the collapsing universe: the story of black holes, by isaac asimov

"PENETRATING"-SCIENCE DIGEST

"The future of the universe: its possible collapse,quasars as 'white holes,' space-time 'wormholes,'and (the) ultimate recycling of the universe . . .The prolific Dr. Asimov, that one-man publisher'slist, has done it again."

-SMITHSONIAN MAGAZINE

"Stimulating and cogent . . . Asimov proves hisreputation as the dean of popular sciencewriters. The most abstract and difficult conceptsare made readily comprehensible in prose aslucid as it is informative."

-TnE Los ANGELES TIMES

"Those with patience to follow Asimov's lead willdiscover that they can grasp the significance ofthe most exciting discoveries in astronomy inrecent decades."

-ST. LOUIS POST-DISPATCi

S#MWMAIC EMOY

B -PC B

PUBLISHED BY POCKET BOOKS NEW YORK

,, POCKET BOOKS, a Simon & Schuster division ofGULF & WESTERN CORPORATION1230 Avenue of the Americas, New York, N.Y. 10020

Copyright D 1977 by Isaac Asimov

Published by arrangement with Walker & CompanyLibrary of Congress Catalog Card Number: 76-53639

All rights reserved, including the right to reproducethis book or portions thereof in any form whatsoever.For information address Walker & Company,720 Fifth Avenue, New York, N.Y. 10019

ISBN: 0-671-81738-8

First Pocket Books printing April, 1978

3rd printing

Trademarks registered in the United States and other countries.

Printed in the U.S.A.

To PHYLLIS AND AL BALK,WHO WERE THERE ON NOVEMBER 30, 1973

CONTENTS

1 PARTICLES AND FORCES 1The Four Forces 2Atoms 8Density 14Gravitation 18

2 THE PLANETS 29The Earth 29The Other Planets 35Escape Velocity 40Planetary Density and Formation 46

3 COMPRESSED MATTER 55Planetary Interiors 55Resistance to Compression 61Stars 67Degenerate Matter 73

4 WHITE DWARFS 81Red Giants and Dark Companions 81Superdensity 87Einstein's Red Shift 93Formation of White Dwarfs 97

vii

viii THE COLLAPSING UNIVERSE

5 EXPLODING MATTER 105The Big Bang 105The Main Sequence 112Planetary Nebulas 119Novas 124Supernovas 133

6 NEUTRON STARS 143Beyond the White Dwarf 143Beyond Light 147Pulsars 152Properties of Neutron Stars 160Tidal Effects 167

7 BLACK HOLES 179Final Victory 179Detecting the Black Hole 186Mini-Black Holes 196The Use of Black Holes 202

8 ENDINGS AND BEGINNINGS 207The End? 207Wormholes and White Holes 214Quasars 220The Cosmic Egg 227

Appendix 1: Exponential Numbers 235Appendix 2: The Metric System 237Appendix 3: Temperature Scales 239

Index

1 PARTICLESANDFORCES

SINCE 1960 the universe has taken on awholly new face. It has become more exciting,more mysterious, more violent, and more extremeas our knowledge concerning it has suddenly ex-panded. And the most exciting, most mysterious,most violent, and most extreme phenomenon ofall has the simplest, plainest, calmest, and mildestname-nothing more than a "black hole."

A hole is nothing, and if it is black, we can'teven see it. Ought we to get excited over an in-visible nothing?

Yes-if that black hole represents the most ex-treme state of matter possible, if it represents thepossible end of the universe, if it represents thepossible beginning of the universe, if it representsnew physical laws and new methods for circum-venting what had previously been considered ab-solute limitations.

In order to understand the black hole, however,we must begin at the beginning and work our waytoward it step by step.

I

2 THE COLLAPSING UNIVERSE

THE FOUR FORCES

There are four different ways in which the vari-ous particles that make up the universe can inter-act with one another. Each of these is a particularvariety of interaction, or to use a more old-fash-ioned but more common term, a force. Scientistshave been unable to detect a fifth force, or yet, tofind any reason why a fifth should be required.

The four forces are listed in order of decreasingstrength in Table 1.

TABLE 1-Relative Strength of theFour Forces

Force Relative Strength *

Nuclear 103Electromagnetic 1Weak 10-11Gravitational 10-39

Every particle in the universe is the source ofone or more of these forces. Each particle servesas the center of a volume of space in which thatforce exists with an intensity that decreases asthe distance from the source increases. The vol-ume of space in which that force can make itselffelt is the force field.

Any particle that can serve as the source of aparticular field will respond to such a field set upby another particle. The response is generally one

* The relative strengths are given in exponential numbers, where 10'stands for 1,000 and 10-"1 for 1/1iOO00,000,000. Some details concerningexponential numbers are given in Appendix I if you're not familiar withtheir use.

PARTICLES AND FORCES

of movement: the particles moving toward eachother (an attraction) or away from each other (arepulsion) unless physically constrained from do-ing so.

Thus, any object capable of producing a gravi-tational field will, if placed in Earth's gravitationalfield, move toward Earth's center-that is, it willfall. The Earth will also move toward the object'scenter, but since it will likely be much larger thanthe falling object, it will rise correspondingly moreslowly-usually, in fact, immeasurably slowly.

Of the four forces two-the nuclear force andthe weak force-make themselves felt only at in-credibly tiny distances of 10-13 centimeters orless. * This is just about the width of the tinynucleus that exists at the very center of the atom.It is only within the nucleus, in the immediateneighborhood of isolated particles, that theseforces exist. For this reason the term nuclearforce is sometimes given to both, and they aredifferentiated by their relative strength into thestrong nuclear force and the weak nuclear force.

In this book, however, there will be little occa-sion to mention the weak force, so we will simplyrefer to the stronger force as the nuclear forceand be done with it.

A given particle is not likely to produce and torespond to each of the forces. Only certain parti-cles, for instance, produce and respond to thenuclear force. Those that do are called hadrons,from a Greek word meaning "strong," since thenuclear force is the strongest of the four. The

I In this book I am using the metric system, which is just aboutuniversally used outside the United States and is used by scientistswithin the United States, too. Some details concerning the metric systemare given in Appendix 2.

3

THE COLLAPSING UNIVERSE

hadrons that are most common and most impor-tant to the structure of the universe are the twonucleons-the protons and the neutron.

The proton was discovered in 1914 by the Brit-ish physicist Ernest Rutherford (1871-1937), andits name comes from the Greek word for "first"because at the time of its discovery it was thesmallest object known to have a positive electriccharge.

The neutron was discovered in 1932 by theEnglish physicist James Chadwick (1891-1974).It carries no electric charge, either positive ornegative. In other words, it is electrically neutral;hence its name.

As early as 1911 Rutherford had shown thatan atom contains almost all its mass in a verysmall region at the center, the nucleus. Once pro-tons were discovered, it was realized that they arerelatively massive particles and must be locatedin the nucleus. The number of protons variesfrom one kind of atom to another. The hydrogenatom has a single proton in its nucleus, the heliumatom has 2, the lithium atom has 3, and so on-up to the uranium atom which has 92. Still moremassive atoms have been prepared in the labora-tory.

But what holds all the protons together in thenucleus, where they are all squeezed into suchclose proximity?

Prior to 1935 only two forces were known-theelectromagnetic and the gravitational. The gravi-tational force is too weak to hold the protons to-gether. The electromagnetic force is strongenough, but it can manifest itself as either anattraction or a repulsion. Between two particlesof opposite electric charge (plus and minus) there

4


is an attraction. Between two particles of thesame electric charge (plus and plus, or minusand minus) there is a repulsion. Protons are allpositively charged and must therefore repel eachother; and the repulsion must be more intensethe closer the protons are to each other. In anatomic nucleus, with protons squeezed togetheruntil they are virtually in contact, the electro-magnetic repulsion must be enormously strong-yet the protons hold together.

In addition to protons neutrons are also presentin the nucleus, but this doesn't seem to help thesituation. Since neutrons lack an electric charge,they neither produce nor respond to an electro-magnetic force. They should therefore neither at-tract nor repel protons. They should neither helphold the protons together nor accelerate thebreakup.

It was not until 1935 that the Japanese physicistHideki Yukawa (1907-) put forth a successfultheory of the nuclear force. He showed that it waspossible for protons and neutrons when very closeto each other to produce an attracting force athousand times greater than the electromagneticrepelling force. What the nuclear force holds to-gether the electromagnetic force cannot blowapart.

The nuclear force works best and keeps thenucleus stable only when protons and neutronsare present in certain proportions. For atomswhose nuclei contain 40 particles or less the bestproportion seems to be equal numbers of protonsand neutrons. For more complicated nuclei therehas to be a preponderance of neutrons, that pre-ponderance growing greater as the nucleus grows

5


more complex. A bismuth nucleus, for instance,contains 83 protons but 126 neutrons.

When an atomic nucleus is forced to have pro-portions outside the region for stability, it doesnot remain intact. Small beta particles (beta is thesecond letter of the Greek alphabet) are given offunder the influence of the weak force until theproportion is adjusted to stability. Other ways ofnuclear breakup are also possible, but all theseways are lumped under the heading of radioac-tivity.

Strong as the nuclear force is, it has its limits.The intensity of the nuclear force falls off veryrapidly with distance, and it can't make itself feltoutside the nucleus. In fact its attractive influencefades considerably when it must extend itselffrom one end to the other of one of the largernuclei.

The electromagnetic force also fades off, butmuch more slowly. The size of the nucleus islimited, since eventually the electromagnetic re-pulsion from end to end will equal the rapidly f ad-ing nuclear attraction from end to end. That iswhy atomic nuclei are so infratiny. The nuclearforce simply won't produce anything larger (ex-cept under the most unusual conditions, whichwe will come to later in the book.)

Now let's concentrate on the electromagneticinteraction, which, as I have said, is produced onlyby those particles that carry an electric charge,and which is responded to only by those chargedparticles. The charge comes in two varieties, posi-tive and negative. The force between positive andnegative is an attraction, while that between posi-tive and positive or between negative and negativeis a repulsion.

6


The proton, with its positive electric charge, isa source of and responds to both the nuclear forceand the electromagnetic force. The neutron, whichis electrically uncharged, is a source of and re-sponds to only the nuclear force.

Then, too, there are particles called leptons,from a Greek word meaning "weak," which are asource of and respond to the weak force but neverto the nuclear force. Some leptons, however, areelectrically charged, and they are a source of andrespond to the electromagnetic force as well as tothe weak force.

The most important of the leptons, as far as or-dinary matter is concerned, is the electron, whichcarries a negative electric charge. (The beta parti-cles produced by unstable nuclei by way of theweak force proved to be speeding electrons.) Theelectron was discovered in 1897 by the Englishphysicist Joseph John Thomson (1856-1940), andit received its name because it was the smallestunit of electric charge then known (or for thatmatter, known today).

The information we now have can be sum-marized as in Table 2.

TABLE 2-Particles and Forces

Proton Neutron Electron

Nuclear force Yes Yes NoElectromagnetic force Yes No Yes

NOTE: There also exist particles like the electron but with a positiveelectric charge. These are antielectrons, or positrons. A proton with anegative electric charge is an antiproton. A neutron with certain otherproperties reversed is an antineutron. As a group these opposites areantiparticles. Just as ordinary particles go to make up the matter allabout us, antiparticles could make up antimatter. Such antimatter mayexist somewhere in the universe, but we have never been able to detectit. Scientists can make tiny quantities of it in the laboratory, however.


ATOMS

Since electrons are not subject to the nuclearforce, they cannot form part of the nucleus. Never-theless, an electron is attracted to a proton, thanksto the electromagnetic force, and tends to remainnear one. Thus, if a nucleus is made up of a singleproton, there is likely to be a single electron heldin its vicinity by the electromagnetic force. Ifthere are two protons in the nucleus, there arelikely to be two electrons held in its vicinity, andso on.

The nucleus and the nearby electrons make upthe atom. (Atom is from a Greek word meaning"unbreakable" because at the time atoms were firstdealt with, it was thought they could not bebroken up into smaller units.)

As it happens, the charge on the electron isprecisely equal. (though opposite in nature) to thecharge on the proton. Therefore, when there are xprotons in the nucleus, the existence of x electronsin the regions just outside the nucleus will meanthat the two kinds of charge will exactly neutralizeeach other. The atom as a whole is electricallyneutral.

Although the electron and proton are equal insize of electric charge, they do not have the samemass.* The proton is 1836.11 times as massive as

I When we say that an object possesses mass, we mean that it takesforce to make it move if It is standing still, or to change its speed ordirection of movement if it is already moving. The more mass it has,the more force it takes. Under ordinary circumstances here on thesurface of the Earth massive objects impress our senses as being"heavy." The more massive they are, the heavier. Still, mass and weightare not identical, and while the meaning is clear if we say that theproton is much heavier than the electron, it is safer to say "moremassive."


the electron. Imagine an atom, then, with 20protons and 20 neutrons in the nucleus and 20electrons in the outer regions of the atoms. Theelectric charge is balanced, but more than 99.97percent of the mass of the atom is in thenucleus.

Yet though the nucleus contains almost all themass of an atom, it makes up only a tiny frac-tion of the volume of an atom. (This is an im-portant point as far as the subject matter of thisbook is concerned-as we shall see.) The diameterof a nucleus is about 10-13 centimeters, while thatof an atom is about 10-8 centimeters.

This means that an atom is 100,000 times aswide as a nucleus is. It would take 100,000 nuclei,placed side by side, to stretch across the atom ofwhich it is part. If you imagine an atom to be ahollow sphere and start filling it with nuclei, itturns out that it would take 101' (a million bil-lion) nuclei to fill the atom.

Now let us consider two atoms. Each one hasan overall electric charge of zero. We might sup-pose, then, that they would not affect each other,that they would be, so to speak, unaware of eachother's existence, as far as the electromagneticforce was concerned.

Ideally, that would be so. If, in various atoms,the charge of the electron were spread with per-fect evenness in a sphere about the nucleus, andif the positive charge of the nucleus were evenlymingled with the negative charge of the electrons,then the electromagnetic force would play no rolebetween atoms.

That, however, is not the way it is. The negativecharge of the electrons is present in the outer re-gions of the atom, and the positive charge of the

9


nucleus is hidden within. When two atoms ap-proach each other, it is the negatively chargedouter region of one that is approaching the neg-atively charged outer region of the other. The twonegatively charged regions repel each other (likecharges repel), and that means that two atomscan only come so close to each other before theyveer away or bounce off.

A sample of helium gas, for instance, is madeup of separate helium atoms forever movingaround and bouncing off each other. At ordinarytemperature the helium atoms move quite rapidlyand bounce off one another with considerableforce. As the temperature lowers, however, theatoms move more and more slowly and reboundfrom each other more and more weakly. Theatoms of the helium gas fall closer together, andthe helium contracts and grows smaller in volume.

In reverse, as the temperature moves higher,the atoms move more quickly, rebound withgreater force, and the helium expands.

There would seem to be no limit to how fastatoms could move (within reason), but there isan easy limit to how slowly they would move. Ifthe temperature drops far enough, a point isreached where they move so slowly that no moreenergy can be withdrawn from them. At that levelof frigidity we reach a temperature of absolutezero, which is -273.18'C.*

Although the helium atom has a charge distri-bution that is quite close to being perfectlysymmetrical, it is only quite close and is not com-

* In this book temperature is expressed by means of the Celsius(centigrade) scale, which is used just about everywhere in the worldbut in the United States and by scientists even in the United States.For details on how that scale compares with the Fahrenheit scale, whichis more familiar to Americans, see Appendix 3.


pletely perfect. The electric charge is not exactlyevenly spread, and as a result, parts of the atom'ssurface are a little less negatively charged thanothers. As a result the atom's inner positive chargepeeps through the less negative areas of the out-side, so to speak, and two neighboring atoms willattract each other very weakly. This weak attrac-tion is called the van der Waals forces because itwas first worked out by the Dutch physicist Johan-nes Diderik van der Waals (1837-1923). As thetemperature drops and helium atoms move moreand more slowly, the force of rebound is eventu-ally not great enough to overcome the tiny vander Waals forces. The atoms stick together, andhelium gas becomes helium liquid.

The van der Waals forces are so weak in thehighly symmetrical helium atom that the tem-perature must drop to as low as 4.3 degrees aboveabsolute zero for helium liquid to form. All othergases have less symmetrical distribution of chargeon their atoms; they therefore experience largervan der Waals forces and liquefy at higher tem-peratures.

Atoms can sometimes attract each other instronger fashion. The electrons in the outer regionsof the atoms are arranged in shells, and the struc-ture is most stable if all the shells are filled. Exceptin the case of helium and a few similar elementsatoms generally have their outermost shell notquite filled, or have a few surplus electrons leftover when that shell is filled.

There is a tendency, then, for two atoms, oncolliding, to transfer one or two electrons fromthe one that has extra to the one that has de-ficiency, which leaves both with filled outermostshells. But then the one that gains electrons has

11


gained a negative charge, and the one that loseselectrons can no longer balance the charge of itsnucleus completely and has gained a positivecharge. The two atoms then have a tendency tocling together.

Or else two atoms, on colliding, share electrons,which then help fill the outermost shell in bothatoms. Both atoms then have filled outermostshells only provided they remain in contact.

In either case, electron transfer or electronsharing, it takes considerable energy to pull theatoms apart, and under ordinary circumstances,they remain together. Such atom combinationsare called molecules, from a Latin word meaning"little object."

Sometimes two atoms in contact are enough toproduce stability. Two hydrogen atoms form ahydrogen molecule; two nitrogen atoms, a nitro-gen molecule; and two oxygen atoms, an oxygenmolecule.

Sometimes it takes more than two atoms in con-tact to fill all the shells. The water molecule ismade up of one oxygen atom and two hydrogenatoms; the methane molecule is made up of onecarbon atom and four hydrogen atoms; the carbondioxide molecule is made up of one carbon atomand two oxygen atoms; and so on.

In some cases millions of atoms can form amolecule. This is because carbon atoms in par-ticular can each share electrons with each of fourother atoms. Long chains and complicated ringsof carbon atoms can therefore form. Such chainsand rings form the basis of the molecules char-acteristic of living tissue. The molecules of pro-teins and nucleic acids in the human body and inall other living things are examples of such mac-


romolecules (macro is from a Greek word mean-ing "large").

Atom combinations in which electrons aretransferred can bring about the formation of crys-tals in which the atoms exist in the countless mil-lions all lined up in even rows.

On the whole, the larger a molecule and theless evenly the electric charge is distributed overit, the more likely it is that many molecules willcling together and that the substance will be liquidor solid.

All the solid substances we see are held togetherstrongly by the electromagnetic interactions thatexist first between electrons and protons, then be-tween different atoms, and then between differentmolecules.

What's more, this ability of the electromagneticforce to hold myriads of particles together ex-tends outward indefinitely. The nuclear interac-tion, which involves an attraction that fadesexceedingly rapidly as distance is increased, canproduce only the tiny atomic nucleus. The electro-magnetic force, which fades only slowly withdistance, can cluster everything from dust par-ticles to mountains; it can produce a body the sizeof the Earth itself and bodies far larger still.

The electromagnetic force is intimately con-cerned with us in more ways than merely makingit possible for us and for the planet we live on tobe held together. Every chemical change is theresult of shifts or transfers of electrons from oneatom to another. This includes the very delicateand versatile shifts and transfers in the tissues ofliving beings such as us. All the changes that goon within us-the digestion of food, the contrac-tion of muscles, the growth of new tissue, the

13


sparking of nerve impulses, the generation ofthought within the brain, all of it-is the result ofchanges under the control of the electromagneticforce.

Some of the electron shifts liberate considerableenergy. The energy of a bonfire, of burning coalor oil, as well as the energy produced within livingtissue, is the result of changes under the controlof the electromagnetic force.

DENSITY

As the atoms or molecules of a given piece ofmatter move farther apart because of rising tem-perature or for any other reason, there comes tobe less mass in a particular fixed volume of thatmatter. The reverse is true if the atoms or mole-cules come closer together.

The quantity of mass in a given volume is re-ferred to as density; so what we are saying isthat when matter expands, its density decreases,and when matter contracts, its density increases.

Scientists, using the metric system, measuremass in grams and volume in cubic centimeters.A gram is a rather small unit of mass, only about1/28 ounce or 1/450 pound. As for a cubic cen-timeter, it is equal to about 1/16 cubic inch.

To give you a typical density, one cubic centi-meter of water has a mass of one gram. (This isn'ta coincidence. The two measures were originallychosen in the 1790s to fit together this way.)This means that we can say water has a densityof 1 gram per cubic centimeter or, in abbreviatedform, 1 g/cm3 .

Changes in density are not just a matter of ex-


pansion or contraction. Different substances havedifferent densities because of the very nature oftheir structure.

Gases have densities much less than that ofliquids, because gases are made up of separateatoms or molecules with little attraction for oneanother. Whereas liquid molecules are in virtualcontact, the atoms or molecules of gases moveabout rapidly, bouncing off one another and inthis way remaining far apart. Most of the volumeof a gas is made up of the empty space betweenatoms or molecules.

For instance, a sample of hydrogen gas pre-pared on Earth at ordinary temperatures andpressures would have a density of roughly 0.00009(or 9 x 10-) g/gm'. Liquid water is a little over11,000 times as dense as hydrogen gas.

The density of the hydrogen could be made stilllower if the hydrogen molecules (or separateatoms, for that matter) were allowed to move far-ther apart. In outer space, for instance, there couldbe so little matter that there is, on the average,only one atom of hydrogen in every cubic centime-ter. In that case, the density of outer space would besomething like 0.0000000000000000000000017g/cm3 -vanishingly small, indeed. Water is about600 billion trillion times as dense as outer space.

Different gases are quite likely to differ in den-sity. Under similar conditions the atoms or mol-ecules making up the gases have just as muchempty space between them. The density thendepends on the mass of the individual atoms ormolecules. If, of two gases, one is made up ofmolecules with three times the mass of those ofthe other, then the density of the first is threetimes that of the other.

15


For instance, a gas with a particularly massivemolecule is uranium hexafluoride. Each moleculeis made up of one uranium atom and six fluorineatoms, and the whole is 176 times as massive asthe hydrogen molecule, with its two hydrogenatoms. Uranium hexafluoride is a liquid that turnsinto gas with gentle heating, and the density ofthat gas is about 0.016 g/cm3. Liquid water isonly 62.5 times as dense as that gas.

Still, any gas, even uranium hexafluoride, ismostly empty space. If such a gas is compressed-if, for instance, it is put into an airtight con-tainer the walls of which are then forced to-gether-the gas molecules are pushed closer toone another, and the density increases.

The same effect is produced even more effi-ciently if the temperature is lowered. The gasmolecules come closer together, and at some low-enough temperature the gas becomes a liquid,where the molecules are in virtual contact.

If hydrogen is cooled to very low temperatures,it not only liquefies, but at 14 degrees above ab-solute zero, it freezes. The molecules are not onlyin contact, but they remain more or less fixed inplace, so that the substance is now a solid.

Solid hydrogen is the least dense solid in exist-ence, with a density of 0.09 g/cm3 , and is only atenth as dense as solid water. However, solidhydrogen, with its low density, is still over fivetimes as dense as the very dense gas uranium hex-afluoride.

In general, the density of liquids and solids alsoincreases as the mass of the individual atoms andmolecules of which they are composed increases.A solid made up of massive atoms is usuallydenser than one made up of less massive atoms.


Usually-however, not invariably. Here the situa-tion is more complex than in the case of gases.

The comparative mass of different atoms isgiven by a figure known as the atomic weight. Theatomic weight of hydrogen is approximately 1, sothe atomic weight of any other atom gives you anapproximate idea of the number of times heavierthan a hydrogen atom it is. For instance, thealuminum atom has an atomic weight of about 27,while the iron atom has one of about 56. The ironatom has 56 times the mass of a hydrogen atomand just a little over twice the mass of an alumi-num atom.

The density of iron, however, is about 7.85g/cm3, while that of aluminum is 2.7 g/cm3 . Ironis almost three times as dense as aluminum.

If iron is made up of atoms twice as massive asthose of aluminum, why is iron three times asdense? Why not only twice as dense?

The answer is that other factors come intoplay. For example, how much room is taken upby the electrons of a particular atom and howcompact the atom arrangement is. Atoms whoseelectrons belly far out from the central nucleusare less dense than you would expect from theirmass, which is, after all, concentrated in the tinynucleus. The electrons represent almost emptyspace and if they spread out and take up moreroom, the density is lowered.

Thus, cesium, with an atomic weight of 132.91,has a density of only 1.873 g/cm3 because itselectrons take up a great deal of room. The muchmore compact atoms of copper, with an atomicweight of 63.54, less than half that of cesium,give copper a density of 8.95 g/cm3 , nearly fivetimes that of cesium.

17


If, then, you want to know the substance withthe greatest known density, you must look amongthe more massive atoms but not necessarily amongthe most massive of all. The naturally occurringelement with the most massive atoms is uranium,with an atomic weight of 238.07. Its density is ahigh 18.68 g/cm3, twice that of copper, but it doesnot set a record. There are no less than four ele-ments with a density greater than that. They,along with uranium, are listed in Table 3 in orderof increasing density.

TABLE 3-Elements of High Densities

Element Atomic Weight Density(g/cm3 )

Uranium 238.07 18.68Gold 197.0 19.32Platinum 195.09 21.37Iridium 192.2 22.42Osmium 190.2 22.48

The rare metal osmium holds the record. Ofthe materials making up the Earth's crust or whichcan be obtained from it, this is the densest. Imag-ine an ingot of pure osmium the length and widthof a dollar bill and 2.54 centimeters (1 inch)thick. That's not a large ingot, but it would weigh5.85 kilograms (a kilogram is equal to a thousandgrams), or nearly 13 pounds.

GRAVITATION

So far in this book we have talked quite a bitabout the nuclear force and the electromagneticforce, and we have dismissed the weak force as


comparatively unimportant for our purposes here.We have barely mentioned the gravitational force,however, and that, as it happens, is the most im-portant of all as far as this book is concerned. Infact, we will speak of it so often that we may aswell save syllables by referring to the gravitationalforce simply as gravitation, when that seems nat-ural.

Gravitation affects any particle with mass,hadrons, leptons, and any combination of these-which means all the objects we see around us onEarth and in the sky.* We can expand Table 2now into Table 4 by adding the weak force andgravitation.

TABLE 4-Particles and the Four Forces

Proton Neutron Electron

Nuclear force Yes Yes NoElectromagnetic force Yes No YesWeak force No No YesGravitational force Yes Yes Yes

Of all four forces gravitation is weakest by far,as was indicated in Table 1. We can demonstratethis, rather than merely state it, by engaging insome simple mathematics.

Suppose we consider two objects with massalone in the universe. The gravitational force be-tween them can be expressed by an equation first

I There are some particles without mass that are not affected in theordinary sense by gravitation. The particles of light and similar radia-tions, called photons, from a Greek word meaning "light," are masslessfor instance. So are certain uncharged particles called neutrinos. Bothof these will crop up later in the book.

19


worked out in 1687 by the English scientistIsaac Newton (1642-1727), and that is:

F(g) = Gd2m (Equation 1)

In this equation F(g) is the intensity of the grav-itational force between two bodies, m is the massof one body, m' the mass of the other, d the dis-tance between them, and G is a universal gravita-tional constant.

We must be careful about our units of measure-ment. It is customary to measure mass in gramsand distance in centimeters. (A centimeter isequal to just about 2/5 inch.) G is measured insomewhat more complicated units that need notconcern us here. If we use grams and centimeters,we will end up by determining the gravitationalforce in units called dynes.

The value of G is fixed, as far as we know,everywhere in the universe.* Its value in the unitswe are using for it is 6.67 x 10-8, or 0.0000000667.Let's suppose that the two bodies in question areexactly 1 centimeter apart, so that d = 1 andtherefore d2 = d x d = 1 x 1 = 1. Equation 1therefore becomes in this case:

F(g) = 6.67 x 10-8 mm'. (Equation 2)

Suppose now that we are dealing with an elec-tron and a proton. The mass of the electron (m)is 9.1 x 10-28 grams. The mass of the proton (m')is 1.7 x 10-24 grams. If we multiply these twofigures and multiply the product by 6.67 x 10-8,

-There is some question about this, a point which will come uplater in the book.


we end up with a final product of 1 x 108 dynes,or 0.00000000000000000000000000000000000-0000000000000000000001 dynes (Here is an ex-ample of why exponential figures are used byscientists in preference to ordinary decimals.)

We can therefore say that for a proton and anelectron separated by 1 centimeter the gravita-tional attraction between them can be representedas:

F(g) = 1 x 10-58 dynes. (Equation 3)

Next let's move on to the electromagnetic forceand set up an equation for its intensity betweentwo charged objects alone in the universe.

Exactly one hundred years after Newtonworked out the equation for gravitational force theFrench physicist Charles Augustin de Coulomb(1736-1806) was able to show that a very similarequation could be used to determine the intensityof the electromagnetic force. The equation is:

F(e) = . (Equation 4)

In this equation F(e) is the intensity of the elec-tromagnetic force between the two bodies, q isthe electric charge of one body, q' the electriccharge of the other, and d is the distance betweenthem. Once again, distance is measured in centi-meters, and if we measure the electric charge inwhat are called electrostatic units, it is not neces-sary to insert a term analogous to the gravitationalconstant provided the objects are separated by avacuum. (Of course, since I am assuming the ob-jects are alone in the universe, there is necessarily

21


a vacuum between them.) Furthermore, if we usethese units, F(e) will also come out in dynes.

If, once again, we assume that the two objectsin question are separated by 1 centimeter, d2 isagain equal to 1 and the equation becomes:

F(e) = qq'. (Equation 5)

Suppose that we are still dealing with an elec-tron and a proton. The two particles have equalelectric charges (even though they are opposite insign), each one being 4.8 x 10-10 electrostaticunits. The product qq' is equal to 4.8 x 10-° x4.8 x 10-10 = 2.3 x 10-'9 dynes.

Therefore for an electron and proton which are1 centimeter apart, the electromagnetic force be-tween them is:

F(e) = 2.3 x 10-41 dynes. (Equation 6)

If we want to find out how much stronger theelectromagnetic force is than the gravitationalforce, we must divide F(e) by F(g). Since both in-tensities are measured in dynes under the con-ditions I've set up, the dynes will cancel, andwe'll end up with a "pure" number, a numberwithout units.

If we divide Equation 6 by Equation 3, we have:

F() 21.3 x 1O-'8 = 2.3 x 103'. (Equation 7)

In other words the electromagnetic force is2,300,000,000,000,000,000,000,000,000,000,000,-000,000 times as strong as the gravitational force.

To get an idea of how enormous this difference


in intensity is, suppose we consider the gravita-tional force to be represented by a mass of onegram. What mass would we then have to use torepresent the electromagnetic force? It wouldhave to be a mass equal to a million bodies themass of our Sun.

Again, suppose that the-intensity of the gravita-tional force is symbolized by a distance equal tothe width of one atom. The intensity of the elec-tromagnetic force would then have to be symbol-ized by a distance a thousand times the width ofthe entire known universe.

Gravitation, then, is by far the weakest of thefour forces. Even the so-called weak force is10,000 trillion trillion times as strong as gravita-tion.

It is no wonder, then, that nuclear physicists,when studying the behavior of subatomic parti-cles, take into account the nuclear force, the elec-tromagnetic force, and the weak force but totallyignore gravitation. Gravitation is so weak that itsimply never influences the course of eventswithin atoms and atomic nuclei by a measurableamount.

This is also the case in chemistry. In all theconsiderations of the various chemical changes inthe body and in the nonliving environment out-side, only the electromagnetic force need be con-sidered-with some interest in the nuclear forceand the weak force in the case of radioactivity-but never gravitation. Gravitation is so weak thatit introduces no measurable effect on ordinarychemical changes.

Then, why should we worry about gravitationat all?


Because somehow it's there and because, de-spite its incredible weakness, it somehow makesitself felt. We realize that every time we fall down.We know that if we fall as small a distance asthat from a third-story window to the ground, weare very likely to be killed by the pull of gravita-tion. We know that it is gravitation that holds theMoon in orbit about the Earth and the Earth inorbit about the Sun. How is this possible for soweak a force?

Let's consider the four forces again. The nuclearforce and the weak force decrease so rapidly withdistance that they need not be considered outsidesuch objects as atomic nuclei.

The electromagnetic force and the gravitationalforce, however, both decrease only as the squareof the distance, and this is a slow enough rate ofdecrease to make it possible for both forces tomake themselves felt at great distances.

There is this crucial difference between the twoforces, however. There are two opposing kinds ofelectric charge and, as far as we know, only onekind of mass.

In the case of the electromagnetic force, thereare attractions (between unlike charges) and re-pulsions (between like charges). Since the elec-tromagnetic force is so strong, the powerful repul-sion between like charges tends to scatter them,preventing any buildup of a sizable number inany one place. The equally powerful attraction be-tween unlike charges tends to pull these togetherquite well, neutralizing the charges. In the end,the positive and negative charges (which arepresent in the universe in equal quantities, as faras we know) are thoroughly intermixed, and no-


where is there anything more than the tiniest ex-cess of either charge.

Therefore, while the electromagnetic interactionis powerful and overwhelming in holding electronsin the neighborhood of the nucleus and in holdingneighboring atoms together, one sizable chunk ofmatter has very little electromagnetic attractionor repulsion for another sizable chunk of mattersome distance away, since in both chunks of mat-ter the two different kinds of charge are so wellmixed that both chunks end up having just aboutzero overall charge.*

Since there is only one kind of mass, however,there is only gravitational attraction. As far as weknow, there is no such thing as gravitation repul-sion. Every object with mass attracts every otherobject with mass, and the total gravitational forcebetween any two bodies is proportional to the totalmass of the two bodies taken together. There is noupper limit. The more massive the bodies, themore gravitational force acting between them.

Consider an object like the Earth, which has amass equal to 3.5 x 1061 times that of a proton.In other words, it is 3,500 trillion trillion trilliontrillion times as massive as a proton. Thereforethe Earth produces a gravitational field that is 3.5x 1051 times that of a single proton. Another wayof looking at it is that every particle in the Earththat possesses mass-every proton, neutron, andelectron-is the source of a tiny gravitational field,

* It is possible to remove some electrons from an object by friction,leaving it with a small positive charge, or to add some electrons, leavingit with a small negative charge. Such bodies can attract or repel eachother and other objects, but the force involved is inconceivably tinycompared to what it would be if all the charged particles in either bodycould exert their full electromagnetic force.

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and all of them melt together and add up to theoverall gravitational field of the Earth.

The Earth also has electromagnetic fields, withevery proton and electron in it acting as a source.The proton fields and the electron fields tend tocancel, however, so that the overall magnetic fieldof the Earth is very small indeed. It is enough topull at the needle of a compass and to deflectcharged particles coming from the Sun and else-where, but it is terribly weak for an object theenormous size of the Earth made up of so manycharged particles.

Therefore, even though the gravitational forceis so much weaker than the electromagnetic forcewhen single particles are being considered, thegravitational force of the Earth as a whole is fargreater than its electromagnetic force. The gravi-tational force of the Earth is strong enough tomake you feel it unmistakably, and to kill you ifyou are not careful.

The enormous gravitational field of the Earthis capable of interacting with the lesser field of theMoon so that the two bodies are held strongly to-gether. Gravitational forces hold the planets andthe Sun together. There are measurable gravita-tional forces between the planets and betweendifferent stars.

Indeed, it is the gravitational force and only thegravitational force that holds the universe togetherand dictates the motion of all its bodies. All theother forces are localized. Only the gravitationalforce, by far the weakest of all, through the com-bination of being long range and of displayingattraction only, guides the destinies of the uni-verse.

PARTICLES AND FORCES 27

In particular, it is the gravitational force that isthe key to any consideration of black holes, so yousee we are on the main highway to them now andmust study the landmarks as we proceed.

2 XTHEPLAN ETS

THE EARTH

ONE EARLY LANDMARK en route to the blackhole (though it was never dreamed of as such atthe time) was the determination of the mass ofthe Earth, something which was carried throughby way of the gravitational force.

Newton had determined that the intensity ofthe gravitational field produced by any object isproportional to its mass. Indeed, that is anotherway of defining mass: that property of matter thatproduces a gravitational field.

This is not how I defined mass earlier in thebook. Then I described it as that property of mat-ter that makes it necessary to use a force of somesort to produce a change in motion of the matter,either in speed or in direction. The greater theforce necessary to produce a certain change in themotion, the greater the mass of the body to whichthe force is applied.

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The first definition of mass given just above issometimes called the gravitational mass. The sec-ond, because it involves the reluctance of matterto undergo a change in its motion, a propertycalled inertia, is referred to as inertial mass. Grav-itation and inertia seem to be two entirely differ-ent properties, and there seems no reason tosuppose that the two kinds of mass shouldmatch each other exactly, that whenever onemass has twice the inertia of another, it also hasa gravitational field of twice the intensity. Never-theless, that's the way it seems to work out. Noone has ever been able to show any distinctionbetween gravitational mass and inertial mass, soit is now taken for granted that the two areidentical.

Thus, the gravitational field of the Earth exertsa force on a falling body so that it undergoes achange of motion, or acceleration, and falls fasterand faster. Since inertial mass and gravitationalmass are the same, we can suppose that the in-crease in the rate of speed with which an objectfalls can be used to measure the intensity ofEarth's gravitation.

This acceleration was first measured back inthe 1590s by the Italian scientist Galileo Galilei(1564-1642). It is equal to 980 centimeters persecond per second. This means that each seconda falling body is moving 980 centimeters per sec-ond faster than it was falling the second before.

Now let us go back to Newton's equation:

F = Gd * (Equation 8)

where F is the intensity of the gravitational field

THE PLANETS

and therefore the value of the acceleration of afalling body, which, as I say, has long been known.G is the gravitational constant, m is the mass ofthe falling body, m' is the mass of the Earth, andd is the distance between the falling body and theEarth. What we're really interested in is the massof the Earth, so let's alter the equation by theusual algebraic techniques to put the m' all byitself on the left-hand side of the equation. Theequation becomes:

Fcl2m = Gm. (Equation 9)

If we have values for every symbol on the right-hand side of the equation, we can multiply thevalue of F by the value of d, multiply the productagain by d, divide this result by G, divide the quo-tient by m, and that will give the value for n',the mass of the Earth.

Well, that looks great, because we do have thevalue of F to begin with, as I have just explained.We also have the value of m, the mass of the fall-ing body, because we can just weigh it on a bal-ance to find the mass in grams.

The distance between the falling body and theEarth is a little complicated. Newton showed thatwhen a body produces a gravitational field, thatfield behaves as though it is produced by all themass of the body concentrated at its center ofgravity. When the body has a shape and proper-ties that fulfill certain conditions of symmetry, thecenter of gravity is at the geometric center of thebody. These conditions of symmetry hold forthe Earth and for all the sizable bodies that weknow of in the universe.

This means that the Earth acts as though its

31


gravitational field originates at its center; d there-fore stands for the distance of the falling bodyfrom the center of the Earth, not from the Earth'ssurface. If the falling body is near the surface ofthe Earth, then the distance is equal to the radiusof the Earth's sphere.

This value was first determined about 240 B.C.

by a Greek geographer named Eratosthenes (276-192 B.c.). He determined the size of the Earth'ssphere from the rate at which its surface curves,which he in turn determined by measuring theangle the rays of the Sun made to different partsof that surface at the same time. The radius (thedistance from the surface of the Earth to its cen-ter) is equal to 637,000,000 centimeters.

Now we have the values of F, m, and d, butas late as the 1700s, we didn't have the value ofG, and until we got the value of G, we couldn'tuse Equation 9 to calculate in', the mass of Earth.

Is there any way we can determine the valueof G?

Well, if G is truly universal, then suppose wemeasure the intensity of the gravitational fieldbetween two lead balls and make use of anotherform of Equation 8. Algebraic techniques canconvert it into:

G = Fd2 (Equation 10)mm'!

We can easily measure the mass of each ofthe lead balls, and that gives us m and m'. Wecan also measure the distance between them, andthat gives us d. If we can then also measure thegravitational force between them and get F, wecan solve the equation for C at once. Then we can

THE PLANETS

put the value of G into Equation 9 and instantlycalculate the mass of the Earth.

There is another catch. Gravitational forces areso incredibly weak in relation to mass that it takesa hugely massive object like the Earth to have agravitational field intense enough to measureeasily. Before we can work with objects smallenough to deal with in the laboratory, we musthave some device that can measure very tinyforces.

The necessary refinement in measurement cameabout with the invention in 1777 of the torsionbalance by Coulomb (who worked out Equation4, which I mentioned earlier in the book). In thetorsion balance tiny forces are measured by havingthem twist a fine string or wire. To detect thetwist, one need attach to the vertical wire a longhorizontal rod balanced at the center. Even a tiny,almost imperceptible, twist would produce ameasurable movement at the end of the rod. Ifthe wire being twisted is thin enough and the at-tached rod is long enough, we can measure thetwist produced by the tiny, tiny gravitational fieldsof ordinary-sized objects.

The wire or thread, you see, is elastic, so there isa force within it that tends to untwist it. The moreit is twisted, the stronger the force to untwist itbecomes. Eventually the untwisting force balancesthe twisting force, and the rod remains in a newequilibrium position. It is by measuring the extentto which the rod has twisted to achieve a newequilibrium that one can determine the intensityof force acting upon it.

In 1798 the English chemist Henry Cavendish(1731-1810) attempted the following experiment:

He began with a rod 180 centimeters long and

33


placed on each end a 5-centimeter-in-diameter leadball. He next suspended the rod from its center bya fine wire.

Cavendish then suspended a lead ball a littleover 20 centimeters in diameter on one side of oneof the small lead balls at the end of the horizontalrod. He suspended another such ball on the oppo-site side of the other small lead ball. The gravita-tional field of the large lead balls would now serveto attract the small lead balls and twist the wire toa new position. From the change represented bythe new position compared with the old Cavendishcould measure the tiny gravitational attraction be-tween the lead balls.

(Naturally, Cavendish enclosed the whole thingin a box and took every precaution to avoid havingthe wire stirred by air currents.)

Cavendish repeated the experiment over andover again until he was satisfied he had a goodmeasurement of F. Since there was no problem inmeasuring the mass of the lead balls or the dis-tances between the large balls and the small ones,he already had m, m' and d. He could now solvefor G in Equation 10 and did so.

Using refinements of Cavendish's experiments,we now believe the mass of the Earth to be 5.983X 1027 grams, or roughly 6,000 trillion trilliongrams.

We can determine the density of any object bydividing its mass by its volume. The volume of theEarth had been worked out correctly, or nearly so,from Eratosthenes's figure for the Earth's circum-ference. Once Cavendish had worked out the massof the Earth, it was therefore possible to determinethe Earth's average density at once. It turned outto be 5.52 g/cm

3.

THE PLANETS

THE OTHER PLANETS

The importance of determining the mass of theEarth lies not only in itself but in the fact that ithas made it possible for astronomers to determinethe mass of large numbers of other objects in theuniverse.

There is the Moon, for instance, Earth's onesatellite, which is 384,000 kilometers from us (akilometer is equal to about five eighths of a mile)and which circles Earth once every 27 1/3 days.

More precisely, both Earth and Moon circle acommon center of gravity. The laws of mechanicsrequire that the distance of each body from thatcenter of gravity be related to its mass. In otherwords, if the Moon were one half as massive as theEarth it would be two times as far from the centerof gravity as the Earth is; if it were one third asmassive as the Earth, it would be three times asfar; and so on.

The position of the center of gravity of theEarth-Moon system can be determined by astron-omers, and it turns out to be located about 1,650kilometers under the surface of the Earth andabout 4,720 kilometers from the center of theEarth. (It is the center that counts in gravitationalaffairs, remember.) The Moon goes around thatpoint, and so does the Earth; Earth's centerwobbles about it every 27 1/3 days.

The center of gravity is 81.3 times as far fromthe center of the Moon as it is from the centerof the Earth, so the Moon has 1/81.3 or 0.0123times, the mass of the Earth. The mass of theMoon is thus 7.36 x 1025 grams, but it is easier

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to express the value as a fraction of the Earth'smass.

Astronomers can go on to determine the massof the other planets of the solar system relativeto that of Earth. One way is by comparing theeffect of a planet on its satellite with that of theEarth on the Moon.

The time in which a small satellite completes itsorbit about its planet depends on two things only:the satellite's distance from the planet's center andthe intensity of the planet's gravitational field.

For instance, the planet Jupiter has a satellite,Io, which is at nearly exactly the same distancefrom Jupiter that the Moon is from Earth. Yet Iocircles Jupiter in 1 3/4 days, while the Mooncircles Earth in 27 1/3 days.

It can be calculated that Jupiter's gravitationmust be 318.4 times as intense as Earth's inorder for Jupiter to be able to whip Io so quicklyabout itself. In other words, Jupiter must have amass 318.4 times that of the Earth. Using thissatellite method and others, one can determinethe mass of all the sizable objects in the solarsystem.

In Table 5 the masses and densities of the nineplanets of the solar system, and of our Moon aswell, are given in order of distance from the Sun.

The intensity of the gravitational field of eachof these bodies is in proportion to their mass, andas you can see, Earth has by no means the great-est gravitational intensity or the greatest massamong the planets of the solar system. There arefour planets more massive than the Earth-Jupiter, Saturn, Uranus, and Neptune. Jupiter isthe giant of the planetary system; it is about 2.5

THE PLANETS

TABLE 5-Mass and Density of the Planets

Mass Density(Earth = 1) (g/cm3 )

Mercury 0.055 5.4Venus 0.815 5.2Earth 1 5.52Moon 0.0123 3.3Mars 0.108 3.96Jupiter 317.9 1.34Saturn 95.2 0.71Uranus 14.6 1.27Neptune 17.2 1.7Pluto 0.1 4

times as massive as the other eight planets puttogether.

The intensity of the gravitational field of eachplanet (or of any body) decreases as the squareof the distance, which means that the relative in-tensity of the gravitational field of two bodies ofdifferent mass remains the same at any distance.

For instance, a spaceship a million kilometersfrom Jupiter's center would feel Jupiter's gravi-tational pull to be 317.9 times as strong as itwould feel Earth's gravitational pull to be if itwere a million kilometers from Earth's center.

If the spaceship were to increase its distancefrom Jupiter's center from 1 million kilometers to2 million kilometers, Jupiter's gravitational fieldwould be only one fourth as intense at the newposition as at the old. If the same thing weredone in connection with Earth, Earth's gravita-tional field would also be only one fourth as in-tense at the new position as at the old. Jupiter's

37


field at its new point would remain 317.9 times asstrong as Earth's field at its new point.

Jupiter's gravitational field would be 317.9 timesas strong as Earth's at every pair of correspondingpoints-but what if the points do not correspond?

There is one important occasion when we wouldbe forced to remain at a different distance fromone planet's center than from another's. That iswhen we are standing on the surface first of oneplanet, then of another, with the two planets beingdifferent sizes.

We can demonstrate this best by comparingEarth with the Moon, since men have stood onboth worlds and have confirmed what theorypredicts.

The Earth's mass is 81.3 times that of -theMoon, and for positions at equal distances fromthe center of each body the intensity of Earth'sgravitational field is always 81.3 times that of theMoon's.

Suppose we are standing on the Moon's surface,though. We are then 1,738 kilometers from theMoon's center. If we are standing on the Earth'ssurface, we are 6,371 kilometers from the Earth'scenter.

The gravitational intensity on the surface of abody is its surface gravity (an important conceptin the story of black holes), and in calculatingthat, we must take into account the differencesin distance from the center. The distance ofEarth's surface from Earth's center is 3.666 timesthe distance of the Moon's surface from theMoon's center.

Gravitational intensity weakens as the squareof the distance, so Earth's surface gravity is weak-ened as compared with the Moon's surface gravity

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by a factor equal to 3.666 x 3.666, or 13.44. Wemust therefore divide Earth's innate gravitationalintensity of 81.3 (compared to the Moon's) by13.44, and that gives us an answer of 6.05.

Thus, although Earth has a mass 81.3 timesthat of the Moon, its surface gravity is only 6.05times that of the Moon. To put it another way,the Moon's surface gravity is about one sixth thatof the Earth.

In similar fashion we can calculate the surfacegravity for all the bodies of the solar system. Thefour giant planets offer a problem because whatwe see as a "surface" is actually the outer edgeof their huge atmospheres, whose thickness wecannot easily judge. We cannot even be certainthat there is a solid or liquid surface anywhere.If we pretend, however, that we can come to restat the top of that cloud layer and calculate theintensity of the gravitational field at that point, wecan call it the surface gravity. With that in mind,we can prepare Table 6.

TABLE 6-Surface Gravity

Surface Gravity(Earth = 1)

Mercury 0.37Venus 0.88Earth 1.00Moon 0.165Mars 0.38Jupiter 2.64Saturn 1.1SUranus 1.17Neptune 1.18Pluto 0.4

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ESCAPE VELOCITYIt is the Earth's gravitational field that lies be-

hind the old saying "Everything that goes up mustcome down." Any object hurled into the air atsome particular velocity is under the constant pullof Earth's gravitation. It therefore loses velocitysteadily until it comes to a momentary halt atsome point above the Earth's surface. Then it be-gins to fall, gaining velocity steadily until it hitsthe ground at the same velocity with which it waswas originally hurled upward.*

If one of two objects is hurled upward at agreater velocity than the other, it will take longerfor it to lose its velocity; it therefore climbs higherbefore the turnaround. It might seem that nomatter how great the velocity with which an ob-ject began its upward climb, that velocity wouldeventually be eroded away. It might climb a hun-dred kilometers, a thousand kilometers, but even-tually the relentless pull of the gravitational fieldwould have its way.

So it would seem-and so it would be if theintensity of the gravitational field did not weakenwith distance.

Earth's surface gravity exerts a certain forceon an object on the surface, which is 6,371 kilo-meters from Earth's center. The intensity of grav-itation decreases as any object subject to that forcerises up from the surface and increases its dis-tance from Earth's center. The decrease in in-tensity is proportional to the square of the

* Actually air resistance complicates the situation and further slowsthe object both going up and coming down. We are going to pretend inthis section, however, that air resistance doesn't exist. That involves onlya small change and doesn't alter the essence of the argument.

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distance-but distance from the center, not fromthe surface.

Suppose we rise into the stratosphere, some 35kilometers above Earth's surface. This is a greatheight by ordinary standards, but the distancefrom the center of the Earth increases only from6,371 kilometers to 6,406 kilometers. That is notmuch of a change; the gravitational intensity atthis height is still 98.9 percent that on the surfaceitself. A human being weighing 70 kilograms onthe surface would still weigh 69.23 kilograms inthe stratosphere. In ordinary life, then, we are notconscious of any significant change in the in-tensity of Earth's gravitation, so we never allowfor that change.

Suppose, however, that an object rises a reallygreat distance, say to a height of 6,371 kilometersabove the Earth's surface. It is then 6,371 +6,371, or 12,742 kilometers from the Earth'scenter. Its distance from the center will have in-creased by a factor of two, and the gravitationalintensity will have decreased to one fourth of whatit was at the surface.

If we imagine an object hurled upward withsuch velocity that it reaches the stratosphere be-fore that velocity is lost, then we see that in thelater stages of its upward flight the gravitationalintensity is slightly lower than it was in the earlierstages. The further loss of velocity is less, then,than would be expected if gravitation intensity re-mained the same all the way up. The object movesup somewhat higher than would be expected be-fore that momentary halt and turnaround.

Next imagine that a second object is hurledupward with an initial velocity double that of thefirst object. By the time the second object has

41


reached the height at which the first object hadlost all its velocity, it will have lost only half itsvelocity. It would now be moving at the velocitythe first object had had to begin with.

Will the second object now climb an additionaldistance equal to the total distance the first objecthad climbed?

No, for the second object is now making itsadditional climb through a region of somewhatweaker gravitation. It loses velocity more slowlyand climbs through a greater distance than thefirst object did from the surface.

Because of the decline in gravitational intensitywith height, doubling the initial velocity of anobject hurled upward more than doubles theheight it reaches. In Table 7 we see the height towhich objects rise above the surface of the Earthat given initial velocities.

TABLE 7-Rising Bodies

Initial Velocity Maximum height above Earth's(km/sec) surface

(km)

1.6 1303.2 5604.8 1,4506.4 3,1008.0 6,7009.6 17,900

As the initial velocity increases, the maximumheight increases too, and it increases more andmore rapidly as the object moves into regions ofweaker and weaker gravitation. Between the firstand last entries in the table the initial velocity has

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increased by a factor of 6, but the maximumheight has increased by a factor of 140.

There comes a point where an object rises sorapidly that its velocity decrease matches the de-cline in gravitational intensity. When it has losthalf its velocity, the gravitational intensity hasalso sunk to half, so that now it would take asmuch time for that weakened intensity to removethe half velocity left than it would have takenthe full gravitational intensity to remove the fullvelocity. The object moving upward continues tolose velocity but at an ever slower pace as gravita-tion grows weaker and weaker. The rising bodynever entirely loses all, and in that case, whatgoes up doesn't come down because it never quitestops going up.

The minimum velocity at which this happensis the escape velocity.

The escape velocity from Earth's surface is11.23 kilometers per second. Anything hurled up-ward from Earth at a velocity of 11.23 kilometersper second or more will go up and never comedown; it will move farther and farther from Earth.Anything moving upward with an initial velocityof less than 11.23 kilometers per second (with nofurther push added to what it already has *) willreturn to Earth.**

* An object that has an initial velocity and no added push is Inballistic flight and must begin with the escape velocity or more to moveindefinitely away from the Earth. A rocket ship, however, can be con-tinually pushed by its rocket exhaust so that, although it may move atless than escape velocity, it can get as far above Earth as desired.However, where living things are not involved, motion in the universeis almost always ballistic motion, with one initial Impulse and no more.

** If an object is moving less than escape velocity but not less thanabout 70 percent of escape velocity, and if it also has a sideways motion,then it may not escape from Earth but may not drop back to the surface,either. It may take up an orbit around the Earth and remain In that

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The value of the escape velocity depends on theintensity of the gravitational field. As that intensitydeclines, the escape velocity declines, too. It turnsout that as we increase our distance from Earth'scenter, the escape velocity declines as the squareroot of that distance.

Suppose we are in space 57,400 kilometersfrom the Earth's center. That would place us ninetimes as far from the center as we would be ifwe were on Earth's surface. The square root ofnine is three, and that means the escape velocityat the height of 57,400 kilometers from Earth'scenter is only one third of what it is at the surfaceof the Earth. At the height it is 11.23/3, or 3.74kilometers per second.

The escape velocity is different for differentworlds. A world that is less massive than Earthand has a lower surface gravity also has a lowerescape velocity from its surface. The escape veloc-ity from the Moon's surface, for instance, is only2.40 kilometers per second.

On the other hand, worlds that are more mas-sive than Earth have higher escape velocities thanit has. In Table 8 the escape velocities from thevarious planets are given, as measured fromthe visible surface (meaning the upper edge of thecloud cover in the case of the giant planets).

It is not surprising that the giant of the plan-etary system, Jupiter, has the highest escapevelocity.

What's more, because it is so voluminous, Ju-piter has a gravitational field that declines withdistance more slowly than Earth's does. Since

orbit indefinitely. An astronaut orbiting the Earth just a couple ofhundred kilometers above the surface must travel at least 7.94 kilo-meters per second to remain in orbit.

THE PLANETS

TABLE 8-Escape Velocities from the Planets

Escape Velocity(km/sec)

Mercury 4.2Venus 10.3Earth 11.23Moon 2.40Mars 5.0Jupiter 60.5Saturn 35.2Uranus 21.7Neptune 24Pluto 5

Earth's surface is 6,371 kilometers from the cen-ter, its gravitation weakens to 1/4 its surfacevalue at a height of 6,371 kilometers above thesurface. At a height of 19,113 kilometers abovethe surface, the distance from the center of theEarth is 4 times what it was at the surface, andEarth's gravitation is only 1/16 its surface value.

Jupitei, however, has a surface that is 71,450kilometers from its center. Therefore one mustrise to a height of 71,450 kilometers above Ju-piter's surface before its gravitation drops to 1/4its surface value, and to a height of 214,350 kilo-meters above its surface before its gravitationdrops to 1/16 of its surface value.

Jupiter's gravitational intensity drops so muchmore slowly than Earth's that at equal distancesfar out in space Jupiter's gravitational intensity is317.9 times that of Earth (what it should be con-sidering their comparative masses), even though

45


Jupiter's surface gravity is only 2.64 times that ofthe Earth.

Jupiter's escape velocity also decreases with dis-tance more slowly than Earth's does. From Ju-piter's surface the escape velocity is only 5.4 timesthat from Earth's surface. The escape velocityfrom Jupiter decreases so slowly with distance,however, that even at a height of 2 million kilo-meters above Jupiter's surface, it is still equal tothat from Earth's surface.

PLANETARY DENSITY AND FORMATION

Despite the size of Jupiter's surface gravity andescape velocity as compared with that of Earth,the impression we ought to get is of surprise atJupiter's feebleness.

Jupiter is after all more than three hundredtimes as massive as Earth and has a gravitationalfield more than three hundred times as intense asEarth's in consequence; yet the surface gravity ofJupiter is less than three times that of Earth, andits escape velocity is less than six times that ofEarth. The same disparity between the gravita-tional intensity on the one hand and the surfacegravity and escape velocity on the other can beseen in the other giant planets.

The reason for this is that the giant planets areso bulky that their surface (their cloud-layer sur-faces, anyway) are anywhere from nearly four toover eleven times as far from their planetary cen-ters as Earth's surface is from its center.

And that is not the whole explanation. Thegiant planets have low densities, which meansthat the matter within them is not compactly

THE PLANETS

packed together but is spread out to take up amore than normal volume by Earth standards.Their surfaces are thus farther out than theywould be if the giant planets were denser.

Suppose we indulge in a fantasy and imaginethat the planet Saturn could somehow be pushedtogether, or compressed, to the point where itsaverage density would be that of the Earth. Itwould have to be compressed to the point whereits volume would be only one eighth of what it isnow. Its radius would only be half what it is now:30,000 kilometers instead of the present 60,000.

Saturn would still have all its mass under theseconditions. Both its mass and the intensity of itsgravitational field would still be 95.2 times thatof Earth. The surface would still be farther fromthe center than is true of Earth, but not so muchfarther so the surface gravity, when Saturn iscompressed to Earth density, would not be 1.15times that of Earth, but 4.60 times.

Suppose we fantasize that Jupiter, too, could becompressed to the average density of Earth. Itsvolume would be only one fourth of what it isnow, and its radius five eighths of what it now is:44,200 kilometers instead of the present 71,400.With its mass intact and its surface that muchcloser to the center Jupiter's surface gravity wouldbe just about 7 times Earth's surface gravity.

Is there any other way in which we can getcloser to the center of a world and therefore in-crease the gravitational intensity? For instance, ifwe burrowed down into the crust of the Earth it-self, would the gravitational force upon ourselvesincrease steadily as we approached the center?

NolSuppose we imagine the Earth had an even

47


density of 5.52 g/cm3 all the way through and thatwe could somehow burrow into it freely. As wedug down, part of the Earth's structure would beabove us. In fact, a whole outer sphere of Earth'sstructure would be farther from the center thanwe were. Newton's mathematics showed that thisouter part would not contribute to the gravita-tional force pulling us toward the center. Only thepart of the Earth that was nearer to the centerthan we were at any particular time would con-tribute to that, and there would be less and less ofit as we burrowed deeper and deeper.

This means that the gravitational pull upon uswould grow weaker and weaker as we burrowedinto the Earth until we reached the very center ofthe planet, when it would be zero. At the centerof the Earth, or of any spherical world, all themass of the world would be pulling at us in thedirection away from the center because it wouldall be above us. It would, however, be pulling out-ward in all directions equally, and the pulls wouldcancel out, leaving us with zero gravity.

If we could imagine a sizable hole at the centerof the Earth, or of any spherical world, therewould be zero gravity at every point within thehole. Science-fiction stories have been written inwhich the Earth was imagined as hollow with aninhabited interior surface lit by a Sun-like objectat the center. Edgar Rice Burroughs's storiesabout "Pellucidar" are an example. Any inhabit-ants of such a world would, however, feel nogravitational pull holding them to that interiorsurface, but would float about freely in the in-ternal space-something Burroughs didn't realize.

No, the only way to increase the gravitationalpull is to compress the entire world, packing all

THE PLANETS

the mass more tightly together so that you canapproach the center while keeping all the massbetween you and the center-a concept that is ofkey importance in understanding the black hole.

The only thing in the universe that can socompress a world is gravitation itself, and it hasdone so in the past, when, for instance, the plan-ets of our solar system were forming.

At the start, the material out of which theplanets were formed was a vast mass of dust andgas. Most of this material was hydrogen, helium,carbon, neon, oxygen, and nitrogen, with hydrogenmaking up perhaps 90 percent of all the atoms.AU of it, slowly swirling in separate turbulentwhirlpools, slowly came together under the weak,but ever sustained pull of the mutual gravitationof all the atoms and molecules.

The more closely the material came together,the more it was compressed, the more the separategravitational fields of the constituent parts over-lapped and reinforced one another. The grav-itational intensity increased, and the furthercompression took place faster-and faster.

Most of the material remained gaseous. Thehelium and neon remained as separate atoms. Thehydrogen atoms combined into two-atom hydro-gen molecules but remained as separate molecules.The carbon atoms each combined with four hydro-gen atoms to form methane molecules, whichremained separate. The nitrogen atoms each com-bined with three hydrogen atoms to form am-monia molecules, which remained separate. Theoxygen atoms each combined with two hydrogenatoms to form water molecules, which remainedseparate.

There were two moderately common elements

49


that didn't remain as separate atoms or as sepa-rate small molecules. These were silicon and iron.Silicon atoms combined with oxygen atoms but, inthe process, did not form molecules that re-mained separate. In this case, the electromagneticforce kept on working to pile more and moresilicon-oxygen combinations together withoutlimit. These combinations, called silicates, couldgrow to be dust particles, then pebbles, then rocksand boulders. Atoms of other elements that wouldfit into the silicate structure were added: mag-netism, sodium, potassium, calcium, aluminum,and so on. It is this mixture of silicates that formsthe rocky materials of the Earth's crust with whichwe are so familiar.

Iron atoms clung to one another for the mostpart, together with other metals, such as cobaltand nickel, that mixed with them freely.

Thus, as the dust and gas swirled inward evermore tightly, ever larger pieces of rock and metal(or combinations of both) formed. Since themetal was denser than the rock, it responded moreto gravitational pull. As a world formed, the metalwould sink toward the center, forming a core,while the rocky material remained in a shell out-side the metal.

The Moon and Mars are built chiefly of rock.Mercury, Venus, and Earth are built of rock andmetal. Tiny solid bits of matter still strew space,and some strike Earth's atmosphere as meteors,which, if they survive to reach Earth's solid orliquid surface, are called meteorites. Some mete-orites are rock, some metal, and some a mixture.

Small worlds like the smaller asteroids are notlarge enough to have a gravitational field intenseenough to hold them together. They are held to-

THE PLANETS

gether by the electromagnetic force within andbetween the atoms, which is, of course, enor-mously more intense than the gravitational forceof such small bodies.

Atoms and molecules that remain separate anddon't build up endless electromagnetically heldcombinations won't cling to worlds by electro-magnetic interaction but can only be held gravi-tationally. The separate atoms and molecules thatmake up a gaseous atmosphere are examples ofthis.

Small worlds lack gravitational fields intenseenough to hold such gases. The Moon, therefore,with a surface gravity only one sixth as strong asEarth's, cannot hold gas molecules and does nothave an atmosphere. What's more, it cannot holdmolecules of liquid that are volatile, that is, thatevaporate and turn into gases easily. For that rea-son the Moon has no free water on its surface.Worlds even smaller than the Moon would alsolack atmospheres and volatile liquids.

Mercury, with a surface gravity 2.3 times thatof the Moon but still only three eighths that of theEarth, has neither atmosphere nor ocean, whileMars, with a surface gravity about like that ofMercury, manages to have a very thin atmosphere-about 0.006 times as dense as ours-togetherwith traces of water.

Why?The answer is that temperature has an effect.

The higher the temperature, the more rapidly theatoms and molecules of gases move, the morelikely it is that some of them will move at speedsgreater than the escape velocity of the planet towhich they belong, the more likely it is that theatmosphere (if any exists to begin with) will dis-

51


sipate into space, and the less likely it is that theatmosphere will have formed in the first place.The lower the temperature, the less rapidly theatoms and molecules of gases move, the less likelyit is that any of them will move at speeds abovethe escape velocity, the less likely it is that theatmosphere will dissipate, and the more likely itis that the atmosphere will form in the first place.

Mars has the same surface gravity as Mercuryhas, but Mars is nearly four times as far from theSun as Mercury is and is therefore considerablycooler. Whereas Mercury's surface can reachtemperatures of 350'C, the average Martian sur-face temperature is only 200C.

Consider Titan, the largest satellite of theplanet Saturn. Titan's surface gravity is probablynot more than half that of Mars, but Titan has asurface temperature of about -180 0C, only 90degrees above absolute zero. It therefore possessesan atmosphere that seems to be denser than thatof Mars and may be almost as dense as that ofEarth.

The less massive an atom or molecule, the morequickly it moves at a given temperature, the morelikely it is that it will escape into space, and themore difficult it is to hold onto as part of azatmosphere.

Thus, the Earth's gravitational field is intenseenough to hold argon atoms (with an atomicweight of 40). It can also hold carbon dioxide,since the carbon atom it contains has an atomicweight of 12 and the two oxygen atoms it con-tains have a total atomic weight of 32, makingan overall molecular weight of 44.

In the same way Earth's gravitational field isintense enough to hold oxygen (molecular weight

THE PLANETS 53

32) and nitrogen (molecular weight 28), but nothelium (atomic weight 4) or hydrogen (molecularweight 2).

If the gradual buildup of material forming aplanet becomes large enough to give rise to agravitational field intense enough to hold evenhelium or hydrogen, the planet then starts to growrapidly, since helium and hydrogen are the mostcommon of the starting materials. The planet, ineffect, snowballs, since the further it grows, themore intense its gravitational field and the moreeffectively it can continue to gather more heliumand hydrogen.

This happens more easily farther from the Sun,where it is cooler and the light gases are made upof atoms and molecules that are moving com-paratively slowly. The result is the formation ofthe giant planets Jupiter, Saturn, Uranus, andNeptune, relatively far from the Sun. It is becausethey are made up largely of the light elements thatthey possess such low densities.

Planets forming closer to the Sun, where tem-peratures are higher, cannot hold onto the lightelements; they are built up chiefly or entirely ofthose less common atoms that can hold togetherby electromagnetic force. Hence it is the smallerplanets of rock and metal, with high densities,that make up the inner solar system.

COMPRESSEDMATTER

PLANETARY INTERIORS

As THE PARTICLES making up a planet cometogether-growing to pebbles, boulders, moun-tains, and worlds-they heat up. Gravitation pro-duces an acceleration motion inward; the largerthe growing fragments become and the faster theymove, the more kinetic energy (kinetic is from aGreek word meaning "motion") they possess. Thelarger fragments, planetesimals, which bang intothe growing world have the energy to gouge outhuge craters. These are eliminated by the crashesand the ever more intense crater gouging that fol-low, until finally the last few remain indefinitely.

We see the craters that mark the last collisionson the Moon, on Mercury, on Mars, and on thetwo small Martian satellites, Phobos and Deimos.We could surely see them on Venus if we couldget a good look under the clouds and on Jupiter's

55


satellites if we could get pictures of them in suffi-cient detail.

Undoubtedly the Earth had its share of craters,too. On the Earth, however, running water andthe action of living things have eroded them, andonly faint traces can be seen.

All the kinetic energy of the crashing togetherof rapidly moving bodies is not lost. Energy can-not be lost; it can only be changed into otherforms. In this case the kinetic energy is turnedinto heat and is concentrated at the center of theworld that is formed. This is true of Earth and,undoubtedly, of all worlds large enough to havereceived a great deal of kinetic energy in the pro-cess of formation. This internal heat is the prod-uct, in the last analysis, of the energy of thegravitational field as it is concentrated more andmore intensely in the process of planet making.

In the case of the Earth evidence was earlygained that the interior is hot. When one digsdeep mines into the Earth, the temperature goesup steadily as one probes deeper. There are alsoindications of internal heat in the form of hotsprings and volcanoes (which probably gave an-cient man the idea of a fiery hell underground).

Modern knowledge of Earth's interior stemsfrom the analysis of earthquake waves, whichtravel through the body of the planet. From thepaths they take, the time it takes them to travel,and the manner in which they make or don't makesudden changes of direction a great deal can beinferred concerning the properties of the Earth'sinterior. The temperature is believed to rise stead-ily all the way to the Earth's center, and at thecenter the temperature may be as high as 5,0000C

COMPRESSED MATTER

(nearly as hot as the 6,0000C of the Sun's sur-face).

The fact that the interior of the Earth is blazinghot means that much of its internal structure was(and still is) in the liquid state after it was formedand after the planet reached something like itspresent size. That means that if it were made upof different kinds of matter that do not readilymix with one another, they would separate, thedenser varieties moving closer to the center andthe less dense varieties floating on top of thedenser ones.

This, indeed, happened. The Earth is chieflymade up of rocky silicates and a metal mixtureof iron and nickel in a ratio of about nine to one.The metal settled in the center, where it nowforms a nickel-iron core. Around it is the silicatemantle. The mantle is solid, for its temperatureat its hottest (which is, of course, at its deepestpoint) is probably no more than 2,7000C, whichis not enough to melt the rock. The core, with aconsiderably higher temperature, is hot enough tomelt the iron; thus the Earth has a liquid core.

The heat in the Earth's interior was originallyformed in the early stages of the planet's history-4,600,000,000 years ago. (A billion years is some-times called an eon, so that we may say the Earthwas formed 4.6 eons ago.) Perhaps by 4 eons agothe major planetesimal collisions were over, andvery little in the way of more kinetic energy wasadded to the Earth. Gravitation had completed itswork of formation.

It would seem that in the 4 eons that have sincepassed, the internal heat should have leaked outof the Earth, and the whole planet should havecooled down. The rock of the mantle and crust is,

57


to be sure, a very poor conductor of heat, so theinternal heat could leak out only very slowlyindeed, but 4 eons is a long, long time.

Actually, though, the Earth has as part of itsconstituents small quantities of elements likeuranium and thorium that by means of the nu-clear force and the weak force slowly break downover the eons and liberate heat. (After 4.6 eonsof existence on Earth half the original uraniumand four fifths of the original thorium still existsintact.) The heat liberated by these radioactiveelements is not very much, but it adds up overthe eons; it is at least as great as the amount ofinternal heat leaking out. What was begun by thegravitational force is now maintained by thenuclear and weak forces; Earth's interior willtherefore not cool down for many eons to come.

Naturally a planet that is larger than the Earthhas received much more kinetic energy in theprocess of formation. In the first place up to hun-dreds of times more mass has come crashing intothe growing planet. Then, too, because of thesteadily more intense gravitational field thosemasses struck at greater speeds. Both mass andspeed contribute to kinetic energy. A large planetwould therefore have a hotter interior than Earthhas (and a small planet would have a cooler one).

Consider Jupiter. In 1974 and 1975 two probes,Pioneer 10 and Pioneer 11, passed quite close tothe planet (within 100,000 kilometers of its sur-face), and from the data received, scientists wereable to estimate the interior temperatures of thevast planet.

The distance from the outer cloud layer ofJupiter to the center is 71,400 kilometers. By thetime a depth of 2,900 kilometers below the cloud

COMPRESSED MATTER

surface is reached (only 4 percent of the way tothe center), the temperature is already some10,0000C, twice as high as Earth's central point.

At a depth of 24,000 kilometers below the cloudsurface, a third of the way to Jupiter's center, thetemperature is 20,000C. At the center itself thetemperature has reached a whopping 54,000C,nine times that of the surface of the Sun.

But it isn't only high temperature that is pro-duced in planetary interiors by the gravitationalinteraction. High pressures are also produced.

Under the action of the gravitational field theoutermost layers of a planet are pulled towardthe center and push against the layers beneath,which are also pulled toward the center and pushagainst the layers beneath them. This series ofpushes is carried on all the way to the center,each deeper layer transmitting the push of every-thing above it and adding its own, so that the pres-sure goes steadily higher as one penetrates deeperand deeper into a planet.

A pressure is often measured as a certainweight distributed over a certain area-the num-ber of grams pushing down on a square centi-meter, for instance. Consider our atmosphere. Itis pulled down against the surface of the Earthby gravitation with sufficient intensity to causeit to push against that surface with considerablepressure.

Every square centimeter of the Earth's surfacereceives the push (or the weight, which is whatthe push is often called) of 1,033.2 grams of air.We can say, then, that air pressure at sea level is1,033.2 g/cm2 , which we can call 1 atmosphere.This pressure is also exerted on our bodies, but

59


in every direction, both inside and out, so itcancels out and we are not aware of it.

The pressure of water in the ocean depths ismuch higher than that of air, since water is muchdenser than air and there is a greater mass of itto be pulled downward. At the deepest part of theocean the water pressure is just over 1,000,000g/cm2 , or about 1,000 atmospheres. Living crea-tures exposed to such atmospheres, both insideand out, are perfectly at ease under such condi-tions. (If, however, a deep-sea animal is lifted tothe surface, the internal pressure declines onlyslightly, while the external pressure declinesenormously. Its cells burst, and it dies. We our-selves would die for reverse reasons if pressuresupon us were greatly increased.)

If we consider the Earth's interior, the pressuresgo up still higher, for rock and metal are denserthan water, and the depths are greater (the col-umns of rock and metal weighing down uponlayers below are longer than the columns of airweighing down upon the surface of the Earth orthe columns of water weighing down upon thesea bottom).

Thus, at a depth of 2,200 kilometers, one thirdof the way to Earth's center, the pressure is al-ready 1,000,000 atmospheres or a thousand timesthe pressure in the deepest part of the ocean. Ata depth of 4,000 kilometers it is 2,500,000 atmo-spheres. At the center of the Earth it is possiblyas high as 3,700,000 atmospheres. This enormouspressure forces the liquid core to stiffen intosolidity at the very center despite its enormoustemperature, so that within the central liquidnickel-iron core there is a small central solidnickel-iron core.

COMPRESSED MATTER

Naturally, once again Jupiter displays evenmore extreme conditions. Its central region holdsup columns of material eleven times as deep asEarth's core does (though the material of Jupiteris less dense than our own) and withstands apressure of as much as 10,000,000 atmospheres.

RESISTANCE TO COMPRESSION

What is it about the material in the interiorof the worlds that makes it possible for them towithstand such enormous pressures?

To answer that, let's consider a table on whosesurface we have placed an object, say a book.Earth's gravitation serves to pull the book down-ward. If the book were able to move freely, itwould fall in response to Earth's gravitation, andit would continue to fall all the way to the centerof the Earth if there were nothing to stop it.

But there is something to stop it: the table. Tobe sure, the table is also pulled downward, butit is stopped from falling by the floor it restsupon, which in turn is stopped from falling by thewalls of the building, which are stopped from fall-ing by the foundations, which are stopped-

If we concentrate on the book and the tableonly, why does not the book, in response to theEarth's pull, simply fall through the table?

It cannot. The book is made of atoms, and sois the table. The outskirts of all the atoms, both ofthe book and of the table, are made up of elec-trons. That means there is an electron surface,so to speak, to the book and an electron surfacealso to the table.

The two electron surfaces repel each other,

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and so much more intense is the electromagneticforce than gravitation that all the pull of thevast Earth cannot force the book through thetable against the resistance of those repelling elec-trons. In other words, the gravitational force iscountered by the electromagnetic force, and anequilibrium is achieved in which the book liesquietly on the table, neither passing through it inresponse to gravitational attraction nor risingabove it in response to electromagnetic repulsion.

If the weight of objects on the table is madegreat enough, however, if enough massive booksare piled upon it, the table will break at someweak point; the atoms making it up will pull apartat a point where the electromagnetic cement isweaker than elsewhere.

If the weight is on some other sort of object,a wax block for instance, the molecules of waxunder the pressure of the weight will slip andslide over one another very slowly. The wax blockwill deform, and the weight will sink into the wax-not into the substance, but down past theoriginal surface because the wax will flow out-ward to get out of the way. (Then possibly it willflow back over the weight.)

Both effects are produced in the Earth underthe weight of its own uppermost layers. There arecracks, for instance, that represent weak points inthe Earth's crust. In fact, the Earth's crust ismade up of a number of large plates foreverpulling apart, coming together, and rubbing side-ways against one another. A sudden motion of thematerial on one side of a crack against the ma-terial on the other is the equivalent of a suddenbreak under stress, and earthquakes result. Somedistance under the surface, where heat makes

COMPRESSED MATTER

the rock more capable of slowly deforming, waxfashion, the heated rock, or magma, can squeezeup through weak points in the harder layersabove and produce a volcanic eruption.

As one goes deeper and deeper into the Earth'sinterior, however, there is less chance for cracksand breaks, and deforming becomes slower. Some-thing else must happen to material at greatdepths and under great pressure. That somethingelse is compression.

In the laboratory scientists are most familiarwith the effects of increasing pressure in connec-tion with gases. Gases are composed of speedingmolecules that are separated from other mole-cules by distances that are large compared withtheir own size. If gases are compressed, the mole-cules are pushed more closely together, and someof the empty space is, so to speak, squeezed out.Gases are easily compressed into smaller volumesby pressure, then. Gases can be compressed to avolume of 1/1,000 their original volume or lessbefore all the empty space is squeezed out andthe molecules are in contact.

In liquids and solids, however, the atoms andmolecules are in contact already and thereforecannot be compressed as gases are, by havingempty space squeezed out. That is why whenliquids or solids placed under the kind of pres-sure that suffices to compress gases, nothingseems to happen to them. Liquids and solids aretherefore said to be "incompressible."

This is sufficiently true under ordinary condi-tions to make it possible for hydraulic presses towork and for steel girders to hold up skyscrapers.Nevertheless, it is not absolutely true.

If pressure is placed on liquids or solids, the

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atoms themselves are compressed; the electronsare driven inward toward the nucleus. This isdone even under the slightest pressures-that ofthe book on the table for instance. The outermostelectrons are driven inward along the plane ofcontact; the amount by which the electrons aredriven inward under the kind of pressures weencounter in everyday life is so microscopicallysmall, however, as to be immeasurable.

As atoms are compressed and the electrons aredriven inward closer to the nucleus, the intensityof the repulsion between the electrons of adjacentatoms (which are also driven together by thepressures) increases. It is rather like compress-ing a spring that pushes outward more and moreforcefully the more it is compressed. In eithercase a new equilibrium is reached. A pressurefrom without compresses the atom or the springuntil the return push from within increases to thepoint where it balances the pressure from out-side.

Although an immeasurable compression suf-fices for ordinary pressure, given enough pressurethe compression of atoms becomes measurableand the electrons are driven inward noticeably.This means that the atoms in substances underpressure take up less room, which means there ismore mass in a given volume-which is anotherway of saying that the density goes up.

We would expect, then, that in Earth's interiorthe densities of the substances making it upshould increase and be higher than they would beif those substances were on the surface under nopressure greater than that of the atmosphere.

Actually the density of Earth's substance doesincrease with depth and with the pressure upon it.

COMPRESSED MATTER

As soon as Cavendish worked out the mass of theEarth, it was immediately evident that the Earthcould not be the same density throughout, that ithad to be considerably more dense in the depthsthan on the surface.

The ocean has a density of 1 g/cm3, and therocks of the outer crust, though differing fromeach other in density, have an average densityof about 2.8 g/cm3 . Yet the Earth's overall aver-age density is 5.52 g/cm3 .

Since the outer layers of the Earth are lessthan 5.52 g/cm3 in density, the inner layers mustbe more than 5.52 g/cm3. To be sure, the interiorcore of the Earth consists of molten nickel-iron,and that is indeed denser than the outer rock.The density of iron, the major component of thecore, is 7.86 g/cm3 here at the surface. That, how-ever, is not quite enough to account for Earth'saverage density. What does account for it is therise in density through the action of pressure andcompression.

The Earth's mantle extends from nearly thesurface down to a depth of about 2,900 kilo-meters, about four ninths of the way to the center.Throughout its extent the chemical compositionof the mantle doesn't change very much, and asample of its substance on the surface would havea density of a little over 3 g/cm3. Its densitygrows steadily higher with depth, however, and atthe bottom of the mantle it is nearly 6 g/cm3. Theaverage density of the mantle is 4.5 g/cm3 .

At a depth of 2,900 kilometers, one passes fromthe rocky mantle into the liquid nickel-iron core,and there is a sudden rise in density, since ironis denser than rock. However, although iron hasa density of 7.86 g/cm3 at the surface, under the

65


pressure of the 2,900-kilometer-deep mantle thedensity of the core at its outer edge is about 9.5g/cm3 . This density rises further as one penetratesdeeper into the core, and at the very center of theEarth it is something like 12 g/cm8 . The averagedensity of the core is 10.7 g/cm 3. Even the maxi-mum density of the core, however, is still onlyabout half the density of osmium at Earth's sur-face. If the Earth's core were made of osmium,the pressure would bring its density to about30 g/cm3 .

(Earlier in the book I said that if the Earth hadan even density throughout, the gravitational pullwould decline steadily as we penetrated beneaththe surface and would reach zero at the center.Because of the changing density in Earth's in-terior this is not quite so. So much of the Earth'smass is concentrated in the relatively smallliquid core-which contains 31.5 percent of theEarth's mass in 16.2 percent of its volume-thatthe gravitational pull actually goes up slightly asone penetrates the Earth, In fact, by the time wefound ourselves, in imagination, on the boundarybetween the mantle and the core, the gravitationalpull on us would be 1.06 times what it is on thesurface. As, however, we penetrated the core, thegravitational pull would finally begin to decreaseand would reach zero at the center.)

At the center of the Earth atoms have onlyabout 85 percent of the diameter they would haveon the surface. The electrons have been drivenin about 15 percent of the way toward the centralnucleus, and that small inward push createsenough outward pressure to balance the veryworst the Earth's gravitational pull inward cando. This is another indication of how much more

COMPRESSED MATTER

intense the electromagnetic force is than thegravitational force.

STARS

We see, then, that all objects up to the size ofJupiter at least are stable, thanks to the electro-magnetic force.

To begin with, individual gas molecules, smallparticles of dust, and larger solid particles thatreach the size of pebbles, boulders, and moun-tains are all held together by the electromagneticforce only. The gravitational force of such smallbodies is so small in comparison that it can beignored.

By the time we begin to deal with objects thesize of large asteroids, the gravitational fields setup by these objects are beginning to pull the mat-ter of the objects inward with noticeable force.The inner regions come under measurable gravi-tational compression, therefore, and this is moreand more the case as the objects under consider-ation grow larger: Moon-Earth-Saturn-Jupi-ter. In every case the atoms of the object arecompressed until the level of compression pro-duces an outward push capable of balancing theinward gravitational pulL

The equilibrium thus established is an essen-tially permanent one.

Imagine a body like Earth or Jupiter alone inthe universe. The gravitational force and theelectromagnetic force in such a world would re-main at an eternal standoff, and the materialstructure of the body itself would remain, as faras we know, in its general overall condition for-

67


ever. There might be minor earthquake quiveringsas the substance of the planet made minor adjust-ments in its position. The planet might slowlycool off till it had no more heat, in the center oron the surface, and its oceans and atmospheremight freeze, but these are what would be called,from an astronomical standpoint, trivial changes.

The equilibrium is not, however, one betweenequals. Although the electromagnetic force is un-imaginably more intense than the gravitationalforce, it is the electromagnetic force that is theunderdog.

The electromagnetic force, huge and intensethough it is to begin with, works only through theindividual atom. Each individual atom deep in theinterior is compressed and can call for no help, soto speak, from its neighbors, who are all equallycompressed. When, therefore, the maximum re-sistance to compression is exerted by one atom,it is exerted by all under the same pressure. If thepressure is further increased, each atom and allthe atoms together come to the end of the row.

The gravitational force, however, incrediblyweak though it is to begin with, will build up in-definitely as more and more matter is grouped intoone place, as each bit of matter adds its owngravitational field to the whole. Though the resis-tance to compression can reach only a certainlimit, the forces producing the compression canincrease without limit.

The electromagnetic force resists compressionand supports (with groans, we might imagine)the pressures of Earth's layers as they are pulledinward by Earth's gravitational field. They sup-port (with more agonizing groans, in our fantasy)the much larger pressures of Jupiter's more

COMPRESSED MATTER

copious layers pulled inward by Jupiter's largergravitational field.

Well, then, what happens if we pile matter to-gether to make a heap even larger than Jupiter?May there not come a point where as the gravita-tional field becomes ever more intense and thepressures at the center ever greater, the atoms thatmust support it all would finally collapse-like atable that breaks at last under a too great weightplaced upon it?

But can we honestly say that heaps of matterlarger than Jupiter are possible? It may be that,for some reason, Jupiter is as large as an objectcan grow.

Of course not. Jupiter may be by far the greatestplanet we have observed, but we have, near athand, closer to us than Jupiter is, an object farlarger still-the Sun.

The Sun is as much larger than Jupiter asJupiter is than Earth. The Sun has a diameter of1,391,400 kilometers, which is 9.74 times asgreat as Jupiter's diameter. It would take nearlyten Jupiters side by side to stretch across the widthof the Sun. Compare this with the eleven Earthsside by side it would take to stretch across thewidth of Jupiter.

And whereas Jupiter is 317.9 times as massiveas Earth, the Sun is 1,049 times as massive asJupiter.

Another indication of the Sun's vast size incomparison with any of the planets, even Jupiter,rests with the matter of surface gravity. At thevisible surface of the Sun, the pull of its gravita-tional field is just 28.0 times that of the Earth's,or 10.6 times that of Jupiter's.

The escape velocity from the surface of the

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Sun is 617 km/sec, which is 55 times that of theEarth and 10.2 times that of Jupiter. In fact, evenat a distance of 149.5 million kilometers from theSun's center the escape velocity from the Sun isstill 40.6 km/sec.

Since 149.5 million kilometers is the distanceof the Earth from the Sun, it follows that theescape velocity from the Sun from a position onEarth is considerably higher than the escape ve-locity from Earth itself. This means that when asatellite is sent to the Moon, Mars, or Venus at avelocity great enough to free it from Earth's gravi-tational pull, it is not necessarily freed from theSun's gravitational pull. Such a satellite may notcircle Earth, but it does remain in orbit aroundthe Sun.

So far only two man-made objects have at-tained velocities that would set them free fromthe Sun as well as from the Earth, sending themhurtling out of the solar system. These are thetwo Jupiter probes, Pioneer 10 and Pioneer 11.This was accomplished by skimming the probesaround Jupiter and letting its gravitational fieldaccelerate them to the proper velocity (the escapevelocity from the Sun being, in any case, smallerat the distance of Jupiter than at our own dis-tance).

There are more important differences betweenthe Sun and Jupiter. Jupiter is much larger thanthe Earth, but it is still a planet. Both Jupiter andEarth are, at least on the surface, cold, and theywould be dark but for reflecting the light of theSun.

The Sun, however, is a star. It shines with alight of its own, bright and blazing.

Is it a coincidence that the Sun is far more

COMPRESSED MATTER

massive than any planet we know and that it isalso blazing with light? Or do the two go to-gether?

We might argue that size and light go togetherand do so in this fashion:

In coming together a world converts the ki-netic energy of the infall of its components intoheat, as we saw earlier in the book. The largerthe world, the greater the internal heat. The Earthis white hot at its center, and Jupiter is far hotterstill.

The Sun, then, being much larger than Jupiter,would also be much hotter in the center-hotenough, perhaps, so that the outer region wouldno longer serve as sufficient insulation to keepthe surface cold. We might argue that the in-ternal heat of an object the size of the Sun wouldbe enough to flow outward in sufficient quantityto keep the solar surface at the white-hot temper-ature of 6,000C.

The trouble with this view of the Sun and itsstructure is that it can easily be shown to be animpossible one.

The Sun, after all, is pouring out energy at avast rate, and it has certainly been doing it forall of recorded history. It seems to have been do-ing it for very many millions of years into thepast, judging from the record of life on Earththrough those past ages. Yet if all the energy theSun had was what it had gained through the ki-netic energy of its formation, then it simplywould not have had enough energy at its dis-posal to be the Sun we know.

In 1853 the German physicist Hermann Lud-wig Ferdinand von Helmholtz (1821-1894) triedto calculate how much kinetic energy would be

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required to supply the Sun's radiation. He decidedthat the Sun would have had to contract from amass of matter 300 million kilometers across toits present size in some 25 million years to pro-duce all the energy the Sun has expended in thattime.

At a diameter of 300 million kilometers, how-ever, the Sun would have filled the entire orbit ofthe Earth, which could then only be 25 millionyears old at the most. But this was impossible.Geologists and biologists were quite certain thatEarth was much older than that.

This meant that the Sun was actually gainingenergy from some source other than its own con-traction, that it was radiating away this energy aslight and heat, and that it could have continuedto radiate for the entire history of the Earth with-out getting any cooler. Throughout the nineteenthcentury, however, no source from which the Sunmight be gaining energy could be worked outwithout introducing difficulties that could not beexplained away.

The turning point came at the turn of the cen-tury, when the structure of the atom was workedout. The atomic nucleus was discovered, and itcame to be clear that there is energy packed in-side the nucleus in amounts far greater than ex-ists among the electrons, from which the morecommon forms of energy are derived.

The Sun is not, therefore, a ball of ordinaryfire at all. It is a ball of nuclear fire, so to speak.Somewhere in its center the energies made avail-able by the nuclear force, a thousand times moreintense than the electromagnetic force, are some-how being tapped.

COMPRESSED MATTER

DEGENERATE MATTER

The average density of the Sun is 1.41 g/cm8 ,a value just a trifle higher than that of Jupiter.This is a density associated with liquids or solidsmade up of the lightest varieties of atoms. It isdefinitely not associated with gases. Even thedensest gas on Earth has a density of only a littleover 1/100 that of the Sun.

What's more, the figure of 1.41 g/cm8 repre-sents only the Sun's average density. Deep withinthe Sun its substance, under the huge pressureof the layers above, which are pulled downwardby the Sun's enormous gravitation, must be com-pressed to a density considerably greater thanthe average.

To be sure, the Sun's outermost layers areclearly gaseous, since for one thing we can see,through the telescope, great gouts of glowing gasshooting upward from the surface. What's more,the surface temperature of the Sun is 6,0000C,and no known substance can remain liquid orsolid at that temperature under ordinary pres-sures.

The interior of the Sun must be considerablyhotter than the surface, but the pressures mustbe enormous. It seemed natural even as late asthe 1890s to suppose that under those pressuresthe solar substance was compressed into white-hot solids or liquids and that this accounted forthe Sun's high density. (This is now known tobe true of Jupiter.)

Close consideration of the properties of the Sunin the first quarter of the present century, how-ever, made it clear that it behaves as though it

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were gaseous throughout, even at its very center.This would have seemed absolutely impossible tothe scientists of the 1890s, but a generation laterit seemed quite natural because by then knowl-edge had been gained of the interior of the atom.It came to be understood that the tiny atom is aloose structure of particles far tinier still.

This is the way it came to appear:Atoms are compressed at the center of the

Earth, and the expansive force of these com-pressed atoms is great enough to hold up all thesubstance of the overlying layers of the planetlike so many miniature Atlases. The atoms areeven more compressed at the center of Jupiter,and these can therefore hold up the far greatermass of that giant planet.

Even the little Atlases have their breakingpoint, however. The mass of the Sun, a thousandtimes as great as that of Jupiter, under the in-ward pull of an enormous gravitation reach andpass the limits of strength of intact atoms. Thepressure at the center of the sun is equal to100,000,000,000 atmospheres, or 10,000 timesthat of Jupiter.

The steady accumulation of matter strengthensthe gravitational intensity to the point where itovercomes the electromagnetic force that keepsatoms intact, and those atoms, so to speak, cavein.

The electron shells are smashed under pres-sure, and the electrons can move about uncon-strained by the shells. They push together to forma kind of unstructured electronic fluid, taking upfar less room than they would as part of shells inintact atoms. As they push together, the electro-magnetic repulsion between them increases fur-

COMPRESSED MATTER

ther; the electronic fluid can withstand a fargreater gravitational compression than intactatoms can.

Within the electronic fluid, nuclei can movefreely and can approach each other more closely,as closely as chance dictates. They can even col-lide with each other.

In ordinary atoms, as they exist on Earth oreven in the center of Jupiter, the electron shellsact as "bumpers." The electron shells of one atomcannot be very far interpenetrated by those ofanother; and as long as the nuclei must remainat the center of these shells, they are kept rel-atively far apart. Once the electron shells aresmashed and the electrons compress into themore compact electronic fluid, the average sep-aration of the nuclei decreases considerably.

Matter in which the electron shells are brokenand in which the nuclei move about in an elec-tronic fluid is called degenerate matter. Degen-erate matter can be much denser than ordinarymatter. It is the nuclei that make up the reallymassive portion of matter, and it is they that arethe true contributors to the mass of any object.If they are forced closer together in degeneratematter than in ordinary matter, there is muchmore mass per volume in the former and, there-fore, a much higher density.

Despite this high density, however, the nuclei,taking up only a millionth of a billionth of thevolume of intact atoms, can still move aboutfreely, just as atoms or molecules do in ordinarygases. Degenerate matter, despite its high den-sity, therefore acts as a gas and has propertiescharacteristic of a gas-a "nuclear gas," if youwill.

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The first discussion of this concept of the Sunas gaseous throughout came in 1907 in a bookby the Swiss astronomer Jacob Robert Emden(1862-1940). The idea was fleshed out and givensubstance in 1916 by the English astronomerArthur Stanley Eddington (1882-1944).

He reasoned that if the Sun were a ball of gasthroughout, with ordinary atoms in the outerlayers and smashed atoms in the inner layers, itought to act like any other gas. When gases arestudied in the laboratory, there is always a bal-ance between any force tending to compress thegas and the temperature of that gas tending toexpand it.

In the Sun the gravitational pull must there-fore also be countered by the internal temperatureof the Sun. The size of the Sun's gravitationalfield and of its compressing effect was known.Eddington set about determining how high thetemperatures in the Sun must be to produce anexpansive effect that would counter it.

The results were astonishing. The enormouscompressions produced by the Sun's gravitationresults in a density of the Solar material at thecenter that must be in the neighborhood of 100g/cm3 , four times as dense as the densest ma-terial on Earth's surface. Yet the Sun, even withso dense a core, behaves as though it were a gasthroughout. The central temperature of the Sunis 15,000,000GC. It takes that high a temperatureto keep the Sun expanded sufficiently to producean overall density of only 1.41 g/cm3 in the faceof its gravitation. (The puzzle about that density,you see, is not that it is so great, but that it is sosmall.)

And what is it that produces so enormous a

COMPRESSED MATTER

temperature at the Sun's core? It was clear byRutherford's time that only nuclear energy wouldsuffice. Nuclear reactions, in which nuclei absorb,give off, and transfer hadrons, produce muchmore energy than the chemical reactions we arefamiliar with, in which atoms absorb, give off,and transfer electrons. The former involves thenuclear force, which is much more intense thanthe electromagnetic force involved in the latter.

The next question, then, was just which nu-clear reactions are involved in powering the Sun.

To answer that question, something had to beknown about the chemical constitution of theSun so that one might begin with a reasonablenotion as to which nuclei exist at the center and,therefore, which nuclear reactions are possible.

Fortunately, the chemical composition of theSun can be deduced from an analysis of its light.Light is composed of tiny waves, and sunlightconsists of a mixture of light of every possiblewavelength.

Different atoms produce lights of particularwavelengths characteristic only of themselves,and on occasion they absorb light of exactly thosesame wavelengths. Sunlight can be spread outby an instrument called a spectroscope into aspectrum, in which all the wavelengths are ar-ranged in order.* In the spectrum are thousandsof dark lines representing wavelengths that havebeen absorbed by atoms in the Sun's outermostlayers. The positions of those lines in the spec-trum can be accurately determined, and from

* We sense different wavelengths of light as difference in color, andthe most spectacular example of a spectrum occurring in nature is therainbow.

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those positions the various kinds of atoms thatdid the absorbing can be identified.

As early as 1862 the Swedish physicist AndersJonas Angstrom (1814-1874) detected the pres-ence of hydrogen in the Sun. Knowledge of theSun's composition increased steadily, and in1929 the American astronomer Henry NorrisRussell (1877-1957) was able to work out theSun's composition in considerable detail.

About 90 percent of all the atoms in the Sun,it turned out, are hydrogen, and it thereforeseems plausible to suppose that the nuclei in thecenter must be predominantly hydrogen nuclei,which consist of single protons. Therefore, thenuclear reactions that would be required to sup-ply the vast stores of energy the Sun constantlyradiates would most certainly have to involve thehydrogen nuclei. There just isn't enough of anyother kind of nucleus to account for all the en-ergy the Sun has been radiating away in its 5billion years of existence.

In 1938 the German American physicist HansAlbrecht Bethe (1906-) used knowledge gainedabout nuclear reactions in the laboratory to workout what might be going on in the Sun.

At the great pressures and densities of the Sun'score the hydrogen nuclei-protons-are veryclose together and are unprotected by intact elec-tron shells. At the enormous temperature of theSun's core they move with a speed far more rapidthan would be possible on Earth. The combina-tion of closeness and speed means that the pro-tons smash into each other very frequently andwith enormous force. Occasionally they remaintogether, fusing into a larger nucleus.

The details of what happens may be under

COMPRESSED MATTER

dispute in minor ways, but the overall resultsseem certain. At the center of the Sun hydrogennuclei fuse to form helium nuclei, the next mostcomplicated specimen. Four protons combine toform a helium nucleus, made up of four nucle-ons-two protons and two neutrons.

Here we have, then, a fundamental differencebetween a planet and the Sun.

In a planet the inward pull of gravitationresults in the compression of atoms, which pro-duces a balancing outward push by the electro-magnetic force.

In the Sun the much greater inward pull ofgravitation can no longer be countered by theatoms' resistance to compression, and the atomsshatter, so to speak, under the pressure. Instead,gravitation is countered by the expansive push ofthe heat produced by nuclear reactions that arenot possible in the lesser temperatures of plan-etary interiors.

No doubt there is some critical mass belowwhich atom compression is sufficient, and thebody is a planet; and above which the centralatoms shatter, a nuclear reaction is ignited, andthe body is a star. Somewhere in the range ofmass between that of Jupiter and the Sun theremust be that critical mass.

Undoubted stars are known which are muchsmaller in mass than the Sun. A star listed incatalogues as Luyten 726-8B is estimated to haveonly 25 the mass of the Sun, yet we can just seeit by the light of its own feeble blaze. Luyten 726-8B is only 40 times as massive as Jupiter, but itis a star and not a planet.

Indeed, Jupiter itself is suspect. It radiates offinto space about three times as much energy as

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it receives from the Sun. Where does that extraenergy come from?

It may be that Jupiter is still contractingslightly and that the kinetic energy of that con-traction is converted into heat. It may also bethat the atoms at the center of Jupiter are at atemperature and pressure that is bringing themto the edge of the breaking point, that a tiny bitof hydrogen fusion is taking place-just enoughto account for a little extra heat leakage from theplanet.

If that is so, Jupiter is at the edge of nuclearignition. There's no fear of actual ignition, ofcourse; it is not large enough and will stay for-ever only at the edge of ignition.

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RED GIANTS AND DARK COMPANIONS

THERE IS A DIFFERENCE between planets andstars that in the long run is more crucial than themere fact that planets are less massive thanstars, or that planets are cold and opaque andthat stars are hot and glowing.

Planets are in a state of essentially staticstability. The equilibrium between gravitation pull-ing inward and the electromagnetic field of com-pressed atoms pushing outward is a perpetualstandoff. It can, as far as we know, maintain it-self forever if there is no outside interference.Were it alone in the universe, Earth might befrozen and lifeless but its physical structure wouldpersist, perhaps forever.

Stars, however, are in a state of dynamic sta-bility, for a star maintains its structure at thecost of something within that is constantly chang-

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ing. The inward-pulling gravitation is, indeed,essentially changeless, but the outer push of tem-perature at the Sun's center, which balances thatpull, depends on nuclear reactions that consumehydrogen and produce helium. The Sun remainswhat it is only at the expense of steadily con-verting 600,000,000,000 kilograms of hydrogeninto 595,800,000,000 kilograms of helium everysecond. *

Fortunately there is such an enormous quan-tity of hydrogen in the Sun that even at this rateof conversion we need not fear anything drastichappening in the near future. The Sun has beenconsuming hydrogen in its nuclear furnace forsome 5 billion years, and even so there is enoughleft for at least 5 to 8 billion additional years.

But even 5 to 8 billion years is not eternity.What happens when the hydrogen is gone?

As nearly as astronomers can tell now fromtheir studies of nuclear reactions and of the na-ture of the various stars they can see, it seemsthat the dwindling of the hydrogen is the preludeto stark changes in a star's structure.

As the Sun, for instance, uses up hydrogenand accumulates helium at the center, the corewill contract further as heavier nuclei concen-trate the inner portion of the gravitational fieldstill further. The core will become denser andhotter. Eventually the heat of the core will beginto rise rather sharply, and the additional heat willforce the outer regions of the Sun to expand enor-mously.

Although the total heat of the Sun's outer re-gions will then be considerably greater than it is

* The missing 4,200,000,000 kilograms is converted into the radiationthat pours steadily out of the Sun in every direction.

WHITE DWARFS

now, it will be spread out over a vastly largersurface. Each bit of surface will have less heatthan it now does, and the new surface will becooler than the present surface is. Where the Sunhas a surface temperature of 6,000C right now,the surface of the expanded Sun will be no morethan 2,500oC. At that lower temperature it willgleam only red hot. This combination of vast sizeand ruddy glow gives this stage of a star's life his-tory the name of red giant. There are stars thathave reached this stage right now, notably Betel-geuse and Antares.

At its fullest extension the red giant into whichour Sun will evolve will be large enough to en-gulf the orbit of Mercury, or even that of Venus.*Earth will then be quite uninhabitable; life onthe planet would have become impossible in theearly stages of the Sun's expansion. (Perhaps bythen mankind, if it still exists, will have leftEarth for homes on planets circling other stars,or in artificial colonies built far out in space.)

By the time the Sun reaches its maximum ex-tension as a red giant, it will have been reducedto the last dregs of its hydrogen. The center ofthe Sun, however, will have by then becomehot enough (with a temperature of at least10,O00,0000 C) to cause the helium atoms thathad been formed from hydrogen atoms over thepast eons to fuse into still larger nuclei and thoseinto larger nuclei still until iron nuclei areformed, each made up of 26 protons and 30 neu-trons.

* Naturally, if a star Is larger than the Sun to begin with, it willexpand even farther. The star Antares is so large that if it were in theplace of the Sun, its giant sphere would include the orbits of Mercury,Venus, Earth, and Mars.


The amount of energy available from the fur-ther enlargement of nuclei is only about 6 percentof the amount originally available from the fusionof hydrogen to helium. Once iron is formed,moreover, matters come to a dead end. No moreenergy from nuclear reactions is available.

After the hydrogen is used up, therefore, andthe red giant is at maximum extension, its re-maining life as an object powered by nuclearreactions has to be less than a billion years-even considerably less.

And as the nuclear reactions dwindle and fail,there is then nothing to resist the inexorable in-ward pull of the gravitational field produced byits own mass. Gravitation has been waiting, pull-ing patiently and tirelessly for many billions ofyears, and finally resistance to that pull has col-lapsed, and the bloated Sun, or any red giant, cando nothing but shrink.

Shrink it does, and it is that which puts ussquarely on the high road to the black hole, withtwo stopping points where we must pause enroute.

The story of the first stopping point begins witha German astronomer named Friedrich WilhelmBessel (1784-1846). He was one of those whotried to measure the distance of stars and was infact the first to succeed.

Stars have a motion of their own (proper mo-tion), but it is very small indeed in appearancebecause they are so far away. (Think how muchmore slowly an airplane very high in the airseems to move against the sky as compared withone that is quite low.)

In addition to the proper motion, stars shouldseem to move in response to the change in angle

WHITE DWARFS 85

from which they are seen from the Earth as itmoves in its large elliptical orbit around the Sun.As the Earth moves around the Sun in this f ash-ion, a star should mark out, in reflection of thismotion, a very tiny ellipse in the sky (providedyou subtract the proper motion and other inter-fering effects). The farther the star, the smallerthe ellipse, and if the size of the ellipse (calledparallax) can be measured by very delicate workat the telescope, the distance of the star can bedetermined.

In 1838 Bessel announced that he had ac-complished the task for a rather dim star called61 Cygni, which, it turns out, is some 150 trillionkilometers from Earth. Even light, which travelsat a speed of 299,792.5 kilometers per secondcannot cover such a tremendous distance quickly.It takes light 11 years to travel from 61 Cygnito us; 61 Cygni is therefore said to be 11 light-years distant from us.

Bessel went on to try to determine the distanceof other stars, and he fixed on Sirius, which fora number of reasons seemed even closer than 61Cygni. For one thing Sirius is the brightest starin the sky, and this brightness might be due toits relative closeness.

Bessel carefully studied the position of Siriusnight after night and noted the manner in whichit very slowly moves relative to the other stars inthe course of its larger-than-average proper mo-tion. He expected the motion to shift in a certainway that would indicate the formation of anellipse in response to Earth's motion around theSun. This ellipse exists, but superimposed on ithe detected a wavering that clearly had nothing


to do with the manner in which the Earth movesabout the Sun.

After a careful analysis of Sirius's puzzling mo-tion Bessel concluded that it moves in an ellipseof its own and completes each turn of that ellipsein about 50 years.

The only thing that can make a star move inan ellipse like that is by having it respond to agravitational field. Nothing else was known inBessel's time that could do it, and nothing else isknown in our time either. What's more, a gravi-tational field large enough and intense enough tomove a star out of its path and force it into anellipse large enough to be measured at a greatdistance must originate in a mass large enoughto be another star.

Bessel could not see anything at all in theneighborhood of Sirius that would serve as thesource of a gravitational field, yet something hadto be there. He decided therefore that there wasindeed a starlike mass in the proper place, butit originated from a star that was not blazing butwas dark. It was a giant star-sized planet, so tospeak. Astronomers therefore spoke of the "darkcompanion" of Sirius.

Bessel went on to note that Procyon, anotherbright star, also has a wavy motion, and there-fore he concluded it also had to have a dark com-panion. It even seemed as though dark compan-ions might be fairly common but that this factwas masked by the impossibility of seeing themdirectly.

Nowadays we would be very suspicious of sucha conclusion. We know that any object with astarlike mass must ignite into nuclear reactionsat the center and blaze if it is to be anything at

WHITE DWARFS

all like our Sun. To be both starlike in mass andto be dark as well would require a set of condi-tions that are widely different from those we arefamiliar with in our Sun.

To Bessel and his contemporaries, however, adark companion was not mysterious at all. It wasa star that, for some reason, had stopped shining.It had used up its entire energy store (whateverthat might be, for Bessel had no way of knowingabout nuclear reactions) and was rolling on, aslarge as ever and with as large a gravitationalfield as ever, but it was cold and dark.

How could Bessel have guessed what an oddobject he had discovered? He certainly could nothave known its connection with red giants, sincethey had not yet been dreamed of in his time.

SUPERDENSITY

The darkness of the dark companions endedin 1862, thanks to the work of an American tele-scope maker, Alvan Graham Clark (1832-1897),Clark was preparing a lens for a telescope or-dered by the University of Mississippi just beforethe Civil War began. (Because of the war it couldnot be delivered, and it went to the Universityof Chicago instead.)

When the lens was done, Clark decided to giveit a final test by actually using it to look at thesky and see how good a job it would do. Hepointed it at the star Sirius in the course of thistest and noted a tiny spark of light in its vicinity,something that was not indicated as being thereby any of the star maps.

Clark at first assumed that the spark of light

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was the result of an imperfection in the lens andthat part of the light of Sirius was somehowbeing deflected. Further tests, however, showedthat there was nothing wrong with the lens. Norcould he do anything that would cause the sparkof light to disappear or change its position. Fur-thermore, that position happened to be exactlywhere Sirius's dark companion was supposed tobe at that time.

The conclusion was that Clark was seeing thedark companion. It was very dim, only about1/10,000 as bright as Sirius, but it was not alto-gether dark. Sirius's dark companion had becomeSirius's dim companion, and it is usually referredto now as Sirius B, while Sirius itself can be calledSirius A. Sirius is now called a binary, or doublestar system.

In 1895 the German American astronomerJohn Martin Schaeberle (1853-1924) detected aspark of light near Procyon. Its "dark compan-ion," was a dim companion, too, and is now calledProcyon B.

Actually this didn't seem to change mattersvery much in itself. It meant that if the com-panions are not totally dead stars, they are atleast dying stars; that although not totally dark,they are flickering out.

By the time, Schaeberle had seen Procyon'sdim companion, however, affairs were changing.

In 1893 the German physicist Wilhelm Wien(1864-1928) had shown that the nature of thelight emitted by any hot object (whether a staror a bonfire) varies with temperature. One canstudy the wavelengths of light emitted and thenature of the dark lines in the spectrum and

WHITE DWARFS

come to a firm conclusion as to the temperatureof whatever it is that is radiating light.

By Wien's law any star that is flickering outand is therefore cooling down on its way to dark-ness has to be red in color. Yet Sirius B andProcyon B are white-dim, perhaps, but white.

Just studying the companions by eye wasn'tgood enough. What was needed was a spectrumso that wavelengths and dark lines could be stud-ied in detail. That was not so easy, since the com-panions are so dim and are so near the muchbrighter stars, which tend to drown them out.

Nevertheless, in 1915 the American astron-omer Walter Sydney Adams (1876-1956) man-aged to pass the light of Sirius B through aspectroscope, producing a spectrum he couldstudy. Once he studied that spectrum, there wasno doubt that Sirius B is not flickering out. It ishot, almost as hot as Sirius A and considerablyhotter than our Sun.

Where Sirius A has a surface temperature of10,0000C, Sirius B has one of 8,0000 C. The Sun'ssurface temperature is only 6,0000 C.

From the temperature of Sirius A, we know howbright each little portion of its surface must be-four times as bright as an equal portion of theSun's surface. We also know how bright thewhole surface must be from its apparent bright-ness when seen from Earth at its distance of 8.8light years. We can calculate that it must radiate35 times as much light as the Sun does; and toproduce that much light (considering how mucheach bit of its surface produces), it must beabout 1.8 times as wide as the Sun is, or2,500,000 kilometers in diameter.

(By the turn of the century, you see, astron-

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omers were beginning to realize that the Sun,which had reigned as the most glorious of allheavenly bodies and upon whose energy all livingthings on earth depend, is, after all, a ratheraverage star and no more. Sirius A is twice aslarge as the Sun, nearly twice as hot, over thirtytimes as luminous. But then, we need not feeldeprived. If Sirius A were to replace our Sun inthe sky, it would be a brilliant light indeed-toobrilliant, for Earth's oceans would boil away, andEarth would before long become a dead world.)

The mystery was Sirius B, however. At its sur-face temperature every bit of Sirius B's surfacemust be giving off not very much less light thandoes an equal bit of Sirius A's surface. To ex-plain, then, why Sirius B should be so muchdimmer than Sirius A, we must conclude thatthere is less surface to Sirius B-a great deal lesssurface. At Sirius B's temperature, it must havea surface only 1/2,800 that of Sirius A.

To have that surface, Sirius B must have adiameter only %3 that of Sirius A, or 47,000kilometers. If this is so, then Sirius B is onlyplanetary in size, for it is roughly the size ofUranus or Neptune. It has only about % the diam-eter of Jupiter and only %0 Jupiter's volume. Ithas in fact a diameter only 3.7 times that of theEarth.

Adams's discovery meant that Sirius B was anentirely new class of star-one that is white hotin temperature and also of utterly dwarfish sizecompared with ordinary stars like our Sun. SiriusB is a white dwarf and, it soon turned out, so isProcyon B.

If Sirius B were not only planetary in size butplanetary in mass as well, there would be no way

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in which it could blaze away so hotly. Objects thesize and mass of Uranus or Neptune simply donot have the kind of pressures at their centersthat would suffice to ignite the nuclear fires.

There was no question, however, of Sirius Bhaving a planetary mass, whatever its size. Itcould not cause a large star like Sirius A to swervefrom its straight-line course, if it were not itselfstarlike in mass. At least not so marked a swerve.

From the known distance of Sirius A and SiriusB from ourselves, and from their apparent sepa-ration in the sky, we can calculate how far apartthey are. Sirius A and Sirius B are on the average3,000,000,000 kilometers apart, so that theiraverage distance from each other is a little largerthan that of the planet Uranus from our Sun.However, while Uranus takes 84 years to swingaround the sun, Sirius B takes only 50 years tocomplete its swing around Sirius A.

From this it can be calculated that the intens-ity of the gravitational fields of Sirius A andSirius B are 3.4 times those of the Sun andUranus. This means that Sirius A and Sirius Btaken together are about 3.4 times as massive asthe Sun and Uranus taken together (or the Sunalone, for Uranus adds so little to the Sun's massthat it can be ignored).

Actually, Sirius B does not swing around SiriusA. The two stars revolve around the center ofgravity of the system. You might imagine themas the two ends of a dumbbell whirling aboutsome point, the center of gravity, along thewooden stick connecting them. If the two ends ofthe dumbbell were exactly equal in mass, thecenter of gravity would be just midway betweenthem. If one were more massive than the other,

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the center of gravity would be nearer the moremassive one, and in proportion to the amount bywhich it were more massive.

In the case of the Sun and any of its planets,the Sun is so much more massive that the centerof gravity is always sufficiently near the Sun'scenter to make it reasonably correct to say theplanet revolves around the Sun. The same is truewhen we speak of the Moon revolving around theEarth-since the Earth is 81.3 times as massiveas the Moon and the center of gravity of theEarth-Moon system is 81.3 times as close to theEarth, therefore, as to the Moon. The same is truewhen we speak of any other planet-satellite sys-tem among the Sun's family of worlds.

In the case of Sirius A and Sirius B, however,the mass is split more nearly equally, so the cen-ter of gravity is well out into the space betweenthem. Both stars circle that center, and boththerefore shift their positions considerably asthey revolve. (If this weren't so, Bessel wouldn'thave noticed a distinct waviness in Sirius's mo-tion across the sky.)

From the orbits of Sirius A and Sirius B thelocation of the center of gravity of the two starscan be determined. From the position of thatcenter of gravity relative to the two stars it turnsout that Sirius A must have 2.5 times the massof Sirius B. Since the total mass of the two starsis 3.4 times that of the Sun, we see that SiriusA, that gorgeous star in our sky, has by itself 2.4times the mass of our Sun, while Sirius B, thatunnoticeable spark, has a mass just a trifle lessthan that of our Sun.

That Sirius A should be 2.4 times the mass ofour Sun is not surprising at all. After all, it is

WHITE DWARFS

larger, hotter, and brighter than our Sun. SiriusB, however, is clearly abnormal. With a size ofUranus or Neptune, it has a mass about equalto our Sun's.

That means it must be very dense indeed. Itsaverage density must be something like 35,000g/m3 , which is 3,000 times as dense as the ma-terial at the Earth's core, and 350 times as denseas the material at the Sun's core.

At the time that Adams worked out the size ofSirius B this was a real stunner, since it washard to accept densities of that sort. And yet, fouryears before Adam's discovery, Rutherford hadworked out the structure of the atom and hadshown that most of its mass is concentrated inthe ultratiny nucleus. Nevertheless, scientists hadby no means gotten used to the notion, and thethought of broken atoms, with the parts of itshrinking far closer together than is ever possiblein intact atoms, was hard to swallow. There wasconsiderable skepticism, therefore, about the pos-sibility of the existence of such white dwarfs.

EINSTEIN'S RED SHIFT

Soon after Adams's discovery, however, a pos-sible way of checking the matter from a com-pletely different direction was worked out.

In 1915 the German Swiss physicist AlbertEinstein (1879-1955) published his generaltheory of relativity. This represented an entirelynew outlook on the universe as a whole. Accordingto this new theory there ought to be some phe-nomena that could be observed that would not bepossible if the older outlooks were correct. For

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instance, when light is radiated by a massivebody, the strong gravitational field of the bodyshould, according to general relativity, have someeffect on the light.

Einstein, building on the work done in 1900 byanother German scientist, Max Karl Ernst LudwigPlanck (1858-1947), had shown that light couldbe viewed as consisting not only of waves, butof waves that are gathered into packets that insome ways act as particles. These light-particlesare called photons, from a Greek word meaning"light."

Photons have a mass of zero when at rest andtherefore do not act as a source of a gravitationalfield, nor do they respond to one in the ordinaryfashion. However, photons are never at rest butalways travel (in a vacuum) at a particular pre-cise speed-299,792.5 kilometers per second. (Sodo all other massless particles.) When travelingat this speed, photons possess certain energies;and although the action of a gravitational fieldcannot alter the speed of photons in a vacuum(nothing can), it can shift the direction in whichthe light is traveling, and it can decrease theenergy.

The shifting of direction was observed in 1919.On May 29 of that year a total eclipse of the Sunwas visible from Principe Island, off the coast ofAfrica. Bright stars were visible in the sky nearthe eclipsed Sun, and their light on its way toEarth skimmed past the Sun. Einstein's theorypredicted that this light would be bent veryslightly toward the Sun as it passed, so that thestars themselves, sighted along the new direction,would seem to be located very slightly fartherfrom the Sun's disk than they really were. The

WHITE DWARFS

positions of the stars were carefully measuredduring the eclipse and then again half a year later,when the Sun was in the opposite half of the skyand could exert no effect at all on the light fromthose same stars. It turned out that the light be-haved as Einstein's theory had predicted it would,and that went a great way toward establishing thevalidity of general relativity.

Naturally astronomers were anxious to makefurther checks on the theory. What about the lossof energy of light in a gravitational field? Lightleaving the Sun must do so against the pull ofsolar gravitation. If the photons were ordinaryparticles with mass, their velocities would de-crease as they rose. Since photons have a restmass of zero, that doesn't happen, but each pho-ton loses a little of its energy just the same.

This loss of energy ought to be detected in theSun's spectrum. The longer a wavelength a par-ticular photon has, the smaller its energy. Inthe spectrum, where light is arranged in orderof wavelength from violet (with the shortestwavelength) to red (with the longest), there isa smooth progression from the high energy ofviolet to the low energy of red.

If sunlight loses energy because it rises againstthe pull of gravitation, every bit of it should endup slightly closer to the red end of the spectrumthan it would if there were no gravitational effect.Such a red shift could be detected by studyingthe dark lines in the solar spectrum and com-paring their positions with the dark lines in thespectra of objects that are subjected only to smallgravitational effects-in the spectra of glowingobjects in laboratories on Earth for instance.

Unfortunately there was no point in looking

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for this Einstein red shift in the solar spectrumbecause the effect is so tiny that even the Sun'smighty gravitational field won't produce enoughto measure.

But then Eddington (who was working out theinternal structure of the Sun and who was veryenthusiastic about the theory of relativity)pointed out that if Sirius B is really both as mas-sive and as tiny as it seemed to be, that might bethe answer. It is not just the overall gravitationalpull that affects light as much as it is the inten-sity at the surface, where the light is given offand where it makes its initial jump into space.

Now, the intensity of the Sun's gravitationalfield is 333,500 times that of the Earth's, butthe Sun's surface is so far from its center that theSun's surface gravity is only 28 times that of theEarth.

What about Sirius B? It has the mass of theSun compressed down into an object the size ofUranus. It has the same gravitational intensityas the Sun has, but you can get much closer tothe center of Sirius B by standing on its surface(in imagination only, of course) than you couldever get to the Sun's.

The surface gravity of Sirius B is, therefore,about 840 times that of the Sun and 23,500 timesthat of the Earth. The Einstein red shift shouldbe much more pronounced in the light leavingSirius B than in the light leaving the Sun.

Eddington suggested to Adams, who was theSirius B expert, that he study the spectrum of itslight again to see if he could detect the red shift.In 1925 Adams tried the experiment and foundthat indeed he could detect the red shift and pre-

WHITE DWARFS

cisely to the extent that Einstein's theory hadpredicted.

Not only did this provide another importantverification of general relativity, but if the theorywas correct, it provided a strong piece of evidencethat Sirius B is indeed as massive and as tiny asAdams had maintained, since only so can it haveenough surface gravity to produce the red shiftthat was observed.

In 1925, therefore, the existence of whitedwarfs had to be accepted. There has been nodoubt about it since.

The enormous surface gravity of Sirius B im-plies an enormous escape velocity. From the sur-face of Earth a missile hurled into the sky withno source of energy other than the initial impetusmust start with a minimum velocity of 11.23km/sec if it is to leave Earth permanently. Fromthe surface of the Sun the escape velocity is 617km/sec. From the surface of Sirius B the escapevelocity is about 3,300 km/sec.

Even 11.23 km/sec is a rapid velocity byearthly standards. A velocity of 3,300 km/sec is,however, enormous. It is 1/g9 as fast as the speedof light.

FORMATION OF WHITE DWARFS

Let's look again, now, at what will happen afterour Sun reaches the red giant stage and uses upall the nuclear energy in its interior. The gravi-tational pull, being then unopposed by the ex-pansive effect of heat, will begin to shrink theSun (as it seems to do now with other stars that


are in that stage) to some point where gravita-tion is opposed by something other than heat.

As it shrinks, it will gain density till it reachesthe point where it might be composed of intactatoms in contact, as planetary bodies such asEarth and Jupiter are. A star-sized mass, how-ever, produces a strong enough gravitational fieldto smash such intact atoms. Thus, the shrinkingwill continue. If it is to be stopped at all, thatstopping must be done by the subatomic particlesthat make up atoms.

What are those subatomic particles, and inwhat manner do they change as the Sun (or anyother star) ages?

To begin with, the Sun, or any star, is mostlyhydrogen. Hydrogen consists of a nucleus madeup of a single positively charged proton that isbalanced by a single negatively charged electronmaking up the rest of the atom.

As the Sun ages, its hydrogen little by littleundergoes fusion, four hydrogen nuclei fusing toform a single helium nucleus. Since a heliumnucleus is made up of two protons and two (elec-trically uncharged) neutrons, we may say thatwhen all the hydrogen has fused and is gone,half the protons in the star have changed to neu-trons. As helium nuclei undergo further fusionduring red-giant formation until finally iron nu-clei are formed, a few more protons are con-verted to neutrons, and in the end the star is a4%5 mixture of protons and neutrons.

What happens to the electrons meanwhile?Every time a positively charged proton is con-

verted to an uncharged neutron, something has tobe done with that positive charge. It cannotvanish into nothing all by itself. Instead, it is

WHITE DWARFS

ejected from the fusing nuclei along with a mini-mum amount of mass. This minimum amount ofmass is enough to produce a particle exactly likethe electron except that it carries a positive elec-tric charge instead of a negative one. This posi-tively charged electron is called a positron. Forevery four protons fused into a helium nucleustwo positrons are formed.

Once a positron is formed, it is sure to collidewith one of the electrons present in the Sun (andin all ordinary matter) in overwhelming num-bers. Although a positive electric charge cannotdisappear all by itself and a negative electriccharge cannot so disappear either, the two maycancel each other if they meet. When a positronand an electron collide, there is a mutual annihila-tion of both electric charge and mass, and the twoare converted into energetic photos called gammarays which possess neither electric charge normass.

In this way about half the electrons in the Sunwill have been destroyed in the course of its life-time as a normal star. The half that remains willbe enough to balance the half of the protons thathave remained as such.

In the conversion from protons to neutrons andin the mutual annihilation of electrons and posi-trons enough mass is lost to be converted into allthe vast quantities of radiation the Sun emits inits lifetime as a hydrogen-fusion reactor. Addi-tional mass is lost because the Sun is alwaysgiving off a stream of protons in all directions,the so-called solar wind.

All this loss is trivial compared to the Sun'stotal mass. By the time the Sun, or any star thatexists in isolation, has completed its red-giant

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period and is ready to shrink, it can have re-tained as much as 98 percent of its original mass;it is this mass that now begins to shrink.

Electrons, protons, and neutrons all have waveproperties as well as particle properties. Thegreater the mass of a particle, the shorter thewaves associated with it and the more pronouncedthe particle properties. The less the mass, thelonger the waves and the more pronounced thewave properties.

Protons are much more massive than electrons-1,836 times more massive. Neutrons are 1,838times more massive than electrons. Protons andneutrons are associated with very tiny waves andare pronounced particles of extremely small size.The electron is associated with comparativelylong waves and it therefore takes up much morespace than protons or neutrons.

As a star collapses, then, past the limit markedby intact atoms, it is the comparatively bulkyelectrons that are brought together in contact, soto speak, first.

Electrons driven into contact are much morecompactly packed than they would be in intactatoms. Thus, Sirius B and the Sun have aboutequal masses, but Sirius B takes up only 1/27,000the space that the Sun takes up. (It's somethinglike the difference in the space taken up by ahundred intact Ping-Pong balls and the spacetaken up by those same Ping-Pong balls brokenup into flakes of plastic.)

Nevertheless, even after the electrons havebeen brought into contact, the much smaller (butmore massive) protons and neutrons, and atomicnuclei made up of them, still find plenty ofroom for movement. These nuclei are much closer

WHITE DWARFS 101

together than they would be if they were part ofintact atoms, but they are still far enough apartso that the distances between them are very largein comparison with their own size.

As far as the nuclei are concerned, a white-dwarf star, dense as it is, is still mostly emptyspace. In Sirius B, for instance, which might al-most be considered as a continuous electronicfluid, the nuclei take up only 1/4,000,000,000its volume. The nuclei, therefore, show the prop-erties of gases.

Naturally a white-dwarf star is not of evenstructure all the way through, any more than anyother massive object is. There is increasing pres-sure as one moves, in imagination, from the sur-face to the center.

A white dwarf has an almost normal skin, anoutermost layer of intact atoms that are pulleddown hard by the intense gravitational pull at thesurface but don't have the weight of other layersabove them. A number of different kinds of atomscan exist in this white-dwarf "atmosphere"-even a small amount of hydrogen that has some-how, through all the life of the star, yet escapedfusion because those particular atoms never hap-pened to make up part of the stellar depths. Theatmosphere may be only a couple of hundredmeters thick.

As we imagine ourselves sinking down intothe material of the white dwarf, these atmos-pheric atoms gradually break down into electronsand nuclei, both moving freely. There, smalldregs of nuclear reactions go on till all the hydro-gen is used up. As we continue to move down-ward, the electrons move into contact and beginto resist further compression. The more tightly


they are compressed, the more strongly they re-sist further compression, and it is this resistancethat finally brings a halt to the contraction of thestar at the white-dwarf stage.

At the core the material of the white dwarf isconsiderably denser than average for the wholestar. The central density may be as high as100,000,000 g/cm3 .

When a white dwarf is formed, it is very hotindeed, since the kinetic energy of the infall hasbeen turned into heat. A white dwarf freshlyformed can have a surface temperature in ex-cess of 100,0000C.

As the white dwarf radiates heat into surround-ing space, however, its energy content must de-crease, and very little of that decrease can bemade up for by the nuclear reactions in the dregsof fairly normal matter that at first remain in itsouter layers. Gradually the white dwarf coolsdown. There are old white dwarfs known withsurface temperatures of not more than 5,0000C.

This loss of heat does not seriously affect thestructure of the white dwarf. Ordinary starswould collapse if they lost heat, since it is theheat produced in the center that keeps them ex-panded against the contracting pull of gravity. Awhite dwarf resists the gravitational inpull by theoutward push of the compressed electrons, andthis does not depend upon heat. The electronsresist further compression as efficiently whencold as when hot.

Presumably, then, the loss of temperature willcontinue, with no significant change in white-dwarf structure, until the white dwarf is nolonger hot enough to glow. It becomes a blackdwarf and will continue to cool further over the

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WHITE DWARFS

eons until its energy content is only the averagefor the entire universe-a few degrees above ab-solute zero.

This is a very slow process, and the entire life-time Qf the universe to date has not been longenough to have witnessed the total drainage ofenergy from any white dwarfs. All the whitedwarfs that have ever formed are still shiningtoday, but given enough time, they will fade.

So far, then, in this book we have discussedtwo kinds of eternal objects-objects, that is, thatcan resist the inward pull of gravity for indefi-nitely long periods of time. There are planetaryobjects, which are small enough in mass neverto have started a nuclear fire, and where gravita-tional compression is forever balanced by theoutward push of compressed intact atoms at thecenter.

There are also (or will be someday) blackdwarfs, which have sufficient mass to have starteda nuclear fire but which, in time, have burnedout, and where gravitational compression is for-ever balanced by the outward push of compressedelectrons.

All the objects we see in the sky outside ourown solar system, plus the Sun within our solarsystem, are not eternal objects. The ordinary starswe see are temporary structures burning theirway down to black-dwarf status (or, as we shallsee, other, even stranger objects) at last.

We can also see clouds of dust and gas ininterstellar space, but under the pull of their owngravitational field much of those clouds will even-tually condense to form stars and work their waydown to the black-dwarf status, also. Some of theclouds may condense into bodies too small in

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mass to ignite the nuclear fire, and they will thenbe planetary bodies. If any of the cloud escapescondensation and joins the thin vapor of indi-vidual atoms, molecules, and dust particles thatspread out between the stars and galaxies, thenthese may be considered separate ultratiny plan-etary bodies.

We remain, then, with planetary bodies andwith black dwarfs as the two classes of eternalobjects in the universe that we have so far dis-cussed in this book.

Several hundred white dwarfs have been ob-served, and that doesn't seem like much amongthe billions upon billions of stars in the sky. Re-member, however, that white dwarfs, althoughbright for their size, are nevertheless dim on thewhole. They are only 1/1,000 to 1/10,000 asluminous as are average ordinary stars and there-fore cannot be seen unless they are very close tous.

We see so few white dwarfs because at usualstellar distances, where ordinary stars are stillbright enough to see and study, white dwarfs aretoo dim to recognize, or perhaps even to see. Theonly way we can really judge the number of whitedwarfs, then, is by studying the immediateneighborhood of the Sun.

In the space within 35 light-years of the Sun,for instance, there are about 300 stars. Of these,8 are white dwarfs. If we assume that this isabout the usual proportion in space generally(and we have no reason to think it isn't), thenwe can say that somewhere between 2 and 3 per-cent of all stars are white dwarfs. There may beas many as 4 billion white dwarfs in our galaxyalone.

5- EXPLODINGMATTER

THE BIG BANG

WHY ARE THERE as many white dwarfs asthere are? Why are there 4 billion in our galaxyalone?

After all, a star doesn't become a white dwarftill it has used up all its nuclear fuel, and ourSun, for instance, still has enough nuclear fuelto last it for billions of years. This may also betrue of countless numbers of the 135 billion starsmaking up our galaxy. Why, then, have 4 billionof those stars run out of fuel, expanded, and thencollapsed?

Or suppose we look at it from the other side.Why are there so few white dwarfs? If billions ofstars have used up their nuclear fuel and col-lapsed, why have not all the stars done so?

In order to answer these questions we mustknow first of all how old the universe is and,therefore, how long ago stars were formed. We

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might then get an idea as to how long they havebeen fusing nuclei and how much remains to befused.

But how can we possibly tell the age of theuniverse?

The answer to that came, quite unexpectedly,out of a consideration of the spectra of stars.

By studying the spectra of stars it is possibleto tell whether a particular star is moving awayfrom us or toward us, and, in either case, howquickly. If the spectral lines are shifted towardthe red end of the spectrum, the star is movingaway from us. If the spectral lines are shiftedtoward the violet end of the spectrum, the star ismoving toward us.

Of course, we might ask how one can tellwhether the red shift of the lines is caused bymotion away from us or by a gravitational effectas described in the previous chapter. The answerto that is that most stars aren't dense enough toproduce a measurable red shift resulting froma gravitational effect. Therefore, unless there isreason to believe the contrary, every observedred shift is taken to be due to motion away fromus.

Naturally, some stars move away from us, andsome move toward us, so that red shifts andviolet shifts are about equal in number.

Beginning about 1912, however, astronomersbegan to study the spectra of the galaxies (whichare vast and distant collections of millions, orbillions, or even trillions of stars similar to ourown Milky Way Galaxy) that lie beyond our own.By 1917 it was clear that all but a couple of theclosest galaxies show a red shift and are there-fore receding from us. What's more, those red

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EXPLODING MATTER

shifts are larger than the ones associated withthe stars of our own galaxy.

As more and more galaxies were studied, itturned out that all the galaxies (except thatsame couple of the closest) have a red shift andthat the size of this red shift increases steadilythe farther the galaxies are from us.

Taking all this into account, the American as-tronomer Edwin Powell Hubble (1889-1953) in1929 advanced what is called Hubble's law. Bythis rule the rate at which a galaxy is recedingfrom us is directly related to its distance from us.That is, if galaxy A is receding from us at 5.6times the velocity of galaxy B, then galaxy A is5.6 times as far from us as galaxy B is.

The rate of increase of the galaxies' speed ofrecession with distance isn't easy to determine.At first astronomers thought that the speed in-creased rather quickly, but newer data has madeit seem that the increase is much smaller thanhad at first been thought. At present astronomersestimate that the speed of recession goes up 16kilometers per second for every million light-years of distance. For example, a galaxy that is10,000,000 light-years away from us is receding ata velocity of 160 km/sec, one that is 20,000,000light-years away from us is receding at a velocityof 320 km/sec, one that is 50,000,000 light-yearsaway from us is receding at a velocity of 800km/sec, and so on.

But why should this be? Why should all thegalaxies be receding from us, and why shouldthis speed of recession be proportional to distancefrom us? What makes us the key to the behaviorof the universe?

We aren't!

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As early as 1917 the Dutch astronomer Willemde Sitter (1872-1934) showed that from a theo-retical standpoint, using the equations of generalrelativity, the universe ought to be expanding.To be sure, individual galaxies and sometimes acluster of anywhere from dozens to thousands ofgalaxies are held together by gravitational pull.But galactic units (either single galaxies or clus-ters of them) that are separated from their neigh-bors by so great a distance that gravitation is tooweak to influence them sufficiently, partake of thegeneral expansion of the universe. This meansthat individual galactic units are all moving apartfrom one another at some constant velocity.

From a viewpoint on any one galaxy it wouldseem that all other galaxies (except those thatare part of the home cluster, if there is one) arereceding. What's more, the constant velocity ofexpansion builds up with distance, so we wouldend with Hubble's law no matter which galaxywe lived in.

If the galactic units spread out farther andfarther from one another as time moves forwardand the universe grows older, then, if we lookbackward in time (like turning a movie film sothat it runs the other way) we would see thegalactic units coming closer and closer to eachother. The universe is more compact, in otherwords, the younger it is; and if we go far enoughback in time, we can see how all the galaxiesmust have been crushed together in one vast col-lection of matter.

In 1927 the Belgian astronomer Georges Le-maitre (1894-1966) suggested that this was ac-tually so-that a certain number of billions ofyears ago the matter of the universe was all in

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EXPLODING MATTER

one place and formed a structure he called theprimeval atom. Others have called it the cosmicegg.

How long the cosmic egg existed, or how it wasformed, Lemaitre did not venture to guess, but atsome moment it must have exploded. This mustsurely have been the greatest explosion the uni-verse had ever experienced; it was the explosionthat created the universe as we know it. TheRussian-American physicist George Gamow (1904-1968) called it the big bang.

Out of the vast outward-speeding fragments ofthe cosmic egg, the stars and galaxies formedeventually, and it is because of the still felt out-ward force of the big bang that the universe isexpanding even today. In the last half centuryevidence for the big bang has accumulated, andnowadays almost all astronomers accept thethought that that is how the universe started.

The big question, though, is when the big bangtook place. Astronomers know (or think theyknow) just how rapidly the universe is expandingnow. If they assume that this rate of expansionhas always been the same and will always remainthe same, then, if we look forward in time, theuniverse will just expand forever and ever; thegalactic units will separate farther and farther.Finally an astronomer looking out at the universefrom Earth will see only our own galaxy andthose other galaxies that form part of our LocalCluster. Everything else will be too far off to see.

On the other hand, if we look backward in timeand assume that the universe will contract stead-ily at a uniform rate, it will come together intothe primeval atom 20 billion years ago.

However, the various galaxies do exert a gravi-

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tational force on one another. This may not besufficient to prevent the expansion, but it willtend to slow it. That means that as we look intothe future, the rate of expansion will growsmaller and smaller, and it will take longer thanwe think before all the distant galaxies outsidethe Local Cluster are lost to sight. Similarly, itmeans that as we look back into the past, thegalaxies come together faster and faster as gravi-tational pull becomes more and more important.Therefore, the time of the cosmic egg and the bigbang must be less than 20 billion years ago.

We are not sure by exactly how much thegravitational force in the universe is slowing therate of expansion. It depends on how much mat-ter there is (on the average) per volume of space-the average density of matter in the universein other words.

If the density is high enough, then the slowingeffect is great enough to bring that rate of ex-pansion to zero eventually. The expanding uni-verse will eventually be brought to a halt. Oncethat happens, the universe under the pull of itsown gravitational forces will begin to contract-at first very slowly, then faster and faster, till thecosmic egg is formed and explodes again. Thiscan happen over and over again, and we willhave an oscillating universe. The American as-tronomer Allan Rex Sandage (1928-) has sug-gested that a cosmic egg forms and explodesevery 80 billion years.

If the density of matter in the universe is justbarely high enough to bring the galaxies to a halt(a density equal to 6 x 10-3° g/cm3 , or about oneproton or neutron in every 350,000 cubic centi-meters of space), then the expansion is slowing

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at such a rate that the big bang must have takenplace about 13.3 billion years ago.

Actually astronomers are not yet certain justhow dense the matter of the universe is, on theaverage, so that we can't be sure exactly whenthe big bang took place or whether the universeis oscillating or not. At the present time the gen-eral feeling is that the average density is not highenough for oscillation, so that the big bang musthave taken place some time between 13.3 and 20billion years ago.

In this book let's make the reasonable assump-tion (subject to change as additional evidence isgathered) that the universe is 15 billion yearsold.

If the universe is 15 billion years old, thatmeans the stars themselves can't be more than15 billion years old.

They might be younger than that, however.The Sun, for instance, must be younger thanthat, or by now it would have consumed its nu-clear fuel, expanded to a red giant, and collapsedto a white dwarf.

Can it be, then, that white dwarfs are the rem-nants of very ancient stars that have been shin-ing since the beginning of the universe, whilethose stars that still shine by nuclear fusion wereformed much later and are much younger?

There is possibly something to that, but it can'tbe the whole answer. Many stars must have beenformed after the big bang, and if they had allreached the white-dwarf stage by now, therewould be far more white dwarfs in our galaxythan in point of fact there are. Then, too, con-sider Sirius A and Sirius B. It seems logical tosuppose that the two stars of a binary were

ill


formed at the same time (just as the Sun andthe planets must have been formed at essentiallythe same time), and yet one is a white dwarfand one isn't.

Can it be that age is not the only factor thatcounts? Do some stars burn nuclear fuel moreslowly than others? Or do some stars have morenuclear fuel to begin with than others? In eithercase, do some stars take longer to reach the stageof collapse than others?

The answer to this question, too, came fromthe studies of spectra.

THE MAIN SEQUENCE

To begin with, a star is born out of a mass ofdust and gas, which swirls slowly and which un-der its own gravitational pull comes slowly to-gether. As this mass of dust and gas (spreadthrough space in the wake of the big bang) comestogether, the gravitational pull becomes more andmore intense, so the process hastens.

As the cloud condenses, the temperature andpressure at the center get higher and higheruntil finally they become high enough to breakdown the atoms at the center and initiate nu-clear fusion. At this moment of nuclear ignitionthe developing star is born.

The period of condensation is not very longcompared to the total multibillion-year lifetime ofa star. The larger and more massive the cloud isto begin with, the stronger the gravitational pullat all stages and the less the time of condensa-tion. A star the mass of our Sun might takethirty million years to reach nuclear ignition,

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while a star with ten times the mass of the Sunmight condense to nuclear ignition in only tenthousand years. On the other hand, a star withonly one-tenth the mass of the Sun might take ahundred million years -to ignite.

Naturally, the stars we see in the sky have al-ready reached nuclear ignition. Once they havereached it, they continue to produce and radiateenergy at very much the same rate for a longperiod. The actual rate at which any star producesand radiates energy depends on how massive it is.

When Eddington worked out the temperaturesinside a star, he realized that the more massivea star, the stronger the gravitational force pullingit together. This meant that the more massive astar, the greater the internal temperature requiredto force it to remain expanded in the face ofgravity. The greater the internal temperature, themore energy will be produced and the more willradiate away from the star. In other words, themore massive a star, the more luminous it willbe. Eddington's rule is called the mass-luminositylaw.

If we study the stars we see, we find that theyform a regular sequence from very massive, veryluminous, very hot stars through stages of smallerand smaller mass, luminosity, and heat down tostars of very small mass, very little luminosity,and quite cool surfaces. This sequence is calledthe main sequence, since it constitutes about 90percent of all the stars we know of. (The other10 percent are unusual stars, such as red giantsand white dwarfs.)

The spectra of the stars of the main sequenceform a sequence of their own. As one movesalong the main sequence toward cooler and

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cooler stars, the spectra reflect the steadily lowertemperatures in the nature of the dark lines theycontain. The stars can therefore be divided intospectral classes according to the dark-line pat-tern.

The spectral classes into which the main-sequence stars are divided are 0, B, A, F, G, K,and M. Of these 0 is the most massive, the mostluminous, and the hottest; while M is the leastmassive, the least luminous, and the coolest. Eachspectral class is divided into subclasses numberedfrom 0 to 9. Thus we can speak of BO, B1, B2,and so on until we reach B9, which is followedby AO. Our own Sun is of spectral class G2.

In Table 9 the mass and luminosity of starsare listed by their spectral class.

Are these stars all equally common?The answer is no.

TABLE 9-The Main Sequence

Spectral Class Mass Luminosity(Sun = 1) (Sun = 1)

05 32 6,000,000BO 16 6,000B5 6 600AO 3 60A5 2 20FO 1.75 6F5 1.25 3GO 1.06 1.3G5 0.92 0.8KO 0.80 0.4K5 0.69 0.1MO 0.48 0.02M5 0.20 0.001

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In the universe generally, large objects are al-ways exceptional and are less common than smallobjects of the same category. There are fewer largeanimals than small animals (compare the numberof elephants to the number of flies), fewer largerocks than small grains of sand, fewer large plan-ets than small asteroids, and so on.

We might expect, then, that there are fewerlarge, massive, and luminous stars than there aresmall, light, and dim stars, and we would be right.The surveys that astronomers have made of thestars they can see and the deductions they havemade from these surveys lead them to supposethat nearly three fourths of all the stars in ourgalaxy fall into spectral class M, the dimmest ofall. The results, in detail, are presented in Table10.

TABLE 10-Spectral-Class Frequency

Spectral Class Percentage Number of Starsof Stars in Galaxy

0 0.00002 20,000B 0.1 100,000,000A 1 1,200,000,000F 3 3,700,000,000G 9 11,000,000,000K 14 17,000,000,000M 73 89,000,000,000

(We can assume, of course, that whatever holdstrue of our galaxy holds true for the vast majorityof other galaxies as well. We have no reason tothink that our own galaxy is particularly unusual.)

The next question is whether the stars of thevarious spectral classes take different times to

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consume their nuclear fuel, and whether sometherefore remain on the main sequence longerthan others and delay the inevitable expansion andcollapse.

If we assume, for instance, that all stars begintheir careers with a constitution that is mostly hy-drogen, the chief nuclear fuel, then we can see thatthe more massive a star, the larger the supply offuel it has. An 05 star, with 32 times the mass,and therefore the supply of nuclear fuel, that theSun has, might (we could assume) take 32 timesas long to consume its fuel and would thereforeremain quietly on the main sequence 32 times aslong as our Sun would, and, for that matter, 160times as long as an M5 star would.

However, stars don't consume nuclear fuel atthe same rate regardless of their masses. The moremassive a star, the more powerfully its own gravi-tational field compresses its matter and the hotterits core must be to balance that gravitational com-pression. The hotter the core must be, the morefuel must be consumed per second to maintainthat temperature. In short, the more massive astar, the more rapidly it must consume its nuclearfuel.

Eddington was able to show, in fact, that as weprogress from less massive to more massive stars,the rate at which they must consume their nuclearfuel increases much faster than the nuclear fuelsupply does. In short, though an 05 star maypossess 32 times as much nuclear fuel as the Sun,that 05 star must consume nuclear fuel over10,000 times as quickly as the Sun, and musttherefore consume its greater supply of nuclearfuel much sooner than the Sun consumes itssmaller supply. Reasoning in the same way, the

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EXPLODING MATTER 117

Sun must use up its nuclear fuel much morequickly than a dim M5 star with only one fifth thesupply that the Sun has.

In short, the more massive a star, the shorterit stays on the main sequence and the sooner itbecomes a red giant and then collapses. The life-span of the various spectral classes are given inTable 11.

TABLE 11-Lifespan on the Main Sequence

Spectral Class Lifespan(years)

0 1,000,000 or lessBO 10,000,000B5 100,000,000AO 500,000,000A5 1,000,000,000FO 2,000,000,000F5 4,000,000,000GO 10,000,000,000G5 15,000,000,000N0 20,000,000,000K5 30,000,000,000MO 75,000,000,000M5 200,000,000,000

Since it is the larger, and less common, starsthat collapse first, here is one explanation for therelative rarity of white dwarfs. No star of spectralclass K or M, which together make up 87 percentof all stars, has had a chance to use up its nu-clear fuel yet, even if each had been burning andradiating ever since the big bang. Only the 0, B,A, F, and some of the G stars can possibly have


left the main sequence, and they make up lessthan 10 percent of all stars.

Even so, we have not entirely explained therarity of white dwarfs. If all the stars in the Gal-axy had been formed soon after the big bang andnone had been formed since, there would be nostars in the Galaxy larger and more luminous thanthe smaller G-class stars. The brighter ones wouldall have expanded and collapsed. But this is notso. There are extraordinarily bright stars in thesky right now-even 0-class stars.

Clearly, the bright stars that now exist cannothave existed throughout the entire lifetime of theuniverse so far. They must have been formedcomparatively recently. Our own Sun (spectralclass G2), m1A be far younger than the universe,or it would be a white dwarf right now. As a mat-ter of fact, it seems to have been formed about 5billion years ago, when the universe was already10 billion years old. And there are places in theGalaxy where stars seem to be contracting towardnuclear ignition right now; and there will be starsforming a billion years from now.

For a long, long time there will remain lumi-nous, shortlived stars in the sky, coming andgoing, while the dwarf stars shine on steadily.

Still, if we assume the universe will expand f or-ever, then eventually all stars, even the smallest,will consume their nuclear fuel, expand, and col-lapse. And many trillions of years from now wemight suppose that the universe would consist ofonly two types of dark "eternal" bodies-blackdwarfs that are the cinders of stars and blackplanetary objects that were never stars.

But if we assume this is the end, will we beright? Does every object large enough to become

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a star end as a white dwarf cooling into a blackdwarf? Or are there objects in the universe evenstranger than the white dwarf?

Yes, there are odder objects still on the horizon.Remember we are heading toward the black holes.

PLANETARY NEBULAS

When a star collapses to a white dwarf, its mass,under the influence of its own gravity, pulls to-gether and contracts, growing smaller and smalleruntil the compressed electronic fluid at the corebecomes resistant enough to further collapse tobear up the weight of the layers of matter above it.

The more massive a collapsing star, the moreforcibly it will shrink and the more tightly it willcompress the electronic fluid.

To make still another analogy, this is rather likethe situation with the tires that hold up an auto-mobile. The weight of the automobile compressesthe air within the tires. The outward push of theair in the tires becomes greater the more it iscompressed, so that eventually it is compressedenough to bear the weight of the automobile. Ifyou then load baggage into the automobile, the airin the tires is compressed further until there isenough outward push to hold up the additionalweight. The more weight there is, the tighter theair within the tire is compressed.

If we think of this in connection with a star,we can see that it is quite likely that the moremassive a white dwarf is, the smaller it must bein size. Thus, a white dwarf star called VanMaanen 2 is only three-fourths as massive asSirius B. Therefore, it does not compress as tightly


and has a diameter about equal to that of Jupiter,or three times that of Sirius B. On the other hand,some comparatively massive white dwarfs are nolarger in volume than our Moon.

But how massive, and how small, can a whitedwarf get? After all, if. we load more and moreweight on a car, the time will come when the ma-terial of the tires will not be strong enough towithstand the greater and greater compression ofthe air. Eventually there comes a point where thetire blows.

Is there also a point where the core of the whitedwarf simply cannot hold up the mass pressingdown upon it. ,

The question was taken up by an Indian-Amer-ican astronomer, Subrahmanyan Chandrasekhar(1910-). In 1931 he was able to show that there isa certain critical mass (Chandrasekhar's limit)beyond which a white dwarf cannot exist, sincethe electronic fluid at that point cannot supportthe weight no matter how compressed it is. Thecore of such a star will simply collapse inward.

The critical mass, Chandrasekhar showed, is1.4 times that of the Sun. The limit could be alittle higher if a white dwarf were rotating rapidly,since then centrifugal force would help lift someof the mass upward. White dwarfs, however, donot seem to rotate fast enough to make this a sig-nificant factor.

Chandrasekhar's limit is not very high. All thestars of spectral classes 0, B, and A, together withthe more massive stars of spectral class F, havemasses that are more than 1.4 times that of theSun. These are also the stars with the shortestlifetimes, and examples of such stars formedin the early days of the universe have surely by

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now expanded and collapsed. Into what did theycollapse? Could some of them have collapsed intovery massive white dwarfs well beyond Chandra-sekhar's limit-thus proving Chandrasekhar'sanalysis to have been in error?

Conceivably so, but the fact is that all the whitedwarfs studied have proved to have masses lessthan Chandrasekhar's limit, and the more suchwe find, the better the limit looks.

Another alternative is that stars more massivethan Chandrasekhar's limit might at some stagebefore or during their collapse have lost some oftheir mass.

This may seem a rather farfetched alternative;how can a star lose mass? The fact is, though,that we know several ways in which a star canlose mass, and a particularly massive star is solikely to lose mass in one of these fashions that wemight as well consider the loss inevitable.

Consider the fact that every star will, when itsstay on the main sequence comes to an end be-cause its supply of nuclear fuel has dropped belowsome critical value, expand to a red giant and thencollapse.

The more massive the star, the hotter its coreby the time of expansion. The combination oflarger mass and greater heat produces a largerand larger red giant. Again the more massive thestar, the more rapidly it contracts when contrac-tion time comes, since the larger is the gravita-tional field that powers the contraction.

Suppose we consider a star, then, that is con-siderably more massive than our Sun and thatbloats up to a rather large red planet. The outer-most layers of the red giant, which are very farfrom the denser inner layers, are under a com-

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paratively feeble gravitational pull. When the starcontracts, then, the inner layers shoot down rap-idly, leaving the outer thinner layers behind. Thecontracting portion of the star heats up ferociouslyas the energy of contracting fall is converted intoheat. The heat blast strikes the outermost layers,falling inward comparatively slowly, and drivesthem outward again.

If a star is massive enough, then, and forms ared giant voluminous enough, only the inner por-tion of it may collapse while the outer portion maybe driven away as a turbulent shell of gas. In thatcase, although the entire star may be above Chan-drasekhar's limit, the portion that contracts maybe below it and may therefore form a white dwarf.

The result, then, is a white dwarf surroundedby a shell of gas. The white dwarf is very hot asit radiates away the vast energies of the rapid col-lapse, and the radiation is in the form of ultra-violet light and even more energetic radiations.The shell of gas absorbs this energetic radiationand reradiates it as a soft-colored fluorescence.

What we see from the Earth, then, is a star witha hazy ring around it. It is a shell actually, but theparts of the gas shell toward us in front of thestar and away from us on the other side are diffi-cult to see because we are looking through a smallthickness of it. On all sides of the star (visible tous), our line of sight is carried through the end ofthe shell, going through a relatively great thick-ness of material. The shell therefore looks like asmoke ring. The most remarkable example of thisis the Ring Nebula in the constellation of Lyra.

Such nebulas are called planetary nebulas be-cause the shell of gas seems to surround the staras though it were in a planetary orbit.

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About a thousand planetary nebulas are known,though, of course, many more must exist that wecannot see. Every one of the known planetary neb-ulas has a small, hot, dense star at the center-probably a white dwarf, though this has actuallybeen demonstrated in only a few of the cases.

If the central stars of planetary nebulas are in-deed white dwarfs, they must have been only re-cently formed, with, as yet, small chance to haveradiated much of the heat they have gained frominf all. And in point of fact, these are the starswith the hottest known surface temperatures,from at least 20,0000C to, in some cases, wellover 100,0000C.

The gas shells we observe seem to have, asnearly as one can tell, a mass equal to a fifth thatof our Sun, but larger shells may be possible, too.Some astronomers suggest that a star might losemore than half its mass in the form of a gas shell,and if that is so, a star up to 3.5 times the massof the Sun can lose enough mass through plan-etary-nebula formation to allow the collapsingcore to drop below Chandrasekhar's limit and forma white dwarf.

Naturally, the gas shell of the planetary nebula,having been driven outward by the energies of thecentral collapse, is moving outward from the star.The rate of this outward motion can be measured,and figures of 20 to 30 kilometers per second aretypical.

As the shell of gas moves farther and fartheroutward, it stretches out over a larger and largervolume, and its matter gets less and less dense.As it moves farther and farther away from thecentral star, any portion of the shell receives lessand less of the star's radiation and produces less

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and less fluorescence. The result is that the shellgrows dimmer and less visible as it enlarges.

In the typical planetary nebula the shell of gasis from a quarter to half a light-year from thecentral star, or about 500 times as far from thecentral star as Pluto is from our Sun.

It has taken perhaps 20,000 to 50,000 years ofexpansion for the shell to move out to this dis-tance, and this is a short time in the lifetime ofwhite dwarfs. The mere fact that the shell isvisible is therefore definite evidence that the whitedwarf formed quite recently.

About 100,000 years after white-dwarf forma-tion the shell of gas will have spread outward andthinned out to the point where it is insufficientlyluminous to be made out from our vantage pointon Earth. It may be, then, that those white dwarfsthat lack a shell of gas, lack it only because theyhave to be well over 100,000 years old.

But the formation of a planetary nebula is notthe only way in which a star can lose mass. Infact, there are a number of ways in which we canencounter exploding matter. The big bang may bethe largest and most magnificent manifestation ofthe phenomenon, but there are "little" bangs ofone sort or another that are yet enormous enoughto be of staggering grandeur.

NOVAS

Anyone watching the cloudless sky night afternight with the unaided eye is presented with whatseems to be a spectacle of unequaled serenity andchangelessness. So much has this changelessnessbeen considered a sign of security in the midst of

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the turbulent world during our recorded historythat any unusual alteration-an eclipse, a shoot-ing star, a comet-was apt to be viewed withfright.

These prominent changes, noticeable to anycasual observer, did not affect the stars, however.They were phenomena of our solar system. To anoccasional careful observer, though, changes ap-peared even in the starry universe. Occasionally anew star would appear in the sky where none hadbeen detected before. It was not a shooting star;it remained in place. But it was not a permanentresident, either. Eventually, it would fade out anddisappear again.

The greatest of ancient astronomers, Hippar-chus of Nicaea (190-120 B.c.), observed such anew star in 134 B.c. and was inspired to preparethe first star map in order that intruders be moreeasily recognized in the future.

A particularly bright temporary star appearedin November 1572 in the constellation Cassiopeia,and a Danish astronomer, Tycho Brahe (1546-1601), wrote a book about it with the title DeNova Stella (which in Latin means "Concerningthe New Star"). From this title the expressionnova came to be applied to temporary stars gen-erally.

In a way the name is a poor one, for the novasare not really new, and they are not truly starscreated out of nothing or out of nonstar material,which then return to nothing, or to nonstar ma-terial.

Once the telescope was invented in 1608, it be-came quite clear that there are uncounted millionsof stars that are too faint to be seen with the un-aided eye. Some of these stars might, for some

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reason, grow much brighter for a short period oftime and then fade again. It could be that a startoo dim to be seen without the telescope mightbrighten to the point of visibility to the unaidedeye and then fade to dimness below the level ofordinary vision again. In the days before telescopesit would then seem that the star had come fromnowhere and returned to nowhere.

This notion would be much strengthened ifsome dim star were actually seen to brighten tothe level of ordinary vision, but it was not till 1848that a nova was actually caught in the act. AnEnglish astronomer, John Russell Hind (1823-1895) happened to be observing a dim star or-dinarily invisible to the unaided eye, when it beganto brighten. It reached a peak in the fifth magni-tude, by which time it was visible as a dim starto anyone looking at the proper spot in the sky.Then it faded.

Once photography was invented, portions of thesky could be photographed at different times, andcomparisons would show whether any star hadchanged brightness. More novas could be detectedin that way; they would not have to be caught inthe actual act of brightening. They did not proveto be as uncommon a phenomenon as had earlierbeen thought. It is now estimated that there mightbe as many as 30 novas per year on the averagein our galaxy.

But what causes a nova?Whatever it is, it must be something violent.

The star that becomes a nova can become thou-sands or even tens of thousands of times as brightas it was to begin with. What's more, the increasein brightness can take place very rapidly-in aslittle as a day, or less. After the peak brightness is

EXPLODING MATTER

reached, the decline is never quite as fast as therise. As the star dims, the rate of further dimmingdecreases, so that in the end it may take years toreturn all the way to its prenova state.

The sudden explosive increase in brightness isvery likely, then, to be explosive in the literalsense. A close study of the spectrum of novasmakes it seem as though shells of gas are emittedby such stars.

Can a nova be a planetary nebula in the mak-ing? Can the nova explosion be the last gasp ofbrightness just before a star collapses to a whitedwarf ?

Probably not. Before the white dwarf forms, thestar should be at the red-giant stage; yet when astar forming a nova has happened to be observedbefore it became a nova, it did not seem to be ared giant. Besides, the mass of gas ejected by anova is only about 1/50,000 the mass of our Sun.A planetary nebula does at least tens of thousandsof times as well.

Can we expect other kinds of explosions thanthose forming planetary nebula?

The chances might seem dim at first. After all,most stars seem to be rather stable-as our Sunis, for instance. The gravitational inpull and thetemperature outpush are in balance, and a starlike our Sun can shine for billions of years with-out any sudden changes in size or temperature atall. There are sunspots, which slightly cool theSun, and flares, which slightly heat it, but thechanges are very small and are microscopic incomparison to those changes that take place innovas.

Not all stars, however, are as stable as the Sun.There are, for instance, stars whose brightness

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varies continually, sometimes with rhythmic regu-larity. This can be because a bright star is partiallyor wholly eclipsed by a dimmer companion thatin its orbit around the bright star passes periodi-cally between it and us.

At other times the variation is due to changes inthe star itself.

In 1784 a Dutch English astronomer, JohnGoodricke (1749-1786)-a deaf-mute who died atthe age of 21-noted that the star Delta Cephei(in the constellation Cepheus) varies in bright-ness. It isn't much of a change: It brightens frommagnitude 4.3 to 3.6,* then fades off to 4.3 again,and repeats this over and over. At its brightestDelta Cephei is only twice as bright as it is at itsdimmest, and this is not likely to be noticed with-out a telescope-and in fact, it wasn't.

The nature of the change, however, is a verystriking one. The star brightens rather quickly,dims more slowly, brightens rather quickly, dimsmore slowly, with great regularity, each cycle tak-ing 5.4 days. In the last 200 years, about 700stars with the same pattern of rather quick bright-ening and slow dimming over and over have beendetected in our galaxy, and all are called Cepheidvariables in honor of the first to be discovered.

Cepheid variables differ among themselves inthe length of their periods. Some have a period aslong as 100 days, and some have a period as shortas 1 day. (In fact, there are a special group ofvariable stars, very like the Cepheids, which haveperiods of 6 to 12 hours and are called RR Lyraestars after the first to be discovered.)

In 1915 the American astronomer Henrietta

* As brightness increases, the value of the magnitude decreases.

EXPLODING MATTER

Swan Leavitt (1868-1921) was able to show thatthe length of the period depends on the mass andbrightness of the star. The more massive andluminous a Cepheid variable is, the longer itsperiod.

Apparently Cepheid variables pulsate, and thatis the reason for their changing brightness. TheCepheid variable has reached a stage in its evolu-tion when the balance of gravitation and temper-ature is no longer smooth. The nuclear fuel supplyis perhaps fading to the point where the innertemperature begins to fail. The star therefore be-gins to collapse, but the very act of collapsing com-presses the interior of the star, speeds up thenuclear reactions, and raises the temperature.That forces the substance of the star outwardagain, and the very act of expanding thins theinterior and cools it so that a compression beginsagain.

The more massive a star, the longer it takes forthe swing in and out to go through a completecycle. This stage is probably short-lived on theastronomical scale, and after a while there will bethe final changes leading to expansion to red giantand then collapse.

Can it be that the novas are Cepheid variablesin which the pulsation has become extreme? Per-haps as the pulsations continue, they grow wilderand wilder until finally the expansion becomes ex-plosive and the outermost section of the Cepheidis blown off in a process that brightens the starvery temporarily, not twofold or threefold, but ten-thousand-fold or more. The loss of the mass mightcalm the Cepheid variable and return it to a stateof sober pulsation again, which, however, may

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after a time swing outward into explosivenessagain. There might be several explosions beforethe final expansion and collapse.

There are, indeed, stars that have been observedto be recurrent novas, which have exploded twiceor even three times in the short period of a littleover a century in which astronomers have watchedsuch stars closely. What's more, all the Cepheidvariables, even the smallest, are considerably moremassive than the Sun. They are large, bright stars-just the kind that would have to lose mass ifthey are to remain within Chandrasekhar's limitand be capable of forming a white dwarf.

It all seems to knit together, but the notiondoesn't stand up. A study of stars that go nova,both before they have done so and after they havefaded again, shows that they are simply not Ceph-eid variables. They are not even large stars; theyare small and dim, even though they have highsurface temperatures.

The combination of smallness and dimness withhigh surface temperatures suggests white dwarfs;yet white dwarfs are so compact and dense andhave such a high surface gravity that they mustbe very stable. How can they undergo an explosiveexpansion?

A suggestion, first proposed in 1955 by the Rus-sian American astronomer Otto Struve (1897-1963), that seems to be gaining favor is that everynova is a member of a close binary, one of twostars that circle each other at a relatively smalldistance. One of them, which we will call A, is thelarger of the two and therefore reaches the end ofits stay on the main sequence before its smallercompanion, B, does. As A expands toward the red-

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giant stage, some of its matter may spill over toB, which is as yet unexpanded. As a result B growsmore massive, and A grows less massive. A canthen shrink directly to the white-dwarf stage, with-out passing through a planetary-nebula stage, eventhough its mass might have been, to begin with,somewhat above Chandrasekhar's limit.

Eventually it is B's turn to leave the main se-quence, its lifespan having been shortened by itsgain of mass at the expense of A. As B expandstoward the red-giant stage, it returns the gift:Some of its matter spills over toward A, which isnow a white dwarf.

The surface gravity of A is extremely intense,and the matter it gains undergoes a sudden com-pression. Since the gained matter will containsome atoms capable of fusion, the compressionmay eventually produce a very rapid nuclear re-action once enough is gathered and once it issufficiently compressed. The nuclear reaction re-leases immense energies that produce a vast flashof light, which accounts for the sudden enormousbrightening we see as a nova, and the expulsion ofthe flashing gas. The nova can recur as additionalincrements of matter leak over from expanding B.

In this way B can eventually collapse to a whitedwarf, even though it had gained enough masswhen A expanded to bring it somewhat over Chan-drasekhar's limit.

Sirius A and Sirius B would be a good exampleof this scenario if they were closer together. Un-fortunately, their average separation is somewhatgreater than that of Uranus and the Sun, so theirimpingement on each other is limited.

When both were formed, perhaps a quarter of a

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billion years ago, the star that is now Sirius B musthave been the larger and brighter of the two, withperhaps three times the mass of the Sun; it wasshining over Earth (then in the age of dinosaurs)with a brightness equal to that of Venus.

Sirius B did not remain on the main sequencelong; it expanded into a red giant and then formeda planetary nebula with perhaps two thirds of itsmust have been captured by distant Sirius A,shifted outward into invisibility, but some of itmust have ben captured by distant Sirius A,whose brightness must have increased and whoselife must have shortened as a result. Had Sirius Abeen considerably closer to Sirius B, it would havepicked up much more of the outer layers of SiriusB and might have gained enough mass altogetherto have left the main sequence itself soon afterSirius B had. In that case it is possible that Siriuswould now be a white-dwarf binary.

As it is, Sirius A will expand to the red-giantstage sometime in the future, and then it will forma planetary nebula. Sirius B is bound to pick upsome of the gas shell, possibly enough of it to flareup as a nova. That should be quite spectacular tothe descendants of humankind who may then bealive and observing.

We now have two methods by which massivestars can get rid of sufficient mass to fall belowChandrasekhar's limit and form a white dwarf.These two methods-the formation of planetarynebulas and the shifting of matter between thepairs of a close binary-work for stars of onlymoderate size, up to three times the mass of theSun. Yet there are still more massive stars. Whatof them? Let us return to the question of novas.

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SUPERNOVAS

Before the days of the telescope the only novasthat were sure to be noticed were those which werevery bright.

The nova concerning which Tycho Brahe wrotehis book, the one that gave the phenomenon itsname, was an example of that kind. Tycho's novaat its peak of brightness was 5 to 10 times asbright as the planet Venus, and perhaps 100 timesas bright as the brightest stable star, Sirius.Tycho's nova could be seen in daylight, and bynight it could even cast a dim shadow that couldbe seen if the Moon were not in the sky.

Then, in 1604, another bright nova appeared inthe constellation Ophiuchus. This one was perhapsonly 1/30 as bright as Tycho's nova, but it wasstill some three times as bright as Sirius. No othernova has since appeared in the sky that has beenas spectacular as these two.

There was an earlier case of such a bright nova,however-one that appeared in July 1054 in theconstellation Taurus. There are no records of itsobservation in Europe, which was then just emerg-ing from a "dark age," during which astronomywas temporarily just about nonexistent. We haverecords, however, from astronomers in China andin Japan.

The 1054 nova, like Tycho's nova, was muchbrighter than Venus. In fact, the 1054 nova wasprobably the brighter of the two and could be seenin broad daylight for 23 days. It slowly dimmedafter it had reached its peak, but it was nearlytwo years before the dimming brought it down be-low the unaided-eye level.

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Why were these novas so much brighter thanother novas. A logical answer seemed to be thatthey just happened to be nearer to us than otherswere and therefore seemed brighter.

In 1885, however, a nova appeared in what wasthen called the Andromeda Nebula (nebula isfrom the Latin word meaning "cloud.") The "An-dromeda Nebula" is a hazy patch of light thatastronomers took for granted was a cloud of dustand gas within our own galaxy. The nova, whichthey assumed just happened to be in the directionof the cloud, wasn't a particularly startling one,for it only reached a maximum brightness of theseventh magnitude and was never bright enoughto see without a telescope.

However, as the Andromeda Nebula was ob-served closely in the years that followed, numerousnovas were found within its confines. That manynovas could not all be found in one direction; itwas too much to ask of coincidence. The notiongrew then that the Andromeda Nebula was a dis-tant group of stars, too dim to make out individu-ally, except when one went nova. Eventually, bythe 1920s, it was generally agreed that one shouldspeak of the Andromeda Galaxy, which is a galaxyfar outside our own, and even larger than ourown.

All the novas observed in the AndromedaGalaxy after the 1885 nova were exceedingly dimand were equivalent to the ordinary novas of ourown galaxy.

The 1885 nova was something else again. It hadto be much brighter than the ordinary novas ineither the Andromeda Galaxy or our own. It wasso bright that all by itself it had momentarilyshone nearly as brightly as all the Andromeda

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Galaxy beside. At its peak it was 10 billion timesas bright as our Sun and was 100,000 times asbright as an ordinary nova. It was what came tobe called a supernova, so the 1885 nova wasnamed, in hindsight, S Andromedae, the S stand-ing for supernova.

Once that was settled, it became clear that thebright novas of 1054, 1572, and 1604 were super-novas of our own galaxy.

Supernovas are much less common in occur-rence than novas are. Astronomers can see themnow and then, here and there, in one distant gal-axy or another. Once a supernova comes intoexistence, it is easy to detect. As soon as a starflares in some galaxy and reaches a peak bright-ness that makes it as bright as all the rest of thegalaxy together, an astronomer knows he has asupernova on his hands. It would seem that thereare, on the average, 3 supernovas per millenniumper galaxy, as compared with 30,000 ordinarynovas. In other words, for every ten thousandnovas there is one supernova.

It is difficult to study supernovas in detail whenthey are located in distant galaxies millions oflight-years away. A supernova in our own galaxywould be much more useful, but through a strokeof ill luck not one supernova has been visible tous in our own galaxy since 1604, so that no suchclose object has ever been investigated telescop-ically. In fact, in the four centuries since 1604,S Andromedae has been the closest supernova tobe observed.

It is clear that the supernova must represent anenormous explosion of a particularly large andmassive star. Nothing else could produce radiationat a rate 10 billion times that of the Sun.

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What's more, shells of gas are blown off by asupernova, shells that dwarf those produced byplanetary nebula in terms of both mass and en-ergy. The best-known example of this is in Taurus,at the site of the great supernova of 1054. Therewe have a large patch of glowing gas.

This patch was first observed in 1731 by theEnglish astronomer John Bevis (1693-1771). In1844 the Irish astronomer William Parsons, LordRosse (1800-1867), examined it closely with alarge telescope he had built and observed that thecloud is filled with irregular filaments that re-minded him of the legs of a crab. He called it theCrab Nebula, and that is the name by which it isknown to this day.

Close study of the gases of the Crab Nebulashows that they are still moving outward at a rateof about 1,300 kilometers per second. (That rateof outward movement, so much greater than inthe case of a planetary nebula, is itself evidenceof the incomparable power of the supernova ex-plosion.) Calculating backwards, it seems that allthe gas was back at the center just about the timeof the 1054 supernova.

Astronomers work backward in other cases. Ifthey find thin wisps of gas in the skies that seemto form part of a shell, they suspect that at onetime, in the center of that shell, a supernova hadexploded. From the speed of expansion of the shellthey can even estimate how long ago the super-nova glowed. Some 14 supernova, including the 3we know, seem to have exploded in our galaxy inthe last 20,000 years. If the number in our galaxywas about the same as in other galaxies, thereshould have been some 60 or 65. The 50 or so wedidn't see, however, must have been in distant

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parts of the galaxy, parts we can't see because ofthe interposition of the dust clouds that hide muchof it from our eyes.

Of the supernova remnants we can detect, thenearest seems to have been one in the constella-tion of Vela. That supernova, which has givenrise to a shell of gas called the Gum Nebula(named for the Australian astronomer Colin S.Gum, who first studied it in detail in the 1950s,and who died in a skiing accident in 1960) has acenter only 1,500 light-years away from us, ascompared with a distance of 4,500 light-years forthe Crab Nebula. The nearest edge of the GumNebula is only about 300 light-years from Earth.

The Vela supernova, which gave rise to theGum Nebula, flashed out some 15,000 years ago,when the Ice Age was just coming to an end. Atits peak, it may have been as bright as the fullMoon for some days, and we may envy those pre-historic human beings who witnessed that mag-nificent sight.

What happens to bring about a supernova?The more massive a star, the higher its internal

temperature at every stage in its evolution. Areally massive star reaches internal temperaturesthat smaller stars never do and never can, andwe must look for events that happen at those veryhigh temperatures to explain the supernova.

The Chinese American astronomer Hong-YeeChiu (1932-) has suggested one interesting ex-planation. The nuclear reactions in the core, hesays, give off two kinds of massless particles thattravel at the speed of light. One kind is the photon,which is the fundamental particle of light and oflightlike radiation. The other is the neutrino.

These two types of particles differ as follows:

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The photons are readily absorbed by matter, sothey are no sooner formed than they are absorbed.They are then reformed and reabsorbed an in-definite number of times, so they can move at thespeed of light only in the tiny, rare intervalsbetween formation and absorption. The result isthat it takes about a million years for photons totravel from the core, where they are formed, tothe surface, where they escape. The draining ofcentral energy by way of photons is thus verysmall, and stars, in giving off photons, radiatetheir energy in a slow, steady way and can there-fore last for billions of years.

The neutrinos that are formed do not react withmatter at all (or scarcely at all), and once formedin the core, they pass through the outer layers ofthe star at the speed of light as though nothingwere there. It takes about 3 seconds for neutrinosto travel from the core of our Sun to its surfaceand then fly out into space. It might take 12seconds for them to travel from the core to thesurface of the largest stars on the main sequence.Any energy given off in the form of neutrinos,then, would leak away almost at once.

In ordinary stars, however, the percentage ofenergy given off in the form of neutrinos is verysmall, so we usually need consider only the pho-tons.

Chiu suggests, however, that at extremely hightemperatures-say, 6 billion degrees-the kindsof nuclear reactions that take place begin to formneutrinos in large quantities. The Sun's internaltemperature right now is only about 15,000,000C,and it will never reach a temperature of 6,000,-000,000°C under any circumstances. Sufficientlymassive stars will do so, however, and when the

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critical point is reached where suddenly vast num-bers of neutrinos are being formed, all of themwill escape from the star in seconds, taking energywith them and draining the core of the energyrequired to keep the star expanded against the in-ward pull of gravity.

As a result the core of the star suddenly cools,perhaps within a matter of minutes, and the starcollapses with a precipitousness far beyond any-thing that can happen in planetary-nebula forma-tion.

In these masive stars, where the core is at the6-billion-degree mark and where the nuclei havebuilt up to the level of iron, the outer layers arestill relatively cool and are still made up of smallernuclei. As one imagines oneself moving outwardfrom the core, one passes through regions in thestar that are less and less evolved, that have moreand more of the smaller nuclei that can combineand yield energy and that are at lower and lowertemperatures, so that fusion reactions are not yettaking place. In outermost regions of the starthere may still even be plenty of hydrogen.

With the sudden, overwhelming implosion ofthe star the temperature as a whole is raised toenormous values because of the conversion ofgravitational energy into heat, and all the nuclearfuel remaining in the star fuses almost at once.This gives rise to the enormous explosion of thesupernova and enables the star temporarily toshine as brightly as an entire galaxy of stars.

In the fury of the explosion two things happen.First, many nuclei that are more complex eventhan iron are formed, for there is a temporary vastenergy surplus that makes the formation of suchnuclei possible. Second, the explosion drives vast


quantities of the star's matter outward as a shellof hot gases containing all the complex atoms thathave been formed, up to those with nuclei of asmuch as five times the size of iron nuclei. Over aperiod of thousands of years this matter graduallyspreads outward, thins, and becomes part of thevery thin gases of interstellar space.

Eventually new second-generation stars formout of the gases that are in part the remnant ofthese old stars.

First-generation stars, formed out of the pri-meval matter of the big bang, are almost entirelyhydrogen and helium, and so must their planetsbe. Nuclei more complex than helium are foundonly in the core of these stars, and there theyare likely to stay-except for supernova explo-sions.

Second-generation stars, like our own Sun, be-gin with complex nuclei that the supernovas havespread far and wide, added in small quantities tothe hydrogen and helium. The planets of second-generation stars, such as Earth, have those nucleias well. Life would be impossible without thoseelements more complex than helium, and all theatoms within our bodies, except for hydrogen,were once at the core of stars that exploded assupernovas.

The enormous explosion of a supernova candrive as much as nine tenths of a star's matterout into space, leaving only a small remnant ofitself to collapse and remain collapsed. It isn'thard to assume that a supernova would alwaysleave a remnant that is smaller than Chandrasek-har's limit, so that no matter how large or smalla star was, it could always shrink to a white dwarf-quietly if it was less than 1.4 times the Sun's

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mass, or with an explosion of steadily increasingferocity as it was more and more over that limit.

Since there are estimated to be three super-novas per millennium per galaxy, and since theuniverse is estimated to be about 15 billion yearsold, there may well have been about 45 millionsupernova explosions in our own galaxy during itshistory. If all of them gave rise to white dwarfs,they would represent about 1 percent of the totalnumber of white dwarfs estimated to exist in ourgalaxy.

That seems reasonable. We can suppose thatonly the very massive stars undergo a supernovaexplosion, while smaller ones reach the whitedwarf by way of planetary-nebula explosions orstill quieter contractions. And there are moresmall stars than large ones, so there should bemany more white dwarfs than there have beensupernova explosions. (It should be remembered,however, that even the "small stars" mentionedin this connection are not much smaller than ourSun. None of the really small stars that make upthe large majority have yet lived long enough toreach the point of expansion and collapse, noteven if they were born at the moment of the bigbang.)

So it might seem that we have a clear pictureof the end of stars, and that end is always thewhite dwarf cooling to the black dwarf. Yet someastronomers were not satisfied-.

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BEYOND THE WHITE DWARF

INDIVIDUAL STARS have been detected with asmuch as 50, possibly 70, times the mass of ourSun. When such a star goes, it will go with anunexampled crash. What's more, when it doesgo, it will have to get rid of 97 or 98 percent ofits mass in order that what is left over will beonly 1.4 times the Sun's mass and can safelycollapse to a white dwarf.

That may happen, of course, but what if itdoesn't? Astronomers know that supernovas getrid of a lot of mass, but there is nothing in theprocess, as far as they know, that says a super-nova must get rid of enough mass to leave a con-tracting body below Chandrasekhar's limit. Whatif, after a supernova explosion, what is left ofthe star has a mass twice that of the Sun andthat this two-Sun mass collapses. The electronicfluid will form and contract-and contract-

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and smash I The inward pull of gravity will simplybe too intense to be balanced by the electronicfluid at its most compressed.

The electrons will then be driven inward todensities at which they cannot really exist.Within the electronic fluid protons and neutronshad been moving about freely; now the electronswill combine with the protons to form additionalneutrons. The electrons and protons are presentin any piece of matter, whether a dust fragmentor a star, in just about equal numbers, so theresult of the union is that the collapsing starwill consist just about entirely of neutrons.

These neutrons will be driven together by thegravitational collapse until they are in virtualcontact. Then, and only then, will the collapsebe halted. The nuclear force, which governs theinteraction of massive particles, keeps the neu-trons from pushing any closer together. Now itis no longer gravitational force being balancedby electromagnetic force as it is in planets, inordinary stars, and even in white dwarfs. It isgravitational force balanced by the nuclear force,which is much stronger than the electromagneticforce.

A star consisting of neutrons in contact iscalled a neutron star. It is composed of a neu-tronic fluid that is sometimes referred to asneutronium. In a sense an atomic nucleus ismade up of neutronium, and, in reverse, a neu-tron star is like a giant nucleus. Neutronium isincredibly dense; it reaches a peak of somethinglike 1,000,000,000,000,000, or 1015, times asdense as ordinary matter.

If a sphere of ordinary matter were convertedinto a sphere of neutronium, its diameter would

NEUTRON STARS

shrink to 1/100,000 the orginal without loss ofmass. Thus, the Earth, which is 12,740 kilo-meters in diameter, would, if it were suddenlyturned into neutronium, be a sphere about 0.127kilometers in diameter. A sphere that size is only1.5 city blocks across, but it would contain allthe mass of the Earth.

Similarly, if the Sun, which is 1,400,000 kilo-meters in diameter, were converted into neu-tronium, it would become a sphere only 14kilometers across. It would have the volume ofa small asteroid, but it would have all the massof the Sun.

It isn't safe, as we shall see, to imagine neutronstars much more massive than the Sun, but justto get a clear picture we can imagine the mostmassive known star somehow converted intoneutronium without the loss of any of its mass.It would be a sphere only 50 or 60 kilometersacross.

Even the cosmic egg has, at times, beenimagined as a gigantic ball of neutronium con-taining all the mass of the universe-a "neutronuniverse," so to speak. It would be 300,000,000kilometers across. If such a cosmic egg were putin the place of our Sun, it would reach out onlyto the asteroid belt, yet it would contain all themass of the 100,000,000,000 stars of our galaxyand of all the stars of 100,000,000,000 othergalaxies.

Nor do we have to imagine only masses aboveChandrasekhar's limit as forming neutron stars.When a supernova explodes, the collapse of thatportion of the star that is not blown away is sosudden that it comes smashing down on the elec-tronic fluid with incredible speed. It is, then, not

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the sheer mass so much as the rapid infall thatbreaks through the electronic-fluid barrier. Oncethe electronic fluid is smashed, that smash isirreversible. The electronic fluid cannot recon-stitute itself. As a result a neutron star with aslittle as a fifth the mass of our Sun may form,with a diameter of only 8.2 kilometers.

The likelihood that the force of supernovacollapse can smash the electronic fluid evenwhen the collapsing mass is under Chandrasek-har's limit makes it look as though supernovasare bound to form neutron stars. White dwarfswill form only when stars too small to explodeas a supernova reach their cycle of expansionand contraction with nothing worse than a plan-etary nebula developed.

In 1934 the Swiss-American astronomer FritzZwicky (1898-1974) and the German-Americanastronomer Walter Baade (1893-1960) were thefirst to speculate about the possible formationand existence of neutron stars. A few years laterthe American physicist J. Robert Oppenheimer(1904-1967) and a student of his, George M.Volkoff, worked out the theory in detail.

But then came World War II, which preoc-cupied scientists to the exclusion of almost every-thing else, Oppenheimer, for instance, headedthe team that developed the nuclear bomb.

Even discounting the pressures of war work,however, interest in neutron stars was not verywidespread among astronomers. After all, thematter seemed hopelessly theoretical. An astron-omer might work out exactly what could happenin a supernova explosion. He might calculatethe manner in which matter might be blownaway, what the speed of collapse might be, at

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what point the electronic fluid would be smashed,and how the neutronium might form-yet itwould all just remain figures on paper.

How could one prove that the theory was cor-rect and that neutron stars exist? Was it reason-able to suppose that an object that is 8 to 15kilometers across and, surely, light-years awaycould be seen?

Even if a neutron star were as intensely brightas the brightest star, its tiny, tiny surface woulddeliver only the feeblest spark. Even if the big-gest and best telescope were focused in its direc-tion, it would show up, at best, as a very dim,dim star. How could one possibly tell it was aneutron star that happened to be close enoughto be made out, rather than an ordinary starthat looked that dim only because it was ex-tremely far away?

Then, why bother about neutron stars?Well, as long as the only important way in

which astronomers could study the sky was byobserving the light given off by objects in it, it wasuseless to bother. As the twentieth century pro-gressed, however, astronomers became more andmore aware of cosmic radiation other than thatof light, and eventually the problem of detectinga neutron star did not seem so impossible afterall.

BEYOND LIGHT

In 1911 the Austrian-American physicist Vic-tor Francis Hess (1883-1964) was able to showthat certain very energetic forms of radiationreach Earth from space, and they were thereforecalled cosmic rays.

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The cosmic rays are composed of very fast,electrically charged atomic nuclei that verylikely originated in the millions of supernovasthat have exploded in our galaxy during its life-time. Because the cosmic-ray particles are elec-trically charged, however, they curve in theirpaths in response to the various magnetic fieldsassociated with stars and with the Galaxy as awhole. They end up reaching us from all direc-tions, and there is no way we can tell from whatspecific direction a specific cosmic-ray particlebegan its travels. While cosmic rays continue tobe interesting to astronomers, they cannot beused to give us information about particularstars.

In 1931 the American radio engineer KarlGuthe Jansky (1905-1950) discovered that thereare microwaves reaching us from the sky. Micro-waves are lightlike radiations without electriccharge, so they travel in straight lines, unaffectedby magnetic fields. Microwaves, as the name im-plies, are made up of waves, as light is, butmicrowaves are about a million times as longas lightwaves are.

Despite this, the micro of microwaves is froma Greek word meaning "small" because micro-waves belong to a group of radiations calledradio waves, and microwaves are the smallestof that particular group. (Microwaves are oftenreferred to as radio waves, by the way.)

Because the microwaves are so long, com-pared with light waves, they have less energy andare less easily detected. Furthermore, the ac-curacy with which a wave source can be pin-pointed decreases as the wavelength increases,all other things being equal. It was therefore

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much harder to work out the point of origin ofmicrowaves than of light. For quite a while,therefore, little was done with microwaves.

The existence of microwaves reaching us fromthe sky, made it clear that stars radiate in allwavelengths. It so happens that the short wave-lengths of ordinary light and the long wave-lengths of microwaves happen to be able to getthrough our atmosphere, while other wavelengthscannot. The atmosphere is more or less opaquefor one reason or another to the wavelengthsshorter than those of visible light, longer thanthose of microwaves, or intermediate betweenthe two.

In the early 1950s rockets began to be sentbeyond the atmosphere into space to observe andmeasure those ranges of wavelengths blocked bythe atmosphere. Rockets could only remain be-yond the atmosphere for short periods of timeat first before returning and plunging back toEarth.

Starting in 1957, however, first the SovietUnion, then the United States began to placesatellites in orbit around the Earth beyond theatmosphere. They could remain beyond the at-mosphere for indefinite periods, and they couldcarry instruments that could detect the full rangeof radiation coming from the sky. With theproper instruments they could detect ultravioletlight, which has wavelengths shorter than thoseof visible light; X-rays, with still shorter wave-lengths; and even gamma rays with even shorterwavelengths.

This roused hope, for violent events involvehigher temperatures and therefore more ener-getic radiation. Any star can radiate light, but

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only violent stars-therefore interesting stars-will radiate X rays, for instance.

As an example, our own Sun emits X raysfrom its thin outer atmosphere, the corona. Thisis because the heat pouring out of the Sun isabsorbed by the thinly spread-out atoms of thecorona, and each atom is therefore raised to atemperature of a million degrees or more. (Thetotal heat of the corona is, however, not verygreat, since although the individual atoms areso hot, there are so few of them.)

Because the Sun is so close, it is the most im-portant emitter of X rays in the sky, but if itwere at the distance of even the nearer stars,its X-ray radiation would be so diluted by distanceit could not be detected. Sirius, for instance, isconsiderably larger and hotter than our Sun, andtherefore undoubtedly emits X rays with severaltimes the intensity that the Sun does. Yet Siriusis at a distance of nearly nine light-years, and itsX rays cannot be detected.

If X rays could be detected at star distances,it would indicate violence indeed, but at firstastronomers didn't think such detections couldbe carried through. Their assumption in the early1960s was that the Sun was the only source ofdetectable X rays in the sky. Nevertheless, therewas some interest in studying the night sky, sinceit was possible that solar X rays might be re-flected from the Moon and that this could giveus some information about the Moon's surface.(This was before astronauts landed on theMoon.)

In 1963 under the guidance of the Americanastronomer Herbert Friedman (1916-) investiga-tions beyond the atmosphere were conducted for

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the detection of X rays coming from the Moon.Such X rays were not detected, but X rays werefound, quite surprisingly, from other directions.In the years since, some satellites have been sentup for no other purpose but to map the sky forX-ray sources, and hundreds of such sourceshave been located.

This gave the universe an entirely new aspect.An X-ray source that could be detected at thedistance of the stars and even, in many cases, atthe distance of the other galaxies, must markevents quite out of the common.

For one thing, the existence of such X-raysources gave rise to hopes that neutron starsmight be detected. When a neutron star isformed, it is, in a way, like an exposed core ofa star and possesses at its surface the temper-ature of a stellar interior. Theoretical considera-tions made it seem that the surface of a neutronstar would glow at a temperature of 10,000,-O00°C.*

A neutron star with a surface at that temper-ature would radiate chiefly in the X-ray region.Consequently, the question arose as to whethersome of the X-ray sources in the sky might notoriginate in neutron stars.

That wasn't the only possibility, of course.X rays might originate from the very hot gasespushed out by supernovas, for instance, just asthey originate from the Sun's corona.

These two possibilities can be distinguished asfollows: A neutron star would be a tiny point inthe sky, while a region of gases would be a dis-

* If the cosmic egg were a gigantic neutron star, its surface tempera-ture would probably be i,000,000,000,000°C at least, and it wouldradiate gamma rays.

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tinct smear. A lot would depend, then, onwhether the X rays seemed to emerge from asingle point or from an area.

A prime suspect was the Crab Nebula. It isthe remains of a tremendous supernova, andthere might be a neutron star somewhere in thecenter of all those gases. And, of course, thegases are there, and they are clearly in energeticturmoil. X rays might come from the suspectedneutron star if one were there, or from the gases,or from both.

In 1964 the Moon was slated to move in frontof the Crab Nebula. As the Moon advanced, itwould cut off the X-ray emission. If the X rayswere coming only from the pointlike neutronstar, they would remain at full intensity as theMoon advanced and then sink suddenly at zero.If the X rays were coming from the gas, theywould decline smoothly in intensity. If the Xrays were coming from both, they would declinesmoothly at first, then experience a sudden drop,then decline further as smoothly as at the start.

A rocket was sent up at the appropriate timeto measure the X-ray intensity from the CrabNebula, and the measurement fell off gradually,more or less, as the Moon advanced. The X raysseemed to be coming from the turbulent gas, andhopes for the detection of a neutron star with-ered.

PULSARS

Meanwhile, however, astronomers had begunworking with microwaves, and the science ofradio astronomy had been rapidly developed toa high pitch of complexity and efficiency. As-

NEUTRON STARS

tronomers learned to use complex arrays of de-tecting devices (radio telescopes) in such a wayas to be able to pinpoint microwave sources withgreat accuracy and to work out their propertiesin great detail.

In the early 1960s, for instance, radio astron-omers became aware that some microwavesources change intensity rather rapidly, as thoughthey were twinkling. They began to design radiotelescopes that were specially adapted to catchthe rapid changes. One such radio telescope wasdevised at Cambridge University Observatory byAnthony Hewish (1924-) and consisted of 2,048separate receiving devices spread out over anarea of 18,000 square meters.

In July 1967 the new radio telescope was setto scanning the heavens, and within a month ayoung graduate student, Jocelyn Bell, was re-ceiving bursts of microwaves from a place mid-way between the stars Vega and Altair-veryrapid bursts, too. At first, she thought she wasdetecting interference with the radio telescope'sworkings from electrical devices in the neighbor-hood. However, she discovered that the sourcesof the microwave bursts move regularly fromnight to night across the sky in time with thestars. Something outside the Earth had to be re-sponsible for it, and she reported the results toHewish.

By the end of November the phenomenoncould be studied in detail. Hewish had expectedrapid fluctuation, but not that rapid. Each burstof microwaves lasted only 1/20 second, andthe bursts came at intervals of 1 1/3 seconds.They came, indeed, with remarkable regularity.They came every 1.33730109 seconds.

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The new instrument picked up these burstsof microwaves easily, for the individual burstswere energetic enough to detect without trouble.Ordinary radio telescopes, however, had not beendesigned to catch these very brief bursts; theyhad detected only an average microwave inten-sity including the dead period between bursts.This average is only 3.7 percent of the burstmaximums, and this had gone unnoticed.

The question was: What does this phenomenonrepresent? Since the microwave source seemsto be a mere point in the sky, Hewish thoughtit might represent some kind of star. Since themicrowaves emerge in short pulses, he thoughtof it as a kind of pulsating star. This was short-ened almost at once to pulsar, and it was by thatname that the new object came tobe known.

Hewish searched for others among the longcharts of previous observations by his instru-ments and found three more pulsars. He checkedthe evidence, and then on February 9, 1968, heannounced the discovery to the world.

Other astronomers began to search avidly, andmore pulsars were quickly discovered. By 1975100 pulsars were known, and there may be asmany as 100,000 in our galaxy altogether.

Two thirds of the pulsars that have been lo-cated are to be found in those directions wherethe stars of our galaxy are thickest. That is agood sign that pulsars generally are part of ourown galaxy. (There is no reason to supposethey don't exist in other galaxies, too, but at thegreat distances of other galaxies they are prob-ably too faint to detect.) The nearest knownpulsar may be as close as 300 light-years or so.

All the pulsars are characterized by extreme

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regularity of pulsation, but of course the exactperiod varies from pulsar to pulsar. The onewith the longest period has one of 3.75491 sec-onds.

The pulsar with the shortest period so farknown was discovered in October 1968 by astron-omers at Green Bank, West Virginia. It happensto be in the Crab Nebula (making the first clearlink between pulsars and supernovas) and provedto have a period of only 0.033099 seconds. It ispulsing 30 times a second, or 113 times as rap-idly as the pulsar with the longest period known.

But what can produce such short flashes insuch a fantastically regular fashion?

So stunned were Hewish and his fellow astron-omers at the first pulsars that they wondered ifit were possible they might be signals from someintelligent life-forms far out in space. Indeed,among themselves they referred to the matteras LGM before the word pulsar came into use-LGM standing for "little green men."

This notion didn't last long, however. To pro-duce the pulses would require 10 billion times thetotal quantity of power humankind could pro-duce. It didn't seem likely that so much powerwould be wasted just to send out very regularsignals that carried virtually no information.Besides, as more and more pulsars were detected,it seemed quite unlikely that so many differentlife-forms would all be zeroing in their signalson us. The theory was quickly dropped.

But something must be producing them; someastronomical body must be undergoing a steadyperiodic change-a revolution around some otherbody, a rotation about its own axis, a pulsation-at intervals rapid enough to produce the pulses.

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To force such rapid changes with the releaseof so much energy would require an enorm-ously intense gravitational field. Astronomersknew of nothing else that would work. Instantlywhite dwarfs came to mind.

Theoreticians got busy at once, but try as theymight, there seemed no way of allowing onewhite dwarf to circle another, or to rotate on itsaxis, or to pulse, with a period short enough toaccount for pulsars. Small and gravitationallyintense white dwarfs might exist, but they couldnot be small enough nor could their gravitationalfields be intense enough for the task. Theywould actually break up and tear apart if theywere to revolve, rotate, or pulse in periods ofless than four seconds.

Something smaller and denser than a whitedwarf was required, and the Austrian-born as-tronomer Thomas Gold (1920-) suggested thatpulsars are the neutron stars that Oppenheimerhad played with theoretically. Gold pointed outthat a neutron star is small enough and denseenough to be able to rotate about its axis in fourseconds or less.

What's more, a neutron star should have amagnetic field just as an ordinary star does, butthat magnetic field should be compressed andconcentrated as the matter of the neutron staris. For that reason, a neutron star's magneticfield is enormously more intense than the fieldsabout ordinary stars. The neutron star as itwhirls on its axis gives off electrons, but theyare trapped by the magnetic field and are ableto escape only at the magnetic poles, which areat opposite sides of the star.

The magnetic poles need not be at the actual

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rotational poles. (They aren't in the case of ourown Earth, for instance.) Each magnetic polemight sweep around the rotational pole in sec-onds or in a fraction of a second and spray outelectrons as it does so (just as a rotating watersprinkler jets out water). As the electrons arethrown off, they curve in response to the neutronstar's magnetic field and gravitational field. Los-ing energy, they may not escape altogether, butthe energy they lose is in the form of micro-waves.

Every neutron star thus shoots out two jets ofmicrowaves from opposite sides of its tiny globe.If a neutron star happens to move one of thosejets across our line of sight as it rotates, Earthwill get a very brief pulse of microwaves at eachrotation. Some astronomers estimate that onlyone neutron star out of a hundred would justhappen to send microwaves in our direction, soof the possibly 100,000 in our galaxy we mightnever be able to detect more than 1,000.

Gold went on to point out that if his theorywas correct, the neutron star is leaking energyat the magnetic poles, and its rate of rotationmust be slowing down. This means that the fasterthe period of a pulsar, the younger it is likelyto be and the more rapidly it may be losingenergy and slowing down.

The most rapid pulsar known, and the onewith the most energetic pulses, is the Crab Neb-ula pulsar, and it might well be the youngest wehappen to have observed so far, since the super-nova explosion that might have left that neutronstar behind took place only 900 years ago. Atthe very moment of its formation the Crab Neb-

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ula pulsar might have been rotating on its axis1,000 times a second, but it would have lostenergy quickly; in the first 900 years of itsexistence over 97 percent of its energy has bledaway until it is now rotating only 30 times asecond. And it should still be slowing, though,of course, more and more slowly.

The period of the Crab Nebula was studiedcarefully, and the pulsar was indeed found tobe slowing down, just as Gold had predicted.The period is increasing by 36.48 billionths of asecond each day, and at that rate it will havedoubled in 1,200 years. The same phenomenonhas been discovered in other pulsars whose pe-riods are slower than that of the Crab Nebulapulsar and whose rate of slowing is also slower.The first pulsar discovered, now called CP1919,has a period 40 times as long as that of the CrabNebula pulsar, and it is slowing at a rate thatwill double its period only after 16 million years.As a pulsar slows, its pulses become less ener-getic. By the time the period has passed fourseconds in length, the pulsar becomes too weakto be detectable. Pulsars probably endure as de-tectable objects for tens of millions of years,however.

As a result of these studies of the slowing ofthe pulses astronomers are now pretty well satis-fied that the pulsars are neutron stars.

Sometimes a pulsar will suddenly speed up itsperiod very slightly, then resume the slowingtrend. This was first detected in February 1969,when the period of the pulsar Vela X-1 (foundamid the debris of the supernova that blazed up15,000 years ago) was found to alter suddenly.

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The sudden shift was called, slangily, a glitch,from a Yiddish word meaning "to slip," andglitch has entered the scientific vocabulary inconsequence.

Some astronomers suspect glitches may be theresult of a starquake, a shifting of mass distribu-tion within the neutron star that will result in itsshrinking its diameter by a centimeter or less. Orperhaps it might be the result of a sizable meteorplunging into the neutron star and adding its ownmomentum to that of the star.

There is, of course, no reason why the elec-trons emerging from a neutron star should loseenergy only as microwaves. They should producewaves all along the spectrum. It should, for in-stance, emit X rays, too, and the Crab Nebulaneutron star does, indeed, emit them. About 10to 15 percent of all the X rays the Crab Nebulaproduces is from its neutron star; it was theother 85 percent or more that comes from theturbulent gases that obscured this fact and dis-heartened those astronomers who hunted for aneutron star there in 1964.

A neutron star should produce flashes of visi-ble light, too. In January 1969 it was noted thatthe light of a dim sixteenth-magnitude starwithin the Crab Nebula does flash on and off inprecise time with the microwave pulses. Theflashes and the period between them are so shortthat special equipment was required to catchthem. Under ordinary observation the star seemsto have a steady light. The Crab Nebula neutronstar was the first optical pulsar discovered, thefirst visible neutron star-up to now the onlyone.

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PROPERTIES OF NEUTRON STARSAstronomers speculate about the detailed com-

position of neutron stars. At the very surfacethere may be a thin layer of normal matter,mostly iron. There may even be a gaseous ironatmosphere, perhaps half a centimeter thick.There are also charged particles such as elec-trons and atomic nuclei that are bound to theneutron star's superintense magnetic field. It isthese, the electrons particularly, that are sprayedout at the magnetic poles and that produce thepulses of radiation that are detected on Earth.

Below that outermost shell of normal matter,are well-packed iron nuclei, bearing character-istics we would think of as "solid," even thoughthis crust is at a temperature of millions ofdegrees. The outer edge of the crust has a densityof only 100,000 g/cm 8, but this rapidly increaseswith depth.

It is this solid surface, with strength nearlya billion billion times that of steel and with"mountains" possibly a centimeter high, thatreadjusts itself every now and again to settledown into a more compact form producing theglitches that slightly decrease the period of rota-tion.

Below the crust, as density increases further,nuclei cannot maintain their integrity, and thematerial becomes a mass of neutrons. Near thecore there may be a sea of still more massiveparticles called hyperons.*

One important property of the neutron star isHyperons can be produced in laboratories, but under earthly condi-

tions they break down in less than a billionth of a second.

NEUTRON STARS

its mass. In 1975 the mass of a neutron star wasdetermined for the first time. The neutron starin question, Vela X-1, turned out to have a mass1.5 times that of the Sun. This was interesting,for the mass was slightly over Chandrasekhar'slimit. No white dwarf could have been thatmassive (although we must remember that neu-tron stars with masses considerably below Chan-drasekhar's limit are also possible in theory).

The mass of Vela X-1 was capable of beingdetermined because that neutron star is part of abinary. Its companion is a massive star of themain sequence, one with 30 times the mass of ourSun. Undoubtedly binaries, if massive enough,can shift matter back and forth as each expands,and end by forming a pair of neutron stars, justas less massive binaries can in this fashion pro-duce a pair of white dwarfs.

Vela X-1 must originally have been the brighterof the pair, and 15,000 years ago, when it be-came a supernova, the companion star may havecaptured as much as a thousandth of the matterblown off by the explosion, gaining considerablyin mass and brightness in consequence and, ofcourse, shortening its own life on the main se-quence. Eventually, in a million years or less,the companion of Vela X-1 will go supernova inits own right, and there may then be two neutronstars rotating about a common center of gravity.The fact that a neutron star can form part of abinary, as Vela X-1 does, shows that when onestar of a pair goes supernova, the other star cansurvive.

The shift of matter from one star to anotheras first one and then the other expands resultsin the conversion of gravitational energy to radia-

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tion, especially where a white dwarf or a neutronstar, with a very intense gravitational field, is in-volved. Up to 40 percent of the mass of mattercan be converted into energy in this way-morethan 100 times the amount of mass that can beconverted to energy by way of nuclear fusion.This is another point that helps explain thebrightness of novas and supernovas.

Next, let's consider some of the gravitationalproperties of a neutron star, taking as our averagespecimen one that has exactly the mass of ourSun but a diameter only 1/100,000 as great.Such a neutron star must have a diameter of 14kilometers and an average density of 1,400,-000,000,000,000 g/cm8 .

If we consider the Sun first, its surface gravityis equal to 28 times that of Earth's surfacegravity. Thus, a person who weighs 70 kilogramson the surface of the Earth would weigh on thesurface of the Sun (assuming the Sun had asurface in the earthly sense and that a personcould survive the experience) just under 2,000kilograms.

Now, if we imagine a body of a given massbeing compressed smaller and smaller, any ob-ject on its surface comes closer and closer tothe center. By Newton's law of gravitation thesurface gravity (assuming the mass doesn'tchange) changes inversely * as the square of thediameter. Thus, if you compress a star so that ithas only 1/2 its original diameter, the surfacegravity is 2 x 2, or 4 times the original. If it iscompressed to 1/6 its original diameter, then the

* By Inversely we mean that surface gravity and diameter change inopposite direction. As, diameter decreases, surface gravity increases; asdiameter Increases, surface gravity decreases.

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surface gravity is 6 x 6, or 36 times the original;and so on.

Sirius B, with a diameter 1/30 that of theSun and a mass just about equal to it, must havea surface gravity 30 x 30, or 900 times that ofthe Sun. Our mythical 70-kilogram person, whocan survive any experience, would on the surfaceof Sirius B weigh 1,800,000 kilograms.

A neutron star with the mass of the Sun anda diameter of 14 kilometers (1/100,000 timesthat of the Sun) must have a surface gravity100,000 x 100,000, or 10,000,000,000 times thatof the Sun. Our 70-kilogram person would weigh20 trillion kilograms.

And what about rotational periods?Our Earth, with a circumference of 40,000

kilometers, rotates on its axis in one day. Thatmeans that a point on Earth's equator, whichmarks out a larger circle in that one day of ro-tation than any other point not on the equatordoes, is traveling around Earth's axis at a con-stant speed of just about 0.5 kilometers per sec-ond. This speed decreases steadily as one movesfarther and farther away from the equator, eithernorth and south, until it is zero at the poles.

A rotational speed sets up a centrifugal effectthat tends to counter the pull of gravity. Thiscentrifugal effect increases with speed of rota-tion, so it is zero at the poles and increases asone approaches the equator until it is a maxi-mum at the equator. The centrifugal effect tendsto pull material away from the axis, and do itmost strongly at the equator, so that we can saythat the Earth has an equatorial bulge. It isn'tmuch. The equatorial diameter (the distancefrom one point on the equator to the opposite

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point, through the Earth's center) is 43 kilo-meters longer than the polar diameter (frompole to pole). The equatorial diameter of Earthis roughly 1/300 longer than the polar diameter,and that is a measure of Earth's oblateness.

Consider Jupiter, on the other hand. Jupiter,the largest planet, has an equatorial circum-ference of 449,000 kilometers and rotates in 9.85hours. A point on Jupiter's equator thereforemoves at a speed of 12.7 kilometers per second,just over 25 times as fast as a point on Earth'sequator.

Despite Jupiter's greater gravity, this enormousspeed of rotation, combined with the fact thatJupiter's substance is composed of lighter ele-ments much less compactly packed than Earth'ssubstance is, results in a larger oblateness forJupiter. Jupiter's equatorial diameter is 8,700kilometers longer than its polar diameter. Itsoblateness is fully 1/16.*

The Sun by comparison has a circumferenceof 4,363,000 kilometers and rotates on its axisin 25.04 days. A point on its equator thereforemoves at a speed of just about 2 kilometers persecond. This is 4 times the speed of a point onEarth's equator, but it is only 1/6 the speed of apoint on Jupiter's equator. The combination ofrelatively slow rotational speed of the Sun, andits huge surface gravity is such that no oblate-ness can be measured. As far as we can tell, theSun is a perfect sphere.

We don't know what the period of rotation isfor Sirius B, or for any white dwarf, but we

* Saturn is a bit smaller than Jupiter and does not rotate quite as fast,but its gravitational field is also smaller, and it is even more ablatethan Jupiter is.

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NEUTRON STARS 165

know that a typical neutron star will rotate inabout 1 second, judging from the period of pulsa-tion of the pulsars. If our 14-kilometer-acrossneutron star rotates about its axis in 1 second,then a point on its equator will be moving at aspeed of about 44 kilometers per second.

This is 3.5 times as fast as a point on Jupiter'sequator, 21.8 times as fast as a point on theSun's equator, and 95 times as fast as a pointon the Earth's equator. Nevertheless, consider-ing the neutron star's vastly intense gravitationalfield, we can be quite certain that its rotationalspeed, fast though it might be by solar-systemstandards, simply can't even approach being ableto lift any material against gravity through acentrifugal effect. The neutron star must be aperfect sphere no matter what. We can be almostas confident that the white dwarf must be aperfect sphere also.

If centrifugal force is not likely to lift the sub-stance of white dwarfs and neutron stars ameasurable distance against gravity, we canimagine that the escape velocity from suchbodies must be high indeed, and we would beright.

Escape velocity varies inversely as the squareroot of the diameter (assuming no change inmass). Thus, if you decrease a star to 1/36 timesits original diameter, then the escape velocityincreases by 6 times (since 6 is the square rootof 36).

Working on this basis, you can see that Sirius B,with a mass equal to that of the Sun and adiameter 1/30 of the Sun, must have an escapevelocity 5.5 times that of the Sun. Since theescape velocity from the Sun's surface is 617


km/sec, that from the surface of Sirius B mustbe 3,400 km/sec.

On the other hand, our neutron star, with itsmass equal to the Sun but with a diameter only1/100,000 as great, must have an escape velocityat its surface that is greater than that of theSun by a factor equal to the square root of100,000, or 316. The escape velocity from theneutron star must be equal to 617 x 316, orjust about 200,000 km/sec.

These figures on escape velocity are particu-larly important to us because they are anothermilestone on the road to the black hole. Let ustherefore present them in tabular form in Table12.

TABLE 12-Escape Velocities

Object Escape Velocity

Kilometers Fraction ofper second speed of light

Earth 11.2 0.0000373Jupiter 60.5 0.00020Sun 617 0.0020Sirius B 3,400 0.011Neutron star 200,000 0.67

For objects of ordinary matter escape velocitiesare tiny fractions of the velocity of light. Evenfor the Sun the escape velocity is only 1/500the velocity of light. In the case of the whitedwarf the escape velocity is 1/100 the velocityof light, and light itself loses a measurableamount of energy in leaving. It was by this lossof energy and the consequent small red shift in

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the light of Sirius B that Adams was able tocheck its dense nature.

A neutron star is likely to have an escapevelocity equal to 2/3 that of light, and the Ein-stein shift would be much greater. We may getX radiation from a neutron star, but if it werenot for the star's intense gravitational effect, Xrays we receive would have far shorter wavesthan they in fact have. And as for the long-waveradiation we get, the visible light waves and themuch longer microwaves, much of that too wouldnot exist were it not for the wave-lengtheningeffects of the neutron star's gravitational field.

TIDAL EFFECTS

There is another gravitational effect that wecan neglect on Earth's surface but that becomesof overwhelming importance in the neighbor-hood of a neutron. This is the tidal effect.

The strength of the gravitational attractionbetween two particular objects of given mass de-pends on the distance between their centers. Forinstance, when you are standing on Earth's sur-face, the strength of Earth's gravitational pull onyou depends on your distance from Earth's cen-ter.

Not all of you, however, is at the same distancefrom Earth's center. Your feet are nearly twometers closer to the Earth's center than yourhead is. That means that your feet are morestrongly attracted to the Earth than your headis because gravitational attraction increases asdistance decreases. This difference in the grav-

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itational attraction between two ends of an ob-ject is the tidal effect.

Under ordinary circumstances tidal effectsaren't great. Let us consider a person (a ratherlarge one) who is two meters tall and who weighs90 kilograms. If he is standing on the Earth atsea level in the United States, the soles of hisfeet are about 6,370,000 meters from the centerof the Earth. Let us say they are at exactly thatdistance. In that case the top of his head isabout 6,370,002 meters from the center of theEarth.

The gravitational pull at the top of his headis (6,370,000/6,370,002)2 times the gravitationalpull at the soles of his feet. This means that thepull on his feet is about 1.0000008 times the pullon his head. This is the equivalent of saying thathe is on a rack with the top of his head and thebottom of his feet being stretched apart by thepull of a weight of 0.000071 kilograms, which isthe equivalent of about four drops of water. Thissort of pull is too small to be felt, and that iswhy we are not aware of tidal effects producedby the Earth on our body.

The tidal effect is greater if an object sub-jected to a gravitational field is larger, so thatthere is a larger drop in the force exerted uponthe object between one end and the other. In-stead of a person, let's choose the Moon.

The Moon has a diameter of 3,475 kilometers,and its center is at an average distance of 384,-321 kilometers from the Earth's center. If weimagine the Moon to be always at that distance(there is actually a slight variation in and outduring the month but not a very large one), thenthe part of its surface directly facing Earth would

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be 382,584 kilometers from Earth's center, andthe part of its surface directly away from Earthwould be 386,058 kilometers from Earth's center.

The gravitational pull on the near side of theMoon, because it is nearer, would under thesecircumstances be 1.018 times that on the farside.

The total force of Earth's gravitational pull onthe Moon (what we would imagine its weightto be if it were resting on a platform attractedto the center of the Earth and 384,321 kilo-meters high) would be 20,000,000,000,000,000,-000 kilograms.

If the Moon were all at the distance of itsnearest surface, then it would weigh 800,000,-000,000,000,000 kilograms more than if it wereall at the distance of the farthest part of the sur-face. You can imagine, then, the Moon beingstretched in the direction toward and away fromthe Earth by that amount of pull; 800 milliontrillion kilograms is no mean pull, and the Moonshows a small bulge in that direction. The diam-eter pointing toward and away from the Earthis slightly longer than the diameter at rightangles to it.

It works the other way around, too. The Moonpulls on the Earth, and it pulls more stronglyon the side of the Earth nearest itself than onthe part farthest from itself. Since the Earth hasa greater diameter than the Moon does, there isa longer distance over which the gravitationalpull can decrease, and that makes for an increasein the tidal effect. The Moon is a smaller bodythan the Earth is and produces a smaller gravi-tational pull altogether, and that makes for adecrease in the tidal effect.

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The decrease wins out. The smaller gravita-tional field of the Moon is more important afactor than the greater diameter of the Earth.If the gravitational effect were all important,the Moon's tidal effect on Earth would be 1/81the Earth's tidal effect on the Moon. Earth'sgreater diameter slightly compensates, and infact the Moon's tidal effect on the Earth is 1/70the Earth's tidal effect on the Moon.

The Earth is stretched in the direction of theMoon by a perceptible amount. The solid ball ofthe Earth stretches by about a third of a meter.The water of the ocean gives more easily andstretches by just over a meter.

There is therefore a bulge in the ocean (anda lesser one in the solid crust) on the side facingthe Moon, and another on the opposite side ofthe Earth, away from the Moon. As the Earthrotates, the land surfaces move into the bulgeand out again, then into the other bulge and outagain. As a result the ocean creeps up the shoreand down again twice a day (in a way stronglyaffected by the shape of the shoreline and otherfactors we need not go into in this book). Thistwo-a-day ocean movement is referred to as thetides, and that is why the phenomenon is re-ferred to as the tidal effect.

The tidal effects of bodies such as the Earthand Moon are not really very large comparedwith the total gravitational force, but they mountup with time. As the Earth turns through thebulges, the friction of the water against the bot-tom of the shallower portions of the ocean, con-verts some of the rotational energy into heat.As a result the Earth is slowly decreasing its rateof rotation and slowly increasing the length of

NEUTRON STARS

its day. The day becomes 1 second longer every100,000 years. That doesn't sound like much,but if this has been a steady rate of decrease, theEarth rotated in only 12.7 hours when it wasfirst formed.

The earth can't lose angular momentum(something that involves its rate of turning)without that being gained elsewhere in the Earth-Moon system. The Moon gains it and is slowlymoving farther away from the Earth as a result,since that is a movement that increases itsangular momentum.

The Earth's tidal effect on the Moon hasslowed the Moon's rotation to the point whereit faces one side to the Earth at all times.

Like gravitation as a whole the tidal effectchanges with the distance between two givenbodies but in a somewhat different way.

Let us suppose the Earth and Moon wereslowly approaching each other. The total gravita-tional pull would increase as they moved closer,varying inversely as the square of the distance.If the Moon and Earth were at half their presentdistance, the gravitational pull between themwould be increased 2 x 2, or 4 times. If theMoon and Earth were at one third their presentdistance, the gravitational pull between themwould be increased 3 x 3, or 9 times, and so on.

The tidal effect increases as the total gravita-tional pull does. The tidal effect increases, inaddition, for another reason.

The tidal effect depends on the size of thebody that is subject to a gravitational field. Thelarger the size of the body, the greater the tidaleffect. However, what counts is not just the sizeof the body but the size of the body compared

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with the total distance of the body from the cen-ter of gravitational pull.

At the present moment the Moon's diameterof 3,475 is just about 0.009 times the distancebetween Moon and Earth. If the distance betweenthe two planets were cut in half, the Moon'sdiameter (which would be the same) would be0.018 times the distance. In other words asthe distance decreased, the tidal effect wouldincrease in proportion to that decrease becausethe Moon's diameter would make up a larger andlarger fraction of the total distance.

You have two factors tending to increase thetidal effects, then-one varying inversely as thesquare of the distance and the other varying in-versely as the distance. If you halve the distancebetween the Earth and the Moon, the tidal effectwould increase 2 x 2 times because of the firstfactor and 2 times because of the second. Thetotal increase would be 2 x 2 x 2, or 8. Now2 x 2 x 2 is the cube of 2, so what we are sayingis that the tidal effect varies inversely as thecube of the distance.

If the distance between two bodies is increasedto 3 times what it was, then the tidal effect isdecreased to 1/3 x 1/3 x 1/3, or 1/27 what itwas. Conversely, when the distance between twobodies is decreased to 1/3 what it was, the tidaleffect is increased to 3 x 3 x 3, or 27 timeswhat it was.

If the Earth and Moon, then, were approach-ing each other, the tidal effect of each on theother would increase steadily and very rapidly.(Whatever the distance, however, the Earth'stidal effect on the Moon would remain 70 timesthat of the Moon's tidal effect on the Earth.)

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Eventually a point would be reached, well be-fore contact was made, where the stretchingeffect on the Moon would be so enormous thatthe very structure of the Moon would crack andbreak. At that moment the Earth, undergoingonly 1/70 the tidal effect the Moon was under-going, would still be able to maintain its in-tegrity, although the enormous ocean tides wouldundoubtedly destroy everything on the land sur-f ace.

In 1849 the French mathematician EdouardA. Roche (1820-1883) showed that if a satelliteis held together only by gravitational pull-if itis a liquid for instance-it will break up if itapproaches the planet it circles by a distance lessthan that of 2.44 times the radius of the planet.This is called the Roche limit. If a satellite isheld together by electromagnetic forces, as ourMoon is for instance, it can come a little closerthan 2.44 times the radius of the Earth beforethe tidal stretching overwhelms and destroys it.

The radius of the Earth at the equator is6,378.5 kilometers, so Earth's Roche limit isabout 15,500 kilometers. This is only about 1/25the actual distance of the Moon. If the Moonwere ever to get that close to the Earth, it wouldbreak up, and its particles would spread out inorbit around the Earth. It would become a set ofrings, like those of Saturn but more massive,and it would no longer exert any important tidaleffect on Earth because the various parts of thering would pull equally in all directions.

The breakup would not continue indefinitely.As the Moon disintegrated into smaller frag-ments, each fragment, being smaller in size,

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would experience a smaller tidal effect. Eventu-ally each fragment would be too small for thedecreasing tidal effect to break it up further.

If an object is small enough, the tidal effectis insufficient to break it up, even when it is incontact with the attracting body. That is why aspaceship can land on the Moon without breakingup and why we and all the other objects on theEarth's surface can remain intact. The tidal ef-fect for objects of our own size and of the sizeof the things we work with is insignificant.

The more intense a gravitational field, how-ever, the more intense the tidal effect and thefiner the powdering of objects that break up atthe Roche limit.

To pass on to gravitational fields more intensethan that of the Earth, let us consider the Sun,which is 333,500 times as massive as the Earthand therefore has a gravitational field 333,500times as intense. The greater diameter of the Sunplaces its surface farther from its center thanEarth's surface is from Earth's center, and sincethe intensity of the gravitational pull varies in-versely as the square of the distance, the surfacegravity of the Sun is only 28 times the surfacegravity of the Earth.

The tidal effect, however, varies as the inversecube of distance. Since the Sun's diameter is109.2 times that of the Earth, we must divide333,500 (the intensity of the Sun's gravitationalfield as compared with that of the Earth's) by109.2 x 109.2 x 109.2, or 1,302,170. Dividing333,500 by 1,302,170, we get 0.256.

It follows, then, that the tidal effect of theSun on objects on its surface is only 1/4 the

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tidal effect of the Earth on objects on its surface.But suppose the Sun were to contract without

losing any mass. Any object on its surface wouldbe closer and closer to its center, and the tidaleffect on it would increase rapidly.

Sirius B has a mass equal to the Sun but hasa diameter only 1/30 that of the Sun. The tidaleffect on the surface of Sirius B would be 30 x30 x 30, or 27,000 times that on the surfaceof the Sun, and 7,000 times what it is on Earth'ssurface.

If we can imagine a human being (two meterstall and weighing 90 kilograms) standing on awhite-dwarf star without being affected by itsradiation, heat, or total gravity, he would stillnot be made seriously uncomfortable by its tidaleffect, even though that effect is so much largerthan on Earth's surface. Multiplying the ter-restrial effect by 7,000 would leave the humanbeing stretched by a pull of only about 0.5 kilo-grams.

What about the Roche limit? Since the Rochelimit is 2.44 times the radius of the body exertingthe gravitational pull and the cube of 2.44 is14.53, the tidal effect produced by any body atits Roche limit is 1/14.53 of the tidal effect itproduces at its surface. If the tidal effect ofSirius B on its surface is 7,000 times that ofEarth at its surface, and if both effects aredivided by 14.53, the ratio still stays the same;the tidal effect at Sirius B's Roche limit is 7,000times that at Earth's Roche limit.

This means that any large object trapped tooclose to a white dwarf will be broken up muchmore finely than it will be if it is trapped too

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close to the Sun or Earth. It also means thatsmall objects that could resist the tidal effects ofSun or Earth at their Roche limits and that wouldremain whole may nevertheless break up underthe influence of a white dwarf.

Let's go further, now, and suppose that an ob-ject with the mass of the Sun collapses to theneutron-star stage and is only 14 kilometers indiameter. An object on its surface will now beonly 1/100,000 the distance to its center as itwould be if it were on the surface of the Sun.The tidal effect on the neutron star's surface istherefore 100,000 x 100,000 x 100,000 timesthat on the Sun's surface, or a million billiontimes that on the Sun's surface and a quarterof a million billion times that on the Earth'ssurface.

A two-meter-tall human being standing on aneutron star and immune to its radiation, heat,or total gravity would nevertheless be stretchedapart by a force of 18 billion kilograms in thedirection toward and away from the neutronstar's center, and of course the human being, oranything else, would fly apart into dust-sizedparticles. Similarly the neutron star at its Rochelimit of 34 kilometers from its center wouldpowder objects finely.

(A second tidal effect arises from the factthat a body on a spherical object has its twosides attracted to the center in slightly differentdirections. This tends to compress the body fromside to side. As long as the body is large enoughso that the surface is virtually flat over the widthof the body, this effect is very small. Even on aneutron star it is small enough to be ignored-

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certainly in comparison with the enormousstretching effect toward and away.)

A human being, even at a distance of 5,000kilometers from the center of a neutron starwould feel a tidal stretch of about 45 kilogramsif the long axis of his body were pointing towardthe star, and that would be painful indeed.

If a spaceship of the future, effectively shieldedagainst heat and radiation, approached a neutronstar at 5,000 kilometers (at which distance itwould merely be a dim starlike object to theunaided eye), there would be no need to be con-cerned about the total gravitational effect. Theship could glide in free fall past the neutron starin a curved orbit and pull away again (if it weremoving at a sufficiently high velocity). It wouldthen feel no gravitation, any more than we feelthe gravitational pull of the Sun as we, alongwith the Earth and everything on it, move aroundthe Sun in free fall.

There would, however, be no way of eliminat-ing the tidal effect, and skimming past at 5,000kilometers would be a harrowing experience. (Atcloser distances the astronauts would be killedand the ship could break up.)

In 1966 the science-fiction writer Larry Nivenwrote an excellent story entitled "Neutron Star,"in which the tidal effects of one nearly destroyan unwary astronaut who comes too close. Itwon a Hugo Award (the science-fiction equivalentof an Oscar) the next year.

Actually, however, the events in the storycould not have happened. Tidal effects are nomystery to astronomers and haven't been sincethe days of Isaac Newton, 300 years ago. Anygroup of scientists capable of building a space-

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ship designed to approach a neutron star wouldcertainly understand the danger of the tidal ef-fect, and the astronaut would be certain (barringequipment failure) to remain at a safe distance.

7 BLACKHOLES

FINAL VICTORY

EVEN NOW we are not through.The nuclear force that keeps neutronium in

being can withstand a gravitational inpull intenseenough to collapse ordinary atoms and even theelectronic fluid. Neutronium can withstand theweight of masses beyond Chandrasekhar's limit.Yet surely, even the nuclear force is not infinitelygreat. Even neutronium cannot hold up massendlessly piled on mass.

Since there are stars up to 50 to 70 times asmassive as the Sun, it is not inconceivable thatonce collapse begins, it may on occasion bepowered by a gravitational fury even greater andmore intense than that which can be withstoodby a neutron star. What then?

In 1939, when Oppenheimer was working outthe theoretical implications of the neutron star,he took this possibility into consideration, too. It

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seemed to him that a collapsing star, if massiveenough, can contract with such force that eventhe neutrons will cave in under the impact; eventhe nuclear force will have to bow to gravitation.

What, then, is the next stopping point of thecollapse?

Oppenheimer saw that there is none-nofurther stopping point. When the nuclear forcefails, there is nothing left to withstand gravita-tion, that weakest of all forces, which whenadded to and added to by the endless pilingtogether of mass finally becomes the strongest.If a collapsing star crashes through the neu-tronium barrier, gravitation wins its final vic-tory. The star will thereafter keep on collapsingindefinitely, with its volume shrinking down tozero and its surface gravity increasing withoutlimit.

It appears that the crucial turning point is 3.2times the Sun's mass. Just as no white dwarfcan be more than 1.4 times the Sun's mass with-out collapsing further, so no neutron star can bemore than 3.2 times the Sun's mass withoutcollapsing further.

Any contracting mass that is more than 3.2times the Sun's mass cannot stop its contractionat either the white-dwarf stage or the neutron-star stage but must go beyond. Furthermore, itappears that any star on the main sequence thatis more than 20 times the mass of the Sun willnot be able to get rid of enough mass by super-nova explosion to make either a white dwarf ora neutron star possible, but must eventually con-tract to zero. For any star of spectral class 0,then, the final victory of gravitation seems asure thing once the nuclear fuel supply runs out.

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(While masses greater than 3.2 times theSun's mass must undergo this ultimate collapseonce the process starts, masses less than that maydo so, as we shall see.)

What happens when this final victory of grav-itation takes place and even neutronium givesway? What happens if a neutron star contractseven further?

For one thing the surface gravity of a con-tracting neutron star goes up steadily, and sodoes the escape velocity, as the surface of theshrinking object gets nearer and nearer that cen-tral point toward which all contraction tends.Already we saw earlier in the book that a neutronstar with the mass of our Sun has an escapevelocity of 200,000 kilometers per second, whichis two-thirds the speed of light.

If the matter in a neutron star continues tocontract and the surface gravity grows evenmore intense, surely there will come a stagewhere the escape velocity becomes equal to thespeed of light. The value of the radius of a bodywhere this is true is called the Schwarzschildradius because it was first calculated by the Ger-man astronomer Karl Schwarzschild (1873-1916).The zero point at the center is called the Schwarz-schild singularity.

For a mass equal to that of the Sun, theSchwarzschild radius is just under 3 kilometers.The diameter is equal to twice that, or 6 kilo-meters.

Imagine, then, a neutron star with the massof the Sun contracting through the neutron bar-rier and shrinking from its diameter of 14 kilo-meters down to one of 6 kilometers. Its densityincreases thirteenfold and becomes 17,800,000,-


000,000,000 g/cm 3. Its surface gravity is 1,500,-000,000,000 times that of the Earth, so an av-erage human being would weigh 100 trillionkilograms if he were standing on such an object.The tidal effect of such an object is 13 times asintense as that of a neutron star.

The most important property of such a super-collapsed object, however, is just the fact thatthe escape velocity is equal to the speed of light.(Naturally, if the object collapses to a size stillsmaller than the Schwarzschild radius, the escapevelocity becomes greater than the speed of light.)

It so happens that physicists are quite certainthat no physical object possessing mass can moveat a speed equal to or greater than that of light.That means that any body at the Schwarzschildradius or less cannot lose any mass by ejection.Nothing that possesses mass can escape its finalclutch, not even such objects as electrons, whichcan, with difficulty, escape from the neutron star.

Things can fall into such a supercollapsed ob-ject, but they cannot be ejected again. It is asthough the object was an infinitely deep hole inspace.

What's more, even light or any similar radia-tion cannot escape. Light consists of masslessparticles, so you might think the gravitationalpull of any object, however great that pull mightbe, would have no effect on light. By Einstein'stheory of general relativity, however, we knowthat light rising against gravity loses some ofits energy and undergoes the Einstein red shift.This has been an established fact ever sinceAdams detected it in connection with Sirius B.When a collapsed object is at the Schwarzschildradius or less, light rising from it loses all its

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energy and experiences an infinite red shift. Thismeans that nothing emerges.

This supercollapsed object acts not only like ahole but like a black one, since it can emit nolight or lightlike radiation. It is in fact called ablack hole for that reason.

The phrase scarcely seems to be appropriatefor an astronomical object whose existence isworked out by abstruse theoretical reasoning. Itis too common and everyday a phrase. Anothersuggested name, therefore, is collapsar, a short-ened version of collapsed star. The dramaticpicture of a "black hole" and the very simplicityof its name, however, seems to insure that itwill continue to be used.

We have then four types of possibly stableobjects:

1) Planetary objects, ranging from individualsubatomic particles up to masses equal to, say,50 times that of Jupiter but no more than that.These are all made up (except for individualsubatomic particles) of intact atoms, and theygenerally have overall densities of less than10 g/cm3.

2) Black dwarfs, which are white dwarfs thathave lost so much of their energy that they canno longer shine visibly. These have masses rang-ing up to 1.4 times the mass of our Sun but nomore than that. They are made up of electronicfluid within which are freely moving nuclei andthey have densities in the range of 20,000 g/cm8 .

3) Black neutron stars, which are neutronstars that have lost so much of their energythat they can no longer shine visibly. These havemasses ranging up to 3.2 times the mass of ourSun but no more than that. They are made up

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of neutronium, with densities in the range of1,500,000,000,000,000 g/cm8 .

4) Black holes, which yield no light, whichcan have masses up to any value, and which aremade up of matter in a state we cannot describeand with densities of any value up to the infinite.

But are these four varieties of objects trulystable in the sense that they will undergo nofurther change no matter how long a time theyexist?

If a member of any of these four classes werealone in the universe, as far as we can tell, itwould prove stable and would never undergoany substantial change. The trouble is, though,that none of these things are alone in the uni-verse. The universe is a vast melange of objectsin the different classes of stability, together withunstable objects such as stars that are evolvingtoward one of the latter three classes or, havingreached one of these classes, are still radiatinglight en route to final blackness and stability.

What happens then?Consider the Earth, for instance. It tends to

lose some of its mass as its atmosphere leaksvery slowly away. It also tends to gain some massas it collides with and retains meteoric matterto the tune of some 35,000,000 kilograms a day.This isn't much, compared with the total massof the Earth, but it is considerably greater thanthe amount of mass lost by the Earth each day.We may say, therefore, that the Earth is veryslowly, but steadily, growing more massive.

In the same way the Sun is constantly losingmass, partly by the conversion of hydrogen tohelium and partly by the ejection of protons andother particles in the form of a solar wind.

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However, it, too, must be gathering dust andmeteoric matter from the space it travels through.

The ability to lose mass is true of all objectsexcept black holes. (It is true of black holes, too,under special cases, according to some speculativesuggestions, as we shall see.) Even neutron starseject electrons, or we wouldn't be able to getthose microwave pulses. And supernovas ejectmasses of matter that can be several times themass of the Sun.

Nevertheless, it can easily be argued that thegeneral tendency in the universe is for largeobjects to grow at the expense of small. Wemight imagine, therefore, (simply as an abstractconception) that a planetary object might event-ually gain so much mass that it will undergonuclear ignition and become a star-a very smallone, of course-that will eventually reach thewhite-dwarf stage and finally become a blackdwarf.

We might also imagine that after a star hassettled down, one way or another, into the pre-sumably stable black-dwarf stage, it might pickup enough mass on its voyage through space tobreak down the electronic fluid and collapsefurther to a neutron star. A neutron star, in thesame way, might gain enough mass to breakdown the neutronium and collapse further to ablack hole-which, it might seem at first blush,can never lose mass and can only gain mass,with no upper limit to that gain.

There is only one object, then, that would trulyappear to be stable through eternity, and that isthe black hole. In the end, then-in the longdistant end-and always assuming that thingswill continue to move in the direction in which

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they now seem to be moving, we might decidethat the universe will consist of black holes only-and finally, perhaps, into one black hole con-taining everything. The entire universe will havecollapsed (as I imply in the title of this book).

Or perhaps it isn't quite that simple. We'llget back to the consideration of what the ultimatefate of the universe might be in terms of blackholes once we consider their properties some-what further.

And certainly the first property we ought toconsider is the matter of existence. In theory,black holes ought to exist; but in fact, do theyexist?

DETECTING THE BLACK HOLE

Detecting a black hole is not easy. Whitedwarfs, because of their small size and dimness,were far harder to detect, as such, than ordinarystars were. Neutron stars, smaller and dimmerstill, were even harder to detect and, if one hadto rely on light radiation alone, might never havebeen detected. It was microwave pulses that gavethem away. Obviously a black hole, which emitsneither light nor microwaves nor any similarradiation, might baffle observation altogether.

Yet the condition is not entirely hopeless.There is the gravitational field. Whatever hap-pens to the mass that seems to be endlesslyadded to, and compressed within, a black hole,that mass must remain in existence (as far aswe know), and it must continue to be the sourceof a gravitational field.

To be sure, the total gravitational pull exerted

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by a black hole at a great distance is no greaterthan the total gravitational pull exerted by thatmass in any other form. Thus, if you are 100light-years away from a giant star with 50 timesthe mass of the Sun, its gravitational pull is sodiluted by distance that it is undetectably small.If, somehow, that star becomes a black hole witha mass 50 times the mass of the Sun, its gravi-tational pull at a distance of 100 light-yearswill be precisely the same as before and will stillbe undetectable.

The difference is this: An object can get muchcloser to a black hole's center than to a giantstar's center, so it can experience an enormouslymore concentrated gravitational pull in the im-mediate neighborhood of a black hole than it evercan near the far-from-the-center surface of abloated star of the same mass.

Can the existence of such enormously con-centrated gravitational intensities be detectedsomehow at great distances?

By Einstein's theory of general relativity grav-itational activity releases gravitational waves,which, in their particle aspect, are spoken of asgravitons (just as the particle aspects of lightwaves are spoken of as photons). Gravitons arefar less energetic than photons, however, andcannot conceivably be detectable unless presentin unusually high energies, and then just barely.Nothing we know of is likely to produce detect-able gravitons-except possibly a large blackhole in the process of formation and growth.

In the late 1960s the American physicistJoseph Weber (1919-) used large aluminumcylinders, weighing several tons each and locatedhundreds of miles apart, as graviton detectors.

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Such cylinders would be very slightly compressedand expanded as gravitational waves passed.Weber detected gravitational waves in this man-ner, and this produced considerable excitement.The easiest conclusion, if Weber's data was cor-rect, was that enormously energetic events aretaking place at the center of the Galaxy. A largeblack hole might be located there.

Other scientists, however, have tried to repeatWeber's findings and have failed, so at this timethe question of whether gravitons have been de-tected or not remains in limbo. There may be ablack hole at the center of the Galaxy, butWeber's route to its detection is discounted now,and other ways of detecting black holes mustbe considered.

One other way, still using the black hole's in-tense gravitational field in its neighborhood, isto study the behavior of light that might be skim-ming past a black hole. Light will curve slightlyin the direction of a gravitational source; and itwill do so detectably, even when it skims pastan object like the Sun, with an ordinary gravita-tional field.

Suppose, now, that there is a black hole lyingprecisely between a distant galaxy and Earth.The light of the galaxy will pass the pointlikeblack hole, itself invisible, on all sides. On allsides the light is bent toward the black hole andis made to converge in our direction. This doesto light gravitationally what a lens does moreconventionally. The effect is, therefore, spokenof as a gravitational lens.

If we see a galaxy that despite its distancelooks abnormally large, we might suspect it is

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being magnified by a gravitational lens and thatbetween it and us lies a black hole.

No such phenomenon, however, has yet beenobserved.

Black holes, however, are not alone in theuniverse. It could be that there is ordinary matterin the vicinity. If so, sizable objects that happento approach too closely will be fragmented intodust and, together with matter already in theform of dust and gas, will be circling in an orbitaround the black hole as an accretion disk about200 kilometers outside the Schwarzschild radius.

Dust and gas moving in an orbit around theblack hole might well stay in such an orbit for-ever if the individual particles were not interferedwith. But mutual collisions bring about a trans-fer of energy, and some particles, losing energy,spiral inward closer to the black hole and even-tually may pass within the Schwarzschild radius,never to emerge again.

On the whole there would be a steady, smallinward leak. Inward-spiraling particles, however,lose gravitational energy, which is converted intoheat, and they are further heated by the stretch-ing and compression of tidal effects. The resultis that they are heated to enormous temperaturesand radiate X rays.

Thus, while we cannot detect a bare black holesurrounded by utter vacuum, we might conceiv-ably detect one that is swallowing matter, sincethat matter will, as its death cry, emit X rays.

The X radiation has to be intense enough todetect across many light-years of space, so it hasto represent more than a thin drizzle of oc-casional dust. There has to be torrents of matterswirling inward, and this means that the black

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hole has to be in pretty specialized surroundings.Black holes, for instance, are perhaps most

likely to be found where there are huge concen-trations of stars in close proximity to one an-other and where mass buildup might most easilyreach the pitch where black-hole formation,sooner or later, will be inevitable.

There are, for instance, globular clusters ofstars in which some tens of thousands or evenhundreds of thousands of stars are clustered to-gether in a well-packed sphere. Here in our ownneighborhood of the universe stars are separatedby an average distance of about 5 light-years. Atthe center of a globular cluster they may beseparated by an average distance of 1/2 light-year. A given volume of space in a globularcluster might include 1,000 times as many starsas that same volume in our own neighborhood.

As a matter of fact, a number of globularclusters have been tabbed as X-ray sources, andthe possibility is that there are indeed blackholes at the center. Some astronomers speculatethat such globular-cluster holes may have masses10 to 100 times that of the Sun.

The central region of galaxies resemble giantglobular clusters containing tens of millions oreven hundreds of millions of stars. The averageseparation in the central regions may be 1/10light-year, and may even diminish to 1/40 light-year at the very center. A given volume of spacein a galactic core may have hundreds of thou-sands, even millions, of stars for every one starpresent in such a volume in our own neighbor-hood.

Such crowding doesn't mean stars are bump-ing one another. Even 1/40 light-year is 40

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times the distance between the Sun and Pluto.Still, the chance of violent events would surelyincrease as the star density in space increases.In recent years there has been increasing evi-dence of explosions at the centers of galaxies,such energetic explosions that astronomers areat a loss to account for the energies released.Could black holes in some form or other be re-sponsible? Possibly

Even our own galaxy is not immune. A verycompact and energetic microwave source hasbeen detected at the center of our galaxy, and itis tempting to suppose that a black hole is presentthere. Some astronomers even go as far as tospeculate that our galactic black hole has themass of 100 million stars, so that it must havethe mass of 1/1,000 of the entire Galaxy. It hasa diameter of 700,000,000 kilometers, whichmakes it the size of a large red-giant star, but itis something so much more massive that it willdisrupt whole stars, tidally, if they venture tooclose, or gulp them down whole before they canbreak up, if their approach is rapid enough.

Perhaps every globular cluster and galaxy hasa black hole at the center, taking in and nevergiving out, relentlessly gnawing at normal matterand always growing. Will they swallow up every-thing eventually? Theoretically, yes, but the rateof doing so may be very small. The universe is15 billion years old, and yet globular clusters andgalaxies still exist unswallowed. There is even asuggestion that central black holes are morenearly the creators of clusters and galaxies ratherthan their devourers. The black hole may havecome first and then served as a "seed," gathering

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stars about itself as superaccretion disks thatbecome clusters and galaxies.

Constructive as a black hole might have beenat first, it is nevertheless swallowing matter now,and however slow the rate, it would not be com-fortable to be near one. If indeed there is a blackhole at the center of every galaxy, the one closestto us is the one at the center of our own galaxy,and that is 30,000 light-years away. This is acomfortable distance, even with a giant blackhole at the other end.

If there is a black hole at the center of everyglobular cluster, the nearest one to us is in thecluster known as Omega Centauri, which is22,000 light-years away-still a comfortabledistance.

So far, however, black holes at the centers ofclusters and galaxies are speculative only. Wecan't see into a cluster or a galactic core to studyits center directly. The vast numbers of periph-eral stars hide it, and any indirect evidence weget in the form of X rays or even gravitationalwaves is not likely to be conclusive in the for-seeable future.

Anything else, then?Suppose we consider not vast conglomerations

of stars but merely pairs of them. Suppose weconsider binaries.

We can tell the total mass of a binary if itsdistance from us and the period of its revolutioncan be determined. If one star looks very smalland yet has a large mass, we can tell it is inone stage of collapse or another. That is how thecompanion of Sirius was detected and how it wasfinally recognized as a white dwarf.

Suppose, then, we have a binary system in

BLACK HOLES

which both members have collapsed into blackholes. The masses, however invisible as a matterof direct observation, are still circling each otherand are still, most likely-if young enough-picking up debris from the matter blown offduring a supernova explosion. Therefore onewould detect a double X-ray in revolution arounda center of gravity. Eight X-ray binaries are nowknown, but as yet the nature of the source inthose cases remains unknown.

What if only one star of a binary collapses intoa black hole? The companion of that black hole,which could easily be many billions of kilometersdistant, will be buffeted by the energy and willfind itself circling through a volume of spacethat is now much dustier than it had been,thanks to the matter ejected in the supernovathat preceded the formation of the black hole.

The companion may grow warmer as it col-lects some of this matter and shorter lived inconsequence, but for the time being it remainson the main sequence. The gravitational pull towhich it is subjected does not increase as aresult of the new black hole it has as a partner;rather it is likely to decrease due to the loss ofmass in the supernova explosion of its partner.

As viewed from Earth, what one would ob-serve would be a normal star of the main se-quence, moving in an orbit about a center ofgravity at the opposite side of which was merelyan intense source of X rays.

Would these X rays indicate the presence ofa neutron star or a black hole? There are dif-ferences that might be seized upon for identifica-tion. The X rays from a neutron star might bein the form of regular pulses matching the micro-

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wave pulses. Two such X-ray pulsars have, infact, been detected, Centaurus X-3 and HerculesX-1. From a black hole the X rays would varyirregularly as matter is swallowed sometimes incopious quantities, sometimes in sparse quan-tities. In addition, if such a point source of Xrays has a mass of more than 3.2 times that ofthe Sun, it must be a black hole. (If a mass morethan 3.2 times the mass of the Sun should some-how prove to be, incontrovertibly, a neutron star,that would upset the entire theory of black holes.So far, such a too-massive neutron star has notbeen found.)

In the early 1960s, when X-ray sources werefirst discovered in the sky, a particularly intensesource was located by rocket observation in 1965in the constellation Cygnus. The X-ray sourcewas named Cygnus X-1.

In 1969 an X-ray detecting satellite waslaunched from the coast of Kenya on the fifthanniversary of Kenyan independence. It wasnamed Uhuru from the Swahili word for "free-dom." It multiplied knowledge of X-ray sourcesto unlooked-for heights, detecting 161 suchsources, half of them in our own galaxy and 3of them in globular clusters.

In 1971 Uhuru detected a marked change inX-ray intensity in Cygnus X-1, which virtuallyeliminated it as a possible neutron star andraised the possibility of a black hole. Now thatattention was eagerly focused on Cygnus X-1,microwaves were also detected, and this made itpossible to pinpoint the source very accuratelyand place it in just next to a visible star.

This star was HD-226868, a large, hot bluestar of spectral class B, some 30 times as massive

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as our Sun. C. T. Bolt of the University ofToronto showed HD-226868 to be a binary. It isclearly circling in an orbit with a period of 5.6days-an orbit the nature of which makes itappear that the other star is perhaps 5 to 8times as massive as the Sun.

The companion star cannot be seen, however,even though it is a source of intense X rays.If it cannot be seen, it must be very small. It istoo massive to be either a white dwarf or a neu-tron star, and the inference seems to be, then,that the invisible star is a black hole.

Furthermore, HD-226868 seems to be expand-ing as though it were entering the red-giantstage. Its matter would therefore be spilling overinto the black-hole companion, which would ex-plain why the latter is so intense an X-ray source.

This is still rather indirect evidence, and notall astronomers agree that Cygnus X-1 is a blackhole. A lot depends on the distance of the binary.The greater the distance, the greater the massrequired of the stars in order to have them haveso short an orbital period, and the more likelyCygnus X-1 is massive enough to be a blackhole. Some astronomers maintain that the binaryis considerably closer than the 10,000 light-yearsits distance is usually estimated to be and thatCygnus X-1 is therefore not a black hole. Theconsensus, however, seems (at least so far) tofavor the black-hole hypothesis.

A few other binaries have since been observedin which one of the pair may be a black hole.These include X-ray sources known as X Perseiand Circinus X-1.

There are also black-hole possibilities whereX-ray emission isn't a factor. In some cases you

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can deduce a very close binary by the behaviorof the spectral lines. Epsilon Aurigae, from thebehavior of its spectral lines, seems to be re-volving around an invisible companion, EpsilonAurigae B. What's more, the spectroscope datamakes it seem that Epsilon Aurigae A, the visiblestar, has a mass 17 times that of the Sun, whileEpsilon Aurigae B, the invisible one, has a mass8 times that of the Sun. Again the combinationof invisibility and great mass indicates the pos-sibility that Epsilon Aurigae B is a black hole(though some astronomers maintain EpsilonAurigae B is invisible because it is a new starin the process of formation, and has not yet ig-nited).

MINI-BLACK HOLES

If black holes exist merely at the centers, ofgalaxies, then there would be only one in ourgalaxy. If they existed also at the center of glob-ular clusters, there would be perhaps 200 of themin our galaxy. However, if they also exist as partof ordinary binary systems, there is the potenti-ality of vast numbers of them. After all, thereare tens of billions of binaries in our galaxy.

What's more, they need not be part of binariesonly. It so happens that the nearby companiongives away the existence of a black hole, whichis why we think of them in connection withbinaries. Black holes might also evolve fromsingle stars, and then, without nearby matter toproduce the X rays and a nearby companion tooffer a measurement of mass, they might beimpossible to detect, but they would be therejust the same.

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Taking all this into account, some astronomerssuspect there may be as many as a billion star-sized black holes in any galaxy like ours. If thisis true and if the black holes are more or lessevenly distributed, the average distance betweenthem is 40 light-years and any -particular starmight be, on the average, 20 light-years fromsome black hole or other.

Of course, it is more likely that the black holesare distributed as unevenly as the stars them-selves are. Ninety percent of all the stars in ourgalaxy (or in any similar galaxy) are locatedin the relatively small central regions. Only 10percent are in the voluminous, but sparsely pop-ulated, spiral arms, where our own Sun is located.It might be, then, that only 10 percent of theblack holes of our galaxy are located in the spiralanms, that they are well spread out here, and thatit is likely that the nearest black hole to us isseveral hundred light-years away.

Of course, in talking about black holes, wehave so far been talking about black holes withmasses equal to those of massive stars, and thereare indeed astronomers who think that the aver-age black hole has a mass 10 times that of ourSun.

It might seem that anything much less couldn'texist, since only star-sized objects could possessa gravitational field large enough to produce acompression intense enough to break throughthe neutronium barrier and produce a black hole.

According to Einstein's theory of general rela-tivity, however, black holes can come in all sizes.Any object possessing mass, no matter how smallthat mass may be, also possesses a gravitationalfield. If the object is compressed into a smaller

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and smaller volume, that gravitational field be-comes more and more intense in its immediatevicinity and eventually becomes so intense thatthe escape velocity from its surface is greaterthan the speed of light. It has, in other words,shrunk within its Schwarzschild radius.

The Earth would become a black hole if itshrank to a diameter of 0.87 centimeter (the sizeof a large pearl). A mass the size of MountEverest would become a black hole if it shrankto the size of an atomic nucleus.

We might go on in this way until we reachthe smallest mass known, that of an electron,but there are subtle theoretical reasons for sup-posing that masses less than 10-5 grams may beunable to form black holes. A mass of 10-5 grams(a speck of matter just visible to the eye) wouldbecome a black hole if it were reduced to a diam-eter of something like 10-lO cm, at which time itwould have a density of 1094 g/cm

3. (At such a

density an object the size of an atomic nucleuswould have a mass equal to that of the entireuniverse.)

But what can possibly compress small objectsinto such mini-black holes. It can't be their owngravitational fields, so it must be some compress-ing force from outside. But what force from out-side can be strong enough to produce them?

In 1971 the English astronomer StephenHawking suggested that one conceivable forcewould have come at the time the universe wasformed-the force of the big bang itself. Withvast quantities of matter exploding all over theplace, some different sections of the expandingsubstance might collide. Part of this collidingmatter might then be squeezed together under

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enormous pressure from all sides. The squeezedmatter might shrink to a point where the mount-ing gravitational intensity would keep it shrunkforever.

There is, of course, no evidence whatsoeverthat such mini-black holes exist, not even as muchevidence as what Cygnus X-1 supplies for star-sized black holes. What's more, some astronomersscout the whole idea and think that there existsonly black holes with masses distinctly greaterthan that of our Sun.

Nevertheless, if mini-black holes exist, then itis likely that there are many more of these thanof the star-sized ones. Can it be, then, that ifthere are star-sized black holes spread at averageseparations of 40 light-years, there might be awhole array of moderate-sized to microscopic-sized black holes at much closer intervals? Mightspace be littered with them? Hawking thinksthere may be as many as 300 per cubic light-year in the universe.

It is important to remember that there is noindication of this whatever. But then, if mini-black holes are thickly spread in space, the totalgravitational effect is tiny, and it can be detectedonly in the immediate neighborhood of the object-a few kilometers away, a few centimetersaway, a few micrometers away, depending on itssize.

To be sure, such tiny black holes must beceaselessly growing, for they will engulf any dustparticle with which they might collide-at leastthat is the usual view of matters. (Hawking alsoadvances subtle reasons for supposing that mini-black holes can lose mass, and that really small

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ones might "evaporate" and explode before theycan gain much mass.)

If a mini-black hole collides with a larger body,it will simply bore its way through. It will engulfthe first bit of matter with which it collides, lib-erating enough energy in the process to meltand vaporize the matter immediately ahead. Itwill then pass through the hot vapor, absorbingit as it goes and adding to the heat, emerging atlast as a considerably larger black hole than itwas when it entered.

(If a mini-black hole enters a larger bodythat has very little in the way of energy of mo-tion, it may become trapped within the body andsink, eventually, to its center where it may gradu-ally eat a hole out for itself and continue to growat an ever slower rate like a parasite consumingits host.)

To be sure, the volume of such mini-blackholes is so tiny, the total gravitation so small,and the volume and emptiness of space so enor-mous that collisions must be rare indeed. In thewhole 15 billion years since the big bang thevast majority of the tiny black holes must havegained so little mass that they are still tiny blackholes and still just about impossible to detect.

In the face of the olds, of course, a mini-blackhole might collide with the Earth. The heat pro-duced as it passes through the atmosphere wouldbe enough to produce spectacular effects thatpeople couldn't help noticing, and its passagethrough the Earth might produce effects as well.

Has it ever happened?We don't know. There are no signs that we

know of that anything like this happened in pre-historic times, but can we be sure? Was Sodom

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destroyed because a mini-black hole struck? Howcan we tell? The destruction might have beencaused by an ordinary meteorite, a volcanic erup-tion, and earthquake, or the whole tale may bemythical. The records aren't good enough.

Has anything happened in historic times thatmight be accounted for by a mini-black hole?One things

On June 30, 1908, what was at first thoughtto be a large meteor strike occurred in theTunguska region of central Siberia. Every treefor 30 kilometers in every direction was knockeddown, and an entire herd of 500 reindeer wasdestroyed. In later years thorough searches of thearea found no craters and no meteor fragments.

Researchers decided that the explosion musthave taken place in the atmosphere. Somethought it might have been a small comet madeup of icy materials that melted and vaporized inthe passage through the atmosphere, creating ahuge bang and peppering the Earth with frag-ments of gravel (embedded in the ice) in sucha way that no noticeable gouges appeared.

Others thought it might have been an exampleof antimatter that struck the Earth. Antimatteris made of material resembling ordinary matterexcept that all the subatomic particles composingit are opposite in properties to the particles com-posing ordinary matter. Antimatter interacts withmatter, converting everything on both sides intoenergy. A particle of antimatter striking thenormal matter of Earth will disappear, taking anequal mass of normal matter with it and pro-ducing a bang equal to that of a hydrogenbomb with a nuclear warhead some 15 or moretimes as massive as itself.


It has even been suggested that the bang wascaused by the wreck of a nuclear-powered space-ship manned by extraterrestrial astronauts.

One other suggestion, however, was that itwas a mini-black hole that did it, one that struck,created a vast explosion as it passed through theatmosphere, entered the Earth at an angle,passed through and absorbed more matter, andemerged at last in the North Atlantic Ocean,where it produced a gigantic water spout and ex-plosion that went unseen and unheard by man.It then proceeded back into space, considerablylarger than when it arrived but still a mini-blackhole.

Of course, this mini-black-hole suggestion isjust speculation, too. Some astronomers pointout that a mini-black hole passing through thebody of the Earth and out the ocean might wellhave set off earthquakes and should surely haveinitiated a tidal wave-yet neither event tookplace in conjunction with the strike of 1908.

There is simply no way, as yet, of either prov-ing or disproving the mini-black-hole explanationof the 1908 event. There may never be a wayunless a similar event happens again at thetime when scientists, with their knowledge of theuniverse vastly advanced over what it was in1908, can study the event as it occurs.

THE USE OF BLACK HOLES

Naturally, any scientist, however dedicated,cannot view the possibility of a collision betweena mini-black hole and the Earth with satisfaction.If the 1908 event had not fortunately struck one

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of the few areas of Earth's land surface on whichno human beings lived for many kilometers inevery direction, there might have been fearfulhuman and property destruction.

One can easily imagine such a strike utterlywiping out Washington, D.C., or Moscow, forinstance, if it happened to be unfortunatelyaimed. The results might so resemble the strikeof a hydrogen bomb that whichever superpowerwas struck might launch a retaliatory strike be-fore learning the truth, and the whole Earthmight be ravished.

Of course, I can't repeat often enough that theSiberian strike might not have been caused by amini-black hole; that there may be no such thingsas mini-black holes; that if there are, the chancesof collision may be far less than that of beingstruck by a meteorite while you are asleep inyour bed.

Still-what if mini-black holes exist?We might eventually learn to protect ourselves

against them. If human beings ever reach thestage where they have observatories and colonieson other worlds of the solar system and in arti-ficial structures in space itself, there may comean opportunity to study mini-black holes in theirnative haunt, so to speak, under conditions thatdon't involve a collision with Earth.

In fact, we can even dream that techniqueswill be developed to capture a black hole bymeans of its gravitational field (very intense inits immediate neighborhood but quite small intotal) and force it to veer in its flight by justenough to effect a miss if it was otherwise head-ing for Earth. That would be a side effect of

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space exploration that might well be worth anyamount of money spent on it.

Those who speculate far in advance of thepresent capabilities of science and who enjoydreaming up fantastic visions of the future *might even find it possible to hope that we arerelatively close to a black hole (though far enoughaway to be safe).

A black hole is, after all, a gateway to enor-mous energies. Any object spiraling into it willin the process radiate a great deal of energy.

Most of the energy in any object resides in itsmass, since each gram of mass is the equivalentof 9 x 1020 ergs of energy. The energy we getby burning oil or coal, for instance, makes useof only a tiny fraction of 1 percent of the massof the fuel. Even nuclear reactions liberate onlya couple of percent of the mass. An object spiral-ing into a black hole or, under certain conditions,skimming it without actually entering it may con-vert up to 30 percent of its mass into energy.

What's more, only certain substances can beburned to yield energy; only certain atomic nucleican be split or fused to yield energy. Anything,however-anything-will yield energy on fallinginto a black hole. The black hole is a universalfurnace, and everything that exists and has massis its fuel.

Perhaps we can imagine some far-advancedcivilization of the future tapping the black holefor the energy it can produce, stoking it withasteroids as we might stoke an ordinary furnacewith coal. In that case, if the galaxy possesseshundreds, or even thousands, of advanced civil-

* This includes myself, since (as the reader may know) I am ascience-fiction writer of some repute.

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BLACK HOLES

izations (as some astronomers suspect it might),it may be those that are reasonably close tosizable black holes who may have the richestsupply of available energy and who flourish asearthly nations do when they are rich in energyresources.

To be sure, it is exceedingly unlikely we willfind massive black holes that we can use as auniversal furnace. Nor might we really be anxiousto find one within too few light-years of ourselves,since the larger they are, the more unmanageablethey are.

Perhaps it is better, until such time as ourtechnology advances sufficiently, to make do withone of the much more common (if they exist atall) mini-black holes and make use of more con-ventional means of gaining energy.

Suppose we find a mini-black hole somewherein the solar system passing through or, evenbetter, orbiting the Sun. We might in each caseseize it by its gravitational field, tug it in thewake of some massive object, and set it up inan orbit around the Earth (if a nervous humanitywill allow it).

A stream of frozen hydrogen pellets can thenbe aimed past the mini-black hole so that it skimsthe Schwarzschild radius without entering it.Tidal effects will heat the hydrogen to the pointof fusion, so that helium will come through atthe other end. The mini-black hole will thenprove the simplest and most foolproof nuclear-fusion reactor possible, and the energy it producescan be stored and sent down to Earth.

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ENDINGSANDBEGINNINGS

THE END?

WE ARE BOUND to be curious about what canpossibly happen to matter that falls into a blackhole.

It is very difficult to satisfy that curiosity. In-deed, all we can do is speculate, for we have noway of telling whether any of the laws of naturethat have so painstakingly been worked out byobserving the universe around us can hold underthe extreme conditions of a black hole. We can'tduplicate those conditions in any way here onEarth, and we can't observe those conditions inthe heavens, since we know of no black hole inour vicinity.

It follows, then, that we can only assume thatthe laws of nature do hold and then try to specu-late what might happen.

One thing that might happen is that the worst

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does not happen or at least is not observed tohappen. How, for instance, can mass compressdown to zero volume and infinite density at theSchwarzschild singularity? This so boggles themind that we must search for something thatwill prevent it.

For instance, Einstein's theory makes it seemthat increasing intensity of gravity has the effectof slowing the passage of time. This is not some-thing we can observe in the universe very easily,for outside of black holes and neutron stars,those gravitational intensities we encounter haveonly a negligible effect on the time rate.

Because of this, if we could observe somethingdropping down into a black hole, we would seeit move more and more slowly as it approachesthe Schwarzschild radius, creeping ever moreslowly until at the Schwarzschild radius we wouldsee it stop dead. However, as it approaches, theEinstein red-shift, also dependent on gravitationalintensity, robs light and lightlike radiation ofmore and more of its energy. The object droppingdownward will grow dimmer as it moves moreslowly, and at the Schwarzschild radius, whereit freezes, it also blacks out. The result is thatwe cannot possibly observe anything within theSchwarzschild radius.

If we imagine an astronaut falling into a blackhole and somehow retaining consciousness andthe ability to be aware of his surroundings, hewould feel no change in time rate; that changeis only something an outsider would see as exist-ing.

The astronaut falling into a black hole wouldpass through the Schwarzschild radius withoutknowing it was any kind of barrier, and he would

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ENDINGS AND BEGINNINGS

keep on falling toward the singularity ahead.However, one way of interpreting the events thatfollow is to suppose that from the standpoint ofthe astronaut the distance before him wouldexpand as he fell, so that though he might fallforever, he would never reach the center. Theblack hole in that view is a bottomless hole.

Although in either way of looking at objectsfalling into a black hole, there is no reaching thecenter, no zero volume, no infinite density-yetthere is also no turning back. The fall is irreversi-ble, so once again let us consider the possibleend of the universe.

If there is truly no way to reverse or neutralizethe black hole, then those that exist now canonly grow; and new ones may form.

If there is a black hole at the center of everygalaxy and at the center of every globular cluster,then in the end (however long delayed) eachgalaxy will become a large black hole surroundedby satellite black holes that are much smaller.

Two black holes can collide and coalesce, buta black hole once formed cannot split up. There-fore we might imagine that sooner or later theglobular cluster black holes in their orbit aroundthe galactic black hole may coalesce with oneanother and eventually with the central one, sothat, given enough time, the galaxy will be oneblack hole only.

Galactic units may consist of one galaxy only,but they may also consist of several galaxies (inextreme cases, several thousand) that are boundtogether by gravitational attraction. Each galaxyin a unit may be a black hole, and these maycoalesce, too.

Can we go on to suppose that all the black

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holes in the universe will eventually coalesce intoone universal black hole?

Not necessarily. The universe is expanding, sothe galactic units (either single galaxies or galac-tic clusters) are steadily increasing their distancefrom one another. Most astronomers seem to feelthat this will continue indefinitely into the future.If so, we have the vision of a universe consistingof billions of black holes, each with a mass ofanywhere from millions to trillions times that ofour Sun, moving endlessly away from one an-other.

The very act of expanding, however, may justpossibly introduce a change.

Back in 1937 the English physicist Paul AdrienMaurice Dirac (1902-) advanced the startlingsuggestion that the intensity of the gravitationalforce generally depends upon the overall prop-erties of the universe. The greater the averagedensity of the universe, the stronger the gravita-tional force is, relative to the other forces of theuniverse.

Since the universe is expanding, the averagedensity of matter is decreasing as it spreads outover a steadily greater volume. It is because ofthe great expansion that has taken place so far(in this view) that the gravitational force is soweak in comparison with the others, and as theuniverse continues to expand, it will grow weakerstill.

Dirac's suggestion has not yet been observedto be true, and many physicists suspect that thegravitational constant (the value of which dic-tates the basic strength of the gravitationalforce) is not only the same everywhere in spacebut does not vary with time, either. Neverthe-


less, if Dirac's suggestion should prove to be true,it alters the picture just described.

As the universe expands and gravitation growsever weaker, those objects held together prima-rily by gravitational force will expand and becomeless compact and dense. This will include whitedwarfs and neutron stars that have alreadyformed, and it will also include black holes. Thetendency will be for all objects to bloat intomatter held together by the electromagnetic forceor not held together at all. Even black holes will,little by little, disgorge, and in the end the uni-verse will be a vast, incredibly thin cloud ofgravel, dust, and gas growing endlessly vasterand thinner.

If this is so, it might seem that the universebegan as a huge mass of compressed matterand will end as a huge volume of thin matter.

This raises the puzzle of where the compressedmatter came from. We needn't worry about thematter as such, for it is just a very compactform of energy, and we might suppose that theenergy has always existed and always will exist-much of it in the form of matter. The questionis, how did the matter come to be compressedinto the cosmic egg to begin with?

We might suppose that if we consider theuniverse to progress from compressed to ex-panded, we are taking into account only half thelife cycle.

Suppose the universe began as an endlesslythin volume of gravel, dust, and gas. Slowly,over incredible eons, it condensed until it formedthe cosmic egg, which then exploded and overequally incredible eons it has been restoringmatter as it had been. We happen to be living

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during the period shortly after (a mere 15 billionyears after) the explosion.

Yet somehow the thought of the universe asa one-shot seems vaguely unsatisfactory. If dis-persed matter could collect itself, coalesce, con-tract, and finally form a cosmic egg, then whymay not the dispersed matter that forms as theend product of the cosmic-egg explosion (whetherit consists of black holes or of dispersed matter)collect itself again, contract once more, and forma second cosmic egg?

Why may not this be repeated over and over?Why, in short, might there not be an endlesslyoscillating universe?

Astronomers have worked out those conditionsthat are required to produce an oscillating one.The choice depends on something like escapevelocity. There is a certain gravitational forceamong the galactic units of the universe gener-ally, and there is an escape velocity associatedwith that force. If the universe is expandingoutward at a velocity greater than the escapevelocity, then it will expand forever and willnever contract. If it is expanding at less thanthe escape velocity, then the present expansionmust eventually come to a halt, and the contrac-tion must then begin.

But is the present observed velocity of expan-sion larger or smaller than the escape velocity?That depends on the value of the escape velocity,which depends on the value of the overall grav-itational force among the galactic units, whichdepends, it turns out, on the average density ofmatter in the universe.

The greater the average density of matter inthe universe, the greater the gravitational force

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among the galaxies, the greater the escape veloc-ity-and the greater the likelihood that thepresent velocity of expansion is not greater thanthe escape velocity and that the universe willoscillate, that it is closed.

Naturally it is difficult to determine the averagedensity of the universe, since it is hard to de-termine how much total mass is present in alarge enough volume of it to be representative ofthe whole. Making use of the best data available,some astronomers seem quite convinced that theaverage density is only about 1/100 the valueneeded for oscillation, that the universe is openand is doomed to expand forever. (If the gravita-tional force is weakening as the universe ex-pands, then an even greater average density isrequired for oscillation, and the apparent densityfalls even further short of that requirement.)

And yet although the arguments against aclosed and oscillating universe seem strong, canthey really be the last word? Clusters of galaxiesthat seem to be held together by gravitationalpull nevertheless don't seem to have sufficientmass to supply that pull. They should be flyingapart in response to the general expansion of theuniverse, and yet they do not seem to be doingso. There is thus what is called the problem ofthe missing mass.

Can that missing mass consist of black holes?Except in a very few cases there is no way ofdetecting black holes, and we don't have the fog-giest notion how much mass is tied up inde-tectably in those black holes of all sizes. It seemsdifficult to believe that black holes account for ahundred times as much mass as do all the visibleobjects of the universe. Yet we are on the very

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borderline of what we can observe and reasonout, and we can't afford to be too certain one wayor the other. The evidence seems to point to anopen, over-expanding universe, but it may bethat, counting the black holes, there is enoughmass to keep the universe closed and oscillatingafter all.

WORMHOLES AND WHITE HOLES

The discomfort over an open, ever-expanding,one-time-only universe is such that astronomersseem to twist and turn in an effort to get awayfrom the evidence that points to it.

Back in 1948 Thomas Gold, along with theEnglish astronomers Fred Hoyle and HermannBondi, tried to get around it by suggesting whatcame to be called the continuous creation uni-verse. The thought was that matter would becreated continuously, an atom at a time, hereand there in the universe. It would be createdat a rate so low that we couldn't detect it.

Nevertheless, as the universe expanded andthe space between galactic units increased,enough matter would be formed to collect intonew galaxies in that space between. On the wholejust enough galaxies would be formed to make upfor the spreading apart of the old ones. Theuniverse would be a vast melange of galaxiesranging from those just forming through all thestages of development to those just dying. Theuniverse would be infinitely large in space andeternally enduring in time. Stars and galaxieswould be born and would die, but the universe

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as a whole would be immortal and would neithercome into being nor go out of being.

This was an attractive theory, but the evidencein its favor was almost nonexistent and nevergrew any stronger. In fact it grew weaker. Ifthe continuous creation universe were what ac-tually existed, then there would never have beena big bang. For that reason any evidence thatseemed to substantiate the big bang tended towipe out continuous creation.

In 1964 American physicist Robert HenryDicke (1916-) pointed out that the big bang, ifit took place 15 billion years ago, must have lefttraces that should even now be visible 15 billionlight-years away (for it takes light 15 billionyears to get here from that distance, and so thelight of the big bang is just arriving now).

The big-bang radiation, of a very energeticand short-wave type, has shifted, because of thisvast distance, far toward the low-energy red endof the spectrum. It has shifted past the red andinto the much longer, lower-energy microwavesection of the spectrum. Since the big bang mustbe visible 15 billion light-years away in any direc-tion, the microwaves must come from all partsof the sky as a background radiation.

In 1965 two scientists at Bell Telephone Lab-oratories, Arno A. Penzias and Robert W. Wilson,demonstrated the existence of a faint backgroundradiation with just the characteristics Dicke hadpredicted. The big bang had been detected, andcontinuous creation has been (at least for now)killed.

That route for avoiding the open universe hasfailed. There are, however, others, and for thoselet us return to the black holes.

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So far we have been talking about black holesthat have only one property-mass. The natureof the mass does not matter. If a kilogram ofplatinum, or a kilogram of hydrogen, or for thatmatter a kilogram of living tissue is added to ablack hole, what is added is a kilogram of masswithout any history of its previous state.

There are two other properties, and only two,that can be possessed by a black hole. One iselectric charge, and the other is angular mo-mentum. That means that any black hole can bedescribed completely by measuring its mass, elec-tric charge, and angular momentum. (It is pos-sible for electric charge and angular momentumto be each zero; but mass cannot be zero, orit is not a black hole.)

While a black hole may have an electriccharge, it can only have it if the mass thatformed the black hole to begin with or that isadded to it afterward has an electric charge. Inpoint of fact the electric charges, positive andnegative, in sizable pieces of matter tend to beequal in quantity, so the overall charge is zero.Consequently, black holes are quite likely to haveessentially zero charge.

Not so with angular momentum. There, in-deed, the situation is reversed, and it is quitelikely that every black hole has a considerableangular momentum.

Angular momentum is a property of any objectrotating on its axis, or revolving around an out-side point, or both. Angular momentum includesboth the speed of rotation or revolution of theobject and the distance of its various parts fromthe axis or center around which it turns. Thetotal angular momentum of a closed system

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(one in which no angular momentum can leakin or out) must be conserved; that is, it canneither be increased nor decreased.

This means that if the distance is increased,the speed of turning must be decreased, and viceversa. An ice skater takes advantage of this whenhe sets up a spin with his arms out-stretched.He draws his arms in toward his body, decreasingthe average distance of the parts of his bodyfrom the axis of rotation, and his rate of spinincreases markedly. He extends his arms again,and he slows down at once.

Every star we know of rotates about its axisand therefore has a large amount of rotationalangular momentum. When a star collapses, tomake up for that, its speed of rotation must in-crease. The more extreme the collapse, the greaterthe gain in speed of rotation. A brand-new neu-tron star can spin as much as a thousand timesa second. Black holes must spin more rapidlystill. There's no way of avoiding that.

We can say, then, that every black hole hasmass and angular momentum.

The mathematical analysis of Schwarzschildapplied only to nonrotating black holes, but in1963 the astronomer Roy P. Kerr worked out asolution for rotating black holes.

In rotating black holes the Schwarzschildradius is still there, but outside it is a stationarylimit, which forms a kind of equatorial bulgearound the black hole as though it were some-thing pushed outward by the centrifugal effect.

An object falling within the stationary limitbut remaining outside the Schwarzschild radiusis semitrapped. That is, it can still get out, butonly under special circumstances. If it happens

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to move with the direction of the turn, the rotat-ing black hole will tend to drag the object aroundlike a stone in a sling and to hurl it back outbeyond the stationary limit with more energythan it entered with. The additional energy isat the expense of the black hole's rotation. Inother words angular momentum is transferredfrom the black hole to the object, and the blackhole slows down.

In theory up to 30 percent of the entire energyof a rotating black hole can be milked out of itby carefully sending objects through the sta-tionary limit and collecting them on the wayout, and this is another way in which some ad-vanced civilizations might use black holes as anenergy source. * Once all the rotational energyis gone, the black hole has only mass; the sta-tionary limit coincides with the Schwarzschildradius. The black hole is then said to be "dead,"since no further energy can be obtained from itdirectly (though some can be obtained frommatter as it spirals into it).

Even stranger than the possibility of strippingrotational energy from the black hole is that theKerr analysis offers a new kind of end for matterentering a black hole. This new kind of end wasforeshadowed by Albert Einstein and a co-workernamed Rosen some 30 years earlier.

The matter crowding into a rotating black hole(and it is very likely that there is no other kind)can, in theory, squeeze out again somewhereelse, like toothpaste blasting out of a fine hole

* Not all astronomers agree with this concept of stripping the rota-tional energy of a black hole. In fact almost anything some astronomerssuggest about a black hole is denied by other astronomers. We are hereat the very edge of knowledge, and everything, one way or the other,is very uncertain and iffy.

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in a stiff tube that is brought under the slow pres-sure of a steamroller.**

The transfer of matter can apparently takeplace over enormous distances-millions or bil-lions of light-years-in a trifling period of time.Such transfers cannot take place in the ordinaryway, since in space as we know it the speed oflight is the speed limit for any object with mass.To transfer mass for distances of millions orbillions of light-years in the ordinary way takesmillions or billions of years of time.

One must therefore assume that the transfergoes through tunnels or across bridges that donot, strictly speaking, have the time character-istics of our familiar universe. The passagewayis sometimes called an Einstein-Rosen bridge, or,more colorfully, a wormhole.

If the mass passes through the wormhole andsuddenly appears a billion light-years away inordinary space once more, something must bal-ance that great transfer in distance. Apparentlythis impossibly rapid passage through space isbalanced by a compensating passage throughtime, so that it appears 1 billion years ago.

Once the matter emerges at the other end ofthe wormhole, it expands suddenly into ordinarymatter again and, in doing so, blazes with radi-ated energy-the energy that had, so to speak,been trapped in the black hole. What we haveemerging, then, is a white hole, a concept firstsuggested in 1964.

If all this is really so, white holes, or at leastsome of them, might conceivably be detected.

That would depend, of course, upon the size

*e This suggestion, too, Is denied by some astronomers.

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of the white hole and upon its distance from us.Perhaps mini-black holes form mini-white holesat vast distance, and we would surely never seethem. Huge black holes would form huge whiteholes, however, and these we might see. Arethere any signs of such white holes?

There may be-

QUASARS

In the 1950s sources of radio waves were de-tected that on closer inspection seemed to bevery compact, emerging from mere pinpoint sec-tions of the sky. Ordinarily, radio sources foundin those early days of the science were from dustclouds or from galaxies and were therefore moreor less spread out over a portion of the sky.

Among those compact radio sources were sev-eral known as 3C48, 3C147, 3C196, 3C273, and3C286. (Many more have been discovered since.)The 3C is short for Third Cambridge Catalog ofRadio Stars, a list compiled by the English astron-omer Martin Ryle (1918-).

In 1960 the areas containing these compactradio sources were investigated by the Americanastronomer Allan Rex Sandage (1926-), and ineach case something that looked like a dim starseemed to be the source. There was some indica-tion that they might not be normal stars, how-ever. Several of them seemed to have faint cloudsof dust or gas about them, and one of them,3C273, showed signs of a tiny jet of matteremerging from it. In fact there are two radiosources in connection with 3C273, one from thestar and one from the jet.

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There was some reluctance, therefore, to callthese objects stars, and they were instead de-scribed as quasi-stellar (starlike) radio sources.In 1964 Hong-Yee Chiu shortened that to quasar,and that name has been kept ever since.

The spectra of these quasars were obtained in1960, but they had a pattern of lines that werecompletely unrecognizable, as though they weremade up of substances utterly alien to the uni-verse. In 1963, however, the Dutch-Americanastronomer Maarten Schmidt (1929-) solved thatproblem. The lines would have been perfectlynormal if they had existed far in the ultravioletrange. Their appearance in the visible-light rangemeant they had been shifted a great distancetoward the longer wavelengths.

The easiest explanation for this was that thequasars are very far away. Since the universe isexpanding, galactic units are separating, and allseem to be receding from us. Therefore, alldistant objects have their spectral lines shiftedtoward the longer waves because that is what isto be expected when a source of light is recedingfrom us. Furthermore, since the universe is ex-panding, the farther an object, the faster it isreceding from us and the greater the shift inspectral lines. From the spectral shift, then, thedistance of an object can be calculated.

It turned out that the quasars were billionsof light-years away. One of them, OQ172, isabout 12 billion light-years away, and even thenearest, 3C273, is over a billion light-years awayand farther than any nonquasar object we knowabout. There may be as many as 15 millionquasars in the universe.

A quasar is a very dim object, as we see it,

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but for it to be visible at all at those enormousdistances, it must be exceedingly luminous. Thequasar 3C273 is 5 times as luminous as ourgalaxy, and some quasars may be up to 100times as luminous as the average galaxy.

Yet, this being so, if quasars were simplygalaxies with up to a hundred times as manystars as an average galaxy and therefore thatmuch brighter, they ought to have dimensionslarge enough to make them appear, even at theirvast distances, as tiny patches of light and notas starlike points. Thus, despite their brightnessthey must be more compact than ordinary gal-axies.

As early as 1963 the quasars were found tobe variable in the energy they emitted, both inthe visible-light region and in the microwaveregion. Increases and decreases of as much asthree magnitudes were recorded over the spaceof a few years.

For radiation to vary so markedly in so shorta time, a body must be small. Such variationsmust involve the body as a whole, and if that isso, some effect must make itself felt across thefull width of the body within the time of varia-tion. Since no effect can travel faster than light,it means that if a quasar varies markedly over aperiod of a few years, it cannot be more thana light-year or so in diameter and may be con-siderably smaller.

One quasar, 3C446, can double its brightnessin a couple of days, and it must therefore benot more than 0.005 light-year (50 billion kilo-meters) in diameter, or less than five times thewidth of Pluto's orbit around the Sun. Comparethis with an ordinary galaxy, which may be

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100,000 light-years across and in which even thedense central core may be 15,000 light-yearsacross.

This combination of tiny dimensions and enor-mous luminosity makes the quasars seem likea class of objects entirely different from anythingelse we know. Their discovery made astronomersaware of the possibility of hitherto unknownlarge-scale phenomena in the universe andspurred them on, for the first time, to considersuch phenomena, including the black hole.

And it is conceivable that there is a link be-tween black holes and quasars. The Soviet as-tronomer Igor Novikov and the Israeli astronomerYuval Ne'eman (1925-) have suggested thatquasars are giant white holes at the other end ofa wormhole from a giant black hole in someother part of the universe.*

But let's take another look at quasars. Arethey really unique, as they seem to be, or arethey merely extreme examples of somethingmore familiar?

In 1943 a graduate student in astronomy,Carl Seyfert, described a peculiar galaxy, whichhas since been recognized as one of a group thatare now termed Seyfert galaxies. They may makeup 1 percent of all known galaxies (meaning asmany as a billion altogether), though actuallyonly a dozen examples have been discovered.

In most respects Seyfert galaxies seem normaland are not unusually distant from us. The coresof the Seyfert galaxies, however, are very com-pact, very bright, and seem unusually hot andactive-rather quasarlike in fact. They show

* This is purely speculative, of course, and the remainder of the bookif, almost entirely speculation, some of it my own.

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variations in radiation that imply the radio-emitting centers at their core are no larger thanquasars are thought to be. One Seyfert galaxy,3C120, has a core that makes up less than oneeighth the diameter of the galaxy as a whole butis three times as luminous as all the rest of thegalaxy combined.

The strongly active center would be visible atgreater distances than the outer layers of theSeyfert galaxy would be, and if such a galaxywere far enough, all we would see by eitheroptical or radio telescopes would be the core. Wewould then consider it a quasar, and the verydistant quasars may simply be the intenselyluminous nuclei of very large, very active Seyfertgalaxies.

But then consider the core of a Seyfert galaxy-very compact, very hot and active. One Seyfertgalaxy, NGC 4151, may have as many as 10billion stars in a nucleus only 12 light-yearsacross.

These are just the conditions that would en-courage the formation of black holes. Perhapsthe mere fact that a certain volume of space issubject to black-hole formation may also makeit subject to the blossoming out of a white-hole.

We can imagine black holes forming here andthere in the universe, each producing an enor-mous strain in the smooth fabric of space. Worm-holes form between them, and matter may leakacross at a rate slow in comparison with thetotal quantity in the black hole serving as sourcebut large enough to produce enormous quantitiesof radiation in some cases. The rate of matterflow may vary for reasons we do not as yet un-

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derstand, and this may bring about the variationsin the brightness of quasars.

There may be many white holes of all sizes,each connected to its black hole (which itselfmay come in any size), and we may be awareonly of the giant-sized ones. It may be that if allblack holes/white holes were taken into account,it would be seen that the wormholes connectingthem may crisscross the universe quite densely.

This thought has stimulated the imaginativefaculties of astronomers such as Carl Sagan(1934-). It is impossible to think of any way ofkeeping any sizable piece of matter intact as itapproaches a black hole, let alone having it passintact through a wormhole and out the whitehole, yet Sagan does not allow that to limit hisspeculations.

After all, we can do things that to our primitiveforebears would seem inconceivable, and Saganwonders if an advanced civilization might notdevise ways of blocking off gravitational andtidal effects so that a ship may make use ofwormholes to travel vast distances in a momentof time.

Suppose there were an advanced civilizationin the universe right now that had developed athorough map in which the wormholes wereplotted with their black-hole entrances and theirwhite-hole exits. The smaller wormholes wouldbe more numerous, of course, and therefore moreuseful.

Imagine a cosmic empire threaded togetherthrough a network of such wormholes, withcivilized centers located near the entrances andexits. It would be as important, after all, for aworld to be located near a transportational cross-

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ing point of this sort as it is for an Earth city tobe built at some harbor or some river ford.

The planets nearest the tunnels might be asafe distance away, but nearer still would beenormous space stations built as bases for theships moving through the tunnels and as powerstations for the home planets.

And how does the wormhole theory affect thepast and future of the universe?

Even though the universe is expanding, is itpossible that the expansion is balanced by mat-ter being shifted into the past through the worm-holes?

Certainly the dozens of quasars we have de-tected are all billions of light-years away fromus, and we see them, therefore, as they were bil-lions of years ago. Furthermore, they are heavilyweighted toward the greater distances and moreremote past. It is estimated that if quasars wereevenly spaced throughout the universe, therewould be several hundred of them nearer andbrighter than 3C273, which is the nearest andbrightest now.

Well, then, do we have an eternal universe,after all, a kind of continuous creation in anothersense?

Has the universe been expanding for countlesseons, through all eternity in fact, without everhaving expanded beyond the present level be-cause the wormholes create a closed circuit, send-ing matter back into the more contracted past tobegin expansion all over?

Has the universe never really been entirelycontracted, and has there never really been a bigbang? Do we think there was a big bang onlybecause we are more aware of the expansion half

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of the cycle involving the galaxies and are notaware of matter sweeping back through worm-holes?

But if there was no big bang, how do we ac-count for the background radiation that is theecho of the big bang? Can this radiation be theproduct of the overall backward flow of matterinto the far past? Can the white holes or quasarsbe numerous "little bangs" that add up to the bigbang and produce the background radiation?

And if all this is so, where does the energycome from that keeps the universe endlessly re-cycling? If the universe runs down as it expands(this is referred to as an increase of entropy byphysicists), does it wind up again (decreasingentropy) as it moves back in time through thewormholes?

There are no answers to any of these questionsat present. All is speculation, including the veryexistence of wormholes and white holes.

THE COSMIC EGG

It must be admitted that the notion that theuniverse is continually recycling is a rather ten-uous speculation.

If we dismiss it, however, we are left with thebig bang-either as a one-time affair if we areliving in an open universe, or as an endlesslyrepeated phenomenon if the universe is closedand oscillating. Either way there is a problem.What is the nature of the cosmic egg?

When the cosmic egg was first suggested, itwas viewed very much as we now view neutronstars. The trouble is that a cosmic egg with all

227


the mass of the universe (equal to the mass of100,000,000,000 galaxies, perhaps) is certainlytoo large to be a neutron star. If it is true thatanything with more than 3.2 times the mass ofour Sun must form a black hole when it col-lapses, then the cosmic egg was the biggest ofall black holes.

How, then, could it have exploded and yieldedthe big bang? Black holes do not explode.

Suppose we imagine a contracting universe,which would form black holes of varying sizes asit contracts. The individual black holes mightbleed away some of their mass through worm-holes, counteracting the overall contraction butnot by enough to stop it altogether (or neitherthe expanding universe nor we would be heretoday).

As the universe compresses, the black holesgrow at the expense of non-black-hole matter and,more and more frequently, collide and coalesce.Eventually, of course, all the black holes coalesceinto the cosmic egg. It loses matter through itswormhole at an enormous rate, producing the big-gest conceivable white hole at the other end. It isthe white hole of the cosmic egg, then, that wasthe big bang that created our expanding universe.This would hold good whether the universe isopen or closed, whether the cosmic egg is formedonly once or repeatedly.

Of course, this solution will only work if worm-holes and white holes truly exist, which is un-certain. And even if they do exist, it will onlywork if the cosmic egg is rotating. But is it?

There is certainly angular momentum in theuniverse, but it could have been created, despite

228


the conservation law, where none had earlierexisted.

That is because there are two kinds of angularmomentum, in opposite sense. An object canrotate either clockwise or counterclockwise (pos-itive or negative if you prefer). Two objectswith equal angular momentum, one positive andone negative, will, if they collide and coalesce,end with zero angular momentum, the energy ofthe two rotary motions being converted intoheat. In reverse, an object with zero angular mo-mentum can, with the addition of appropriateenergy, split to form two subobjects, one withpositive angular momentum and the other withnegative angular momentum.

The objects in the universe may all have angu-lar momentum, but it is very likely that someof that angular momentum is positive and somenegative. We have no way of knowing whetherone kind is present in greater quantities than theother. If such lopsidedness does exist, then whenall the matter of the universe collapses into acosmic egg, that cosmic egg will end up with anamount of angular momentum equal to the ex-cess of one kind over the other.

It may, however, be that the amount of angularmomentum of one kind in the universe is equalto the amount of the other kind. In that case,the cosmic egg, when it forms, will have noangular momentum, and will be dead. We can'trely on wormholes and white holes for the bigbang, then.

What else?Just as angular momentum of two opposite

kinds exist, so matter of two opposite kindsexists.

229


An electron is balanced by an antielectron, orpositron. When an electron and a positron com-bine, there is a mutual annihilation of the twoparticles. No mass at all is left. It is convertedinto energy in the form of gamma rays. In thesame way, a proton and an antiproton will com-bine to lose mass and form energy; and so willa neutron and an antineutron.

We can have matter built up of protons, neu-trons, and electrons; and antimatter built up ofantiprotons, antineutrons, and antielectrons. Inthat case any mass of matter combining withan equal mass of antimatter, will undergo mutualannihilation to form gamma rays.

In reverse, mass can be formed from energy,but never as one kind of particle only. For everyelectron that is formed an antielectron must beformed, for every proton an antiproton, for everyneutron an antineutron. In short, when energy isturned into matter, an equal quantity of anti-matter must also be formed.

But if that is so, where is the antimatter thatmust have been formed at the same time thatthe matter of the universe was formed?

The Earth is certainly entirely matter (exceptfor vanishingly small traces of antimatter formedin the laboratory or found among cosmic rays).In fact the whole solar system is entirely matter,and in all probability so is the entire galacticunit of which we are part.

Where is the antimatter? Perhaps there arealso galactic units that are entirely antimatter.There may be galactic units and antigalacticunits, which because of the general expansion ofthe universe never come in contact and neverengage in mutual annihilation. Just as matter


forms black holes, antimatter will form anti-black holes. These two kinds of black holes arein all respects identical except for being madeup of opposite substances.

If the universe was ever, in the past, con-tracting, black holes and anti-black holes formedeven more easily; and as contraction continued,the chances of collision between two black holesof opposite nature and a consequent enormousmutual annihilation increased. In the final co-alescence there was the greatest of all greatmutual annihilations.

The total mass of the universe disappeared andwith it the gravitational field that keeps the blackhole, and the cosmic egg for that matter, inexistence. In its place was incredibly energeticradiation, which expanded outward. That; wouldbe the big bang.

Some period after the big bang the energy,becoming less intense through expansion, wouldbe tame enough to form matter and antimatteronce more-the two forming separate galacticunits by some mechanism that, it must be ad-mitted, has not been worked out-and the ex-panding universe would take shape.

From this view of the big bang as the mutualannihilation of matter and antimatter, it doesn'tmatter whether the cosmic egg is rotating ornot, or whether it is alive or dead.

Yet we have no evidence that there exist anti-galactic units. Can it be that for some reason wedo not as yet understand the universe consistssimply of matter?

We might argue that this is impossible; theuniverse cannot consist simply of matter, as thatwould make the big bang impossible. Or we

231


might think of a way of accounting for the bigbang even in a universe of matter only, and evenif, on contracting, that universe forms a cosmicegg that is not rotating and is therefore a deadblack hole.

Well, according to the equations used to explainthe formation of black holes the size of theSchwarzschild radius is proportional to the massof the black hole.

A black hole the mass of the Sun has aSchwarzschild radius of 3 kilometers and is there-fore 6 kilometers across. A black hole that istwice the mass of the Sun is twice as large across-12 kilometers. However, a sphere that is twiceas large across as a smaller sphere has eighttimes as much volume as the smaller sphere.It follows that a black hole with twice the massof the Sun has that twice the mass spread overeight times the volume. The density of the largerblack hole is only one-fourth the density of thesmaller black hole.

In other words, the more massive a black holeis, the larger and the less dense it is.

Suppose our entire galaxy, which is about100,000,000,000 times the mass of our Sun,were squeezed into a black hole. Its diameterwould be 600,000,000,000 kilometers, and itsaverage density would be about 0.000001 gramsper cubic centimeter. The galactic black holewould be more than 50 times as wide as Pluto'sorbit and would be no more dense than a gas.

Suppose that all the galaxies of the universe,possibly 100,000,000,000 of them, collapsed intoa black hole. Such a black hole, containing allthe matter of the universe, would be 10,000,-000,000 light-years across, and its average den-


sity would be that of an exceedingly thin gas.Yet no matter how thin this gas, the structure

is a black hole.Suppose the total mass of the universe is 2.5

times as large as it seems to astronomers to be.In that case the black hole formed by all thematter of the universe is 25,000,000,000 light-years across, and that happens to be about thediameter of the actual universe we live in (asfar as we know).

It is quite possible, then, that the entire uni-verse is itself a black hole (as has been suggestedby the physicist Kip Thorne).

If it is, then very likely it has always been ablack hole and will always be a black hole. Ifthat is so, we live within a black hole, and if wewant to know what conditions are like in a blackhole (provided it is extremely massive), we havebut to look around.

As the universe collapses, then, we mightimagine the formation of any number of relativelysmall black holes (black holes within a blackholel) with very limited diameters. In the lastfew seconds of final catastrophic collapse, how-ever, when all the black holes coalesce into onecosmic black hole, the Schwarzschild radiussprings outward and outward to the extremity ofthe known universe.

And it may be that within the Schwarzschildradius there is the possibility of explosion. Itmay be that as the Schwarzschild radius recedesbillions of light-years in a flash, the cosmic eggat the very instant of formation springs outwardto follow, and that is the big bang.

If that is so, we might argue that the universecannot be open whatever the present state of the

233


evidence, since the universe cannot expand be-yond its Schwarzschild radius. Somehow theexpansion will have to cease at that point, andthen it must inevitably begin to contract againand start the cycle over. (Some argue that witheach big bang, a totally different expandinguniverse with different laws of nature gets underway.)

Can it be, then, that what we see all aboutus is the unimaginably slow breathing cycle(tens of billions of years in and tens of billions ofyears out) of a universe-sized black hole?

And can it be that separated from our universein some fashion we cannot as yet grasp, there aremany other black holes of various sizes, perhapsan infinite number of them, all expanding andcontracting, each at its own rate?

And we are in one of them-and through thewonders of thought and reason it may be thatfrom our station on a less-than-dust speck lostdeep within one of these universes we havedrawn ourselves a picture of the existence andbehavior of them all.

234

APPENDIX 1

EXPONENTIAL NUMBERS

NUMBERS CAN, FOR convenience, be writtenas multiples of 10. Thus, 100 = 10 x 10; 1,000= 10 X 10 X 10; 1,000,000 = 10 X 10 X 10x 10 x 10 x 10; and so on. A short way ofwriting such numbers is to indicate the numberof lOs involved in the multiplication as a smallnumber (or "exponent") to the upper right ofthe 10.

Thus, if 100 = 10 x 10, we can say that100 = 102. In the same way 1,000 = 103 and1,000,000 = 106. As it turns out, the exponentequals the number of zeroes in the large number.The number 1,000,000,000,000,000,000,000,000,-000,000,000,000 (a trillion trillion trillion) has36 zeroes in it and can be written 1036.

The exponential system also works for frac-tions. The number 1/100 is 1/102, and there aresound algebraic reasons for writing it as 10 -2.In the same way 1/1,000 = 1/103 = 1 0 -3 and

235


1/1,000,000 = 1/106f = 10-6. If you write sucha number in decimals, the exponent is alwaysone greater than the number of zeroes. Thus1/1,000,000 = 0.000001, where five zeroes are tothe right of the decimal point, so that the ex-ponential figure is 10 6. If you want to countthe single zero usually put to the left of thedecimal point, the exponent equals the numberof zeros.

Thus 0.0000000000000000000000000000000-00001 (or one-trillionth-trillionth-trillionth) is10 -6.

If you have a number such as 6,000,000, it isequal to 6 x 1,000,000 or 6 x 106. In the sameway 45,200,000 is equal to 4.52 x 10,000,000 =4.52 x 107. And 0.000013 is equal to 1.3 x0.00001 = 1.3 x 10 4.

APPENDIX 2

THE METRIC SYSTEM

THE METRIC SYSTEM builds up measure-ments in units of ten exclusively, as opposed tothe common system where the buildup can be byalmost any digit, so that twelve inches make afoot, three feet make a yard, and 1,760 yardsmake a mile.

The metric unit of distance is the meter, andit can be built up (or down) by stages of tenthrough a series of prefixes:

1 kilometer = 10 hectometers = 1,000 meters1 hectometer - 10 dekameters = 100 meters1 dekameter = 10 meters1 meter1 decimeter = 1/10 meter1 centimeter = 1/10 decimeter = 1/100 meter1 millimeter = 1/10 centimeter = 1/1,000

meter

There are other prefixes, too, both larger and

237


smaller. For instance, a megameter is 1,000 kilo-meters; and a micrometer is 1/1,000 millimeter,but these are rarely used.

This simple use of 10 as stages of measure-ment makes the metric system far more simpleto learn and use than the common system. As aresult the entire civilized world, except the UnitedStates, has gone metric. Someday we will too.

Since a meter is equal to 39.37 inches, or1.094 yards, a kilometer is 1,094 x 1,000 or1,094 yards. This comes to 0.621 miles or justabout five eighths of a mile. A centimeter, on theother hand, is 39.37 divided by 100 or 0.3937inch-or just about two fifths of an inch.

A cubic centimeter is 2/5 x 2/5 x 2/5 or0.064 cubic inch-which makes it about onesixteenth of a cubic inch.

Another metric measure used in the book in-volves mass. Here the basic unit is the gram. Thisis a rather small unit, since it is equivalent to0.035 ounce, or a little more than a thirtieth ofan ounce. A kilogram = 1,000 grams = 0.035 x1,000 ounces = 35 ounces or about 2.2 pounds.

Other more complicated measurement units,such as "dynes" (mentioned early in the book),can be built up out of centimeters, grams, andseconds. Time units such as seconds, minutes,days, and years remain the same in the metricsystem as-in the common system.

APPENDIX 3

TEMPERATURE SCALES

THE ENTIRE CIVILIZED world, except theUnited States, uses the Celsius temperature scalein which the freezing point of water is set at0 degrees and the boiling point of water at 100degrees. The United States will some day adoptthis system but as of now it still uses the Fahren-heit scale in which the freezing point of wateris set at 32 degrees and the boiling point of waterat 212 degrees.

The number of degrees between freezing andboiling of water is 100 degrees in the Celsiusscale and 180 degrees in the Fahrenheit scale.Therefore a Celsius degree is 180/100 or 9/5 thesize of a Fahrenheit degree. Conversely a Fahren-heit degree is 100/180 or 5/9 the size of a Cel-sius degree.

You cannot convert one into the other just bytaking into account the difference in size ofdegrees. There is also the question of the dif-ferent position of the zero, which in the Celsius

239


scale is at the freezing point of water, and inthe Fahrenheit scale is 32 Fahrenheit degreesbelow the freezing point of water.

To convert, then, you must use the followingequations:

degrees F = 9/5 (degrees C) + 32degrees C = 5/9 (degrees F) - 32

INDEX

Absolute zero, 10Acceleration, 30Accretion disk. 189Adams, Walter Sydney, 89,

93, 96Aluminum. 17Andromeda Galaxy, 134Angstrom, Anders Jonas, 78Angular momentum, 171, 216Antares, 83Antiblack holes, 231Antieleciron. 7Antigalaxies, 230Antimatter, 7, 230, 231Antineutron. 7Antiparticles, 7Antiproton, 7Atom(s), compression of, 63-

64collapse of, 74ff.diameter of, 9

interaction of, 9light and. 77structure of, 4, 8

Atomic weight, 17

Baade, Walter, 146Background radiation, 215Ballistic flight. 43n.Bell, Jocelyn, 153Bessel, Friedrich Wilhelm, 84-

87Beta particles, 6, 7Betelgeuse. 83Bethe. Hans Albrecht, 78Bevis, John. 136Big bang. 109

evidence for, 215Binaries, black holes and, 192-

96neutron stars and, 161, 162

241

INDEX

Black holes, 183ff.angular momentum of, 216,

217cosmic egg and, 227-28,

229detection of, 186ff.energy from, 218galactic centers and, 190galactic civilizations and,

225globular clusters and, 190interior of, 207, 208matter transfer and, 218,

219number of, 195, 196properties of, 216rotating, 217size of, 232-33universe as, 233, 234X rays and, 189ff.

Black dwarf, 102, 183Black neutron star, 183-84Bolt, C. T., 195Bondi, Hermann, 214Brahe, Tycho, 125Burroughs, Edgar Rice, 48

Cavendish, Henry, 33-34Centaurus X-3, 194Centrifugal effect, 163Cepheid variables, 128-30Cesium, 17Chadwick, James, 4Chandrasekhar,

Subrahmanyan, 120-21Chandrasekhar's limit, 120-21Chemical reactions, 77Chiu, Hong-Yee, 137, 221Circinus X-1, 195Clark, Alvan Graham, 87-88Close binary, 130Collapsars, 183Compression, 63, 64

Continuous creation, 214Copper, 17Core, Earth's 57

density of, 65Corona, solar, 150Cosmic egg, 109

angular momentum and,229

antimatter and, 230, 231black hole and, 228, 229formation of, 212size of, 145surface temperature of, 151

Cosmic rays, 147Coulomb, Charles Augustin

de, 21, 33Crab Nebula, 136

neutron stars and, 152pulsar in, 155, 157-58, 159

Crystals, 13Cygnus X-1, 194

Degenerate matter, 75Delta Cephei, 128De Nova Stella, 125Density, 14ff.Dicke, Robert Henry, 215Dirac, Paul Adrien Maurice,

210

Earth, 52age of, 57crust of, 65density of, 34electromagnetic force and,

26escape velocity from, 40-44gravitational force and, 26,

30-31interior of, 47, 48, 57internal densities of, 64, 65internal pressures of, 59

242

internal temperatures of,56, 57

mass of, 34mass changes of, 183-84mini-black holes and, 201,

202oblateness of, 164rotation of, 163, 170, 171size of, 32structure of, 49-50tidal effects and, 167, 168,

169Earth-Moon system, 35Earthquakes, 56Eddington, Arthur Stanley,

76, 96, 113, 116Einstein, Albert, 93-94, 218Einstein-Rosen bridge, 219Electromagnetic force, 2

atomic structure and, 6, 7Earth and, 13energy and, 14universe and, 24-26

Electron(s), 7Electronic fluid, 75Electron shells, 11-12Emden, Jacob Robert, 76Energy, 14

black holes and, 202-05,218

planet formation and, 55Sun and, 71-72

Eon, 57Epsilon Aurigae B, 196Equatorial bulge, 163Eratosthenes, 32Escape velocity, 40ff.Exponential numbers, 2, 235-

36

First-generation stars, 140Friedman, Herbert, 150Forcess, 2

Force fields, 2

Galactic center, 188black holes and, 190

Galaxies, clusters of, 108recession of, 106, 107

Galilei, Galileo, 30Gamma rays, 99, 149Gamow, George, 109Gases, 11

compression of, 63density of, 14, 15

Glitch, 159Globular clusters, 190Gold, 18Gold, Thomas, 156, 214Goodricke, John, 128Gravitational constant, 20-21

value of, 32ff.Gravitational force, 210

relative strength of, 2, 19-23universe and, 24-25

Gravitational lens, 188Gravitational mass, 30Gravitational waves, 187Gravitons, 187Gum, Colin S., 137Gum Nebula, 137

Hadron, 3Hawking, Stephen, 198HD-22868, 194-95Helium, 10, 11

liquefaction of, 11Sun and, 79

Helmholtz. Hermann LudwigFerdinand von, 71

Hercules X-1, 194Hess, Victor Francis, 147Hewish. Anthony, 153Hind, John Russell, 126Hipparchus, 125Hoyle, Fred, 214

INDEX 243

Hubble, Edwin Powell, 107Hydrogen, density of, 15

fusion of, 78Sun and, 77

Hyperons, 160

Inertia, 30Inertial mass, 30Interactions, 2lo, 36Iridium, 18Iron, density of, 17, 65

Earth and, 50, 57

Jansky, Karl Guthe, 148Jupiter, 36

escape velocity from, 46gravitational field of, 36, 45internal pressures of, 61internal temperatures of,

58-59nuclear reactions and, 80oblateness of, 164, 165rotation of, 164

Kerr, Roy P., 217Kinetic energy, 55

Leavitt, Henrietta Swan, 128-29

Lemalitre, Georges, 108Leptons, 7Life, supernovas and, 140-41Light, 77

gravitational field and, 94,95

speed of, 182Light-years, 85Local Cluster, 109-10Luyten 726-8 B, 79

Macromolecules, 12-13Magma, 62

Main sequence, 113ff.Mantle, Earth's, 57

density of, 65, 65-66Mars, 50, 52Mass, 8, 29-30Massless particles, l9nMass-luminosity law, 113Mercury, 50, 52Meteor, 50Meteorite, 50Metric system, 3, 236Microwaves, 148Mini-black holes, 198

Earth and, 200, 202evaporation of, 200number of, 200possible uses of, 202-05

Missing mass, 213Molecules, 12Moon, 152

atmosphere and, 51escape velocity from, 44gravitational field of, 35rotation of, 171surface gravity of, 38tidal effects and, 168, 170

Mutual annihilation, 99

Ne'eman, Yuval, 223Neutrinos, 16n, 137Neutron(s), 4

mass of, 100Neutronium, 144"Neutron Star," 177Neutron star(s), 144

density of, 162detection of, 152diameter of, 162escape velocity from, 165magnetic fields of, 156, 157mass of, 145, 160maximum mass of, 180microwaves and, 157

244 INDEX

pulsars and, 155-58rotation of, 164structure of, 160, 161surface gravity of, 163surface temperature of, 151tidal effects and, 176X rays and, 150-51, 152

Newton, Isaac, 20, 29, 177NGC 4151, 224Niven, Larry, 177Novas, 125

binaries and, 130, 132bright, 133number of, 126white dwarfs and, 130, 132

Novikov, Igor, 223Nuclear force, 2

nucleus and, 6range of, 3

Nuclear fusion, 99Nuclear reactions, 77Nucleon, 4Nucleus, atomic, 5

diameter of, 9forces within, 5structure of, 6

Ocean, 60Omega Centauri, 192Oppenheimer, J. Robert, 146,

179-80Optical pulsars, 159OQ172, 221Orbital velocity, 43nOscillating universe, 212Osmium, 18

Parallax, 85Penzias. Arno A., 215Photography, 126Photons, 19n, 94, 138Pioneer 10 and 11, 58, 70

Planck, Max Karl ErnstLudwig, 94

Planetary nebulas, 122-124Planetesimals, 55Planets, 55

density of, 37, 46, 47escape velocity from, 45formation of, 48, 49mass of. 37structure of, 48, 49surface gravity of, 39

Platinum, 18Positron, 7, 99Pressure, 59, 60Primeval atom, 109Procyon, 86Procyon B, 88, 89, 90Proper motion, 84Protons, 4

mass of, 100Pulsars, 154

lifetime of, 158light and, 159nature of, 155-58neutron stars and, 155-58number of, 154period of, 155period changes of, 157, 158X rays and, 159, 194

Quasars, 221distance of, 222luminosity of, 222Seyfert galaxies and, 223-

24size of, 222variability of, 222white holes and, 223

Radioactivity, 6Radio astronomy, 152Radio telescopes, 153Radio waves, 148

INDEX 245

INDEX

Rainbow, 77n.Recurrent novas, 130Red giants, 83Red shift, gravitational, 95Red shift, recessional, 95Ring, Nebula, 122Roche, Edouard A., 173Roche limit, 173Rockets, 149Rosen, 218Rosse, William Parsons,

Lord, 136RR Lyrae stars, 128Russell, Henry Norris, 78Rutherford, Ernest, 4, 93

Sagan, Carl, 225Sandage, Allan Rex, 110, 220S Andromedae, 135Satellites, 149Saturn, 164n.Schaeberle, John Martin, 88Schmidt, Maarten, 221Schwarzschild, Karl, 181Schwarzschild radius, 181, 182

mass and, 232, 233Schwarzschild singularity, 181Second-generation stars, 140Seyfert, Carl, 223-24Seyfert galaxies, 223, 224Siberia, 201, 202Silicates, 50Sirius, 150

binary system of, 91, 131-32

dark companion of, 86diameter of, 89mass of, 92motion of, 86surface temperature of, 89

Sirius A (see Sirius), 88Sirius B, 88

density of, 93

diameter of, 90escape velocity from, 97,

166mass of, 93surface gravity of, 96, 163surface temperature of, 89tidal effects and, 174-75

Sitter, Willem de, 10861 Cygni, 85Solar wind, 99Solids, 17, 18Spectral classes, 114

frequency of, 115lifetime and, 117luminosity and, 114mass and, 114

Spectroscope, 77Spectrum, 77Stars(s), 70

birth of, 112changes among, 124, 125chemical composition of,

140collapse of, 119ff., 139, 143-

45, 182end stages of, 184first-generation, 140ignition of, 79lifetime of, 115-17mass of, 143motion of, 105parallax of, 85proper motion of, 84pulsating, 129second-generation, 140temperature of, 88unstable, 128

Starquake, 159Stationary limit, 217Strong nuclear force, 3Sun, 69

central density of, 76central pressure of, 75, 76

246

central temperature of, 76chemical composition of,

77, 140density of, 73energy of, 72, 78escape velocity from, 69-70,

166evolution of, 82-83gaseous nature of, 75, 76hydrogen fusion in, 82lifetime of, 82mass of, 69mass change of, 183rotation of, 164spectral class of, 114surface gravity of, 69, 163surface temperature of, 71tidal effects and, 174, 175X rays from, 150

Supernovas, 135ff.formation of, 137-39gaseous remnants of, 136number of, 135internal temperature of, 138

Surface gravity, 37-39

Telescope, 125-26Temperature scales, 11, 237Thomson, Joseph John, 7Thorne, Kip, 2333C120, 2243C273, 220, 221-223C446, 222Tidal effects, 167ff.

distance and, 171, 173matter breakup due to, 173,

174Tides, 170Titan, 52Torsion balance, 33Tycho Brahe, 133

Ultraviolet light, 149Universe, age of, 110- 11

antimatter in, 230black hole as, 232, 233contracting, 227, 228end of, 210expanding, 108, 109, 226,

227gravitational force and, 26origin of, 108oscillating, 110, 212

Uranium, 18Uranium hexafluoride, 16

Van der Waals, JohannesDiderik, 11

Van der Waals forces, 11Van Maanen 2, 119Vela supernova, 137VelaX-1, 158Volkoff, George M., 146

Water, 14Weak force, 2

range of, 3Weber, Joseph, 187Weight, 59White dwarfs, 90

central density of, 102formation of, 97ff.mass of, 119novas and, 130, 131number of, 104planetary nebulas and, 122-

24pulsars and, 155structure of, 101surface temperature of, 102

White holes, 219quasars as, 223

Wien, Wilhelm, 88Wilson, Robert W., 215Wormholes, 219Uhuru, 194

INDEX 247

248 INDEX

X Persei, 195X ray(s), 149

black holes and, 189ff.globular clusters and, 190neutron stars and, 151, 152pulsars and, 159

X-ray pulsars, 194

X-ray sources, 151, 152binary, 193

Yukawa, Hideki, 5

Zwicky, Fritz, 146

WILLTHEUNIVERSE EXPAND FOREVER?

COULD THE SUN EXPLODEIN OUR UFETIME?

In a world of starquakes, anti-matter, red giantsand white dwarfs, a star more massive than

our own sun can disappear into a black hole fromwhich not even light can escape.

When this happens, the laws of physicshave no meaning.

Here is one of the great detective stories of modernscience, followed to its conclusion

by one of the most respected scientists writingtoday. It is a totally absorbing investigation

of a phenomenon,onlyrecently discovered, that may explain the mysterious

30-megaton blast that flattened aSiberian forest in 1908- and that may,

ultimately, be responsiblefor the collapse of the present universe.

"Cosmic drama"-Publishers Weekly"A Renaissance man born out of his time, Asimov's

the greatest explainer of the age." - Carl Sagan

SELECTED BY 10 BOOK CWBS

the collapsing universe: the story of black holes, by isaac asimov

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