main sequence lifetimes

Main Sequence Lifetimes

• Time on Main Sequence– How much fuel it has (Core H)– How fast it consumes the fuel (Luminosity)

hrs 6gal/hr 2.5gal 15

nconsumptio of RateGas ofQuantity

drive

drive

t

t


LMyrs

LxMx

t

kgxL

kgxkgxM

MMnconsumptio

fuelt

lifetimeMS

Star

cemainSequen

10

)(19

)(29

19)(

2930H Core

H Core

H Core

10102102

102~1

102)102(1.

1.0~Luminosity

M


LMyrst lifetimeMS

1010

• Our Sun M = 1 M() and L = 1 L()

• tMS-lifetime = 1010 years = 10 billion years

• Large Mass Bright Star M = 10 M() and L = 105 L ()

· tMS-lifetime = 1010

· tMS-lifetime = 106 years = 1 Million years

yearsLM

5

11

)(5

)(

1010

1010

Nuclear Fusion and Forces of Repulsion

• For Hydrogen repulsion of 2 (1+) charges– At 1 Atomic radius Frepulsion= 2.3 x 10-8 N

• For Helium repulsion of 2 (2+) charges– At 1 Atomic radius Frepulsion= 9.2 x 10-8 N

• Ratio of forces 9.2/2.3~4x• For Hydrogen, we had 2 pairs of H fused to make 1

Helium.• For Helium, we need 3 pairs of He to fuse to make 1

Carbon so ratio 3/2(4) = 6x 6x as much force

Nuclear Fusion• Hydrogen Fusion requires temps ~ 7 Million K

• Helium Fusion requires temps ~ 100 Million K– A bit more than 6x (~14x)

• Energy from Helium fusion ~0.1 Energy released in Hydrogen fusion

• All stars > 0.5 M() can create Helium burning Temps of 100 million K

Nuclear Fusion

• High Mass Stars create 100 Million K by contracting Core a little.

• Low Mass Stars create 100 Million K by contracting Core a lot!

• If a Low Mass Star contracts Core a lot, Core can become Degenerate!!

Degenerate States of Matter• Normal Matter only one atom may exist in a

particular energy state. This causes atoms to have some spatial separation.

• Degenerate Matter many atoms may exist in the same energy state. This causes atoms to become quite close together.

Degenerate Matter

• Super-Fluids

• Super-Conductors

• Bose-Einstein Condensates

Super-Fluid

http://london.ucdavis.edu/~zieve/Research/creep.jpg

Super-Conductor

http://sci-toys.com/scitoys/scitoys/magnets/levitation_closeup.jpg

Bose-Einstein Condensates

http://math.nist.gov/mcsd/savg/vis/bec/3D.00007.jpg

Bose-Einstein Condensates

•http://science.nasa.gov/headlines/y2002/images/neutronstars/magnetar_huge.jpg

Degenerate Core of a Star• Gas atoms so close act like Solid!• Heat a Gas, Changes in Both Volume and

Pressure• Heat a Solid, Small Changes in both Volume

and Pressure.

High Mass Star (Normal Gas Core)• Fusion releases Energy Heats Gas• Heated Gas Gas Expands due to increase

Pressure• Expanded Gas Cools Gas • Cooling Gas decreases Nuclear Fusion rate• Decreased Nuclear Fusion Rate Pressure

drops• Gas Contracts Increased Temps Increased

Fusion

• Gas properties regulate Nuclear Fusion

Low Mass Star (Degenerate Core)• Fusion releases Energy Heats Gas (Solid)• Heated Solid No Increase in Pressure• No Increase in Pressure No Expansion• No Expansion No Cooling• Increased Temperatures Increased Nuclear

Rate• Increase Nuclear Rate Increased Release of

Energy• Increased Temps etc……

• No Regulation of Nuclear Fusion Helium Flash!!

Helium Flash• Explosive release of energy• Usually restores Degenerate Core back to

normal Core• Helium Flash Ends First Red Giant Phase of

Low Mass Stars and start Yellow Giant Phase• High Mass Stars do not have a helium flash• High Mass Stars go originally to Yellow Giant

Phase and then expand into Red Giants• Onset of Helium Burning often cause stars to

become unstable (Variable Stars)

0 0.5 1 1.5 2 2.5-6

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

f(x) = − 2.03319992589272 x − 1.46664841474245

Average Absolute Magnitude vs Log(P) for Cepheid Variable Stars

DW Donovan 2013-03-13

Log of Period, Log(P), (unitless)

Ave

rage

Abs

olut

e M

agni

tude

, M, (

Uni

t-le

ss)

http://www.jwst.nasa.gov/orbit.html

Lagrange Points

Mass Mystery???

• Both stars in a binary form about same time• More massive stars evolve faster• Red Giant star (on left) is less massive than Main

Sequence star (on right)

• Solution Mass Transfer!!!

More Massive Star is Dimmer??

• Β Lyrae • More Massive Star is Dimmer

• Solution – Accretian Disk blocks some of light!!

Stellar Evolution in a Globular Cluster

In the old globular cluster M55, stars with masses less than about 0.8 M are still on the main sequence, converting hydrogen into helium in their cores. Slightly more massive stars have consumed their core hydrogen and are ascending the red-giant branch; even more massive stars have begunhelium core fusion and are found on the horizontal branch. The most massive stars (which still have less than 4 M ) have consumed all the helium in their cores and are ascending the asymptotic giant branch.

Dredges• 1rst – After Core H ceases

– Relative abundance of Carbon, Nitrogen and Oxygen changed at surface

• 2nd – After Core He ceases– Again Relative abundance of C, N, and O changed

• 3rd – After during AGB (if M > 2 M() )– Prominent Carbon compounds. C2, CH, CN – Strong C absorption lines in spectra– Carbon Star!!

TT Cygni is an AGB star in the constellation Cygnus that ejects some of its carbon-rich outer layers into space.

Some of the ejected carbon combines with oxygen to form molecules of carbon monoxide (CO), whose emissions can be detected with a radio telescope. This radio image shows the CO emissions from a shell of material that TT Cygni ejected some 7000 years ago. Over that time, the shell has expanded to a diameter of about ½ light-year.

Later Stage of Low Mass Stars• Helium Shell burning decreases as its fuel is

used up• Dormant Helium Shell provides insufficient

pressure to support Dormant Hydrogen Shell• Hydrogen Shell contracts, Heats up, Re-ignites!• Helium produced in Hydrogen Shell adds to

Helium Shell Fuel• Hydrogen Burning re-heats Helium Shell, Small

Helium Flash!!• Helium Shell Burning Pushes Star out again• Outer layers detach!! Planetary Nebula!!

Planetary Nebulae• Thermal Pulses happen in increasingly shorter

intervals over time• 1 M() loses about 40% of its mass this way• As outer layers are ejected, hot core exposed• Core Temp ~ 100,000 K emits UV radiation• Radiation ionizes gas creating Fluorescence

glows• Radiation also propels gas outward in

increasingly larger rings• Non-symmetric radiation creates hour-glass

shapes

1980’s • Two “Neutrino Telescopes” went into operation

– Kamiokande (U-Tokyo and U-Penn) detector in a zinc mine in Japan

– IMB (U-Cal at Irvine, U-Michigan, and Brookhaven) detector in a salt mine in Ohio

• Neutrinos interacts with a proton in the water creating a supersonic positron

• Positron moves faster than the speed of light in water creating a shockwave effect known as Cerenkov radiation

http://ncas.sawco.com/condon/text/s6c06f1b.htm

http://www.pbs.org/wgbh/nova/barrier/boom/images/cone.jpeg

http://www.sonicbooms.org/T38/T38c3.jpg

http://www.simulationinformation.com/sonic%20boom.jpg

http://www.anomalies-unlimited.com/Odd%20Pics3/Images/shuttlesonic.jpg

http://www.physlink.com/Education/AskExperts/ae219.cfm

http://dept.physics.upenn.edu/balloon/cerenkov_radiation.html

http://www.physlink.com/Education/AskExperts/ae219.cfm

Solar Neutrinos Vs Supernova Neutrinos??• Energy

– Solar Neutrinos ~<1 MeV– Supernova Neutrinos ~>20 MeV

• Measuring Properties of Cerenkov radiation, the speed of the e+ which created the radiation can be found

• Speed of e+ gives originally energy of neutrino which collided with proton that created the e+

February 23, 1987• 12 second burst of neutrinos detected

– Kamiokande detected 11 Neutrinos– IMB detected 8 Neutrinos– The Earth was subjected to a neutrino flux of approximately

1016 neutrinos– Supernova emitted 1058 neutrinos in about 10 seconds

160,000 years ago• Approximately 100x the Energy the Sun has emitted in

its entire lifetime!!• About 100x the amount of light energy the Supernova

emitted• Approximately 10x the total luminosity of the stars in

the entire observable universe at the moment

February 23, 1987

• 3 hours later Light arrived from Supernova 1987 ????

• Neutrinos not blocked by gas layers of the star• Light created only after shockwave reached the

outer-most layers of the star

Why was SN 1987A Unusual?

• Peak Intensity about 0.1 of intensity of other observed Supernovas

• Confusion over whether progenitor star was a Red Supergiant or a B3 I Blue Supergiant?

• Pop I or Pop II star? • Possible Pop II meaning it oscillated between Red and

Blue Supergiant.

Supernova 1987A

• In Blue Supergiant phase, radius is about .1 of size than when in Red Supergiant phase

• When explosion occurred more mass closer to core, more energy needed to push outer layers away, less available for creating brighter light

• Type II Supernova

*****

Types of Supernovas• Type II do have prominent Hydrogen Lines• Type I do not have prominent Hydrogen Lines

in their spectra• Type I further subdivided into

– Type Ia which has strong absorption lines of Si– Type Ib which does not have Si but does have

absorption lines of He– Type Ic which has neither

http://csep10.phys.utk.edu/guidry/violence/sn87a-rings.html

*****

http://apod.nasa.gov/apod/image/0402/sn1987a_acsHubble_full.jpg

*****

http://physics.uoregon.edu/~courses/BrauImages/Chap21/FG21_08A.jpg

• Type II, Ib, Ic are found near sites of new star formation.

• Type Ia found in galaxies where there are no ongoing star formations

Supernova leftovers

• Remnants – Gasses and elements

• Core Relics – Neutron Stars– Black Holes

• Why More Supernovas in other Galaxies??– Ought to see about 5 per century based on what we

see in other galaxies (~100 remnants seen with radio in other galaxies)

– Last Supernova in our Galaxy 1604 – Kepler– 1572 Brahe– 1054 China

• Interstellar dust blocks best star forming regions from our view

• Neutrons form :• Supernova’s Create many reactions• Neutrons first discovered in 1932 Chadwick• Zwicky (Caltech) and Baade (Mt. Wilson

Obs) Proposed parallel to White Dwarf, Neutron Star

• White Dwarf uses Degenerate e- pressure to sustain outer layers weight

• Neutron Star uses Degenerate n pressure• Neutrons can with stand more force, hence

1.4 M() limit no longer applies

nep

Improbabilities for a Neutron Star • Thimbleful would weigh 100 million tons Density 1017 kg/m3

• Recall 1 teaspoon of White Dwarf weighs ~ 5.5 tons!!Density 109 kg/m3

1 M() White Dwarf would have a diameter of 10,000 – 12,000 km, Size of Earth!!

1 M() Neutron Star would have a diameter of 30 km (19 miles), Size of large city!!

http://www.astro.umd.edu/~miller/nstar.html

1960’s Cambridge England • 1967 Anthony Hewish’s Research Group from

Cambridge University finish 4 ½ acre radio telescope array

• Jocelyn Bell, Graduate Student, discovers regular pulses of radio noise from one location in the sky.

• Period of Pulses was 1.3373011 seconds

Sources of Pulsing • Little Green Men (aliens)

– Several Sources found across sky Periods range from 0.25 s to 1.5 s

• Variable stars (cepheids, etc)– Variation in intensity is on order of days, weeks, not

seconds!• White Dwarf Pulses (Acretion disks, Hot Spots)

– Would require rotations less than 1 second at their diameters, not likely

• Eclipsing Binaries – Again too short a period, stars would literally have

to be overlapping to create that kind of period

Sources of Pulsing • Crab Nebula (left over of the 1054 Supernova)

Period is 0.033 seconds or 30 pulses per second

• No White Dwarf could withstand such a rotation• Source of Pulsing must be smaller and more

dense than a White Dwarf• Mid 1960’s belief was White Dwarfs accounted

for all dead stars in our Galaxy

Why So Fast in Spinning • Conservation of Angular Momentum

– Ice Skaters– Sun

– RS= 696,000 km TS = 27 days

– Neutron Star

– RN = 30 km TN = 4.33 x 10-3 s (231 turns/sec)

Where is Radiation Coming From?• Magnetic Field is Connected to Gasses of Star• As Star is compressed, Magnetic Field is

concentrated• Radius changes by a factor of 10-5m• Surface Area (4 R2) changes by 10-10 m2

• BEarth = 10-4 Gauss• BSun = 1 Gauss• B White Dwarf = 106 Gauss• B Neutron Star = 1012 Gauss• BMRI = 104 to 105 Gauss

Where is Radiation Coming From?• Time-Varying Magnetic Fields Create Electric

Fields, Strong E fields induced near surface

http://micro.magnet.fsu.edu/primer/java/electromagnetic/

http://www.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html


Fields, Strong E fields induced near surface• Large amount of Energy available (Rotational

Kinetic Energy) Pair Production (e-, e+ )

http://commons.wikimedia.org/wiki/File:Pair_Production.png

http://www.studyblue.com/notes/note/n/chapters-8-10-/deck/1661893



Kinetic Energy) Pair Production (e-, e+ )• Strong E and B fields create Forces which

push created particles along field lines




push created particles along field lines• Accelerated Charges Radiate!! (antennas)

http://www.kshitij-school.com/Study-Material/Class-12/Physics/Electromagnetic-waves/Production-of-electromagnetic-waves-by-an-antenna.aspx




push created particles along field lines• Accelerated Charges Radiate!! (antennas)• Two Narrow beams of Radiation• Lighthouse Analogy

http://scatteredglimpses.wordpress.com/2011/08/02/the-lighthouse-and-the-searchlight/

Synchrotron Radiation Accelerating Charged Particles Radiate Electro-magnetic

(EM) Waves (Photons)Magnetic Fields can change a charged particle’s direction

of motion Acceleration!Such radiation removes energy from charged particle

http://www.ndt.net/ndtaz/content.php?id=850

http://scienceforums.com/topic/11645-7-reasons-to-abandon-quantum-mechanics-and-embrace-this-new-theory/

Where is Radiation Coming From?• Why not Blackbody Radiation???

• Blackbody also has radiation at most wavelengths, but it is strongest in the visible and higher at the star’s temperatures.

• Pulsars are strong in Radio as well as other radiations

• Sun is weak in Radio– Sun’s Radio source is also charged particles

moving within its magnetic field

• Over 1000 Pulsars discovered by using Radio Astronomy

• Estimated 100,000 or more waiting to be found in disk of Galaxy

• Periods range from 8.51 s to 0.00156 s (641 rotations a second)

• Not all Supernova Remnants have Pulsars• It appears that only Type II Supernovas

produce Pulsars• Supernovas often asymmetrical• Pulsar may move relative to the Remnant

moving

• No Sign of Pulsar in Supernova 1987A

Energy Output

• Sun 4 x 1026 Watts

• Crab Nebula 3 x 1031 Watts

• Crab puts out 100,000 x Sun’s Energy

• Pulsars lose Energy as they Radiate• Less Energy Slower Rotation• Crab Pulsar is gaining 3 x 10-8 S per day• Energy is going to Radiation Including

Synchrotron radiation (energy created as e- move in circular orbits)

• Generally the slower a pulsar rotates the older it is.

• Exceptions!!

Pulsars gradually slow down as they radiate energy into space

• The pulse rate of many pulsars is slowing steadily• This reflects the gradual slowing of the neutron star’s

rotation as it radiates energy into space• Sudden speedups of the pulse rate, called glitches, may

be caused by interactions between the neutron star’s crust and its superfluid interior

• Solution – Mass transfers from companion star– First star is high mass– Type II Supernova creates neutron star– Pulsar originally fast, slows as usual over time– Companion ceases to be main sequence and

expands past its Roche Lobe– Neutron Star’s strong gravity captures mass which

is either leaving on its own from Red Giant, or is just removed as Red Giant’s gravity not strong enough to hold it

– Mass from Red Giant strikes rotating Neutron Star with large speed and at an angle to increase star’s rotation, hence Speeding Up Pulsar!

Models of Pulsar• Construct Picture that fits Data• Composition• Mass• Rotation Rate• Energy Output• Magnetic Field• Induced Currents• Glitches!!!

Dec 27, 20047 Spacecraft overloaded by intense burst of

radiation lasting ~0.2 Sec.Pulsar SGR-1806-20 15,000 pc away

(Sagittarius) 1014 x Luminosity of Sun 300,000 years needed for Sun to emit that

much energy.Pulse rate before burst was 7.47 SecPulse rate after burst was 7.47 SecRotational Kinetic Energy not source of burstMagnetar!!

Magnetars

When Neutron stars form if they have a large enough rotation rate P<0.005 sec, Magnetic field gets compressed and enhanced.

B = 1015 G ~ 1000x normal Neutron StarHuge B field creates tremendous stresses that

are relieved by “starquakes” that emit the large amounts of energy seen.

*****

Pulsating X-ray sources are also neutron starsin close binary systems

• Magnetic forces can funnel the gas onto the neutron star’s magnetic poles, producing hot spots

• These hot spots then radiate intense beams of X rays• As the neutron star rotates, the X-ray beams appear to

flash on and off• Such a system is called a pulsating X-ray variable

• Sometimes Companion Star’s Gas is gaining so much energy from the gravity of the Neutron Star that when it strikes the Neutron star it creates a “Hot Spot” on the star which then can radiate X-rays. -- Pulsating X-Ray Sources!!

• Neutron Star’s Magnetic Field will direct this gas to either its North or South Magnetic Pole creating two hot spots on Star

• Eclipsing Binaries can create “Off Times”

The fastest pulsars were probably created by mass transfer in close binary systems

• If a neutron star is in a close binary system with an ordinary star, tidal forces will draw gas from the ordinary star onto the neutron star

• The transfer of material onto the neutron star can make it rotate extremely rapidly, giving rise to a millisecond pulsar

• 1982 Pulsar PSR 1937+21 – Period 2.558 ms 642 rotations per second

• Rapid spinning suggests very young pulsar• It’s rate of decrease in its spinning, suggests

very old pulsar??• Discovery of millisecond Pulsars!! - Over 50 all

with periods between 1 and 10 ms (rotations of 100 to 1000 per second)

• All ms Pulsars are in binary systems!!

Explosive thermonuclear processes on white dwarfs and neutron stars produce novae and bursters

• Material from an ordinary star in a close binary can fall onto the surface of the companion white dwarf or neutron star to produce a surface layer in which thermonuclear reactions can explosively ignite

• Explosive hydrogen fusion may occur in the surface layer of a companion white dwarf, producing the sudden increase in luminosity that we call a nova

• The peak luminosity of a nova is only 10–4 of that observed in a supernova• Explosive helium fusion may occur in the surface layer of a companion

neutron star• This produces a sudden increase in X-ray radiation, which we call a burster

Nova vs Supernova• Luminosity peaks

~105 L()

• Energy Radiated 1037 J

• Hydrogen Fusion occurring on Surface of White Dwarf in Accreted material

• Repeated Novas

• Luminosity peaks ~109 L()

• Energy Radiated 1044 J

• Hydrogen Fusion occurring inside White Dwarf

• White Dwarf destroyed, No Repeats!!

Nova vs X-Ray Burster• White Dwarf Star• Hydrogen Fusion

occurring on Surface of White Dwarf in Accreted material

• Neutron Star• Helium Fusion occurring

on Surface of Neutron Star in Accreted material

• White Dwarf’s Mass Limits 1.4 M()

(Degenerate e- pressure)• Neutron Star’s Mass Limits 2-3 M()

(Degenerate neutron pressure & Strong Nuclear Force)

• Gamma Ray Bursters????

Like a white dwarf, a neutron star has an upperlimit on its mass

• The pressure within a neutron star comes from two sources• One is the degenerate nature of the neutrons, and the other is the

strong nuclear force that acts between the neutrons themselves• The discovery of neutron stars inspired astrophysicists to examine

seriously one of the most bizarre and fantastic objects ever predicted by modern science, the black hole

What if Neutron Star M > 2-3 M()??

• vescape for a Neutron Star is ~ ½ c (speed of light)

• vescape for a mass > 3 M() is > c !!!

• Black Hole

Einstein’s Postulates• Theory of Relativity – The laws of Physics must

have the same form in all inertial reference frames

F = ma F’ = m’a’ m’ = 3(m +b)

• Theory of Constancy for the Speed of Light – All Observers measure the same speed of light

Another way is c < or = to 2.998 x 108 m/s in a

vacuum.

Special vs General Relativity

• 1905• Two frames of reference differ by constant v• Train Paradox• Twin Paradox

• 1915• Two frames of reference differ by constant a• Tidal Forces• Theory of Gravity

http://www.nap.edu/html/oneuniverse/images/motion_47.jpg

Special vs General Relativity

• 1905• Two frames of reference differ by constant v• Train Paradox• Twin Paradox

• 1915• Two frames of reference differ by constant a• Tidal Forces• Theory of Gravity

http://astronomyandspace.blogspot.com/2010/06/quote-john-wheeler.html

"Mass tells space-time how to curve, and space-time tells mass how to move.“

- John Wheeler

http://users.rcn.com/zap.dnai/astronomy/gravity.htm

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/bend2.gif

http://science.nasa.gov/headlines/y2004/images/einstein/lensing_med.jpg

http://chandra.harvard.edu/photo/2003/apm08279/apm08279_grav_lens.jpg

• This is one of the first multiply-imaged sources discovered in 1979 (by Walsh, Carswell and Weymann). Points A and B are images of the same distant source (quasar 0957+561), produced by light bending round a closer massive object that produces no image on this photograph.

http://www.upscale.utoronto.ca/GeneralInterest/Key/relgen.htm


• This is one of the first so-called 'giant arcs', C12244-02, viewed by the Hubble Space Telescope.

• In this case the foreground galaxy, shown by the bright spot at the centre of the picture is so perfectly aligned with the distant galaxy that the image of the latter becomes an almost perfect Einstein Ring. This picture was taken using the Hubble Space Telescope, by J.L. King, University of Manchester.


http://leo.astronomy.cz/grlens/fig1.gif

Mercury’s orbit changes orientation at a rate of 574 arcsec (about one-sixth of a degree) per century.

Newtonian mechanics predicts that the gravitational influences of the other planets should make the orientation change by only 531 arcsec per century.

Einstein was able to explain the excess 43 arcsec per century using his general theory of relativity.

The Precession of Mercury’s Orbit

• Doppler Red-Shift – the radiation is changed (longer wavelength) because of relative motion between the source and the observer.

• Gravitational Red-Shift – the radiation is changed (longer wavelength) because either time or space changes.

• Doppler Red-Shifts can never indicate motion greater than c

• Gravitational Red-Shifts can imply motion greater than c but it is because the space or time was changed, not local faster than c travel!!

• The general theory of relativity also predicts the existence of gravitational waves, which are ripples in the overall geometry of space and time produced by moving masses

• Gravitational waves have been detected indirectly, and specialized antennas are under construction to make direct measurement of the gravitational waves from cosmic cataclysms

Test #4 Gravity Waveshttp://spaceplace.nasa.gov/en/kids/lisa_fact2.shtml

• The Laser Interferometer (in-ter-fear-AH-muh-ter) Space Antenna (LISA) is a space mission that will be able to detect some of these gravitational waves, like a huge astronomical microphone. If NASA decides to pay for this mission, it will be launched around 2015.

1993 Nobel Prize in Physics (discovery in 1974) http://nobelprize.org/physics/laureates/1993/press.html

http://casa.colorado.edu/~ajsh/redschbig_gif.html

Black Holes

• Well is infinitely deep, not finite as in a normal massive object

• 10 M() Black Hole affects a range of about 1000 km• Cannot “see” Black Holes• Must detect effects of Black Holes

Case for HDE 226868 (Cygnus X-1)

• Irregular x-ray Source, some variations (flickering) are 1/100 s

• Objects cannot flicker faster than time for light to travel across their diameter

• Since nothing travels faster than c, a flicker of 1/100 s implies diameter is less than 3000 km across (< ¼ Earth’s diameter)

• Our Sun has a diameter of 1.391 x 109 m• So it could flicker (1.391 x 109 m)/(3.00 x 108 m/s) = 4.64 seconds


• Radio bursts show source at same point in sky as star HDE 226868

• Spectroscopy identifies HDE 226868 as a B0 Super Giant with a surface temp of 31,000K Such stars do not emit significant x-rays

Case for HDE 226868 (Cygnus X-1)• HDE 226868 can’t be alone, must be binary• Doppler shifts of spectra reveal a pattern of

shifting of 5.6 days Confirming binary nature of star

• Knowledge of other Supergiants, speculate mass of HDE must be about 30 M()

• Companion must be about 7 M()

• 7 M() too large for Neutron Star, must be black hole

• X-rays not from black hole, but from accretion disk. Gravitational energy raises T to several Million K


• What if HDE were not 30 M()?• Companion could be only 3 M()

• Neutron Star then!!

Other Possible Black Hole Candidates• V404 Cygni

– Visible star period 6.47 d – Variation of radial velocity > 400 km/s– Lower limit on Companion mass > 6.26 M()

• A0620-00 Monoceros– Orbital period of binary 7.75 h– Companion Mass > 3.2 M() Most likely 9 M()

Black Holes in Binary Systems

• One star undergoes Type II Supernova and forms black hole

• Neutron star or White dwarf accretes enough material from the other star

• Pair of Neutron Stars emit Gravity waves as they come together and combine to form a black hole

M87• Use Newtonian Mechanics

• Doppler shifts give periods and telescopes give distances, Mass found

• Dark Matter

32

2 4 RGM

T

Categories of Black Holes

• Supermassive ~1 Million to 1 Billion M()

• Stellar ~10 M()

• In 2000 Missing Link 500 M() Black Hole found in M82

Categories of Black Holes

• Supermassive ~1 Million to 1 Billion M()

• Stellar ~10 M()

• In 2000 Missing Link 500 M() Black Hole found in M82• Primordial Black Holes?? Hawking 1970’s Masses on order of MEarth to 5 x10-8 kg

(1/40 mass of a water drop)

Schwarzschild Radius

• Find Radius of a 10 M() Black Hole

2

2cGMRSch

mxmR

smx

kgxkg

NmxR

Sch

Sch

4

28

302

211

100.3500,29

1000.3

)1099.1)(10)(1067.6(2

Black Holes• Non-rotating Star Collapses inside event horizon, non-rotating

Black Hole (Schwarzschild) is formed• Once Star is inside Event Horizon, collapse cannot be

stopped• Inside event horizon, we have no knowledge, it is believed

that Time and Space are mixed• Outside event horizon, Time must move forward• Inside event horizon, Space must move to center• Information Sink, once inside event horizon, Universe outside

loses all knowledge of object• 2014 Hawking changes his mind about information loss

http://www.space.com/24454-stephen-hawking-black-hole-theory.html



Describing a Black Hole• Mass – Put object in orbit

• Charge – should be near zero, if initially charged or possesses large Magnetic field, charges will be attracted to balance and Magnetic field will be reduced by radiation

• Angular Momentum – Put two satellites in orbit in opposite directions, ergo-region is a distortion of spacetime that is pulled with the spinning Black Hole, creates different periods for satellites

Black Holes Losing Energy (Mass)

• Penrose Process – Give up rotational energy

• Evaporation (Hawking Radiation) – Only likely in small mass Black Holes

Milky Way Galaxy

• Hindu’s thought Milky Way was source of Ganges

• Greek word Galactos (“milk”)

Early Views of Galaxy• Assumed we are at center of Galaxy• Galaxy cannot be spherical since the star

density is not uniform in all directions.• Herschel reasoned disk shape• Kapteyn used brightness and relative motion of

stars to determine a diameter of 17 kpc (~55 ly), too small !!

• Shapley using the Cepheid variable work of Leavitt reasoned we are 2/3 of the way from the center to the edge, about right!!

• Shapley found a diameter of 100 kpc too large!.

Globular Clusters• ~106 stars in a spherical volume few hundred

light years in diameter• Ordinary stars and Open Clusters are usually

found in the plane of the Galaxy, Globular Clusters are found in a spherical distribution which was found to be centered not around our Solar System but around a point in the direction of Sagittarius

• Shapley measured distances to the RR Lyrae variables in the globular clusters.

• Shapley’s Value of the galaxy’s diameter of 100 kpc is 2 x actual value.

• Shapley did not account for dimming of stars by interstellar extinction!!

Parts of a Galaxy• Main Disk ~ 50 kpc diameter, ~0.6 kpc thick• Central Bulge ~2 kpc in diameter, not likely to

be a flattened sphere, but is elongated. Perhaps peanut shaped.

• Halo – Traced out by Globular Clusters• Halo Stars have very elliptical and higher

velocity than main disk stars• Globular Clusters have Pop II (metal-poor)

stars• Main Disk has more Pop I stars Spiral Arms

have lots of Hot O and B stars which trace out Spiral arms

Find New Stars• Stars mostly made of Hydrogen• Find Hydrogen regions (remember H II

regions??• Visible light from Excited H requires e- go

from n=3 to n=2 or n=4 to n=2, etc Cold interstellar space e- not likely to be in any orbit other than n=1

• e- still emit photons, but they are in Radio region of E-M Spectrum

Mapping out the Galaxy• H clouds emit radio waves• Since they are moving radiation is Doppler

shifted• Only radial (to Earth) velocity found this way• All objects rotating have same angular speed• Objects farther from center of rotation have

larger linear speed

Period of Sun around Galactic Center

rsMillionYeaP

yrP

pckm

skmpcP

vRP

7.223sec10156.3

1sec1006.7

11009.3

/220)8000(2

2

715

13

Galactic Mass??

)(1041

2

7

316

28

3

2211

2

2

32

32

2

103.91085.1

sec10156.31

11009.3

)102.2()8000(

1067.6

4

4

4

MkgM

yrpc

m

yrpc

kgNm

M

PR

GM

RGM

P

Galactic Mass??

• Previous calculation only considers mass inside of Sun’s orbit.

• Adding mass outside of Sun’s orbit pushes mass of Galaxy to >1012 M() ~ 200 Billion Stars!

• Observed Mass is ~10% of this mass???• Rest of Mass must be DARK MATTER

What is Dark Matter?

• Dark Matter is matter that cannot be detected with today’s technology.

• It’s existence is inferred from observed gravitational effects.

• Observation of star groupings outside of Milky Way suggest a Dark Matter Halo 2 to 4 x larger in diameter than Visible Halo

Examples of Dark Matter• Neutrinos (possibly small mass), could be a large fraction

of Dark Matter• WIMPS (Weakly Interacting Massive Particles) –

previously mentioned in lowering Sun’s core temp• MACHOS (Massive Compact Halo Objects), some

evidence of low mass MACHOS (~10-6 to 0.1 M() ), from microlensing of starlight.

• Density waves exist independent of medium• Vwave ≠ Vmaterial

• Weather Systems

• Hot O and B stars have short Lifetimes• ~3 to 15 Million years• Age of Galaxy ~ 10 Billion years• Stars don’t live long enough to get away from Spiral Arms

Problems with Density Wave Model

• Where does the energy come from to sustain spiral density waves?– Galaxy itself (bar at center could produce the asymmetric

gravitational attraction necessary– Interactions between galaxies

• According to the theory of self-propagating star formation, spiral arms are caused by the birth of stars over an extended region in a galaxy

• Differential rotation of the galaxy stretches the starforming region into an elongated arch of stars and nebulae.

Self-Propagating Star Formation• Galaxy without spiral arms• Stars begin to form

– Radiation from new hot stars compress gasses creating some new stars

– Supernovas compress additional gasses creating more new stars

• Newly formed stars travel at same speed but as seen earlier make spiral arms because of lagging behind

Density waves Vs Self-Propagating Star Formation

• Density waves create Spiral Arms which then create Stars

• Self-Propagation create Stars which then form Spiral Arms

Variety in Spiral Arms

The differences from one spiral galaxy to another suggest that more than one process can create spiral arms.

Galactic Nucleus?

• Strong Radio source• Synchrotron Radiation• Appears to have ~ 3 Million M() in a volume 1 AU in

diameter

• Black Hole??

main sequence lifetimes

Documents