Review of Stellar Evolution
The Hertzsprung-Russell diagram shows the relationship between color (temperature) and brightness (luminosity) for stars
•
About 90% of all stars
(including the Sun) lie on the
Main Sequence.
• Stars maintain this relationship between color and magnitude during core hydrogen burning.
•
A star
’s location along the Main
Sequence depends on mass
(higher mass stars sit at brighter luminosities along the
Main Sequence).
• Main Sequence is just one phase of a star
’s life
•
Astronomers use the
Hertzprung-Russell diagram to trace the evolutionary stages of stars of different masses.

Stars form out of clouds of gas and dust (which can be several hundred light years across) in our Galaxy (the Interstellar Medium stuff between the stars). The atoms and molecules in these clouds are moving with speeds according to the temperature of the cloud.
If the cloud is cold enough, the particles will begin to come together due to the attractive force of gravity.
The first several stages of star formation take about 2 million years as the densest pockets collapse first leading to fragmentation. Stars initially form in these groups or clusters.
Pockets with mass < 0.08 M sun will not achieve high enough temps to become a star
(brown dwarfs). The following scenario is for gas spheres with 0.08 M sun
< M < 7 M sun

Protostar (position 4 on HR) – after ~ million years
•the opaque center of the collapsing cloud fragment continues to contract and gain mass as material “ rains ” onto it.
•The contraction leads to continued heating (position 5) which builds pressure on the core and starts to slow the collapse.
Star (6) - after ~30 million years
• central core temperature reaches 10 million degrees K .
• nuclear fusion begins in the core (burning Hydrogen into
Helium and releasing energy/light).
• contraction continues very slowly until the star reaches equilibrium on the Main
Sequence (position 7)

On the Main Sequence , the contraction stops because gravity and radiation pressure exactly balance each other. The nuclear reactions occur at exactly the right rate to balance gravity. Thus the star
’s mass determines its luminosity on the Main Sequence
(more gravitational pressure from higher mass means higher luminosity).
Nuclear reactions slowly convert Hydrogen to Helium in the core. A new star begins with about 91%
Hydrogen (H) and 9%
Helium (He).
In the core of a star with a mass similar to the Sun, the conversion of H to He will take ~ 10 billion years (its
Main Sequence lifetime).

When the H in the core runs out:
Nuclear reactions stop
Core pressure decreases
Core contracts and gets hotter - heating overlying layers
H to He burning moves to a shell and reactions occur faster than before (less gravitational pressure from upper layers)
The star becomes more luminous
The hot shell causes the outer layers to expand and cool
The star moves off the Main Sequence and up the Red Giant Branch (positions 8 to 9). This takes about 100 million years.

Red Giant Branch - the core continues to get hotter as the outer layers press down (the star is called a Red Giant at this time – no longer a main sequence star).
When the core reaches 100 million degrees, conditions are hot enough to begin burning the Helium to Carbon
The onset of this burning causes the temperature & luminosity to rise sharply in a runaway explosion called the Helium Flash (position 9).
Eventually the core expands, density drops and equilibrium is reestablished.
The core structure is now readjusted during Helium core burning and the total luminosity decreases .
During core Helium burning, the star is on the Horizontal Branch of the HR diagram (position 10).

Helium-to-Carbon burning occurs stably in core, with Hydrogen-to-Helium burning in a shell until the core Helium runs out in ~20-50 million years.
The increased shell burning causes the outer layers to expand and cool once more.
The star moves up the asymptotic giant branch over the next ~10,000 years and becomes a red supergiant (position 11).
The star looks like this, with both a
Helium and Hydrogen burning shell and a
Carbon, non-burning core.

White Dwarf
As the Carbon core continues to contract and heat, the shell Helium burning grows more intense.
Helium flashes occur in the shell .
Surface layers pulsate and are eventually ejected.
The hot, tiny core is now called a White
Dwarf and is surrounding by a Planetary
Nebula (emission line nebula)
The white dwarf has ~1/2 the star ’s original mass since the other half is expelled in the planetary nebula. They are small (about the size of the Earth) and extremely dense (10 6 g/cm 3 ).

Red Giant

Nova – accreted Hydrogen gas from binary partner star onto WD surface becomes so hot due to the strong gravitational field, it burns off quickly and violently every few weeks to every couple of years.
The white dwarf eventually gets cooler and fainter as it no longer produces any light via nuclear reactions (position 13).
Unless a WD is in a binary partner, it will become impossible to detect after several million years. However, if it is in a binary system, the
WD can accrete material from its neighbor star and can reveal itself as a recurring event known as a Nova.

Degeneracy Pressure – supports White Dwarfs
Degenerate gas - compressed/cooled gas such that all electrons are in lowest energy levels allowed by exclusion principle
Pauli Exclusion principle
– two particles in close proximity cannot be in the same quantum state (i.e. quantum numbers that describe energy level, spin must differ).
Degeneracy Pressure results from the Heisenberg Uncertainty principle
Δp Δx ≥ h/2π
Since the particles ’ locations are extremely confined, momentum is very uncertain and particles are moving extremely fast  this leads to a high pressure for a degenerate gas.
The particles have “Heisenberg speeds” of
Δv = Δp/m e
P degen
~ (h/2π)n e
1/3
= (h/2π) 2 n e
5/3
/m
/m e e
(eq.18.8)
(eq.18.11)
Chandrasekhar found the maximum pressure exerted by a degenerate electron gas with Δv  c allowing for special relativistic effects and carbon/oxygen composition. This pressure corresponds to a maximum mass
 1.44 M sun
(Chandrasakhar limit)

Mass-Radius Relationship for White Dwarfs
Equating hydrostatic equilibrium pressure with electron degeneracy pressure gives


•In high mass stars (> 7 M

), outer layers of star squeeze and heat the core to ignite
Carbon…then Oxygen,
Neon, etc.
•MS life of such a star is
~30Myr(7M

/M) 3
•As each fuel gets exhausted in the core, its burning moves to a shell -
Onion skin structure
•Formation of Iron is the final stage

Why is Iron formation the end of the line?
56 Fe has the highest binding energy per nucleon - very stable.
Any reaction involving iron (fission or fusion) requires energy.
With no more sources of energy, and Fe fusion taking energy from the gas, pressure support in the star ’s core is lost.
The core quickly collapses under its own weight….

In these higher mass stars, the iron core reaches and exceeds the
Chandrasekhar limit (1.44M

) and the core cannot be supported by electron degeneracy pressure - core continues to collapse very quickly – less than 1/10 second!
The 56 Fe atoms use any energy produced in the collapse, so the core does not heat up.
Iron atoms get destroyed in the ever collapsing core and the protons then combine with electrons in the star to produce neutrons and neutrinos e + p = n +
 e
Eventually, the neutrons are so close together they “ touch ” : neutron degeneracy pressure.
The neutron core then halts the collapse causing outer material to bounce outward and leaving behind a Neutron Star.

Electrons run out of room
(quantum states to occupy) and prevent further collapse. Protons and neutrons still free to move
Stronger gravity=>more compact
Electrons and protons combine to make neutrons.
Neutron degeneracy prevents further collapse.
Much more compact.

Supernova!
During the explosion, nuclear reactions take place rapidly and can produce elements heavier than iron.
Material is dispelled into the interstellar medium to be incorporated into later generations of stars.
Crab Nebula - result of a supernova recorded by
Chinese astronomers in 1054
AD – appeared as bright as
Venus and visible in the daytime sky

Lightcurves show a rapid increase in brightness followed by fading over several months.
A supernovae explosion can exceed the luminosity of an entire galaxy (max
L sn
~10 9 L sun
)
Total energy output:
Neutrino energy ~ 10 46 J
Kinetic energy of ejected gas ~ 10 44 J
Photon energy ~ 10 42 J
(compare with Sun ’s lifetime energy output of 10 44 J)

Aside on Spectroscopy in Astronomy…
1
2
3

Absorption line spectrum for a star (the
Sun)
Emission line spectra of different elements

Spectra of supernovae reveal differences:
Type II SN – do show H absorption lines
Type I SN – do not show H absorption lines
Further divided:
Type Ia SN – no H or He lines
Type Ib SN – no H but do show He lines
Type II and Ib are thought to be the same thing, except that Ib completely lost their
H rich outer layers in a strong stellar wind and then underwent core collapse.
Type 1a are completely different
•WD eventually “ builds up ” material that was not completely ejected during nova explosions
• Added mass causes gravity to squeeze the WD allowing Carbon to finally start burning.
• Carbon burns all over the WD at once
(not just in core) and the star explodes in a carbon-detonation supernova.

New Type 1a SN discovered last year in galaxy M82!
Supernova 2014J
• 11th magnitude source
• visible in amateur telescopes
• Type Ia (exploded white dwarf)
• debris expanding at 20,000 kilometers per second
• Distance ~ 12 million lightyears

Type II Supernova Remnants
Optical -
Veil Nebula
IR - CasA
Generally have strong magnetic fields and contain many charged particles
Electrons spiral around the field lines - spiraling motion of charged particles produces synchrotron radiation polarized light
Radio - CasA
X-ray - CasA
Optical - SN1987A

Degeneracy Pressure – supports Neutron Stars
Neutrons obey Pauli exclusion principle similarly to electrons and can exert degeneracy pressure at high densities
P n
~ (h/2π) 2 n n
5/3 /m n
(eq.18.36)
Since the star is all neutrons and

= n n m n
P n
~ (h/2π) 2

5/3 /m n
8/3
Recall, for electron degeneracy
P e
~ (h/2π) 2 n e
5/3 /m e
(eq.18.11)
Thus, electron degeneracy pressure is greater by m n
/m e
~ 1839 (at a given density). But since the density of a neutron star is much greater than a white dwarf, neutron degeneracy pressure is greater in a neutron star than electron degeneracy pressure in a white dwarf.

Problem time
Compute the ratio of neutron degeneracy pressure to electron degeneracy pressure.
Density of WD = 2x10 6
Density of NS = 2x10 14 g/cm 3 g/cm 3
P ns
/P wd
= (ρ ns
/ρ wd
) 5/3 x (m e
/m n
)
For a 1.4M

NS with r = 15km, what is the acceleration of gravity at the surface?
g ns
= GM ns
/R ns
2 = 8.3 x 10 13
Compare with Earth ’s gravity g earth cm/s
= 10 3
2 cm/s 2
Tidal effects are also important on the surface of a neutron star dg/dr = 10 8 cm/s 2 /cm or 100,000 times the acceleration of gravity on the Earth per cm.

Neutron Star size compared to New York City
Mass: 1.4 - 3 M

Radius: 10 -15 km
Density: 10 11 kg/cm 3
(eq 18.41)
1 cm 3 weighs as much as Mt. Everest!

Neutron star rotation
Since angular momentum is conserved, any original rotation of the star is amplified in the shrunken core.
J = I

(I is rotational inertia,
 is angular velocity)
I = (2/5)MR 2 for rotating sphere
Imagine a star like the Sun becomes a neutron star


R

2 =

R 2
(

/


) = (7x10 5 km)/(15 km) 2 = 2x10 9
If the Sun rotates once in 30 days, the period of the neutron star is
P ns
= (2.7x10
6 s)/(2x10 9 ) = 1.35 x 10 -3 s or 1000 times per second!

Magnetic Fields
•Faraday’s Law tells us that the magnetic flux through a surface remains constant
•Thus, neutron stars have strong magnetic fields since
BR 2 = constant and the star ’s original magnetic field now runs through a smaller surface area.
•Beginning with the Sun’s magnetic field, the neutron star would have a field 2 x 10 9 times stronger.

 Possible existence of neutron stars was first realized in the 1930s in theory only.
 Believed to be too small to be observed
(although some nearby and recently formed NS have hot enough surfaces (T~10 6 K and L~0.2L
sun to be detected in X-rays)
)
 In 1967 an accidental discovery in radio astronomy revived interest in neutron stars via the discovery of the first pulsar .

The first pulsar was discovered in 1967 by a graduate student,
Jocelyn Bell, who measured this radio signal from an unresolved source (named LGM-1).
Her advisor Antony Hewish was studying the scintillation
(twinkling) of radio light from distant sources caused by charged particles in our solar system.
This required observations with time resolution of ~1/10 th
– not previously attempted for radio sources.
second
The rapidly varying source they detected showed a regular pulsation with a period of
1.337 s.
Since then, about 500 pulsars have been discovered in our Galaxy

For a rotating star, the rotation must not be so fast that objects on the surface lose contact with the surface (i.e. gravity must be greater than the force required to keep a point moving in a circular path).
R = [(G/4π 2 )mP 2 ] 1/3 where P is the period, R is radius
Rules out normal stars and WD which do not have strong enough surface gravity leaving neutron stars as the best candidates.
1) Strong magnetic fields capture particles from NS atmosphere and produce
“ hot spots ” at the magnetic poles.
2) Accelerated particles at hot spots emit beamed synchrotron radiation.
3) If the rotation axis is different than the magnetic field axis, then the radiation beam rotates like a searchlight.

4) The rotating searchlight is like a lighthouse, which we see as a pulsar if we happen to lie in the searchlight beam.
5) Not all neutron stars will be observed by us as pulsars because the searchlight might not intercept Earth. The pulsar would visible to about ~20% of potential observers

The pulse period gives the rotation period of the neutron star.
Typical periods are 0.03 to 1 seconds, or 1 to 30 rotations per second
The beamed radiation appears in the radio, but sometimes also in
X-rays, visible, infrared. Emission mechanism not entirely understood though most is likely synchrotron radiation – magnetic field accelerates charged particles which spiral around field lines.
Visible light images of the Crab
Pulsar during “on” and “off” separated by only hundredths of a second

Crab Pulsar P = 0.033s
This pulsar is responsible for replacing much of the energy radiated away via synchrotron emission from the remnant (about 10 5 L sun
)
Chandra X-ray (left) and
HST optical (right) movie showing real time shock waves from the pulsar into the surrounding interstellar medium

More than half of all stars are in binaries.
White dwarfs in close binaries lead to novae (mass transfer followed by Hydrogen burning on the surface of the white dwarf).
Neutron star binaries can behave similarly (mass transfer followed by Hydrogen burning on the surface).
Time scales are shorter (explodes every few hours) and the bursts are hotter (appearing in X-rays) because stronger surface gravity.
Neutron star
X-Ray Bursters

Neutron stars in Close Binaries
The hot accretion disk and hot spot are constant sources of X-rays, with bursts (fueled by fusion) going off every few hours.
Millisecond Pulsars:
Infalling accreted material orbits faster than the NS spin and can spin-up the rotation over time causing some neutron stars to spin almost
~1000 times a second

 Just as there is a limit to the mass that can be supported by electron degeneracy, there is a limit to the mass supported by neutron degeneracy
(Tolman-Oppenheimer-Volkoff limit: ~3M sun
)
 If mass is greater than this, there is nothing to halt gravitational collapse
 The result is a stellar core that becomes a black hole

Detection of Black Hole candidates in binary systems
BH in binary system with normal star
As star evolves, it evolves and swells to size larger than Roche limit
Tidal force of BH strips away outer layer. Gas is compressed and heated to 10 6 K.
Forms accretion disk with characteristic spectrum - X-rays from innermost (hottest) parts with visible – infrared from outer part
We measure masses from orbital parameters (Kepler ’ s Laws).
If dark companion has M > 3 M sun
, likely BH candidate.

Observational Evidence for Black Holes: Cygnus X-1
•Bright X-ray source
•Optical images show an O type star (blue supergiant) with m v
=9 implying a mass of 15 M sun
•Spectroscopic binary with P=5.6 days
•Variability of 0.07mag implies orbit inclination of 30 degrees
•Period combined with velocities from orbital parameters yields total system mass of ~23M sun
•Mass of unseen companion: 8M sun
(or at least more than 4M sun
)
•X-ray variability implies small source of origin (5ms -- <1500km)
•Black hole!
Gamma-ray image
X-ray variability over 1 minute

Observational Evidence for Black Holes: Cygnus X-1
Problems with black hole conclusion
•Possible that the spectrum of the companion is produced by different mass star
•Orbit inclination has some uncertainty
•Triple-star system?
For years, Cyg X-1 was the only strong candidate for stellar black hole, but there are currently over
~30 likely black hole candidates in our Galaxy
See http://www.johnstonsarchive.net/relativity/bhctable.html
and http://blackholes.stardate.org/objects/ for current lists

Other examples:
LMCX-3
•X-ray source in Large Magellanic Cloud
•Companion is 17th mag B3V star
•Spectroscopic binary - P=1.7 days
•Does not eclipse - constrains inclination
•Estimated mass of compact object: 4 to 11M sun
Nova Mon 1975
•Transient X-ray source
•Optical companion is a K-dwarf (better mass estimate)
•Spectroscopic binary - P=7.8 hours
•Estimated lower-limt mass of compact object: 3 M sun
V404 Cygni
•spectroscopic binary
•P=6.47 days
•Cool subgiant (0.6M
sun
) orbiting dark companion with M=6M sun