ionize anything, pretty much. It just goes through, like they're [? transparent ?]. Radio waves, microwaves, infrared don't do anything. We need things up at least out to that and probably well into the X-rays, which have enough oomph in every photon to actually slam into a nitrogen or oxygen and knock the electron out. !!BRIAN: Right. !!PAUL: But the trouble is, remember, black body spectrum we've talked about. To get X-rays, we're going to need temperatures of millions of degrees. And the sun is 6,000 degrees, 5,700, or something like that. That peaks in the visible. So how can the sun produce something with enough energy to produce the ionosphere We know the ionosphere is there. !!BRIAN: Well, maybe we just need to take a good look at the sun and not posit what the sun looks like to our eyes, but what it looks like at high energies. !!PAUL: OK. So we want to actually see if X-rays are coming from the sun. The trouble is if you look at different wavelengths here, here are probably wavelengths at the bottom here. And here's how much of them get through the atmosphere. !!And you can see that most wavelengths in the X-ray, X-rays don't get through the atmosphere, which is kind of weird. Visible light gets through mostly, when it's not cloudy. There are various particular infrared wavelengths that get through we've spent a lot of our lives observing in these different windows over here. !!And radio waves get through, no trouble at all. But X-rays don't. This is kind of odd, because the X-rays penetrate. They go through the human body. !!Superman has X-ray vision and can look at guns in people's pockets, and things like this. But it's the same trouble. X-rays, because they ionize stuff, have so much energy, if you put them through a lot of anything, they will ionize and get stopped. So the atmosphere above us is very, very thick. X-rays can get a few meters through the air. But they certainly can't get through 10s of kilometers of air. !!So I'm kind of curious that Superman X-ray vision would be pretty useless. He wouldn't be able to see more than a couple of meters away. And there also would be no light for him to see by. We see because you get sunlight coming down, bounced off Brian, so I can then see him. But there are no X-rays coming through. !!So I'll have to have an X-ray torch. Maybe if Superman had an X-ray torch, he could shine X-rays. But then they wouldn't bounce back if I was trying to see what was in Brian's pockets . !!The X-rays would just go straight through out to the side. So I'd need an accomplice to run round the far side and far X-rays so I could see it. So I think X-ray vision's pretty useless, really. !!

BRIAN: But it does tell us, getting back on to the point here, that if we're going to go out and look at the sun, we're not going to do it from Earth. We're going to have to do it above Earth. !!PAUL: Which, until the 1940s, was impossible. But during the Second World War, some very clever Germans invented ways of getting things up into space. And so after the war, people were trying to figure out, could we use these new rockets that Germans have come up with to get a detector high enough to actually see if the X-rays are coming in. !!So first thing we needed was a detector. And that here is basically what's called a proportional counter. And it's very similar to a Geiger counter. !!You get some gas in a container. You have a very thin window at the front. And you make the thickness of that window just right so it will let X-rays through, but it won't let ultraviolets and visible light and so on through. And if an X-ray will get in here, and will get into the gas, and it will ionize. It will knock an electron out. !!And then you put a very strong negative voltage on this cathode in the middle here. And that will start-- that means that the electron will start accelerating towards it, and it'll accelerate really fast if you put enough voltage. As it moves closer and closer, it'll hit other atoms and ionize them, giving you more electrons, which in turn will go and hit more electrons, and more electrons, until you get a huge pulse of electrons hits the wire. !!BRIAN: You've got a big cascade. So one electron then cascades into this whole flood of electrons. !!PAUL: Enough that you can detect. So you should pick up a big pulse of-- !!BRIAN: Electricity, effectively, when you measure it. !!PAUL: And so you can count those X-ray photons. Then you use them for getting into space. And so you generally use one of these things, a V-2 rocket. !!BRIAN: A good use of a V-2. !!PAUL: Yes. My father, growing up in London during the Second World War, had a bad use of the V-2. He was sitting in his lounge, eating his breakfast when there was a huge explosion at the end of the street. One of these things had landed on the end of the street. !!His main memory of the fact was that it blew out all the windows in his house and got ground glass into his sugar bowl. And sugar was rationed. And they couldn't eat that sugar. All that lovely sugar that looked perfect. And they couldn't eat it from then onwards until the next ration came through because it had glass all over it. It's funny what people remember about these things. !!BRIAN: So we could go through and use something like this to look at the sun. So let's see what the sun looks like with a modern detector. !!PAUL: OK, so here's a modern movie of the sun in X-rays. !!BRIAN: Ooh. So you can see the sun is glowing in X-rays. But not the disk of the sun. It seems to more almost be like a fog of stuff above the sun that's glowing in X-rays. !!PAUL: And these lumps of extra [INAUDIBLE] are generally over the sun spots. So somehow it seems that-- well, the surface of the sun is much too cold. The surface of the sun is black at X-rays. We're getting it above, which is weird. !!Normally, in a star, you think it's hot in the middle, cold as you go further out. And that indeed is what happens in the sun generally-- several million degrees the middle, going down to only 6,000

at the surface. Only 6,000 degrees. Only an astronomer could say that. But then when you get above the surface, it gets hotter again, but only in sports near flares. !!BRIAN: So that's a very complicated process that we're not going to talk too much about. But it involves magnetic fields, and particle acceleration, and all sorts of other processes for another course. !!PAUL: And there are people who spend their lives studying it. !!BRIAN: But it does-- the sun is very nearby. It's only 150 million kilometers. But that's 100,000 times closer-- or even more so-- than the next nearest star. And we can barely see the sun in X-rays. So it seems like the end of X-ray astronomy as we know it. !!PAUL: Yes. That's what a lot of people thought, X-ray astronomy is just going to be the study of the sun. And that was interesting, because the ionosphere, that's importance for military communications and things, which is why [INAUDIBLE] people were funded to do this. But was that going to be the end of X-ray astronomy? Was there anything else they could see? !!I mean, the sun is, what, about 10 to the 11 meters away. The nearest other stars 10 to the 16 meters away. So that's 10 to the 5 times further away. Flux goes as one over distance squared. So that means anything else like the sun is going to be 10 to the 10 times fainter, 10 billion times fainter. !!BRIAN: So that means we're going to need 10 billion times bigger telescope to see these things. !!PAUL: It could well be there are some stars out there that emit a lot more X-rays than the sun, because they're harsher or have more flares. But 10 billion's a very big number-- !!BRIAN: That's a big number. !!PAUL: --to overcome. So at this point, it may have been that X-ray astronomy was over. However, some of the research in the field didn't give up. !!Nowadays, probably, they would've got no more funding to keep on their research. But back then, there were some people who thought, well, let's give it a go. We don't know until we see. !!And it occurred to them that there might be one other source, this one over here, the moon that might emit measurable amounts of X-rays. I mean, how does the moon emit X-rays? The moon isn't that hot. Well, the idea was that the solar wind, these particles flung out at half the speed of light from the sun-- protons and most protons-- will smash into the moon. And maybe when they smash into the moon, they were liberate X-rays. !!BRIAN: So this is some version of the Large Hadron Collider, just the nature's version on the moon. So you could crash things in, and you get flashes of light and other activity. And not a foolish way to go and create some interesting conditions to observe. !!PAUL: Yeah. And the calculations were very uncertain. But it looked like maybe if you build a better detector-- certainly the one that picked up the sun wasn't going to be enough-- but if you built one that was maybe 100 times better than that, then maybe we could pick up the moon. !

V7.3 PAUL: OK. So how do you make a detector that's maybe 100 times better. So you could hope to see the moon? Well there were a couple things they could look at. One thing you could do is make

this shield at the front-- this thin screen-- even thinner. So a lot of experimentation was done. They actually used a mica sheet at the end. That made them somewhat more sensitive. !!But the main problem was that for every x-ray that came in and generated a pulse of electricity, there were many cosmic rays-- protons and electrons moving at high speed, orbiting around the earth's upper atmosphere-- that crashed into this, and generated pulses as well. And those were far more common than the x-rays. !!BRIAN: Yeah. So, we forget that x-rays are one thing out there. But these cosmic rays caused by the sun-- and it turns out from things around the galaxy-- are very common. And ultimately, if you produce an electron, however you do it-- whether you're an x-ray or just a high-speed particle-- you're going to get the same signal. There's no way to tell the difference on this. !!PAUL: The sun was so bright on x-rays, that they could measure a background level of signal, then we'd point to the sun-- they'd see more. But that was not going to work for these fainter signals like what you might get from the moon. The needed some way to get rid of the background. !!And luckily, the thing is, that these cosmic rays as we call them as they come through, they might come through. They might generate electron here. But they're going to keep going. They go out the back. And, what you could is put another detector at the back, or maybe another detector at the sides, and all around the place. Because any cosmic ray that goes through is going to hit this and hit that. It's going to generate a pulse of electricity here and a pulse of electricity behind. !!And you have some clever electronics that says, if there's a pulse here and a pulse there at almost the same time-- ignore it. !!BRIAN: Yep. !!PAUL: But if there's a pulse here and not a pulse there, it's probably an x-ray. And we should pay attention to it. !!BRIAN: Right. And that can improve the sensitivity of the detector to x-rays by a factor of 100 or so. Because you're getting rid of all that noise. It's sort of getting rid of the fog of the stuff you don't want. !!PAUL: So they got this working. They would have detectors that were about 100 times more sensitive than the first ones. And then they needed to launch it. They launched it on an Aerobee rocket in 1962. They had-- a little port would open at the side here. And as the thing would move around, it would survey the sky as it spun around. And sure enough, they picked up a signal. A really strong signal. !!BRIAN: Really big signal. So there's the moon, which they thought they might be able to see. And it looks like maybe they did see it. But there's something way bigger than the moon-- !!PAUL: It's not quite at the same place. !!BRIAN: Yeah, it's not quite at the same place. And it's much, much brighter than it appears to be, that the moon is. !!PAUL: So, they picked up a signal-- a really strong signal. Such a strong signal that the x-rays from the signal, whatever it is, are enough to actually appreciably ionize the upper atmosphere. But it's not coming from the moon. Where is it coming from? !!Well, they tried to map where it's happening. Here's a map of the sky. And this box is the area. Somewhere in this box must be where this x-ray source is coming from. !!

BRIAN: But there's no bright stars or anything there. There's not really anything there. !!PAUL: It's quite close to the galactic center, but not very close. It's in the Milky Way. There are maybe 100,000 or a few millions visible stars in that area. Because the accuracy was very imprecise they knew is was coming from vaguely this area. They didn't pin down very accurately where it was coming from. But none of the stars are particularly interesting. !!So it looked like somehow a fairly normal-looking star, at best-- or maybe something quite different that's even fainter than a normal star-- was putting out such a huge flux of x-rays that it could ionize the upper atmosphere. !!BRIAN: Well, you would certainly need something pretty big and pretty hot to do that. !!PAUL: So let's work out how hot you'd need it. !

V7.4 PAUL: OK. So let's try and work out how hot this mysterious x-ray source, Scorpius X-1, must be. Now we know that if something is emitting like a black body, then the peak wavelength-- it's going to be called 2 constant, which is roughly 3 by 10 to the minus 3 divided by the temperature. !!What wavelength are these things emitting? Well, they emit all the way out to x-rays-- let's say, x-rays of about 10 kiloelectron volts in energy. For photons, the higher the energy, the shorter the wavelength. So short-wavelength photons pack a big punch, whereas long-wavelength ones, like radio waves, are very weak. !!So this energy corresponds to a very short wavelength, about 10 to the minus 10 of a meter. 0.1 nanometer-- about the size of an atom, which is indeed why we use x-rays to study atomic structure, and crystalline structure. !!So, if you plug this wavelength into here, we can rearrange it so we get T equals 3 by 10 to the minus 3, over 10 to the minus 10, which comes out as a whopping 30 million Kelvin. So that's 3 by 10 to the 7 Kelvin. So wow. That's hot. I mean, the sun at 6,000 degrees is positively icy in comparison. !!But that poses a problem. If it really is that hot, and it's radiating as a black body, then it must radiate an absolutely staggering amount. You should remember, the Stefan Boltzmann equation tells you that the power radiated per unit area is equal to the-- power is equal to area, times the Stefan Boltzmann constant, times T to the 4th power. And as our temperature is so enormous, that's going to be absolutely colossal. So the power per unit area is going to be absolutely staggering. !!Which means that probably this object has to be quite small. If it had a very big area-- say as big as a red giant star, and also a temperature that's high-- it would be blindingly bright even by day. It is a very, very bright source. It emits enough x-rays to appreciably ionize the upper atmosphere. But it's not that bright. The luminosity in fact is about 2 by 10 to the 31 watts. You can determine that by looking at the x-ray flux and factoring in the distance by the normal inverse-square equation. !!So given that luminosity, we know that that must equal, if it's a black body, A sigma T to the 4th. So we know that L equals the area. If it's a sphere, that's 4 pi r squared, sigma the Stefan Boltzmann constant, which is 5.67 by 10 to the minus 8, times T to the 4th. And we know the temperature up here. !!

So from this, we can work out the radius of this object, again, assuming it's a sphere. So what we can do is, we that r squared equals L over 4 pi sigma T to the 4th. Take the square root of both sides. And we find that r equals square root of L over 4 pi sigma T to the 4th. !!And if we plug in the temperature-- 30 million degrees-- Stefan Boltzmann constant 5.6 by 10 to the minus 8, and the luminosity, 2 by 10 to the 31, that comes out as roughly 6 kilometers. Not 6,000 kilometers, or 600,000 kilometers, or 6 light years, or 6 astronomical units-- 6 kilometers, the size of a suburb. !!So, whatever these things are that are emitting this huge amount of x-rays, they must be extremely small. !

V7.5 !BRIAN: So Paul, we need something really small and really hot, and that's great, because we have something in our inventory out in space called a neutron star that just perfectly fits this bill. !!PAUL: But would a neutron star be this hot?!!BRIAN: Well, so a neutron star, if we remember, is formed when a massive star, 10- 20 times the mass of our Sun, runs out of nuclear fuel in its centre and collapses down and it forms a neutron star, and the centre of that star is literally billions of degrees when the neutron star is born, so the neutron star is going to be born really really hot. !!PAUL: So it sounds like a really good hypothesis here, that these things, these X-ray sources, are neutron stars let behind from supernovae. And further evidence for this came from the second one of these X-ray sources discovered. If you take an optical picture of the part of the sky where it came form, the X-rays, this is what you see. This is a picture we've seen before.!!BRIAN: Yes, this is the Crab Nebula. This is where in 1054 the Chinese saw a "Guest Star” that is, what we would now call a supernova, and we can literally see the interior of that big star that exploded a thousand years ago expanding, and so, here we have something hot and small. Seems to me, like, it's game over, we have our explanation, it's a neutron star. !!PAUL: yes, this would be a very short lesson if that were the case. But things get a little bit more complicated, as so often the case in astronomy. One problem - this was the second X-ray source discovered, and sure enough, this sits right in the middle of a supernova remnant. But how about the first one, the one that's called Scorpius X-1, because it's in the constellation of Scorpius an incredibly bright X-ray source. Do you supernovae recently in Scorpius?!!BRIAN: Ahh, no, I don't, and we've got a pretty good record of them as well, we certainly didn't see anything explode, and it doesn't sounds like there's even any supernova remnant in that part of the sky. !!PAUL: So that would indicate that if it was produced by a supernova, the supernova must have been quite a long time ago - long enough that we have no records and that the blast wave has faded out of visibility, but that's - how long does it take a blast wave to fade to invisibility? !!BRIAN: Oh, it's a couple of hundred thousand years before a supernova fades, but you're right, a hundred-thousand years is a long time, because of course that neutron star is really hot and really small, it puts out a lot of energy and it's going to cool and not be so hot and not so bright. !!PAUL: Yup, so that's one puzzle, that not all these X-ray sources, in fact the majority of X-ray sources aren't associated with nice supernova remnants like this and there's also another problem.

If it was the neutron star in the middle that was producing the X-rays, then you'd expect an X-ray image just to show a little dot in the middle all the radiation would be coming just from that neutron star, smaller than a pixel in the centre. !!BRIAN: So when they took their picture, did they see a little dot in the centre? What did they see?!!PAUL: Well, to begin with, they couldn't quite tell more than that it was coming from vaguely from somewhere around here but they used a very cunning trick. They waited until the Moon came across this part of the sky. And as the edge of the moon went across, it will block out X-rays, and if everything was coming from a little dot in the middle, you'd see full X-rays, full X-rays, and suddenly, when the limb of the Moon crosses it, it will drop to nothing right away. But they did their measurement - it was a really hard one to do because the sounding rockets were very unreliable, it was hard to launch them at exactly the right time to get precisely to the time when the Moon was crossing exactly the right place, but they managed it, and what they found was that instead of having an abrupt drop in X-rays at the moment when the limb of the Moon crossed the middle, they had a more gentle drop in brightness of X-rays, so it didn't suddenly, it went away more gradually, about the time it takes the Moon to cross a fair portion of this. !!BRIAN: So that's interesting because, you get a sense of how this would work if you've ever seen a total solar eclipse. The Sun is really really bright, and then when that final bit of the Sun gets covered up, and when that final bit of the Sun gets covered up, it just instantly turns black, and what you're sayings is that as this was a slow process, that seems to indicate that whatever is glowing in the X-rays had to be actually, the X-rays themselves had to be not really really small on the sky but actually quite broad, so that seems a little different than that idea that all the X-rays are coming from the neutron star. !!PAUL: And if you get a modern X-ray image of this part of the sky, you can indeed see - this is where the X-rays are coming from, and they are not all coming from a dot in the middle but actually are mostly coming from the sort-of whirlpool-y shape around things. !!BRIAN: OK, so we have something that still makes me happy there in the centre, but most of the X-rays are coming from outside it in this sort of windy bit and stuff, so I can imagine there's lots of shocks and things, but those only last for thousands of years, so you get X-rays a little bit, but then there's got to be a source of energy that keeps things going, even from those shocks.!!PAUL: we need something to get get the nebula and excite it. And curiously enough, about the same time that these observations were being made, a theorist called Franco Pacini came up with a possible explanation. The idea was that of course when a, stars have magnetic fields, and the star that presumably formed the neutron star had magnetic fields, and it could be that when it collapsed to form the neutron star, it dragged its magnetic field lines in with it, and so what was originally a fairly spread-out magnetic field became an incredibly concentrated magnetic field.!!BRIAN: a really powerful magnet. !!PAUL: Yeah, a good analogy of this is rubber bands Let's imagine that this whole room was full of rubber bands running from the roof to the floor, and I get an armful of them, and then pull them tight, and then go around in circles like this, I'm going to get this really tangled knot of rubber bands, that would probably fling me back around again at the end, and the same thing might happen in this case, you've got the star, neutron star, which is presumably due to conservation of angular momentum, is going to be spinning really fast by the time it's formed. !!BRIAN: So that's like the analogy of the person doing the figure skating and bringing their arms in and speeding up. I always do it with phone books and a chair - it's quite fun when you are bored at the office. Take the phone books in and spin yourself around in your chair. !!

PAUL: So, you have a really strong magnetic field rotating like crazy. In fact, if you do the calculations, the amount of energy you get in just one cubic metre of that magnetic field would be enough to power the entire world. !!BRIAN: Wow, OK. !!PAUL: And it's spinning really fast, that means it's constantly changing, and whenever you get a magnetic field that is changing, it generates an electric field, which generates a magnetic field, and you've got electromagnetic waves, in this case they would be very low frequency radio waves, with a frequency of maybe only one hertz which means a wavelength of three hundred thousand kilometres, so this is far too long wavelength for anything we can pick up, and in fact it wouldn't get out of the nebula, but the idea is that these incredibly low radio waves with enormous energy would come out and get mopped up by the electrons in the nebula, and it would excite them and give them lots of energy, which would produce shocks and X-rays and everything we see. !!BRIAN: what you're really going to do is you're going to transfer the energy of that one point four solar mass rotating neutron star and you're going to transfer that energy, and there's a lot of energy, that’s like the world's biggest fly-wheel, and through this process you're going to transfer that energy out into the nebula, and then you are can get shocks or something, to give you the X-rays. !!PAUL: Yesh - it sounds like it almost might work.!!BRIAN: OK!!!!V7.6 PAUL: And now our story of the discovery of neutron stars takes an unexpected twist. We're going to switch from x-ray astronomy, wich is one new technology at the time, to radio astronomy, another new technique of a time. !!We've talked about radio astronomy in its early days before, back in the first course in the series when we were talking about the discovery of quasars. And back then, one of the leading institutes for the radio astronomy was in the United Kingdom, the University of Cambridge, my alma mater. And some people there at the Lord's Bridge Radio Observatory were trying to look not for neutron stars but for what's called interplanetary scintillation. !!You know if you look at a star at night, it seems to twinkle and that's because of the bubbles of hot and cold air coming through the atmosphere. But it turns out that if you look at the radio waves from a distant quasar, they get a similar effect not due to our own atmosphere but actually due to bubbles of differently ionized material moving around in the galactic wind. !!They had a plan to do this is they came up with a new radio telescope. This radio telescope wasn't much to look at it. It looked like a paddock full of sheep, full of wooden posts with wires dangling between it. They needed the sheep to keep the grass down because our poles are too close to get a lawnmower in there. !!So just a whole bunch of wires dangling on posts all over the place. Mostly the clever stuff was in the receivers at the end who collected the signals from these things. And what this telescope was capable of doing was looking for very rapid changes in signals which is what they were expecting with scintillation. !!

BRIAN: Yeah. So Paul, a young woman at the time, Jocelyn Bell, was doing her Ph.D., was looking at the signal. And it turns out that this was a fixed telescope. And so it looked up into the sky and as the sky went by, different quasars or radio sources would come into view and you can look at them for a little bit and see how they might twinkle. !!But then they had a source come by that Jocelyn Bell realized looked funny. It was scruffy. It had a pattern that looked fuzzy and didn't look like anything else. And they wondered what it was and they changed how they read the radio signals because before they were looking at something every couple seconds and they looked at it at much higher resolution. And when they did that, they saw a ping, a ping every 1.33 seconds. And that was why-- what would be going ping in the cosmos? !!PAUL: And then a ping. And then a ping. And then a ping every 1.32 seconds. !!BRIAN: Yeah, and very regularly. !!PAUL: I mean if I ever see that in observatory you do occasionally. You see something flashing like that, you think it's a satellite or a plane going over. They must have thought early on that it was some sort of terrestrial interference, but they were soon able to rule that out. !!BRIAN: Yeah, because the interesting part of this is that remember this is looking up into the sky and so one day you'll see it and then it'll go around-- the earth will rotate. You won't see it. And then you'll see it. !!And when they saw it come up the next day, they saw it 23 hours, 56 minutes, and 4 seconds later. And that number rings a bell to we astronomers because that is what we call the sidereal revolution time of the Earth, rather than the time it takes to rotate back to the same place on the Sun. !!PAUL: Yes. You think that the Earth rotates every 24 hours, but in fact, it's a little bit different than that. That's how long it takes for the Sun to come back to the same place as seen from us, but because we're going around the Sun it's one part and 365 different. And that small difference was what they were seeing. !!So that meant that whatever this was it wasn't on Earth because anything on Earth, like you're the milk float or someone jamming-- someone turning on their phone receiver at the same time would be at the same calendar time, not the same sidereal time, unless it was another astronomer perhaps. !!BRIAN: That's right. So what would be coming from space going ping at 1.33 seconds almost exactly? Well, they made a joke of it being little green men, but it turned out to be something far more interesting, I think. !!PAUL: Yeah. Judging by Bell's memoirs about this time. They didn't seriously think it was aliens to begin with, but for a while they started to think, well, maybe it is, maybe we should be telling the prime minister or something about this. !!But then eventually they discovered a second bit of stuff somewhere else, and this time they found another one of these pulsing signals, the different period. And before on the file, these had been found all over the place. At that point, it became clear. It wasn't going to be aliens. They weren't going to be all over the place. !!It had to be something natural, but what is there that's going to be natural, out in deep space, beyond our solar system, it's putting out a lot of power to pick up radio signals here, but that would do a ping every half a second or every 1.3 seconds or something like that? !!

BRIAN: So you can imagine something pulsing, but probably aren't big capacitors or something in space that we would make things pulse here on Earth. So maybe we could have something rotating, and for whatever reason there's a hotspot on it, that every time it rotates you'd see it. !!PAUL: Or some sort of eclipse that goes around or something like that. But even so it's very fast. When we think-- like an exoplanet that goes around the Sun in four days is hooting around, going at some enormous speed. 1.3 seconds? I mean, that's just ridiculous. Wouldn't it just fling itself to pieces from the centrifugal force? !!BRIAN: Well, I think the Earth certainly would. So maybe we need to do a calculation and see exactly what we're up against here. !!PAUL: OK. So let's do that calculation. !

V7.7 PAUL: Let's try to estimate how fast something can spin without spinning itself to pieces. So let's assume we have a spherical something with a mass that's-- give it a solar mass, roughly, to get some specific numbers. And it's rotating with a particular period, p. So p is how long it takes to spin around once. !!Now if we look at something on the surface. So here it's spinning around, something on the surface. The question is can it stay on the surface or will it get flung off to space by the rotation. Now this object is going to have a downward gravitational force and there's going to be a normal force from the surface. !!And it's moving in a circle, a circle of radius r. Now we know that for anything to move in a circle at radius, r at some velocity, v. There has to be a net force towards the middle, a centripetal force of m v squared over r. Where m is the mass of whatever it is sitting on the surface. !!Now in that case it'll be contributed by the difference between the gravitational force and the normal force. If something's spinning very slowly, the gravitational force and the normal force will be equal and opposite. So as to leave the object lying on the surface. If it's spinning faster, the normal force will be reduced but the gravitational force will stay strong. !!As it spins faster and faster and faster, the normal force will shrink away to zero. So at the crucial moment when something's about to be hurled off the surface, the gravitational force all by itself with no normal force taken-- in fact, it's supplying the centrifugal force. If something spins even faster still, then it would have to fly off into space. Normal force can't pull down unless somethings [? bolted ?] down. !!So if something is spinning such that gravity cannot supply the centripetal force, it must fly off. So the critical dividing line, when things are just about to spin off, we'll set that equal to the gravity. Given by the normal equation. !!OK. So that's telling us how to balance-- this is going to happen. Now we also know what the velocity is, we know the period. Now the velocity. It's going to go all the way around every period. So the distance it travels 2 pi times the radius, that's the circumference of the circle divided by the velocity. It's got to be equal to the period. !!Which means that the velocity equals 2 pi r over p. Now let's plug that into here. We end up with m v squared, so it's going to be 4 pi squared r squared over p squared. And then there was the 1/r. r equals G, the mass of the whole object, which is the mass of the sun. Mass of the lump on the surface over r squared. !!

And what can we do here? Well the mass of the lump cancels out. That cancels with one of these. We put that r up to that side. So we end up that I have r cubed over here equals G M sun. P squared moves up to the top and the 4 pi squared moves down to bottom. !!And we can then take the cube root. And we get that r equals cube root G M period squared over 4 pi squared. Now for the first pulsar we know the period is about a second. So we put one second into here and we assume it's got the mass something like the mass of the sun. !!We find out that this critical radius comes out at about 1,500 kilometers. Now bear in mind that is an upper limit. If it gets bigger, centripetal force is larger, gravity gets weaker. So the centripetal force will be much bigger than gravity. So things will fly off. !!But it could be much, much smaller than this. What's interesting about this number is that it's smaller than the size of a white dwarf. Which is, if you remember, about 5,000 or 6,000 kilometers. So what this is telling us is that a white dwarf cannot spin where it goes around like every second or so. !!It just can't spend that fast the surface layer will be flung off into space. So we have to look at something here which is smaller and denser than a white dwarf. !!V7.8 PAUL: So it looks like these things really do have to be neutron stars. They have to be so small and so dense to be able to spin so fast without flinging themselves to pieces. So it sounds like a good theory. !!BRIAN: It does. Well Paul, we have the Crab Nebula, which we thought might have a neutron star in it. Wouldn't it be wise to look there for a pulsar? !!PAUL: And people did, and indeed it was seen very soon. There is indeed a pulsar in here. !!BRIAN: And from memory, it's pulsing at 30 times a second. So, much faster than the first pulsar that was discovered. But they can measure that it's slowing down quite rapidly, and so in the future, it will be not spinning nearly as fast as it is now. !!PAUL: So that would make sense, because it's going to start off spinning very fast. But the spinning, as we've said, is generating energy beaming out this low-frequency electromagnetic radiation which is heating up the whole nebula around it, and producing the x-rays we can see, and that energy loss will slow it down. And so that all seems to work. It's radiating energy out, getting rid of the angular momentum, slowing down. And the first pulsar discovered only goes around every 1.33 seconds, will indeed be one that's now blown it's nebula away and has slowed down steadily. So that all seems to make sense. !!BRIAN: It does. !!PAUL: So it seems that we're getting something like this-- a spinning neutron star, firing a beam out each pole-- well, not exactly out of the pole, but at some offset angle, maybe the magnetic field lines, magnetic pole-- the mechanism by which this happens is a bit unclear. But what we do have is this incredible electromagnetic field, if you just took the energy in one square meter of magnetic field around one of these things, it's more energy in one square meter than all energy the human race has generated since the advent of industrialization. !!BRIAN: So they're very powerful. !!

PAUL: And this magnetic field is spinning very fast. If you've got that much energy, that much magnetic field spinning fast you're going to get something coming out. !!BRIAN: Right. !!PAUL: And the details are rather complicated, but it seems you can get this lighthouse-like beam spinning around. !!BRIAN: And so in the case of the Crab Nebula, that neutron star, that thing that's much bigger than our sun, that's much the size of Canberra is going to be turning 30 times a second. That's an amazing amount of energy there, if we think about it. And it'll be putting out all that energy into the nebula around by moving those electrons back and forth and that's going to generate a lot of energy. But that's also going to sap the neutron star of its rotation, and that's why it's decelerating over time, and why eventually it won't be spending at 30 times a second, it'll be going once a second or even slower. !!PAUL: So we seem to have a coherent picture of the Crab Nebula and things like that, of the pulsars. That the supernova explodes, produces an incredibly magnetized spinning neutron star, and this generates energy that ionizes and energizes the nebula and causes it to slow down, and has also generated these beams and pulses. So it seems that neutron stars really do exist. !!V7.9 BRIAN SCHMIDT: All right Paul, so we've shown that neutron stars and these pulsars seem to be related to the centers of supernova remnants at least in the case of the Crab Nebula. But we still have that first source SCO x1, which is this big bright thing. It's not blinking at all like a pulsar. It's just really bright in x-rays. Maybe we need to look at that one a little more carefully and see what's going on there. !!PAUL FRANCIS: Yes, there's a whole bunch of these x-ray sources, and not associated with supernova remnants that we can see. So what could be going on here? We first of all had to get better positions. Knowing it somewhere in that part of the sky isn't going to help us. !!So some experiments are done where they've actually put obstacles in front of the x-ray detector, these patterns of greens would actually call shadows in the background, like a collimator and use that to work out more precisely where the x-rays are coming from. !!BRIAN SCHMIDT: So if you had a lot of things, you would actually see the pattern. And depending on where the pattern or the shadow is cast, you could just tell the direction. !!PAUL FRANCIS: --or that angle, yes. !!BRIAN SCHMIDT: --because it wasn't very easy, especially back then to make x-ray mirrors. Although interestingly enough, we can do it now. !!PAUL FRANCIS: Yes, you have the extras bounce at a very glancing angle. And that was the latest missions they had back when they didn't have the capability to do that. But with things like this and with all the various clever trick and techniques the pioneer x-ray astronomers were able to narrow down where some of these x-ray sources were coming from. And it looked like ordinary stars. !!BRIAN SCHMIDT: Ordinary stars? But how can an ordinary star produce lots of x-rays? That doesn't make sense at all. !!

PAUL FRANCIS: Yeah, and we've talked about the sun that produces x-rays. There's flares. But this is far too much energy for any conceivable flare to produce. So to my mind, that's telling us we've got to look at binary here. !!Maybe there's a normal star, and there's something much more exotic orbiting it, or the star's orbiting the exotic thing. And when we see the normal star, we're not actually seeing where the x-rays are coming from. We're seeing something close to it, like just we had for the dwarf and classical novae. !!BRIAN SCHMIDT: OK, so we can test that idea. !!PAUL FRANCIS: Yeah, how are we going to test it? Well, the next clue came from the first x-ray astronomy satellite, Uhuru. Because up until then, people had kind of thought these things might be varying in brightness, but it's very hard. You launch a sounding rocket. You get a couple of minutes data, or maybe 10 minutes data. Then it comes down again. !!How do you know it's really varying? So it'd be great if you could put an x-ray detector in space and leave it up there so it could sit up and look at the same thing for a long time and see if it's changing. And this is the first one that did it. And very early on, it was able to show that some of these compact x-ray sources really were pulsing, just like pulsars and x-rays. !!BRIAN SCHMIDT: It was pulsing in the x-rays. !!PAUL FRANCIS: Yes. !!BRIAN SCHMIDT: OK. !!PAUL FRANCIS: Pulses from the first one was much slower than x-ray, the radio pulses you get, much further apart. !!But there's more than that. The pulses weren't particularly regular. Sometimes, the pulse would be close together. And sometimes, it'd be further apart. Now, that should sound like something we did in the last course about exoplanets. !!BRIAN SCHMIDT: Right, so if they are closer together, so that would mean if I'm coming towards you, then the pulses would get pushed together. And then when I went away from you, you sort of get the Doppler effect to light. !!PAUL FRANCIS: Yeah. If I'm pulsing towards you and I'm moving towards you, the light from the first pulse or the x-rays from the first pulse sets off. Then if I move forward, by the time the next pulse comes, it's a bit closer together. So then we're going to bash together. If I'm moving away, there'd be a bigger gap between each wave of pulses. !!BRIAN SCHMIDT: Right. !!PAUL FRANCIS: So it kind of looks like a normal star. And we've got x-rays which are moving towards and away from us-- and presumably sideways as well, but we can't measure that with this effect. !!BRIAN SCHMIDT: So if this is going on, we would also expect that the big normal star that we see to be moving around and showing Doppler effects as well. !!PAUL FRANCIS: And eventually, the optical telescopes are good enough to see this. And exactly the same thing we've seen, that when the x-ray thing is moving towards, the star is moving away from us, and vice versa-- again, very much like what we talked about for the dwarf novae. !!

So it seems like what we're talking about here is something like this. We have, similar to dwarf novae, a heavy thing-- in this case, a neutron star rather than a white dwarf. And we've got-- in one of thes cases, [INAUDIBLE] will seem like this. And here it comes out. !!And we've got a star which is spitting gas through its Roche lobe in the stream onto this disk, only now, it's rather different because it's falling all the way down to the neutron star surface rather than a white dwarf surface. And because a neutron star has a big mass and is much smaller, there's a lot more energy to get out of that. So instead of emitting the ultraviolet light that they've got from the dwarf novae, this is coming out as x-rays. !!BRIAN SCHMIDT: Right, and so we would have a huge amount of mass, a huge gravitational potential to give us the amazing amounts of energy and high temperatures that we need to explain this phenomenon. !!PAUL FRANCIS: And this is also going to do rather strange things to the neutron star. Because remember, this neutron star probably had a supernova a long time ago. We didn't see any supernova [INAUDIBLE] around it. And so it should have slowed down. But we're going to get this gas and secretion just spinning around and falling down, but that's going to speed it up again. !!BRIAN SCHMIDT: Right, because you have to conserve the angular momentum of the stuff again. And so you would expect these stars to be spinning, if they've been accreting for a long time, potentially very quickly. !!V7.10 BRIAN: So Paul, these neutron star binaries are pretty wild. They have huge amounts of energy. It seemed to me to have a huge amount of potential to fill the sky with interesting objects. You got any ideas of what you think are maybe the most interesting objects in the sky? !!PAUL: Well, I think possibly the weirdest of this whole category would have to be SS 433, which was like a compete bombshell to the astronomical community when it was covered back in the 1970s. !!BRIAN: It's got a good name too, sounds important. !!PAUL: Yes. And normally, if you look at the spectrum of one of these x-ray binaries, you'd expect to see a particular emission line-- say, h alpha-- from the gas around the disk. Now, this particular object, SS 433, was observed here in Australia at the Anglo-Australian Observatory. And it was an x-ray source and a faint radio source. !!And it seemed to have a sort of nebula around it that might have been the remains of a blast wave of something. So it was an interesting target. And when they looked at this, they got a spectrum. And sure enough, it had the big line there-- but also, the line over here. !!BRIAN: Ooh. !!PAUL: And another one hiding behind you. !!BRIAN: And over here too. !!PAUL: But they didn't see that one. The original data only covered this range, because the spectrograph's weren't too good back then. And this caused a lot of puzzlement, because they'd look up-- OK, line here. And what you normally do is you look at a line, and you look up the list of

elements and see which one showed up at that wavelength. But there wasn't any really obvious plausible element that showed up at that wavelength. !!BRIAN: Hm. !!PAUL: So what's going on? Some mystery Kryptonite or something like this? A new, weird element? !!BRIAN: New element, but in a good way. Astronomers think of the universe as being the world's greatest laboratory. So maybe it's a new element. !!PAUL: But well, they went to re-observe it a bit later, and they're gone. !!BRIAN: OK, so-- !!PAUL: So what do you think when that happens? Do you think you've already stuffed up your spectrum somehow? !!BRIAN: Well, when I see something really weird, I just assume there was a little glitch. A cosmic ray came in and wasn't right, yeah. !!PAUL: OK, so they thought maybe it was a bit funny, but maybe you shouldn't publish that maybe. !!BRIAN: Yep. !!PAUL: So avoiding, sweeping under the carpet a little bit. However, when more observations were made-- this time in California-- people discovered that first of all, there were two of these things. But also, they came and went. They came back. !!And they moved around, so it actually moved backwards and forwards in wavelength in a symmetrical way. So you see, they'd go both in closer towards the line, and both further away from it. Now, what could cause that? !!BRIAN: Well, my sense is it's probably not a bunch of new elements being synthesized. But it strikes me as something that seems related to the Doppler shift somehow. !!PAUL: Yeah, I mean, an element can't move around. It's going at the same wavelength. So this is presumably something that's moving. And given there are two of them roughly symmetric-- they're not exactly on either side of this-- maybe it's this line, but there's some gas coming out from this thing moving towards us and going away from us. !!BRIAN: So what's the implied velocity of the gas? !!PAUL: Well, these are a long way separated. We're talking at more than 20% of the speed of light to make this happen. !!BRIAN: 20% of the speed of light? !!PAUL: Yes. !!BRIAN: Wow, OK. So that's a lot. That's a pretty amazing velocity indicated. But the amazing thing, is, of course, we have a neutron star here, so almost a black hole. So you really can't imagine getting things up to that type of speed potentially. !!

PAUL: Yeah, but that was-- you'd think there would be stuff falling. And maybe there's stuff falling in from one side and falling in from the other side. And so this stuff that's blue shift to it is on the far side falling in. And that stuff that's red shift is on the near side going in. !!But when they actually observed this thing with modern radio telescopes, what you see is something like this. It's a corkscrew. Now, you're the expert on corkscrews here, Brian. !!BRIAN: Ah, yes, although mine tend to be used for extracting things, not just playing around in space. !!So let's see. We have literally this amazing corkscrew in both directions. Now, that's sort of sounds like a jet, but a jet which is being precessed, I can't-- I'm not coordinated enough to do both arms. But if I do that with a fire hose, which I do sometimes on a hot day, I'll get a corkscrew out. !!And if the fire hoses are stuck out, then they'll kind of go like that, like a kayaker. And you'll get exactly that thing. But it's a jet moving at 20% of the speed of light. !!PAUL: Yes, and we know-- the first course, we talked about quasars and how they had these jets squirting out. This is not a quasar. It's a neutron star binary in our own galaxy. But it seems to have the same sort of thing-- two jets being squirted out opposite directions. !!But as you say, they are precessing. They're moving around something like this. And that's a bit weird. So what's going on here? !!I guess the idea would be that this is normal, a star that's donating mass which is forming an accretion disc and swelling down to the neutron star in the middle. But somehow, as gas comes in, some of it goes out at this enormous speed. !!And this is a bit weird. I mean, why should be stuff falling in produce stuff going out? It's, in fact, embarrassing that we actually never observe stuff falling into these things. We only infer it indirectly. But all we ever see is stuff coming out. !!But we know this is common whenever we have a disk. So for example, a protoplanetary disk, because it was covered in the first course. We get jets coming out from this. We've got bipolar outflows. We know that quasars get a disk around a black hole, and that produces a jet. !!So It seems to be generically true that you get jets quite often. But why are you getting a jet in this one and not all the other X-ray binaries? !!BRIAN: Well, it's not obvious to me why you would get it. But it is interesting that if you have a big mass here and this thing, it might precess around like a giant top. The earth precesses around every 26,000 years. !!PAUL: Because of the moon pulling on it. !!BRIAN: Yeah, the moon and the sun interaction. So it's not completely crazy. But that whole process of how to create a jet from in-falling material is one of those sort of mysteries of the universe still. !!PAUL: It probably has something to do with magnetic fields. Whenever we don't know what's going on, we invoke magnetic fields. !!BRIAN: That's right. Now interestingly enough, Paul, with our SkyMapper telescope, we were out looking around for objects-- in our case, some of the first, oldest stars in the universe. And we look at them by finding things that are very funny colors. And we found an object that sort of looks like

this. It's not exactly the same. But we found something that seems to be having jets shooting out at a large speed in a way analogous to this. !!But it's in a very funny location. It's not towards where young stars are in the galaxy. It's kind of off a long ways away from the galaxy. So it's maybe a sort of a dead version of this, like a really old version of this or something. We're not sure. We still need to get more data. But it's one of the exciting things that you can find. There's really nothing else like it that anyone's ever discovered before. !!PAUL: OK, so maybe SS 433 is not alone in the universe. !!V7.11 BRIAN SCHMIDT: So we've seen that massive stars, when they run out of their nuclear fuel, they collapse down in the form of supernovae. And in that process, leave a neutron star behind, an incredibly dense ball of neutrons, about 10 kilometers, even less, across, but more than the mass of the Sun, where gravity is as extreme as you can possibly imagine. And there are literally hundreds of millions of these things scattered around our Milky Way. And we see them as glowing, hot balls that emit in the X-rays, or even gamma rays sometimes. And we also see them as these peculiar, pinging, radio objects we call pulsars. They really are remarkable objects. !!PAUL FRANCIS: And the study of them is still ongoing. But in many ways, their biggest use now is not studying themselves, but because of what they can tell us about other things, particularly these pulsars that spin very fast. Remember that when they first form, they're spinning at maybe once a second. They have a very strong magnetic field and they slow down fast. !!After all, they lose most of the magnetic field. But they're probably drifting off somewhere deep in space. But if they're in a binary, as we've just talked about, they can mass onto them. And that can spin them back up. And some of these things are spinning only at millisecond periods, like a thousand times a second. And they're called "millisecond" pulsars, curiously enough. !!And these turn out to be fantastically accurate clocks. These pulsars, which may be a thousand times a second, are better than any clocks we can measure on Earth. !!BRIAN SCHMIDT: Well actually, Paul, it turns out humanity has finally gotten one step up in front of those pulsars for accuracy. It appears we finally are able to beat pulsars with the best, new atomic clocks, and through really precise measurement. So they are amazing atomic clocks. And imagine being able to put atomic clocks around the galaxy? Think of all the interesting physics you could do. !!PAUL FRANCIS: We've already talked about one thing in the Exoplanets course. The fact that because they're sending their pulse out so precisely, if one of them has a planet around it that cause it to wobble backwards and forwards-- not by very much-- we're only talking meters here-- but that can be measured with such exquisite precision that they can find very low-mass planets around these things. We talked about that in the last part of this course. !!But perhaps even more exciting is the use of these things to probe the physics of strong gravity. There's another Nobel Prize, of course, in this. !!BRIAN SCHMIDT: Yeah. That's right. So Hulse and Taylor discovered a binary pulsar. That is, two pulsars going to around each other, where you could go through and see the one pulsar that was the easiest to see and use it to time what's going on. And it turns out there's all sorts of interesting relativistic effects, general relativistic effects. That is, things that only Einstein's gravity predicts. !!

And one of the things is gravitational radiation. So as one neutron star goes around the other, it will let off gravitational radiation. And that will cause its orbit to essentially get closer and closer to the other object over time. So the whole thing will essentially speed up a little bit over time. !!And that was seen. And general relativity predicted exactly what was seen in this binary pulsar, and led eventually to the 1993 Nobel Prize. !!PAUL FRANCIS: Yes. Of course, general relativity is normally very hard to test on Earth because the gravity just isn't strong enough. If you had a black hole in our lab, it would be pretty easy. But luckily, we don't. !!So these neutron star binaries are one of the few places where you can actually test this theory. And so far, its come up with flying colors in these extreme environments. !!BRIAN SCHMIDT: And one of the other things is that there you are inferring the existence of gravitational waves because you're seeing essentially the energy that's left the system. !!PAUL FRANCIS: It has to be going somewhere. !!BRIAN SCHMIDT: That's right. But these same objects, because they're amazing atomic clocks, give us the opportunity to maybe directly detect gravity waves. So imagine you see two objects orbiting each other and letting out gravity waves. Those waves cause space to do that. And when space gets bigger and smaller, if it's bigger, then it takes longer, for example, the radio waves to get through that part of space. And if it's shorter, it's quicker to get through that part of space. !!So imagine you have really big gravity waves, that are billions of kilometers across. Then if I look that direction at a set of pulsars, and compare it to a set of pulsars that direction, I'll suddenly see that those pulsars will slow down, while these stay the same speed. And then, eventually, those might slow down or speed up. And that would be caused-- or be a way to detect space sort of stretching and contracting due to gravity waves. !!PAUL FRANCIS: So the race is on to discover gravity waves at the moment. They've been inferred from microwave background observations and from the pulsar measurements, but never directly measured. There are labs around the world trying to measure it and they're getting pretty close now. But maybe the astronomers will get there first and discover them via this effect on the radiation coming from pulsars. !!BRIAN SCHMIDT: Right. So pulsars really are one of the great toolboxes that astronomers would have. There has literally been three sets of Nobel Prizes now related to them. !!And so the interesting thing is is there anything even more interesting than neutron stars? And many of my colleagues, who study them, say no. !!PAUL FRANCIS: Yes. And so we've started with white dwarfs. And they're pretty violet. But neutron stars put them in the shade. What could come worse? !!Well, we know that the neutron stars are held up by neutron degeneracy pressure. And that's not stronger than electron degeneracy pressure that holds up white dwarfs because neutrons are move massive. Therefore, they have to have a lot more energy because they can get close to the speed of light. And there's got to be limit then. !!Eventually if you pile mass on a neutron star, it's going to do the same. It's going to see it's own Chandrasekhar limit, do the same thing that a white dwarf does, and collapse. And then what happens then? Well, that's a topic for our next video. !!

Lesson 8: Special Relativity!

V8.1 BRIAN SCHMIDT: So we've seen some of the most amazing stars in the universe, white dwarfs the size of the Earth, neutron stars the size of a small city, but all the same mass as the Sun. But now let's move on to the most amazing of the stars, the idea of a black hole, a star even denser than a neutron star. !!PAUL FRANCIS: And this concept goes all the way back to at least the 18th century. Back then, some philosophers came up with the idea of dark stars. And the idea here was that you might have a star whose gravity was so strong that light couldn't escape it. !!Back then, they thought of light as being like a ball. So here's my light particle, a photon, if you like. And the idea was that the light would be shining. And you have a brightly shining star, such that it would go up. But the gravity would be so intense, it would come back down again. !!BRIAN SCHMIDT: So it wouldn't have escape velocity. !!PAUL FRANCIS: No. It wouldn't have escape velocity, just like this ball doesn't have escape velocity. It comes back down again. So the photons would come up and come back down. !!So you would have a star, but according to their idea, it might look very much like a normal star if you were up close it. But the light would never escape. The gravity was too intense. And so it will be invisible. !!And, of course, there could have been billions of these stars around the galaxy. They could be looming and approaching us just right now, on their way to kill us. And we wouldn't know because the light can't get out. !!BRIAN SCHMIDT: Um. So to understand this, we need to understand light a little better because that ball is not really a very good example of how light really works. !!PAUL FRANCIS: Yes. And, in fact, the true idea of a black hole is altogether weirder than this. And so to understand that, we're going to have to talk about Einstein's theory of special relativity. And that's what we're going to do for the next several videos. !!Now, the first clue from this came maybe in next century, the 19th century, with the discovery of electromagnetic waves. Now back in the early 19th century, people like Faraday had shown that there was electric fields and magnetic fields. And it was eventually realized that if you change an electric field, like you, say, have a wire and you suddenly apply a voltage to it, there's a change in the electric field. And that directs a magnetic field. It makes a compass twist. !!But likewise, if you change a magnetic field, like by taking a magnet and waving it around, that makes an electric field. That's how dynamos work. You whirl magnets around to make electric currents. !!But the idea was, towards the end of the 19th century, that Maxwell came up with, so if a changing electric field can produce a magnetic field, and a changing magnetic field can produce an electric field, that maybe we don't need wires and magnets at all. They can just go about, winding themselves through space. !!You have a changing electric field. That makes a magnetic change. That makes an electric field change. That makes a magnetic field change. And the two of them just keep wandering through space, supporting each other. !

!BRIAN SCHMIDT: So once you start one of these things going, you just sort of get this thing going on, right? !!PAUL FRANCIS: Yeah. And no need for wires or batteries. It could just sustain itself. !!They did the calculation. And you get the wave that looked like this, with the two components at right angles to each other. And it conveys the speed. !!So it depends on two constants that can be measured in the laboratory, the constants of the electrostatics and magnetic fields. And it came out with the velocity. And when they did the calculation, the velocity came out as 300,000 kilometers per second. !!BRIAN SCHMIDT: Ah. !!PAUL FRANCIS: And that's a curiously familiar number. !!BRIAN SCHMIDT: That is an interesting number. That sounds an awful lot like the speed of light. !!PAUL FRANCIS: Yeah. So this was an amazing breakthrough. That we had light and we had electric fields and things. And people didn't realize it had anything to do with each other. And what did magnets have to do with light? !!But we found out is that, in fact, they're the same thing. That an oscillating electric and magnetic field actually produces light and it comes out with that speed. !!So this led to the whole understanding of light for the first time. It led to the discovery of radio waves. So that's probably one of the greatest technologically useful discoveries of all time, along with the thermodynamics of steam engines. !!But there was a philosophical puzzle here. Because here's the speed and that speed is absolute. It doesn't say with respect to what or where it's launching from or anything. It's always the same speed. !!BRIAN SCHMIDT: So that's saying that if we think light is actually this electromagnetic waves, it's sort of saying you might expect light to always have the same speed, no matter what's going on in your life. And that can lead to some interesting problems. !!PAUL FRANCIS: Yeah. And the problems that leads to, we'd have to go back to Galileo to understand. Galileo came up with the idea-- it's Galileo's theory of relativity, which in its own way was every bit as amazing as Einstein's theory. In fact, even more so, I would say. !!And the first idea is that let's say we take Brian and put him in a box-- !!BRIAN SCHMIDT: Yup. !!PAUL FRANCIS: --a soundproof, lightproof box that lets no forces through. You have all the physics equipment you like in there. You can do any experiment you like. But can you tell where you are? !!BRIAN SCHMIDT: So, for example, if I'm moving, then I might expect the ball that I drop inside my box to have a different trajectory if I'm moving? Well, no, not if the ball is moving with me. !!PAUL FRANCIS: Yeah. So the curious thing is that not only can you not tell where you are-- so you don't know whether your box is an Alpha Centauri or downtown Canberra-- unless there's some

force. You open the window or feel the gravity coming in from outside. But if you're floating freely in space, you can't tell where you are because as long as it's the same everywhere. !!So no experiment you do will give different answer wherever you are. So you can't tell it anyway, without looking outside where you are-- without looking at something out that is relative. !!But worse than that, you can't tell if you're moving. Now, this was a big controversy back in Galileo's time. He was proposing that the Earth went around the Sun, so that when the pope was sitting in his chair at St. Peter's, he's actually moving at an enormous speed here, 30 kilometers a second around the Sun. !!And his opponents thought this was ridiculous. If you could move at these enormous speeds, wouldn't you feel it? You'd get blown back or something. But Galileo pointed out, no. !!Actually, you can't feel motion. You can feel acceleration. When you start moving, when you put your foot down on the accelerator, you can feel that. !!BRIAN SCHMIDT: Yeah. !!PAUL FRANCIS: But if you're just moving at a steady speed, you can't tell. And he used the example of being on a rolling galley, one the Venetian navy fleets. !!You could be doing experiments in the cabin there. It feels rocking. That's acceleration. You can see that if it's just going nice and steady on a smooth sea. !!You drop things. They appear to land at your feet. They don't suddenly fly off sideways, even though you're moving. !!BRIAN SCHMIDT: And we get this same feeling throughout our lives. For example, if you've ever been able to look out the window of a plane, when suddenly the plane gets towed back, you often can't feel the acceleration. And all of sudden you look outside and you realize that, wow, outside's moving. Ah-- or is it you moving? It's kind of hard to tell. !!And indeed, the whole idea of Galilean relativity is it doesn't really matter. Either is equally valid. !!And we use this type of idea, I guess, throughout our lives. And we sort of take it for granted. But you really can't tell what's fixed and what's not. It's only when you say the Earth is special, that you sort of have that reference point. !!PAUL FRANCIS: Yes. Because we think of the Earth as being stationary. I think that I'm standing here, not moving. But, of course, I'm on the Earth, which is spinning at a thousand kilometers at hour, right here at Canberra, moving around the Sun at 30 kilometers a second. !!The Sun is moving around the galaxy at 200 kilometers a second. The galaxy is falling into the Virgo Cluster. The Virgo Cluster is falling into the Great Attractor. !!So what, if any of these things, constitutes rest? And Galileo's key insight is we don't know, but we don't care. Because any motion that's uniform, we can't tell the difference. If we can't measure the difference, it makes no difference. !!So there is no such thing as a universal standard of rest. Motion is entirely relative; hence, relativity. So an important concept. But as we'll see, that gets us into trouble. !

V8.2

PAUL: So here's the problem. We've said that we can't tell if we're moving. There's no absolute frame of motion. But we have the speed of light that is always the same. !!Now how do those two things conflict with each other. Well, let's imagine that there are two of us and I'm on a boat. And I'm going to this direction whereas you're stationary. You're sitting there on the quay-side OK. !!Now let's say you shine a torch that way and that light from that will go out at 300,000 kilometers a second. But let's say I, as I come along here, shine a beam of light past you and I'm moving towards you at, say, 1 meter per second. What speed is that light going to be going at when it goes past you? !!BRIAN: Well, intuition says it should be going your velocity plus the velocity of light. So if you're going 1 meter per second, then it'll be 300,000 kilometers per second, plus your 1 meter per second. And that means that if we shoot our torches off at the same time-- !!PAUL: Mine's going faster than yours. !!BRIAN: --your light's going to pass my light. !!PAUL: Yeah. So that conflicts with this equation we just had back here which said it was that speed but it didn't say where it was launched from. It just said that speed. So we're now violating Maxwell's equations. !!And it'd be really bad if, for example, I was going along at the speed of light and shining a torch backwards. Because then as I came past you, I'm going at 300,000 kilometers a second that way. I'm just trying to go out backwards. So what speed would the light be then going past you? !!BRIAN: It would just be stuck there. That would be pretty cool theater trick. !!PAUL: Yeah, just a frozen light. But that can't work because remember what produces a magnetic field is a changing electric field. What produces a electric field is a changing magnetic field. So it just simply is not changing. !!BRIAN: Yeah, so that would be problematic. !!PAUL: They have to move to exist. !!BRIAN: So to give some people some intuition, I grew up in Alaska. And Alaska, one of the things you do, is you get in snowball fights. Now I had an OK arm, but not a great arm. So I could only throw a snowball at about, oh maybe, 50 kilometers an hour. !!But one of the tricks we used to use as we would get in the back of a pickup-- that is a car that has an opened backside-- and we'd drive along the road at maybe 50 kilometers an hour so that when I threw my snowball at you it would go 50 kilometers an hour that I could throw plus the 50 kilometers an hour the car. !!So it certainly works for snowballs because trust me, a hundred kilometer an hour snowball hurts a lot more than a 50. And this trick really did make the snowballs travel a lot faster. !!PAUL: So we have a choice here. So one possibility would be that exactly the same thing that works for snowballs works for light, that if I'm going fast and I shine a light forward, it'll go faster. So in that case, we've violated Maxwell's theory. We've said that light doesn't always travel at the same speed. It can go faster or slower, depending on where it gets launched. And then it could be stationary. !!

Einstein's famous [INAUDIBLE] fly a spaceship alongside a light wave, and it would be stationary which it can't happen because electromagnetic waves have to move to work. They have to move at that speed to work. So that's one problem. !!But maybe it's not like that. Maybe when I'm running forward and I shine my torch, instead of going at 300,000 kilometers a second, it goes at 300,000-- 300,000 plus 1, it just goes at the same speed no matter. Even if I'm running at half the speed of light, it doesn't go at 1.5 times below. But it still goes at 1 times the speed of light because it's always going at the same speed relative to some universal frame of reference. !!BRIAN: OK. But that means that if I'm in-- let's just I'm in a box or I'm in this room, and we know, for example, the Earth is traveling at 30 kilometers per second around the Sun. !!So let's say the Earth's motion's in that direction. That means that if I shine a torch that way and I measure how fast light moves that way and I measure how fast it goes that way, I should be catching up or going behind it. !!So it travels the same speed, but I'm moving, and so I should be seeing, catching up with the light at least in one direction. I should be able to see it, should see a different speed of light if I'm in a box. !!PAUL: So we've got a paradox. There's a conflict between Galileo's idea of relativity but there's no absolute frame of reference and Maxwell's idea that electromagnetic waves. !!And there are two possibilities. One is that when you shoot light it goes out at your speed plus its own speed. In which case, Maxwell's did because I can go different speeds and even be stationary. !!The alternative is to say that light always goes a speed with respect to some sort of fixed background. In that case, Galileo's wrong because we can then run around even in a locked box and find it for moving by sending light into different directions and seeing how fast they. go because one or other of these has to be wrong. !!BRIAN: Yes. Well, OK. I always believe that when it's hard to tell the best thing to do is to do an experiment, but it doesn't seem to me why Galileo might not be wrong or why Maxwell might not be wrong. Reality is going out and looking. !

V8.3 PAUL: So by about the late 19th century, people had figured this paradox out and experiments were done, the most famous of which is the Michelson and Morley experiment to actually see if the speed of light was constant even though the earth was moving. And the answer came back that the speed of light did seem to be constant in every direction. Along the direction or back or sideways. !!BRIAN: That's crazy, Paul. So I go-- we're moving in this direction and I measure the speed of light, that direction, and I get the same answer as that direction? It's like light seems to know what to do based on what I'm doing. That seems impossible. !!PAUL: Well, it make sense if the earth is stationary because we've now found a universal frame of rest and that frame of rest is the Earth. The Earth is stationary. !!BRIAN: So the Earth isn't rotating once a day and it's not revolving around the Sun? !!PAUL: Well now maybe Aristotle was right and the Earth is stationary and the Sun really is going around us and we're not rotating. It's the universe that's rotating around us. !

!BRIAN: OK. I'm not feeling better about this. !!PAUL: What else can we do? The speed might seem to be the same in directions. !!BRIAN: So maybe there's some weird way light travels, that light travels in an ether. And although the Earth's moving, the ether isn't moving. !!PAUL: Or it's moving with us. Yeah. So back then, people thought that-- we know the other sort of waves. For example, water waves move in water. Sound waves move in air. So maybe light waves moving something we can't quite see that was called luminiferous ether, which means that thing what makes life waves happen. I guess it's the dark energy of its time. !!BRIAN: Absolutely. So you would have this ether be moving along with the Earth. !!PAUL: Yeah. So the Earth would have to have a chunk of ether around it, which I have colored in this light blue over here. And the idea would be that that was following the Earth around its orbit, which is why when we made measurements here, the light seemed to travel at the same speed in all directions. !!But if there were any astronomers on Venus or on Mars or the Sun trying to do experiments, they would have their own chunk of ether around them and they would also find themselves at rest. So this gets away with the horrible problem of the whole universe rotating around us. !!BRIAN: OK, but it does mean that if I look to here that there's going to be a different piece of ether here and a different piece of ether here where light travels at different speeds presumably. And I know that if you change speed-- for example, if you put something in water where the speed of light is slower in the water, you get these refraction effects and so that you end up seeing two images or you see light bend, and very useful for making a lens, but it's not-- it means that Venus is going to be distorted and things. !!PAUL: Yes. We all did the calculations and if there were a chunk of ether following the Earth around another chunk following Venus and the Sun and the galaxy and so on, that would explain the Michelson-Morley experiment that the speed of light was the same in all directions. But we'd then start getting horrible effects whenever the light went through these ether boundaries. The alternative would be that the ether for the entire universe is centered on the Earth and following us around the Sun. !!BRIAN: And that violates the Copernican principle that we're not a special place in the universe. !!PAUL: That sounds pretty crazy. !!BRIAN: So we have another paradox, it seems. !!PAUL: Different version of the same paradox. So it doesn't look like we're moving. According to the experiments, the light's going at the same speed in all directions, but we know we're moving. So what the hell's going on here? !!BRIAN: So I don't know. I think we're going to have to think harder about crazy ways to fix this problem. !!V8.4

BRIAN: So when you want to solve a physics problem, you always have to choose your frame of reference, and you usually choose your frame of reference to make it easy to solve. So for example, if I'm going to drop a ball, for example, here on planet Earth, I don't choose a reference frame of the Earth rotating and the Earth going around the sun. I choose just right here in this room. !!So if I drop this ball, it goes straight to the ground. So if we look at this from a mathematical point of view, we want to choose a reference frame, which is really fixed to the place that you're interested in. So let's try that. !!PAUL: Yeah, so let's imagine we've got two barges. There's a front barge and that's you on it. I've painted you in green. !!BRIAN: Oh, that's me. Good. !!PAUL: I'm over here. I'm the invisible man on this one. And this will be the coordinates you're using, your x, y and zed-coordinates. And also, a clock to measure time. And I'm measuring with respect to this. So if I'm doing my experiment here, I would use these coordinates on that tree, and you would use those. !!The question is how do we convert between these things? So let's-- if you're just doing your own experiment, Galileo relativity tells you everything should work fine in your coordinates. The same if I'm doing things on my barge, everything should work fine for me. !!But what happens if I'm looking at you as you drift past? How would I measure what you're doing? Well, that all seems to make sense. This could be a place where we can solve this mystery. Because if there's some funny thing going on with the conversion, maybe that can help us get of this whole problem. !!BRIAN: Right, so this conversion of what you see in your frame of reference compared to what I see in my frame of reference is called a transform. It's a complicated name for something that's pretty simple. It's just how we convert from your point of view to my point of view. !!PAUL: Yep. So what we're going to do now is go through what you would expect to be a common sense transform. This is probably something that any physics student has used a million times without even thinking about it, without giving it a name-- converting from one set of coordinates to another. !!So we're going to do the what you would expect some common sense, and then we're going to start mucking it up and playing with it and see if we can come up with some relativity. But first of all, let's just leave our common sense on-- we'll turn it off a bit later-- and see what we would expect the common sense transform to be. !!So the key thing here is going to constitute an event. We've got to wave there. That was you, waving. An event, in relativity, is something that is located both in space and in time. So there was particular time and a particular position where you waved. !!BRIAN: Right, and so there was a position. So let's look at that, the event. And so at some point, I'm going to have a coordinate. The clock will have a time. And we want to see how my version of coordinates in time compare to yours. And that's the notion of the transform. !!PAUL: Yeah, so you're measuring with respect to your x, y, and zed and t. And I'm measuring with respect to my x prime, y prime, zed prime and t prime. So let's look at how we do this. So this is the actual moment, a freeze frame from the image when you've waved your hand up. !!BRIAN: I've done it. !

!PAUL: So the place is here, so there's your x-coordinate. y-coordinate is 0. And there's the zed-coordinate. And your time t is measured by your clock. !!BRIAN: Right !!PAUL: And the question is if I try to measure that same event-- I'm looking at you as you go past-- when would I measure as the x, y, zed and t coordinates? So that's with respect my coordinates, which are fixed to my barge. !!BRIAN: Right, so our barges are on the same piece of water. So we're going to have these new coordinates, which we're going to call x prime, y prime, zed prime, and t prime, which are your versions of my event. !!PAUL: So we're measuring with respect to my rulers, when did you raise your hand. !!BRIAN: Right. !!PAUL: Well, the easy one is zed, the height. !!BRIAN: Right, because we're on the same body of water in this case and we have the same reference frame. !!PAUL: So we're measuring zed prime off the same basis, so the height of your hand will be exactly the same. !!BRIAN: Right. !!PAUL: Now, the y-coordinate will be a bit different, because you're off to the side. But that will just be a constant offset, which will be however far apart we are. So let's see. You're a meter to the side over there. Then whatever y-coordinate your hand is, mine will be that plus a meter, plus whatever the separation is. That's also pretty easy. !!Time would also be easy. And presumably our clock's not going to change. Ha, ha. Who would come up with an idea like that? !!BRIAN: Your watch and my watch will have the same, yep. !!PAUL: Yep, so the time that you measure in t prime should be the same. So the transform there is very easy. It's the same time, same zed. The y is just offset by a constant. The tricky bit is going to be the x, because-- !!BRIAN: I'm moving. !!PAUL: You're moving relative to me. And we're both moving in this case. What matters is the relative speed. !!So as you go that way, if you raised your hand now, as opposed to raised it a bit later-- if you raised it a bit later, you'd be further over. So what x prime I measure is going to depend not only on what x you had, but also on what time you raised it, if you raised it later. Because of course for you, you're raising it at the same place, same x every time. But for me, its going to change. !!BRIAN: And it depends on my velocity. !!

PAUL: Relative to me. If we have the velocity relative to me-- because I'm doing this way and you're moving that way. So we take your velocity and subtract mine so we get the relative speed-- and call that v, then my coordinates-- you will have moved a distance of v times t. !!And it's your x. So the x prime I measure will be your x plus that v times t. So the longer you wait before raising your hand, the bigger mine will be. !!BRIAN: OK, that seems straightforward enough. !!PAUL: OK, so this is a common sense, actually wrong, transform. So we get x prime is just-- I measure x for your hand raising event is just what you measure plus v times t. Since it's the same y-- it's just offset by a constant-- I haven't bothered showing that. And the time is the same. !!So that's common sense. But remember, we've got this paradox. We've got light traveling at the same speed and violating Galileo's relativity and what the hell's going on here. Perhaps we could muck up with these. Perhaps we could play with these. !!BRIAN: Hmm, sounds like a good idea to me. I can't think of anything else to do. !!PAUL: Yeah. Everybody's stuck here. !!V8.5 PAUL: So we've got this paradox that we'd like everybody to measure the same speed of light, even if they're moving. So if I'm running along here, I should measure speed of light, but you looking at me should also measure the same speed of light from me. !!And that's weird. And so we're going to do some violence to common sense to common sense to make this to work. !!Now we've had this transform, the common sense transform, a Galilean transform. And that says, that if I'm going fast, and I follow something forward, that thing should be going even faster. The velocity should add. !!So we're going to need to do some violence to that. There are various possibilities we could do. We could, for example, change lengths. So if I'm running forward and I throw something, to me it's going to go at one speed, and it's going to be at a different speed for you. So maybe it's because time speeds up or slows down for me, or maybe the lengths change. !!BRIAN: So I bet you mathematically, if we sit down and do some algebra, we can calculate a transform in which the speed of light is the same for everyone. But it's going to mess other things up that we hold to be true, I think. !!PAUL: Yes, we're in a tough situation. I mean, the transfer we just talked about is so common sense. Velocities adding up, positions adding up. It's just saying your time is my time. That's what common sense tells us. But if we're going to make this work, we need to come up with a transform that does violence to that in order to keep the speed of light sacred. !!BRIAN: Well, desperate time calls for desperate measures. So let's figure out what happens if we keep the speed of light constant for everyone. !!PAUL: So it turns out that if you want the speed of light to be constant for everybody at every time, there's only one set of transforms that can do it. And this was worked out by Lorentz just before Einstein got there independently a year later. And these are those. !

!Here's our common sense transform, which tells us that, in my frame of reference, it's just your frame of reference plus velocity times time. But Lorentz said it's the same thing. x prime equals x plus vt. This is a constant gamma in front. !!What's gamma? Gamma is this rather weird thing down here. So it's 1 over 1 minus root v squared over c squared. So v is velocity, c is the speed of light. If velocity is much less than the speed of light, that's going to be a very small number. Squared is even smaller. 1 minus is going to be about one. So it's approximately 1 over root 1, which is 1 over 1, which is 1. !!BRIAN: Right. !!PAUL: So what that means is to slow speeds, this equation and that equation are pretty much the same. !!BRIAN: Right, because we have, that is 1, so for slow speeds it's just x plus vt, exactly what we have. !!PAUL: And that's a good feature of this relativity theory, that it behaves like good old Galileo stuff when speeds are low. It doesn't disprove-- you're not going to fall off your bicycle just because new theories come up. It behaves like the old one, so that was necessary. !!For z, there's no change. Time it's a bit weirder still. Once again, when you make velocity very low, this comes out as the same as that. But what you'll see in here is, once again the gamma plus the velocity times the position over c squared. So this actually depends on where you are, as well as the time. So that's a bit weird. !!What's the gamma? Here's what gamma looks like. I've plotted gamma against velocity of the function of the speed of light. And what you can see is, when you're going much less than the speed of light, it's pretty much done, 1. !!BRIAN: So even at 40% of the speed of light, it's almost 1. But when you get up to-- !!PAUL: Yeah, our faster space crafts are about here on the scale. About 2 pixels in. !!BRIAN: 99.9% of the speed of light, then this number starts becoming really weird, like bigger than 5. !!PAUL: And it starts heading off to infinity as you start going up to 1. When you get v equals c, that's 1 over 1 squared, which is 1. So 1 minus 1, which is 0, 1 over root 0, which is infinity. !!BRIAN: So that means as I start going closer and closer to the speed of light, our relative velocities are, this number is going to become much bigger than 1. Which means it's going to be like the distance between us is more than just this x plus vt. It's got this extra factor in it. !!PAUL: Yeah, so if you're off sitting there with a ruler, you'll think your ruler is a meter long, but I won't. I've got a different length for it. !!And also your time, your clock might think an hour has passed, and I think a different amount of time has passed. And even worse than that, let's say you have two clocks at different ends of your boat that are different times according to me because of different x-coordinates. !!BRIAN: Oh OK, so that's really going to break some of the things that we think as being just part of nature around us, right? It means-- !!

PAUL: So we've got three real problems here. And if you do the sums, you find the first effect is time dilation. If you race past me, for your point of view nothing's changed. Your clock's running at normal time, yeah, it's going fine. Your rulers are all the right length, the speed of light in all direction's the same for you. But when I look at you, to me you seem to be going really slowly. You're-- !!BRIAN: So if you're looking at my clock, it's like it slowed down as I go away from you. !!PAUL: And you seem to be talking very slowly. !!BRIAN: Yeah, okay. !!PAUL: But then, curiously enough, from your frame of reference, you see the same for me. For me, I think I'm fine, but you look at me, and I would appear to be going really slowly and my clock would be moving-- but to me I'm perfectly fine. !!BRIAN: OK, and what about this link? We saw that links are messed up as well. !!PAUL: Yeah, so to me, if your length in the z-coordinate looks, so normal so you're as high as you ever were-- !!BRIAN: But I'm not moving in that direction, yes? !!PAUL: Yeah, if you're moving this way, you're much thinner. So you seem to shrink along the direction of your motion. But from your point view, you look perfectly normal. !!BRIAN: I'm completely normal, but you look shrunk as well. !!PAUL: Yes. And possibly even the worst thing is simultaneity, that things appear-- if you look at this equation back here, you see that two things that happen at the same time from your frame of reference , if they're at different x-coordinates will appear at different times for me. So let's say, for example, you did-- [GESTURING], open both your hands simultaneously, because they're at different x-coordinates, I will think you opened one of them before the other. !!BRIAN: So in other words, if I drop a ball out of two hands, when I drop them, of course from my point of view, those balls are going to hit the ground at the same time-- !!PAUL: But from my point of view, you dropped them at different times and they hit the ground at different times. !!BRIAN: Right, so that means things happen at different times depending on where you are and how fast you're moving, relative to what's going on. !!PAUL: And even in different orders. So for example, if you're going this way, from my point of view, you dropped this one first and then that one. But then, if it's someone going the other way, it might appear you're dropping them the opposite way around. So it's making cause and effect different. What happened first? !!BRIAN: Hmm. That's pretty deeply disturbing. !!PAUL: It is indeed. So these three weirdnesses, time dilation, length contraction, simultaneity removed-- but they do you solve the problem of light. !!So the idea is, let's say you're trying to measure the speed of light. So you're driving on your barge, you've got a torch in your hand , and you turn it on at some point. Or your turned it on as an event

here, it turns on, and a bit later there will be a second event over here when it's picked up by the receiver. !!BRIAN: Right. !!PAUL: So you've got event one event two and from your frame of reference, you'd measure when event one happened when you turned the light on. When event two happened, you'd take the difference in time, the difference in distance, divide one by the other, and look at the speed of light. !!For my point of view, I'd use the Lorentz transform. I'd measure when the first event happened to convert it from your xyz and t to my x-prime, y-prime, z-prime, and t-prime. And I'd convert the second event using those equations. And it turns out, that if you do that, I will measure the same speed of light as you did. So-- !!BRIAN: At least we will get what we seem to see in nature, at least, so that would be good. !!PAUL: From my point of view, you are doing the experiment really slowly and your experiment has shrunk. But I thought you were going to change the answer, it turns out those two things just happen to cancel out and get the same speed of light. !!BRIAN: OK. !!PAUL: Now this is a bit complicated. So what we're doing is, you either take it from trust in us that these things will work, but I'll also put in an appendix calculation where I actually show that the Lorentz transform actually does give you the same speed of light. And I will show how it changes time and changes length. !!If you don't want to do the math, don't worry, you don't need it for the exam. And just feel free to skip over to the next thing. !!But if we do muck up the transform to explain this constancy, the speed of light, this is the price you pay for it. !!BRIAN: Very profound things that should happen in nature. And of course, the best thing to do is to go out and test these things to make sure that they really do happen in nature. Or else we know that it's an interesting idea but it's wrong. !!PAUL: We'll have to find some other way out of the paradox. !!V8.6 BRIAN: All right. Today I have with us Dr. Craig Savage who's a physicist here at the Australian National University. And one of the things he's developed is some visualization tools to look at relativity in sort of a real world way. And so, Craig, why don't you take us on the C Highway here? !!DR. CRAIG SAVAGE: Sure. Well, this is what I call the desert road simulation. And this is an artificial world, sort of like a computer game world, in which we've artificially made the speed of light 1 meter per second. So instead of being 300,000 kilometers per second, it's just 1 meter per second. !!So this is a very unusual world. But apart from that, everything is physically correct. And in this little movie, what we're going to do is accelerate down the road that you can see there. So we're going to start off some distance back from where you can see in the image at the moment, and we're just going to start from rest and keep accelerating down that road and look and see what happens. !

!BRIAN: OK. !!DR. CRAIG SAVAGE: So I'll start it up. !!BRIAN: And as I see here, we have checkmarked, "Aberrations." So aberration is distortion caused by the fact that things get lengthened or shortened. !!DR. CRAIG SAVAGE: That's right. Well, ultimately it's caused by the fact that we're traveling at a speed near the speed at which the light is traveling. So normally in everyday life, the speed of light is so fast that it doesn't matter how fast we;re traveling. Light is just traveling essentially infinitely fast. In this world, it's different. As soon as we start moving, our relative motion to the light actually starts to matter. !!BRIAN: OK. So let's see what happens. !!DR. CRAIG SAVAGE: So start up. And what you've got to remember in this, because it's very unusual, is that we're starting from rest and constantly accelerating towards the front, towards the building. But you can see, it looks like it's getting further away. !!BRIAN: It's getting further away. Yeah. !!DR. CRAIG SAVAGE: But we only ever are moving towards it. At the top right, is our speed. It's a fraction of the speed of light. C means the speed of light, and down at the bottom is the gamma factor, which I think you've encountered before. !!BRIAN: That we've discussed, yes. !!DR. CRAIG SAVAGE: That tells you how strong your relativistic effects are. The hole in the clouds that you can see started off when we are at rest, directly above us. And now it's in front of us. You can see these strange curving and aberration effects that are occurring. !!BRIAN: So, we're right now passing the building it seems. !!DR. CRAIG SAVAGE: I'm going to pause it so we can talk about that. The little inset that's just next to you, Brian, there's a green arrow there which shows the direction of motion. That's us. And you can perhaps see the building. It's really little map. !!BRIAN: So this is the building here. !!DR. CRAIG SAVAGE: That's the buildings. This is the rest frame of the building or the world frame. And the purple pyramid shows the field of view of the camera. So that's what we're seeing on that main screen. So what you can see right now at this point where I've paused it, we're traveling at 0.946 the speed of light-- although we're paused so we're not actually moving. But everything, it's just like we've stopped the motion. You can see the building's behind us in the world frame. !!BRIAN: Right. !!DR. CRAIG SAVAGE: But we can see the building in front of us, so we're seeing behind us. And that's one of the magic things in relativity. You can see behind you. !!BRIAN: So what's really going on here is the light here was emitted and we've sort of caught up to at some level. !!DR. CRAIG SAVAGE: That's right. !!

BRIAN: It's headed out, trying to go like that. And we're going like that. And we ended up meeting up here in the forward. And that's one of the things that causes that aberration. !!DR. CRAIG SAVAGE: And that'll become a little bit clearer as we look at some more stuff. But It's quite mind boggling that once you start moving around at the same speed as light is moving, you can even see behind you. !!BRIAN: OK. !!DR. CRAIG SAVAGE: So I'll keep that going now. !!BRIAN: Yep. !!DR. CRAIG SAVAGE: Just finish that off. !!BRIAN: All right. so we're going, keep going. !!DR. CRAIG SAVAGE: Now, this one is what it would really look like if all the physics was in there-- except we've got the speed of light 1 meter per second. So it's still that artificial speed. But previously, I'd turned off the relativistic Doppler effect, which is a change in color. And I'd also turned off something called the headlight effect, or sometimes the beaming effect, which is an intensity change. And you'll see why I've turned them off once I show you the movie. !!BRIAN: So that density, just to remind people, we know what the Doppler effect is. That's the stretching. But if I'm coming towards a light, as I'm going towards it very quickly, I get more and more photons per second coming from that light. So that's going to make the light much brighter. !!DR. CRAIG SAVAGE: It is. Yes that's right. And you'll see that when I turn all those things on, it's kind of less interesting. Or at least it's hard to see the aberration effects that we saw before. So this is the more realistic one, but it's a little bit harder to understand. !!BRIAN: OK. !!DR. CRAIG SAVAGE: Let it go. Otherwise it's exactly the same. We're just going to accelerate down the road. Again you can see things look like they're getting further away even though they're not. You can now see colors starting to change, and the major effect is the brightening directly in front of us. And as we accelerate more and more, it just gets brighter and brighter in front of us and dimmer and dimmer behind us. !!BRIAN: And it becomes more and more concentrated the closer to the speed of light we get. And you'll get this really bright thing where everything coming towards us is incredibly bright. !!DR. CRAIG SAVAGE: And you can see a slight Doppler rainbow around that bright bit as well. !!BRIAN: And although we can see behind us, we really almost can't. Because although light is coming from behind us, it's so faint that it's almost impossible to see. !!DR. CRAIG SAVAGE: That's right. So moving on. This animation-- which all this stuff I must say was created by Antony Searle, who I think you taught a long time ago. !!BRIAN: He took this class back in the 1990s when I first started teaching it. Yeah. !!DR. CRAIG SAVAGE: That's right. Antony did some pretty amazing work creating the software which produced these videos. In fact, he was integral to everything that we're going to see today. !!BRIAN: And he did this as an undergraduate? !

!DR. CRAIG SAVAGE: He did this as an undergraduate in his second year. In fact, it was ever an Easter weekend where he dropped into my office on the Easter Thursday and asked what I was doing. And I said I was trying to create simulations of relativity, and I didn't know how to do it. I couldn't do it. !!And he managed to do it over the Easter weekend. I don't think he slept much. But he came in on the Tuesday morning and had a working application which did everything I'd been trying to do for a long time. And I was just absolutely blown away. !!And the project has gone on from there. But Antony wanted to use the tram motif, the idea that Einstein had thought about motion in terms of trams moving through Bern, the city in which he lived in in Switzerland. And what you can see when you look at these images of the tram is how it changes. In fact, what you're seeing right now in that stop motion is a length-contracted tram. So the tram is moving at about 86% the speed of light. So the length/contraction factor is about 2, so it's half its normal size. !!BRIAN: OK. So let's put the image in motion and get a sense of how it goes. So we can see there's all sorts of-- !!DR. CRAIG SAVAGE: It'll repeat. It'll repeat through. !!BRIAN: --interesting effects. So as it goes by, it actually sort of, gets squished. !!DR. CRAIG SAVAGE: It's going to come in again. There we go. !!BRIAN: Comes through. !!DR. CRAIG SAVAGE: And you can see that as it gets towards the center, we see the true-length contraction. What we're seeing at this point in the frame is length contraction mixed up with some speed of light effects. So some relativistic optic effects so it looks longer. But actually in the center, what you see is the pure length-contraction effect. And you might also notice that we can see the back of the tram at this point. !!BRIAN: You can see the back of the tram even though it's sort of in a place where you normally wouldn't be able to see it. !!DR. CRAIG SAVAGE: Non-relativistically, you should be able to see the front of the tram from this perspective but not the back. But relativistically, it's the other way around. And that's something called Terrell rotation. Objects appear not only to length contract but also to rotate around. !!BRIAN: OK. !!DR. CRAIG SAVAGE: I can tell you that. !!BRIAN: Put it through. And as it goes by-- !!DR. CRAIG SAVAGE: Length contraction. !!BRIAN: --that length contraction. Gets squished. Goes out of frame. !!DR. CRAIG SAVAGE: Now we're jumping into the perspective of the tram and try and understand a bit more the things that we've been seeing so far. !!So this shows what you might think of as rain falling down vertically. But you could also think of it as photons of light falling down vertically. These are the photons that get into your eye or onto the

camera, enable you to see things. And what we're going to do is jump into the frame of the tram-- that is move along with the tram-- and look at what happens to those raindrops or photons. !!BRIAN: So here we're looking at from the perspective of just standing outside and watching the tram go by. !!DR. CRAIG SAVAGE: Now we've jumped into the tram frame. And if you look carefully, you can see that those raindrops or the photons are falling down diagonally. !!BRIAN: Right. !!DR. CRAIG SAVAGE: That's a very familiar effect. If you ride your bike through the rain or drive your car through the rain, you see exactly the same thing. The apparent angle of those raindrops changes. They seem to come from front. !!BRIAN: All the rain always hits the front windscreen, not the back windscreen of the vehicle. !!DR. CRAIG SAVAGE: Photons are very much like rain. So they do the same thing. They rotate around so that from the perspective of you moving through the rain or through the light, you see it rotate around in front of you. !!BRIAN: OK. !!DR. CRAIG SAVAGE: Now this diagram here-- I'll move it back a little bit so that we can start from rest. This shows light coming from a 360 degree circle around you. The green dot is us, and we're going to be accelerating through this animation. !!And what will happen is the direction we see the light coming from for each of those arrows will rotate around to where we see it coming from. In the world frame, it's always coming in like this. But as we accelerate, the aberration effect or that raindrop effect that we just saw happens. And this is what happens. Keep your eye on the arrow at the back. !!BRIAN: All right. So we're going through, and we have light coming in all directions around us. And as we get closer and closer to the speed of light, it seems-- because of the aberration-- that things behind us are put in front. And that collapses all the light to be concentrated in that little headlight effect that we saw-- the searchlight effect that we saw. !!DR. CRAIG SAVAGE: That's right. !!BRIAN: And so that's why things look so bright here is all the light is concentrated. !!DR. CRAIG SAVAGE: No arrows back here, so it's very dark back here. So, bright in front as we saw. Dark behind. And remember this arrow? It started off back here. We're now seeing in front of us something that in the rest frame or world frame is behind us. And that's exactly what we saw in the first desert road animation. !!BRIAN: We managed to collapse the entirety of the sky, more or less, all the way into that front little bit. in front of us. !!DR. CRAIG SAVAGE: That's correct. And it just keeps going as you get closer and closer to the speed of light. !!BRIAN: And interestingly enough is that, in our first set of lectures where we just talked about one of the ideas of gamma ray bursts, is that instead of traveling-- If you're traveling very fast and instead of the light around, you put a light bulb here, and you figure out what it's going to do. It's

going to do exactly the same thing as what it sees. And so that means all the light in the light bulb, almost none of it will go back here. All of it will be pushed out here and beamed. !!DR. CRAIG SAVAGE: You just reverse the direction of everything. That's right. !!BRIAN: That's right. So it ends up looking like a searchlight, a little light bulb with the same effect. OK. Great. !!DR. CRAIG SAVAGE: OK. So that's the end of these videos. !!BRIAN: OK. Well, my understanding is we can go through and we can play around a little bit in real time. !!DR. CRAIG SAVAGE: We can. !!BRIAN: And so I'm going to let you do that here. now. Thanks. !!DR. CRAIG SAVAGE: Excellent. !!V8.7 BRIAN: All right, Craig. Here we are in your real time, special relativistic world. Tell us about where we're at. !!CRAIG: Well, this is an interactive game-like simulation, unlike the videos that we had before. Antony Searle, also was involved in creating this, but another undergraduate student, Lachlan McCalman, also contributed enormously to the development of this software. So what we've got here is a little bit more complex world than the one we saw before, where we just had a building and a sign. !!There's all sorts of things here. But what you can see at the moment is some trees and a road. And I'm going to do exactly the same thing. I'm going to accelerate with constant proper acceleration down that road, and we'll see what we see. Here we go. If you look very carefully, you should be able to see the speed and orange at the top left of the screen. So we're accelerating towards those trees. !!BRIAN: Everything's moving away, and that's because those arrows are coming around. And despite that moving forward, things look like we're moving back. But now we're going off and we're actually coming up to the walls and things as we go through. So eventually-- !!CRAIG: So I just went through something there. !!BRIAN: So eventually, when we accelerate-- although initially things look further away-- eventually we catch up with things and they start appearing closer again. OK, good. So one of the interesting things that we can do with this is we can look at-- let's look at the trees, if we go through and accelerate here again. !!CRAIG: Yep. And I can do things like turn the Doppler effect on and off as well. So that's with the Doppler effect on. !!BRIAN: So that's not very interesting because everything just looks dark. !!CRAIG: That's right, yeah. And part of what happens is that we shift the infrared and ultraviolet into the picture as well. !

!BRIAN: So the trees look bent over. Again, that's the aberration-- not just in the one dimension, but in the two dimensions. !!CRAIG: That's correct. !!BRIAN: All right. !!CRAIG: It's a bit hard to steer relativistically. !!BRIAN: Yeah, I can imagine that it would be very easy to hit a tree when everything's distorted. !!CRAIG: That's right. !!BRIAN: Now Craig, my understanding is that you have also some other worlds. !!CRAIG: That's right. !!BRIAN: For example, one that has, for example, a bunch of cubes, where we can get a sense of what things look like. !!CRAIG: Yes, that's fascinating. Yes. So I call it the cube lattice. And what I'll do is give you a perspective on that just by pausing, but giving us a high velocity. So this is a freeze frame at high velocity. Because I'm traveling at high velocity, the image has-- or the world has-- collapsed up in front of me, so I can see a lot of it now which I couldn't see before. !!BRIAN: Which you can really because this is-- really, if we were going no speed at all, we would have just this big set of cubes that was perfectly square. And we really see what the aberration looks like. We take this big field of view and we collapse it down. And we end up with this bulging thing in the middle and sort of almost a pin question. !!CRAIG: So this is a lattice of hollow cubes. These cubes are hollow through all three axes. And what we're going to do, when I unpause it, is fly through the center one. So that's a wall of these hollow cubes. And behind it are actually two other walls. So we'll fly through this one and then through two more. So let me start that up and see what happens. !!BRIAN: So we're coming very quickly. Now, this is kind of akin to what Luke Skywalker did in the first Star Wars movie. But it didn't look like this in the movie. he's going really fast-- !!CRAIG: It's really hard to get through a hall, whoops. !!BRIAN: --on the surface. And trying to turn and get something into a little hole looks really, really challenging. !!CRAIG: It is. !!BRIAN: Because everything is so distorted. !!CRAIG: And distortions change as you change your direction of relative motion. !!BRIAN: Right. All right, so Craig, my understanding is that people can download this. !!CRAIG: That's correct. !!

BRIAN: People who are taking the class. And so we'll provide the link so they can have their own little play. And you can try to experience the relativistic world in real time yourself. So let's finish off with a trip across the solar system. !!CRAIG: Let's do that. !!BRIAN: All right, Craig. Let's take a trip to Saturn from the Earth. !!CRAIG: OK. So, in the initial part of this movie we'll see the Doppler effect as we move away from Earth. So you can see that the blue oceans went green and the land masses went red, and also the background stars redden somewhat, due to the Doppler effect. !!BRIAN: So that's the Milky Way there. That's all been turned into kind of a dull color. I'm color blind, but it looks kind of boring now. And here we're going to go by one of our sister ships. This is a-- !!CRAIG: That's right, a little solar sailor. It's deploying its solar sail right now. !!BRIAN: So this is the way that-- presumably, we're in something like this ourselves that we can speed up very quickly. !!CRAIG: Well, it's interesting how fast you might be able to go in a solar sailor. Probably not quite as fast as we're going in this simulation, but maybe a few hundredths the speed of light is a possibility. !!BRIAN: Oh, so we're speeding up towards it which means it looks further away. That always gets me. !!CRAIG: Yes, It's very disconcerting. !!BRIAN: But eventually, the distance will catch up. And as we go through, we get incredibly weird distortions. And we've got to go, it looks like, right into the sun. !!CRAIG: That's right. Well, of course the sun is out there in the sky but it collapsed around into the front of us, wherever it was. !!BRIAN: Now, we've had the entire sky wrapped around and we're coming up on Saturn, which looks very distorted. !!CRAIG: Very strange. !!BRIAN: So traveling at 99% of the speed of light's going to help us get there quickly because that means that you have all that length contraction from our perspective of the distance, which means the time's contracted. !!CRAIG: That's correct. !!BRIAN: So normally, from the sun to Saturn, 83 minutes at the speed of light. But if we're traveling 99% of the speed of light, then that time is going to be reduced substantially from our point of view. !!CRAIG: That's right. !!BRIAN: Although from the sun, it looks like it still took us 83 and some extra bit of time. !!CRAIG: It's very strange, yes. !!

BRIAN: All right. So, travelling at the speed light, very high speed, is going to be useful to get there. But once you get there, you're going to have to think about what you look at because Saturn's ring doesn't look flat anymore. It looks warped. !!CRAIG: Yeah. The reason that we stopped at Saturn and we're doing some orbits around it at the moment is because spherical objects, strangely enough, stay looking spherical. So they're not very interesting. !!BRIAN: I'm getting kind of seasick. !!CRAIG: Yeah. !!BRIAN: I think I want to go slower when I visit Saturn myself. !!CRAIG: Yes. You probably wouldn't want to orbit it at that speed. !!BRIAN: Well, that should give people pause to think about their trip to Saturn sometime in the distant future. !!CRAIG: Well, we're going to finish off with the finale of flying through the rings. We accelerate up, and, of course, that makes Saturn move away as we're familiar with now but we're going to-- !!BRIAN: Oh, so we're coming at night at the speed of light. !!CRAIG: Very fast. !!BRIAN: And we're catching up. And as we go through, it does not look like a ring system at all. But still very interesting. And we can see the Milky Way-- the entirety, which fills the whole sky-- wrapped in to that tiny little part of the sky do the aberration. OK, well, thank you very much, Craig. That was a wonderful tour of the relativistic world and our solar system at nearly the speed of light. Thank you very much. !!CRAIG: Thank you. !!V8.8 PAUL FRANCIS: So we've seen that the speed of light is really a very fundamental limit. This to me is really annoying. I'm a great science fiction fan, and it's always a real pain-- the stupid law of physics that says you can't go faster than the speed of light. Just to mention Star Wars. So let's go to Alderon-- 200 years later you arrive. It makes a very unexciting story. !!When I was a kid I used to try to think about ways around this. One idea a lot of people have about beating the speed of light limit is that in the course of history of science, there have been many limits to speed. Back when the first railways were coming along, people thought you can't go more than 30 kilometers an hour-- the stress will shake people to pieces. And of course that's long since been passed. Then much more recently there was the speed of sound limit-- aircraft can't penetrate the sound barrier. They penetrated it very shortly afterwards. !!So is the speed of light a barrier like that? That's just waiting for some future technology to break it? And what would happen if you built a really powerful rocket, and you got to 99% of the speed of light-- then you put your foot down on the accelerator? Would you just cruise past the speed of light? !!

BRIAN SCHMIDT: Unfortunately it seems, as near as we can tell with our understanding of special relativity, that really is a hard limit because light is always going the same speed no matter what you're doing. So no matter what you do-- you're going 99% of the speed of light? Light leaves you at the speed of light. You want to press the accelerator down? You want to go 99.9% of the speed of light? !!Well, you don't go over 100% because you always have the speed of light going at the speed of light away from you. And the way this is all compensated for is because time ends up being dependent on your reference frame. !!PAUL FRANCIS: So your own frame of reference. So let's say I'm accelerating, and I accelerate, accelerate, accelerate. All of a sudden I stop for a rest. I shine a beam of light forward. It's going away at 300,000 kilometers a second. Then I accelerate, accelerate, accelerate, use my antimatter drive and whatever. And I shine a light forward, and it's still going at the same speed. And no matter how fast I go, I shine a light, it goes exactly the same speed. I can't catch up. !!BRIAN SCHMIDT: That's right. You can't violate it, but it does have some interesting-- I would say science fiction like-- effects. So imagine I start heading towards Alpha Centauri at 4.3 light years. Now if I shoot a photon off, it's going to take 4.3 years to get there. Unless I'm actually on a rocket ship. Because of that time dilation, when I'm heading towards Alpha Centauri and I go faster and faster, Alpha Centauri looks closer and closer to me, and the amount of time it takes for me to get there ends up being very short. It ends up being, if I go fast enough, a few seconds-- within my frame of reference-- to get there. So I can get to Alpha Centauri in a few seconds. !!PAUL FRANCIS: It sounds like you're breaking the speed of light limit, but not really. From your frame of reference, going at 99.9% of the speed of light, light is still going at C faster to you. The reason why it takes such a short time to get there is because Alpha Centauri is no longer four light years away. It's actually only a few meters away. !!BRIAN SCHMIDT: That's right. !!PAUL FRANCIS: Because of the length contraction. But if you're flying past and I'm looking at you, from my point of view it's not-- Alpha Centauri is still four light years away because I'm stationary. What's different is your time seems to have slowed down. But to you the time doesn't seem to have slowed down. To you, my time seems to have slowed down. !!BRIAN SCHMIDT: Right. So we can imagine doing an experiment-- which I'd love to be able to do-- is I build a rocket ship. I head out right now at almost the speed of light to Alpha Centauri. I go visit it. I come back a few seconds later, and I'm going to tell you all about it. !!PAUL FRANCIS: Yeah. We're about the same age, but when you came back, I'd now be eight years older than you. !!BRIAN SCHMIDT: That's right. And I would be confused because it only took a few seconds-- hey, what were you doing getting old? And this seems crazy, but there are ways we can actually test it in the lab. !!PAUL FRANCIS: Yes, you can routinely get a particle, some type of particle that for example would only last a millisecond left to itself, and then bring it up to 99 point a few nines percent of the speed of light, and it can last for hours or weeks. So this is something that's not just a purely theoretical thing. We can test this and do test it all the time in our labs. !!For example, there are natural particles, muons, at the upper atmosphere. And normally they wouldn't penetrate the atmosphere. But because they're going so close to the speed of light, their clock slows down from our frame of reference. So they can penetrate the speed of light from their own frame of reference. Time is going normal, but the atmosphere is much shortened. !

!BRIAN SCHMIDT: And that's just a little small, little bit. And they've even done it more directly, I think, for people's senses. They've taken these atomic clocks, which keep very precise time. And you would have two of them. You put one of them in an airplane, and the other one not. And then they come back, and they see that indeed the clocks have become disentangled, essentially. They're no longer on the same time, due to this exact effect. So it's real. It's crazy-- !!PAUL FRANCIS: But it is real. !!BRIAN SCHMIDT: But it is the universe we seem to live in. !!PAUL FRANCIS: And going back to this accelerating faster than light business. If I'm trying to accelerate, no matter how fast I accelerate, the speed of light is always going faster than me. It's a bit like most skills in the real world-- no matter how good you get at something, you realize there are people that are better than you at whatever you want to do. So it's not so much that I can't go faster than light. It's that no matter how fast I go, light is still going C faster. But if you're looking at me, what do I seem like? !!BRIAN SCHMIDT: Well, if I'm looking at you trying to go fast, well then you end up looking very, very squashed. Because of these distortions, this contraction, you end up looking almost like a sheet of paper moving off into the distance. So you look very funny. !!PAUL FRANCIS: My time slows down. Also my mass appears to go up. So when I'm at 99.9% of the speed of light and I put my foot on the accelerator, my mass is now maybe thousands of tons. !!BRIAN SCHMIDT: That means you're going to need a lot energy to do it. !!PAUL FRANCIS: Yeah. !!BRIAN SCHMIDT: Because that energy to get going faster and faster becomes enormous, and getting the last few nines, the amount of energy could end up being the entire energy in the universe to go that fast. !!PAUL FRANCIS: So from someone else's point of reference, what stops you getting faster than the speed of light-- as you get close to the speed of light, your time slows down, and also your mass goes up. So you'd need an infinite amount of energy to add another 0.9 or another 0.99 to it. So without all the energy of the universe and then some, you can never actually penetrate the speed of light. !!BRIAN SCHMIDT: That's right. So this is not just a hard limit to pass, it probably is a hard limit to pass. !!PAUL FRANCIS: A very fundamental limit. !!Anyway, now we'd like to talk about-- to take this back to black holes. And to do this we're going to have to introduce a new form of diagram-- one that combines both space and time. So let's talk about that. !!Lesson 9: Black Holes!!V9.1

BRIAN: All right, Paul. This relativity stuff's pretty interesting. But I thought we were gonna be talking about black holes. And I know black holes involve relativity, but I also know they involve gravity. So how does this all hang together? !!PAUL: Well, to put gravity into this whole relativity picture, we're going to have to introduce a new type of diagram, a sort of space/time diagram, because it includes space and time, curiously enough. !!BRIAN: Ah, I see. So we've got the x-coordinate and the y-coordinate. And we don't have a zed-coordinate. !!PAUL: Yeah. No, because, reality, space is three-dimensional. You've got x, y and zed-coordinates. And then you add an extra dimension of time. It becomes four-dimensional. And at that point, your brain dribbles out of your ears. !!BRIAN: Yeah. I don't deal with four dimensions very well. !!PAUL: So what we've done here is I've just thought about the fourth dimension. For purposes of simplicity, we just have to space dimensions, x and y. And we'll have t vertically. !!BRIAN: I see. So if you are here at the origin, then I've got a little bit of an x and a little bit of a y, so I'm here. And then I'm standing still and moving forward in time. So I'm moving up in time because I'm not doing anything. I'm just continuing to exist. !!PAUL: Yep. So a stationary object is just a vertical line in this diagram. So you are moving through time. No one can help doing that. But you're not moving in space. !!BRIAN: OK. Simple enough. !!PAUL: But let's say we had a line like that. So what's going on here? !!BRIAN: Ooh. So this time, it looks like I'm moving forward in time, but I'm moving in the x direction and then back. So that's sort of me doing this. !!PAUL: And then coming back again. !!BRIAN: There we go. !!PAUL: Yeah. So if something's moving, you get a slope. In this case, it's a slope this way because you moved that way. So your x is increasing , while time goes up. And then you come back again. !!BRIAN: OK. Fair enough. !!PAUL: OK? How about that? !!BRIAN: Oh, that looks like I'm going to have to be acrobatic. So that looks like the same basic idea, but I've got to move a lot more and then come back. So it's gonna be like-- !!PAUL: Yep. So you've got to move and come back in the same time you were before. But the change in x is bigger, so you're moving faster. !!BRIAN: OK. !!PAUL: So in general, any sort of curve like this slope indicates speed. And the bigger the slope, the faster you're going. That leads to the idea of the fastest thing of all-- light, we've just been talking

about. Let's say there's an event down here at the bottom of the cone. And let's say it flashes out light in all directions. !!Now light will be going at a 45 degree angle in this thing, if you scale the coordinates correctly. And so there'll be a cone, which is where the flash is, a hollow cone. So if you're anywhere on this cone, you will see that flash. If you're further out, then the flash won't have reached you yet. If you're further in, the flash went past sometime in the past. !!BRIAN: OK. So that means, just to get our heads around it, we start off at a flash here. And then a very short time later-- so for example, if I shot a light off right now, you're about 2 meters away. OK? So that means a few nanoseconds. !!There's this little circle that everyone can see that flash for that very short period of time. And then as each moment in time moves forward, that circle goes further and further out. And so you get in this space/time diagram this cone out. OK, I think I've got that sorted. !!PAUL: OK. So what this also means, of course, is because you can't travel faster than light, it means anything outside the cone cannot be influenced by an event down there at the base of the cone. So no matter what happens there-- the biggest explosion, the most-- I don't know-- anything what you can imagine that happens down there can have no effect out here because, even at the speed of light, it can't get that far. !!Anything inside the cone could, in principle, be affected. If it's actually on the cone, light could affect it. But if it's inside the cone, it could be the light comes out here, then bounces on a mirror and hits the edge, or you leave a videocassette that drifts upwards here and then sends a message out on the later time, or you actually fly a spaceship there. !!So basically, only things inside can be influenced. Only the place inside the cone is where you can go, because you can only go slower than light. So you've got to be somewhere inside this cone, no matter how good your rocket is. !!BRIAN: OK. So that cone is almost like, what we would call in astronomy, a horizon where you really can't get past, no matter what you do. !!PAUL: That's right. It is a horizon. So saying, the only thing that can be influenced by that point is in here. Or if we are up here at a later time, if we're inside the cone, we can see what happened down there. !!BRIAN: OK. So now let's add some gravity. Now what happens? !!PAUL: Well, the idea is that gravity tilts the cones. So let's imagine this blue line is something heavy-- star, neutron star, whatever it might be-- and we've got a whole bunch of cones from a whole bunch of different events in a grid all over the place. So out here, a long way away from this mass, the cones are vertical as normal, so things can go in any range of directions along a line here. But when you get closer, you see these cones are tilted over, pointing towards the mass. !!BRIAN: And that's sort of because gravity, the way we think of it through Einstein's version of relativity for gravity, we're sort of warping the fabric of space. And so the cones fall over a bit, depending on which way space is bent. !!PAUL: That's right. In Einstein's theory of general relativity, which we'll cover again in the "Cosmology" course, what happens is that gravity warps space time. And that has the effect of causing these cones to tilt over. We'll go back and do far more of that later on. !!BRIAN: OK. !!

PAUL: So if you're here, your natural motion will be down the middle of the cone, which will bring you in. Let's call it falling. !!BRIAN: Yep. !!PAUL: But still have a choice. You can go at the speed of light, so you can still escape in that direction or that direction. But if you make the mass really big, you tilt the cones over further. !!BRIAN: Ooh. So now this is kind of interesting, because these cones right here are more than 90 degrees over, which means, all directions-- no matter how fast I travel-- I can't get back away. I'm stuck. !!PAUL: Yep. So you take one of these cones over here. And your choice is basically you can't stay where you are, because only the cone further in is possible. So your choices, you can only go in slowly or go in very, very fast. But nothing you can do will cause you to stay where you are. !!BRIAN: So that means that nothing I can do, even if I'm light, I can't get away from this mass moving forward in time. Now that's beginning to sound like a black hole. !!PAUL: It is, indeed. !!BRIAN: Ah-ha. !!PAUL: Remember, we talked about the original idea of a black hole as being like a normal star with a normal surface, and the light will just come up and go down. We've now seen a rather different picture where the light that's emitted will go down right from the moment it's emitted. !!And also, the matter can't sit there, because matter goes slower than light. So everything has to move in. In a state of rest, it has to move in faster and faster. But no matter how much it struggles-- even if it struggles away at the speed of light-- it's still sitting in one of the cones here, and it still has to go in. !!BRIAN: OK. So, all right. So these black holes seem-- I guess I get how do these light cones and curved space all come together. I guess one could imagine, maybe, thinking of this in terms of how big they might be. !!PAUL: Yeah. And it seems they can't have a size, because the stuff has to go in. And there's no stopping it. It's not as though the light cones suddenly stop pointing upwards again. Then it's the closer you get, the more they're tilted over, so they can't seemingly have a solid surface. The matter must go all the way down to zero size. !!BRIAN: Wow, that's hard to imagine, hard to visualize. We'll have to [CLEARS HIS THROAT] have to think about that. !!V9.2 PAUL: So because of these light cones being tilted over, a black hole can't have a solid surface. In principle, it must be a single point. But it still weighs as much as the whole whatever it is that formed the black hole did before, probably a big star or something. So you're talking about a very big mass, 10 to the 31 kilograms, say, in 0 size. !!BRIAN: All right. But we always talk about the radius of a black hole or its event horizon. So that seems to tell you something has a size. So how do we reconcile that? !!

SPEAKER 1: Well, really, the size is 0. I've drawn this little blue circle there. But of course, it would be far smaller than a pixel, so it would be literally 0 size. You don't normally like having infinities in your equations. But here, your density is your mass divided by the volume. The volume is 0, so any mass at all gives you infinite density. And that starts being really nasty if you have infinity in there. !!But when people talk about the radius of a black hole, they're actually not talking about the radius in the center. It really is, as far as we know, just a dot, 0 size, smaller than the head of a pin. But there is a sort of radius out here which is called the event horizon. This is not the actual radius of anything solid. There's nothing actually physically there. You would straight through it without noticing. !!What it is is the line of no return. This is the line at which those cones are tilted so that they're vertical on the edge. So once you're inside here, you have to move in. You can't stay stationary. Anywhere else, if you try and go as fast you can at the speed of light, you could in principal stay where you are and even move out. But once you're inside this radius, all motions take you in. !!BRIAN: OK. So that means what you're saying is if made out of the right stuff, I could literally travel across that event horizon and there's not a sign in space that says event horizon or anything. There's nothing there. It's not the surface of the black hole. It really is just the point of no return. !!PAUL: Yeah. So it's maybe a sign, abandon hope all ye who enter here. But there's nothing going past. You could fly quite happily through here. Just if you wanted to turn around and come back again, that's when you start finding the trouble. !!And this is also called the Schwarzschild radius after the theorist who derived it. And it's got this form here, 2GM over the speed of light squared. So you can work it out. It turns out to be pretty small if Earth was to collapse down to a black hole, which will give you about 8 millimeters of this. !!BRIAN: 8 millimeters? !!PAUL: Yes !!BRIAN: Like that big? !!PAUL: Yep. So if you've got something that's-- that's for the Earth to collapse down-- for the sun to collapse down, we're talking about the radius of a few kilometers. Still pretty small. If you had 100 million solar masses collapse down, you might get about an astronomical unit out, which is still pretty small for the scale of something the weighs that much. So these things are absolutely tiny. !!BRIAN: OK. So imagine, then, I'm in a spaceship-- or let's just say I'm in a circular spaceship traveling near the black hole-- !!PAUL: OK. There's one coming in behind you. !!BRIAN: Which is grey in this case, it looks like. As I come through, I speed up, I speed up, I speed up , and just, bing, I go away. !!PAUL: Yes. And from your point of you, you'd just be moving steadily inwards, moving steadily inwards. You would feel nothing dramatic happen when you cross the event horizon. But from my point of view, as you got closer and closer to the event horizon, the light coming out-- let's say you send a flash every second. The flashes to begin with will arrive every second. But as you came closer and closer, each photon will have to struggle its way out of this intense gravity, so the flashes will come further and further apart. What that means is from my point of view, you will appear to slow down. So that last scream as you went across the event horizon would appear indefinitely extended. !!

BRIAN: And I would just sort of fade away as I fell into the black hole. !!PAUL: But also you'll get more and more red shift, because the photons have to struggle their way out here, and so the red shift will get greater and greater and greater. So at the moment you're scattering visible light towards me, but that might become infrared, and then radio, and then 100-kilometer long radio waves or something as that last infrared scream disappears down the event horizon. So for you, you would just be going pretty fast. !!BRIAN: There's one thing I think we should just make sure people understand at this point. If I'm here and for some reason find myself at rest outside of a black hole, I will fall into a black hole. But of course, normally one does not find themselves at rest around a planet in the same way if we were suddenly to stop here on Earth, the Earth would fall into the sun. It's the fact we're orbiting the sun. So this isn't really a very realistic way of looking at things, is it? !!PAUL: Yes. Here's a more realistic one that we have given a bit of a sideways motion. We showed this back in the first course when we talked about quasars. Even a very small sideways motion is enough to stop you falling into the black hole. You just whip around it in an elliptical orbit. !!BRIAN: OK. Very good. So in this case, presumably, that elliptical orbit went inside that horizon, that Schwarzschild radius, then I wouldn't come out again. !!PAUL: Indeed. But as long as you stay outside-- you actually have to stay outside a bit further outside. Because actually when you're really close in, the normal orbital rules don't work because your mass goes up and time slows down. And so it actually turns as the radius just outside the Schwarzschild radius where there are no stable orbits. But as long as you stay outside that-- and that's very, very small. So if its an earth-mass black hole, that might be 12 millimeters or something like this. That's a very small target to hit. So by and large, black holes are not very deadly. !!BRIAN: Well, OK. I'm just trying to think what it would be like for me to try to orbit a black hole at 12 millimeters. Would that look like? !!PAUL: If you're going around a back hole, the trouble is not the orbit. You just get around. The trouble is that the orbit is going to be different for different parts of you. !!BRIAN: Because I'm a lot bigger than 12 millimeters. !!PAUL: Yes. So here's a simulation of a person orbiting a black hole. !!BRIAN: Very nice likeness of me. Oh, I'm getting-- oh, that's not-- oh, I really don't want to try to do that. !!PAUL: I don't know. You're very limber, I'm sure. !!This is what's technically called spaghettification. You get turned into spaghetti. What's happening is different parts of your body are at different distances from the black hole, and so they orbit at different speeds. Say for example, your feet were closer to the black hole. They would have to orbit faster for centrifugal force to balance gravity. So each time you go around, you get more and more stretched out. This word spaghettification means turned to spaghetti, and it's my 8-year-old son's favorite word. !!BRIAN: So this is the same idea of what we called tidal forces, where parts of your body get pulled on more than other parts of your body, and you tend to get ripped into shreds or turned into spaghetti in this case. !!PAUL: Yes, that's right. What's killing you is not the gravity, it's the change of gravity across your body. If you're very, very small, so the gravity is not very different in different parts for you to be

OK. The larger you are, the more different the gravity will be on one side as opposed to the other, and so the more likely something like this is to happen to you. !!BRIAN: OK. !!PAUL: So they can be deadly. !!BRIAN: So we're not going to be orbiting the Earth as a black hole anytime soon, it looks like. !!PAUL: Well, if you were a good long way out, like 10 meters, it would be OK. But if you start to get to within millimeters or so, then you would be in big trouble. !!BRIAN: I'm thinking even 10 meters might be a bit ugly. !!V9.3 BRIAN: So we've seen how gravity distorts space and causes the way that light travels out to be essentially distorted. That the light cones become bent such that if you get enough stuff in a single place, that light literally cannot leave that vicinity. All paths lead to the center. And this leads to the idea of a singularity, a point where, essentially, mass is concentrated with a horizon, or a sphere, around it which effectively is a no-go zone-- a place where once you pass there is no way out. It's not a signpost. It's not a fence or anything. But it is a place that once you go past, there's no coming back from. !!PAUL: Yeah. So this is a theoretical idea. This is what would happen if you have enough matter and you shrink it small enough. But the real question is, do they actually exist in the real world? There are plenty of theoretical things that could exist, that are consistent, but don't actually happen to really occur. So presumably to form a black hole, you need to get an awful lot of mass and squeeze it down to a small enough size that it's inside its own event horizon. How could you actually physically do that? Wouldn't degeneracy pressure stop you? !!BRIAN: So, clearly it's not going to be an easy thing to happen. And that's just as well. We don't need a universe full of black holes. Probably wouldn't be very good for our lives. But in the supernovae that I study, really big ones, we think maybe there's an avenue to form one. So the idea is that normally when a supernova forms, the core shrinks down and is stopped by neutron degeneracy pressure. So the neutrons push back. And it turns out that if you have about one and 1/2 solar masses' worth of staff, the neutrons keep, essentially, the material at a radius of about 7 or 8 kilometers. And that is about three times bigger than the radius of a black hole. But as you get bigger and bigger stars, instead of being limited by maybe one and 1/2 solar masses in the center, we think that the process of the supernova isn't able to keep that much material out. And you'll pile on, and you could grow that central object to maybe 10, 20, or 30 times the mass of the sun. !!PAUL: So this would be a star that maybe started with 100 times the mass of the sun or something might produce a 20 thermomass neutron star in the middle. !!BRIAN: Right. But a 20 solar mass neutron star, we think, is a bit of an oxymoron, because if you take that degeneracy pressure, it turns out that when you add material to a neutron star, like a white dwarf, it tends to want to get a little smaller. !!PAUL: So the more massive the neutron star is, the smaller it is, not the bigger, because the extra pressure pushes it down, like you talked about for white dwarfs. !!BRIAN: And there seems to be a crossover point, given our understanding of neutrons and how they push on each other, that when you reach more than about two times the mass of the sun, the

radius of the neutron star ends up being less than that no-go radius of the Schwartzchild radius. And so at that point, we think these things must become black holes. !!PAUL: At that point, because, of course, neutron stars, even the ones we know about, are not much bigger than the event horizon. So if you shrink it down by another factor of two or three it can be inside its event horizon. And then, of course, the cones are tipped over, so no pressure up could conceivably stop it from collapsing all the way. If our understanding of relativity is correct. !!BRIAN: That's right. And so once you pass that, you essentially end up with all paths leading to that single point. And you end up with this event horizon of a few kilometers across and presumably a singularity in the center created by a very massive star. Now, these massive stars are very rare, but we do see them, even in our own galaxy and nearby galaxies. So we seem to know they exist. And we seem to have indication, especially gamma ray bursts. The only way we know how to get enough energy to form a gamma ray burst is to not have a 1 or one and 1/2 times the solar mass neutron star, but more like something that's 10 or 20 solar masses in the center. !!PAUL: OK. So that's one way we could conceivably form black holes. But presumably there are some others. Like If you had two neutron stars in close orbit. We know there's at least one neutron star binary out there. They will lose energy because of gravity waves, and presumably spiral together. And if they collided together and gave you something again over this roughly three solar mass limit, would that collapse to form a black hole? !!BRIAN: Probably. Again, those collisions can be very messy. We think they may well also produce another form of a gamma ray burst, and for the gold and uranium in the universe as well. But the interesting question is, as they come together, we think the less massive of the two neutron stars gets disrupted and sort of shredded to bits. And presumably most of that stuff is spinning around very quickly. And we think most of it will eventually collapse onto the other neutron star and form a black hole. There is some small chance that it would be ejected by the process and not fall on and bring the thing up. But that's a very good way to make another black hole. Probably not a 10 solar mass one, but maybe a three solar mass one. !!PAUL: Would it also be possible to do it more gradually? We've talked about these x-ray binaries, where you get a secondary star like Cygnus X1 dumping matter on a neutron star. But if you dump more and more matter on it, it will get more and more massive, and at some point, just like we talked about for the type 1A supernova, you might go over this limit and collapse to form a black hole. !!BRIAN: I think in principle it's possible, but I think in practice it's very difficult. And the reason is it's just very hard on a neutron star to actually get the material to settle down and go and settle on the neutron star. It produces so much energy that you will accumulate a little bit, but in order to have enough material settle down in practice, it looks pretty difficult to do that. And so I wouldn't be willing to rule it out, but I don't think we have any evidence at this point that it does happen. !!PAUL: OK. So we've got this theoretical concept of black hole, and we've got some at least halfway plausible mechanisms to produce it, but all relies on general relativity working in this regime of intense gravity where it's never been tested. In the lab, we can only test in relativity to maybe one decimal place or two decimal places. We can get rather more accurate measurements of it from the case of binary pulsars and things like that where we can see the gravity web coming out. But still, though, none of these tests come anything close to the conditions in a black hole. It's always very dangerous to take a theory and extrapolate it far beyond where it's been tested. So could it be that, in fact, they don't exist, and that there's some new law of gravity that comes in when the gravitational forces becomes so big it stops it all happening? !!BRIAN: Well, in science, as you know, nothing is ever ruled out. You always want to test, and since we haven't yet observed a black hole directly, it is certainly worthwhile to go out and look around

the universe and see if what general relativity predicts is true. And to look for increasingly extreme cases to the point where maybe we eventually are able to find a black hole. !!PAUL: OK. So in the next part of this course, we want to talk about the observational evidence for the existence of black holes. !!V9.4 BRIAN: All right, Paul. These black holes sound like a good idea theoretically, but as an observer, I like to see things before I believe them. Now black holes by their very name seem to conjure up a problem. How on earth are you going to see something which no light can get out of? !!PAUL: Yes. And astronomy is the ultimate noncontact sport. You can look, but you can't touch for anything outside our own solar system. And how can you see something that doesn't emit any light? Or any radio waves? Or any sort of waves? !!Even gravity waves couldn't get out of a black hole. Any sort of wave is going to be trapped in there so how are you going to see these things? !!BRIAN: Well, one thing when we looked at the spaghettification of myself, I would certainly be screaming as I got ripped apart like that. So if-- OK, you can't hear me scream in space, but it does conjure up the idea that as I get ripped apart, if I were a star or something I'd probably make a pretty interesting display. !!PAUL: Yeah, and remember we saw that for the dwarf novae. The lights from the dwarf novae was coming not from the white dwarf, but from the mass that was spinning round it going faster and faster and radiating gravitational potential energy. So if something falls into a black hole-- we talked about this in the quasar section of the first course-- there's a lot of energy before it goes into the event horizon. !!Going from infinity to 2 or 3 Schwarzschild radii out. You could liberate maybe 30% of the rest mass' speed. If it bumps into something else in there, you can perhaps radiate. !!BRIAN: Right. So you have a star come by, it'll get ripped apart if it were to come by, then all the gas would probably collide with each other and want to radiate all that energy. As it radiates the energy, then it wants to get closer and closer. So you could imagine getting a big, it's probably a disk of material form around the thing that is going to get heated up from all the stuff colliding. Radiate that gravitational energy away, and that should glow pretty brightly. !!PAUL: Yeah. So we can't see the black hole itself, but maybe we could see stuff swirling down its throat. Another possibility though if you remember in the exoplanets course we couldn't see the exoplanets, but we worked out they were there by their effect by making the star wobble backwards and forwards. So maybe if there's a black hole around, you will see stars wobbling backwards and forwards or doing loop de loops or something around it. And we could tell there was something dark and massive there. !!BRIAN: Ah, so I'd use the motion of the stars themselves to infer how much gravity is there. OK. That makes sense. We weigh the sun, for example, by the Earth's motion. !!PAUL: Yeah. And in fact, it's a combination of these two things that leads to probably the best case study of a black hole. If you remember going back to x-ray astronomy, they found all this strange x-ray resources, and some of them turned out to be neutron star binaries. But one of the very early discovered ones, Cygnus X-1, turns out is not a neutron star binary or it's probably not. !!

The star, just like the other binaries we talked about, we've got a star going loop de loops around something that emits x-rays. But that it's going around rather faster. And the star is very massive. It probably weighs something like 10 or even more solar masses. !!BRIAN: So this is a giant-- blue super giant. So that's sort of like-- !!PAUL: not small red stars like the other ones we were talking about. !!BRIAN: OK. So that's a star like Rigel in the constellation of Orion. So that's a big 10 to 20 solar mass star that is young and burning very brightly because it has a big nuclear reactor because it has so much mass to compress its interior so much. !!PAUL: Yeah. Can you imagine the Doppler effect of the star? You can see it moving back [INAUDIBLE] at pretty high speeds. So as we've done many times before in the series of courses you can work out the mass of what it's going around. And that mass comes out as 10 to 20 solar masses. !!If it was going around a neutron star-- it actually wouldn't be because it's so massive the neutron star would be going around it. It wouldn't be wobbling very much. So to have it wobbling as much as we see, it must be going around something. That's pretty damn heavy. !!BRIAN: All right. So we have something that's 10 or 15 times the mass of the sun, yet seems to be very small. Now neutron stars we know a bit about. We know they're made out of neutrons. And we know that when you have a neutron star and you start adding material to it, it starts becoming smaller. !!PAUL: It's just like the white dwarfs do. It's a rather strange situation when you make them heavier, they get smaller. !!BRIAN: And so we know that a neutron star even if it's 1 and 1/2 times the mass of the sun is already only 8 or 9 kilometers across. And we know that's very close to a black hole. So if I make one 15 solar masses across, I think, given our understanding of neutrons, that that thing would be smaller than the Schwarzschild radius. And so it almost has to be a black hole if it's that heavy and small. !!PAUL: Yeah, once it's compressed that much, no matter what force is holding it up, it can't. Has to fall in. !!BRIAN: Yeah. OK. !!PAUL: We also know this thing is flickering in x-rays on time scales of even milliseconds, which also implies it's only [? light ?] milliseconds across and therefore, very small. So we seem to be looking at something that's very small and very massive and that sounds like a black hole. !!Here's an artist's impression of it. We don't know for sure. It's certainly consistently. We can't think of anything else that could have that mass given our understanding of neutrons, but maybe our understanding of neutrons is rather deficient. !!People have been trying very hard to look at the x-rays coming from the central region and see if there's really conclusive proof that it is actually falling down a hole rather than bouncing off a surface. And it all seems to be consistent with that. There's probably some evidence there that it's actually falling into something, not just hitting a surface, but it's very model dependent and not, perhaps, 100% sure. But probably between 98% or 99%. !!

BRIAN: But unfortunately, we can't go out and take a picture that looks just like this right now. Instead, we are relegated to an artist's impression of what we think it might look like, but I think the bets are in that we have a pretty good case for a black hole in this case. !!V9.5 BRIAN: So Paul, we often find these quasars we talked about in our first course in the centers of some galaxies. The only way we think we can power those quasars is that quasar to have a giant black hole in the center. So it strikes me that maybe it would make a lot of sense to look at the closest galaxy and at its center and see what's going on there. And that closest galaxy, of course, would be the Milky Way, our own galaxy. !!PAUL: Yes. So let's zoom in to our own Milky Way Galaxy from the European Southern Observatory. So there is Sagittarius showing the stars. !!BRIAN: That's the Milky Way. We're going to go right into the center of it. So we're zooming in and you're literally looking at 10 billion stars there to begin with. !!PAUL: And as you zoom in, we change our wavelengths from optical to infrared, because the center is shrouded by huge amounts of dust, so we can't see the visible wavelengths. But if you go to longer and longer wavelengths, you can see through the dust. !!BRIAN: OK. And what we're going to end up here at the very end, is we're going to take an image here, where we made it look very fancy with adaptive optics that we talked about in the first course, where we get rid of the effects of the atmosphere and use an eight-meter telescope. !!PAUL: And here we've modeled what you've seen in that previous image. The previous image is of real data. And now we're actually modelling it. So we're trying to fit that. And what you can see is there are stars, that on the time scale is 15 years' worth of data, are actually moving around. If we close in we can try and work out what's an orbit that's consistent with their motion. And it looks like they're all going around a point over here. So if you see something going like this, there must be a mass there. You work out how much mass is necessary to explain the motion. If it's accelerating really fast, it must be very massive. !!BRIAN: So how much do we need to get those stars to move? !!PAUL: Best estimates are about 4 million times the mass of the sun. !!BRIAN: 4 million times the mass of the sun. Wow, that's a lot. !!PAUL: It must be small, because some of these stars are getting very, very close. If it was big, like it was a cluster of neutron stars or something, they'd be [? passed ?] inside the cluster of neutron stars. So it's got to be no more than a few light-hours across. !!BRIAN: A few light-hours across. So that's inside our solar system to Pluto. And 4 million suns' worth. So I can imagine packing 4 million suns in that space, but I can't imagine keeping all those suns in there, because they're going to collide, and there's just really no way to do it. !!PAUL: And if you've got that much mass, the event horizon is going to be an astronomical unit or so anyway. !!BRIAN: OK. So it sounds like this is a smoking gun for a black hole. !!

PAUL: Yep. That much mass, that much-- not much light coming out, huge amount of mass, small space-- that certainly sounds like a black hole. !!V9.6 BRIAN: So Paul, I'm pretty convinced by the evidence we've seen that there really is a big black hole, a million plus solar mass black hole, in the middle of the Milky Way. You think our Milky Way is alone or is it sort of normal? !!PAUL: Well, people have tried to look at whether there's a massive black hole in the middle of other galaxies. And it's a very tricky thing to do because we can't trace individual stars. I mean, it's hard. It's really on the edge of our technology even in our own galaxy, a mere eight kiloparsecs away-- whereas any other galaxy is much further away. But you can use a Doppler effect and look at the fractal stars that are moving fast, towards and away from you. And if you zoom right in the middle of pretty much any galaxy that's near enough to do this work, you do indeed see the stars in the middle are moving at some enormous speed. !!BRIAN: So I'd go in, and I'd take a spectrum here and one here as fine in detail as I could. And I'd see that that side's moving away. This side's coming towards us. And I infer a rotation speed for those stars. !!PAUL: It could be rotation, or it could be the stars are just falling in and out of the gravitational well and coming back and forwards. !!BRIAN: Ah, so the swarm-of-bees motion as well. !!PAUL: Yes. !!BRIAN: Either way. !!PAUL: But the mass means the bees are swarming really fast. !!BRIAN: Yep. OK. Very good. !!PAUL: And that seems be what's the case. But the middles of galaxies are typically what we understand-- this galaxy like our own-- are typically what we call a "bulge." Here's an edge-on view of a galaxy. You can see it puffs up in the middle. This is the bulge of a galaxy. We talked about this in "Microlensing" back in the Exoplanets course. And it seems that the black hole lives in the middle of the bulge, and its properties are very closely related to that of the bulge. Here's a view of a bulge in another galaxy, and black hole's right in the middle. And the properties of the bulge-- which is how many stars it's got, how bright it is, its size-- all seem to correlate very strongly with the mass of the black hole in the middle. !!BRIAN: All right. So you've got a bunch of stars which took lots of time to form and presumably form by some process that makes stars. And then you have this giant, supermassive black hole in the center. And you're saying that those things seem to go hand in hand. That's not at all obvious to me why that would be true. !!PAUL: Yeah, presumably it's telling us something about how all this formed. We don't really know, as you talked about in the previous course, about how these giant black holes formed. But maybe whatever process formed the giant black hole also forms the swarm of stars around it. Or maybe even there's some sort of feedback cycle. So that, for example, let's say you've got gas flowing in that's forming stars and forming the black hole at the same time. And if it's coming in too fast, the

black hole forms and lights up as matters are created to it like a quasar and blows stuff back out and stops the formation again. So maybe there's some sort of feedback cycle going on here. !!BRIAN: Yeah, I'm not sure. Especially since we can't really figure out even how to make big black holes, it turns out. It's one of the big mysteries is how do you make giant black holes? !!PAUL: I mean, it's gotta be a big clue. But the other thing you can think of is disk galaxies like our own Milky Way have relatively small bulges. But there are galaxies which have very big bulges, in fact are almost all bulge. Here you've got the disk here in the Sombrero Galaxy but a huge great bulge is actually most of the galaxy. And you get galaxies which are entirely bulges. We call them elliptical galaxies, and these ones you'd expect to have really massive black holes. And indeed that what you seem to find. !!BRIAN: Right so this one, for example, has a black hole that we believe is greater than 10 to the 9, a billion times the mass of our sun. And it's a galaxy that's about 100 times bigger than the Milky Way as well so it sort of falls in. But yeah, a billion solar mass black hole. And so short a time to make it, because how you going to create something that big? !!V9.7 PAUL FRANCIS: So, we've seen that we get these clusters of stars in the black hole. We don't see the black hole, it's just surrounded by light, we only infer its presence. But if you remember back to the first course in the series, there are some galaxies which have massive black holes, which are radiating like crazy. These are called the quasars, perhaps thought to be a disk of gas swirling down the throat of one of these massive black holes. !!Here's a zoom in of one of these things left over from that course. So, here's a galaxy, and we're going to zoom in on it, and right in the center you'll see the dot of light. That's where we expect the black hole to be and will morph into another image in a second, and-- !!BRIAN SCHMIDT: That dot of light is outshining all the billions of stars, right? So, very powerful. !!PAUL FRANCIS: Now, if we zoom in, we can see the dot in the middle, and actually blasting out light in both directions. !!BRIAN SCHMIDT: So, Paul, what fraction of galaxies look like this? !!PAUL FRANCIS: Only very few. Most galaxies, they all, as far as we can tell, have this massive black hole in the middle. Most of them are not shining like this. Then we zoom right in the middle, and we get this disk around the black hole. So, what's going on here? We get these incredibly luminous things in some fraction of galaxies, but most, we don't. !!BRIAN SCHMIDT: OK, so I guess we have to ask ourselves the question, what makes something like this bright? Why would it be bright? And presumably it's bright because it's got an energy source. !!PAUL FRANCIS: Yes. There are two possibilities for why every galaxy has a black hole, why doesn't every galaxy have a quasar? And one possibility is maybe they do have something, but it's hidden from us. We know that the middles of galaxies are very dusty places, so it could be that actually far more galaxies have quasars than we think, but they're hidden by dust clouds. !!BRIAN SCHMIDT: So, Paul, you've gone out and you've looked in red light, so you can look better through the dust. What do you find? !!

PAUL FRANCIS: Well, it seems that for every quasar we see, there are probably two or three more that are hidden. !!BRIAN SCHMIDT: OK, so-- !!PAUL FRANCIS: But that's still a very small fraction of galaxies. In most cases we see there is a black hole, but there's no quasar there. !!BRIAN SCHMIDT: So maybe they're more like a strobe light that's only on occasionally and then switches on, off, on, off, so that they have that energy source, but not all the time. !!PAUL FRANCIS: Yes, it could be something to do with feeding. I mean, presumably you've got a black hole that's going to eat everything that's got a low enough angle and momentum to fall in, and maybe that's why you get the quasar phase where it gobbles on everything around it. Then, after a while, anything that's going to fall in has fallen in, and so the only thing that's going to be left are those that orbit and never come that close. At that point, it might go quiet. !!BRIAN SCHMIDT: So, I guess the question is why you would have much stuff? You mean, you say low angle or momentum, but when the galaxy forms, well, that stuff gets beaten up into submission with or without a black hole there. So, what would cause there to be a bunch of stuff that is able to go into the black hole? Strikes me that most of the time, there would be much stuff at all, just would keep orbiting. !!PAUL FRANCIS: We know there were-- quasars were very common in the early universe of him that's when you first form the galaxy and things are all mucked up and confused, but we still have some quasars today and so something must have stirred these things up. !!BRIAN SCHMIDT: So if at some point in the future about 3 billion years the Andromeda Galaxy, which has a big black hole, and our Milky Way, which seems to have a black hole, are going to merge. Now, that strikes me as a good way to stir stuff up, so maybe it's galaxy mergers that give us this supply of gas. !!PAUL FRANCIS: Indeed, people have thought this idea for decades now, that maybe what's happening is you get a massive black hole in the middle of the galaxy. Early on, it's very bright, because there's forming the galaxy. Once the galaxy settles down to a sedate middle age, everything could have been eaten has been eaten. It's not shining, but then every time you get a galaxy collision, and that will drive stuff in. There's only one problem; if you look at colliding galaxies and non-colliding galaxies, the rate at which you see quasars seems to be about the same in both of them. !!BRIAN SCHMIDT: How long does it take for a quasar to light up once galaxies collide? !!PAUL FRANCIS: Well, that could be a way out of this. It could be that the galaxies collide and drive the gas in, and then the collision settles down, but the gas is still working its way down the center where we can't really see it, and so it could be that the quasar phase happens well after the collision. Or it could be some minor collisions where a very small galaxy forms into a bigger one, like the magnetic clouds would eventually pass through the disc of our own galaxy and fall in. There's another dwarf galaxy currently falling into our own Milky Way, and maybe it's these really small things that are much harder to see that come in and funnel the gas into the center. !!BRIAN SCHMIDT: Yeah. I suppose we don't actually need that much mass, even to shine as bright as a quasar, if you're falling into a giant black hole. !!PAUL FRANCIS: Yeah. So, there do seem to be massive black holes in the middle of pretty much every galaxy, but only a very small fraction of them are shining, and we're not quite sure why. !!

V9.8 BRIAN: All right, Paul. You've dedicated a lot of your life to going out and looking at quasars. What's the weirdest quasar that you've seen? !!PAUL: Well, most quasars look blue. This is a true color picture of a quasar I took. And it looks blue. And this is what you'd expect because here's what the spectrum of a quasar looks like. !!You remember that you've got the accretion disc. We talked about these around white dwarfs. The inner bits are going to be incredibly hot, 20,000, 30,000 degrees so they're going to have a spectrum that peaks up here. And then as you go further and further out, you're going to have bits that peak at lower and lower wavelengths. And altogether you get a spectrum that looks like this. !!And why does that look blue apart from the fact I colored the graph in blue? Well, let's look at something that looks sort of white or maybe slightly yellowish. The sun. This is what the spectrum of the sun looks like. !!And if you compare the two, you have to bear in mind the human eye perceives as green light at these sort of wavelengths. So these sort of wavelengths in the middle, the two spectra aren't that different. The human eye perceives as red the wavelengths down here. !!And in this case, the sun is actually much brighter than the quasar relatively speaking. But when you go down here to the wavelengths the human eye perceives as blue, the quasar is much brighter. So you've got something that's much more blue light and much less red light so it's going to look blue. !!BRIAN: OK. Makes sense to me. !!PAUL: OK. Well, this is all making sense. But this is a normal quasar. This is what most quasars look like. !!But if you search for quasars not in optical wavelengths, but, say, in gamma rays or radio or high-frequency x-rays or something like that, you find a lot of quasars that are this color. !!BRIAN: So what color is that? I'm colorblind, Paul. But it's not blue. !!PAUL: It's not blue. It's a kind of pinky, purple, sort of rather revolting color actually. I think it was my college colors back at Cambridge. And you shouldn't get this from an accretion disc. Accretion discs should be very hot. As the gas swirls down the throat of the black hole it should be 30,000 degrees. You should be getting blue light, damn it. !!BRIAN: OK. !!PAUL: And if you look at the spectrum of this, it's quite different. There are no emission lines, no absorption lines, no anything. Just the dead, flat line. !!BRIAN: Kind of looks like it's a dead object if this was its heart, OK? !!PAUL: Yes. !!BRIAN: So nothing. And remind me what a quasar looks like normally. !!PAUL: OK. Well, the quasar would look like this blue line here. So there's no way you'd mistake the two. And in fact, this line keeps on going out to enormous wavelengths. This is just optical light, but it keeps on going all the way out to the hardest gamma rays we can measure and out the way to the lowest frequency radio we could measure. Pretty much dead flat the whole way. !

!Why is it this horrible shade of pinkish purple? Well, you compare it to the spectrum of the sun again, which is what the human eye perceives as white. And it's below the sun at green wavelengths, but above at both ends both blue and red. So we get something with lots of blue and red, but not much green. !!BRIAN: You get purple. !!PAUL: Yes. !!BRIAN: Or pink. !!PAUL: And in fact, you get exactly this color. So what could be causing this? These things are seriously weird. First of all, it's a totally strange spectrum that goes over such an incredible range all the way from hard gamma rays to the furthest radio. !!They're also very strongly polarized. Normal light sometimes the light rays are going up and down, and sometimes they're left and right. For a normal thing, like a black body it's a mixture of the two. But these ones are often very strongly just one or just the other. And sometimes even change from one to the other. !!BRIAN: OK. So normally, you don't get polarized light from spheres. You'd need to have something that's really pointy in one direction or something. !!PAUL: Yeah, like a radio transmitter or something. Radio transmitters give you polarized light. And then these things vary on time scales of minutes even sometimes. !!BRIAN: Minutes? !!PAUL: They often are called intraday variables, which means normally a quasar is never going to vary within one day, but certainly on time scales of hours and sometimes even faster than that. And they seem to change in brightness. !!BRIAN: Well, that seems to be faster than how long it would take light to get across one of these supermassive black holes. It's 8 minutes from here to the sun, for example. !!PAUL: Yeah, so these things are-- !!BRIAN: So they're violating any sort of common sense. !!PAUL: It seems to be whatever it's coming from, it's coming from an incredibly small location, smaller even than the very small area already you're talking about for the event horizon of these black holes. !!BRIAN: Now you said these things are really bright in the radio. Now when you have really bright sources in the radio, you can look at them in detail there. So doesn't that mean we could go in and we could put radio telescopes on different sides of the planet of the Earth, look up and use the whole Earth's diameter as a giant radio telescope? !!PAUL: Yes. This is called very-long-baseline interferometry, when you combine telescopes all over the world and sometimes even in space. And if you use that-- this is actually from the Hubble Space Telescope. It was first discovered using as radio telescopes. !!You look right in at the center of these things. What you can see is usually a bright blob, which we think is the center and then a bunch of blobs sort of making a one-sided jet. So lots of these

quasars have two-sided jets. These ones seem to have one-sided jets. They squirt stuff out of one direction only as far as we can see. !!And you can look at these lumps in the jet and you can actually see them moving out because of the superb resolution of these sorts of telescopes. So you see this blob is a certain distance from the center here. And as time goes on, it's getting further away. These all are moving out from the center. !!BRIAN: And so these lines are showing what you would expect if something was moving at six times the speed of light. !!PAUL: And that's the real puzzle. You can work out how fast these things are moving out, and they seem to be going considerably faster than light. !!BRIAN: Well, that would be a problem for what we've already talked about in this course I would think so perhaps, we need to investigate this a bit further. !!PAUL: OK, so let's try and figure out how we measure these speeds and what could be wrong with this. !!V9.9 PAUL: So how can we explain this apparent faster than light motion? Surely that's impossible. Well, to get our heads around this, we have to think about what precisely we are measuring. !!What we'll do is we'll have a telescope. A radio telescope to be precise, a network of radio telescopes, very long baseline interferometry. And we will see the nucleus of our quasar and a blob. And at one time it's here, and at a later time, it's moved to there. Now what we can measure is the change in position, delta r. And we know the change in time, delta T. That's the time between our observations. OK. And we therefore infer that the velocity equals delta r divided by delta T. Seems pretty straightforward, but there are two complications here-- one involving the r and one involving the T. !!Let's start off with the complication involving the r. We are measuring the apparent sideways motion. But in addition to moving sideways away from the quasar, these blobs may be moving towards us or away from us. !!So let's imagine we are looking from over here. And we have a quasar, and it's squirting blobs out at this angle here. All we actually see is this component of the motion. We don't see that component of the motion at all. So that distance is r And this angle here, the angle to the line of sight is theta. What we observe is delta r is actually-- delta r observed-- is actually the real r times sine theta. If something's moving straight towards us for example, we won't see it move at all. The blob will just sit on top here. If it's at right angles, then the r observed is the same as the r actually moved. And if it's somewhere in between, it's going to be some fraction given by sine theta. !!So does that solve our problem? Well, no. That's going to make delta r observed smaller. So it's going to mean our velocity will appear less than the true velocity. It's not going to make it appear more that the true velocity. So that means it must be going even faster than light to-- at least what we observe if it's at some angle. So that's important, but it doesn't really help us. !!What else can we look at here? Well let's see what's wrong with the delta T. Now delta T, remember we're taking two observations at two different times separated by delta T. And we see the radiation that was coming from there is now coming from there. But there's a complication

here. Once again, let's imagine that a quasar is firing a blob of plasma close to the line of sight. And once again we have an angle theta in here. !!Now you might think that the time that elapses for the quasar between there and there is the same as the time that elapses on Earth between the observations. But you'd be wrong. Because let's imagine some light sets out from here. It's going to travel this distance to reach the Earth. But light coming from here only has to travel a smaller distance to reach the Earth. Because it's got a smaller distance to go than that light, it will appear relatively earlier. !!So what is the delta T observed? Well, imagine we have a pulse that sets out from here. And there's some time there, T. And another pulse gets from there. On the pulse that set out from here, we have traveled a distance CT. Meanwhile this blob has traveled a distance along the line of sight which is that length there, which is r cos theta. !!So the light coming from here has a head start on the light coming from there. It's not starting from the same place. So the time interval that we observe on Earth will not be the time interval that takes light to get from there to there, but only the time difference it takes light to get from there to there. That distance there is going to be CT minus r cos theta. !!OK. So let's combine these things. Apparent velocity, the v observed, is going to be apparent distance, which is going to be r sine theta. Over the apparent time. Apparent time is going to be CT minus r, and r is just v times T. So it's vT cos theta. All divided by C. That's the extra distance light has to go, divided by the speed of light. And also up here, we know that r is actually just equal to vT again. So that comes out. Let's make the substitution beta equals a fraction of the speed of light. That comes out as beta sine theta. All over 1 minus beta cos theta times the speed of light. So that's how fast things are going to appear to travel. !!Now, this top, this sine theta, is going to make things appear slower. But the bottom, the 1 minus beta cosine theta, if beta is quite close to the speed of light and theta is small and therefore cosine theta is close to 1, you get a 1 minus a number that's almost 1. So that could make the bottom very small and make the apparent velocity very large. Is it enough to cancel out the sine theta effect? Well, let's do a calculation of that. !!I've produced plots of the apparent velocity as a function of angles to the line of sight for different values of beta. Here's a plot for beta equals 0.7, so something travelling at 70% of the speed of light. And what you can see here is that at angles of around 40 to 50 degrees, the apparent motion is actually faster than the true motion. At small angles or large angles, it's much less. !!A speed of 0.7c wasn't enough to give us apparent superluminal motion. But here's a plot for 0.9c, and you see now that at angles of between 20 to 30 degrees from line of sight, the apparent velocity can be up to twice the speed of light. So we are getting superluminal motion. !!If we take the velocity even further still, all the way up to 0.99% of the speed of light, you can see that you get extremely fast speeds, up to 7 times the apparent speed of light, for angles are only about 10 degrees off the line of sight. !!So that's our explanation for this apparent superluminal motion. The quasar is firing something very close to the line of sight to the Earth. Because it's so close to the line of sight of the Earth, its apparent sideways speed is reduced. But on the other hand, the light from this thing almost catches up with the light from earlier epochs, which means that the time is enormously compressed. If we take two observations a year apart, it could well be light that was actually emitted 100 years apart, but because it's going 99% of the speed of light, it's almost caught up with the lights from the earlier bits. !!And so it turns out that for angles not quite on line of sight, but only a small way off, and speeds very close to the speed of light, this effect of catching up with its own light and therefore

compressing the time more than compensates for the small angle and gives us motions which can be extremely fast. !!It also explains the one sided nature of the jets. Probably these quasars are also firing a jet out that direction. But if you remember from relativity, when something's moving close to the speed of light most of its radiation is beamed out in a narrow angle forwards. So what's happening is light from blobs going this way mostly comes out in these directions. And the light from a blob in this direction mostly comes out in these directions. So we just can't see the blobs over here. They're beaming the light in a different direction. We only see the ones on this side, which explains why the jets are so one sided. !!The compression of time because it's almost catching up with its own light also explains how these things can vary so very, very fast. They're actually not varying that fast. It's just that they're varying and moving towards us, so the apparent time variation is compressed because of the motion. !!So it all seems to fit together. !

V9.10 !PAUL: So we've seen things that look very much like black holes, both in binary systems and in the middles of galaxies. But, Brian, is the evidence enough to convince you that black holes really exist? !!BRIAN: Well, the evidence is pretty compelling. We think we understand neutrons, for example, and it's kind of hard to imagine how you can make a 10 solar mass neutron star, given our understanding of neutrons. And when we look in the center of our Milky Way, the idea that you can have a million plus solar masses, material, in something the size of the solar system, and it not being a black hole, seems unlikely. That being said, so we've got something that, sort of, it smells like a black hole and feels like a black hole, but we have a problem. Sort of by definition, it's kind of hard to look like a black hole. !!PAUL: Now there's a lot of stuff in the popular press coming out of the work of people like Stephen Hawking and Roger Penrose talking about possible really weird things in black holes. Like black holes might actually shine if they're very small. Or there's been some speculation about if you fall through a rotating black hole you might go through a wormhole to another dimension. Things like this. What do you make of all this sort of stuff? !!BRIAN: I never really know what to make of it, because ultimately science is about theories with predictions. But we don't know a lot about how gravity works at this level. This is sort of going sort of beyond general relativity. And it's beginning to also mix in quantum mechanics, and that's a mixture we don't understand. That's one of the great unsolved mysteries of the universe. !!PAUL: Yes. You remember we talked about it back when we were talking about the Big Bang. We have quantum mechanics, which deals with very small things, and relativity, which deals with very massive things. Normally one or the other works perfectly in our labs on Earth. The only places where we need both are either the Big Bang-- entire universe, no size, or a black hole-- if you bite into the 30 kilograms, no size. And the things don't match at all. So. Given we have a theory which we know doesn't really work, especially when you get down to near the singularity, what are we to do? We have to be guided by experiment, but we haven't got any black holes in our labs. !!BRIAN: Yeah. I think what's really quite remarkable is just how much our observations are able to progress. So, for example, I was just visiting Europe and was being shown an experiment to use radio telescopes across the continent to image the black hole in the center of our galaxy. And although you don't expect black holes to emit, they can cast shadows. So imagine if you can image

that thing the size of a solar system in the middle of the galaxy and see the shadow of the black hole. That might pretty well cinch it for you. !!PAUL: Yes. I guess I don't really want a black hole in my lab, but if you've got one a nice safe distance away, like eight kiloparsecs, you can get these exquisitely good measurements, maybe we could really start putting some constraints on all of these white, weird, and wonderful theories from that. !!BRIAN: And you never know where things might pop up where you least expect it. One of the theories of Stephen Hawking is the idea that black holes get very small, they evaporate very quickly. And you essentially are able, through quantum mechanics and the Heisenberg Uncertainty Principle, to create out of nothing a particle pair, one on this side of the black hole and one on that side. The one outside can escape. And so that is a very characteristic prediction. !!PAUL: We're talking about black holes are the mass of atoms here, not the ones you can talk about astrophysically. And so they would have to have been created by some strange process back the very early universe if they exist at all. !!BRIAN: Absolutely. And an Australian, John O'Sullivan, was out looking for these in the '70s, and never found them, when they were first predicted. But he was able to go out and invent Wi-Fi from some of the ideas that he had in going and looking for these things. But you never know. Maybe there are small little black holes, but they're rare enough that we haven't yet found it. So you never know with science where new ideas might pop up. !!PAUL: So. Black holes. Seriously weird. Possibly even much weirder than we think. Because we don't have any in our lab, we can't tell. So I guess the future is trying to make really, really detailed astronomical observations of these black holes that are at nice safe distances, and trying to see whether all these wonderful theories that people are coming up with actually bear much resemblance to reality or not. !!BRIAN: Absolutely. !!!!!!!!!!!!!