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Chapter 18 The Bizarre Stellar Graveyard. What is a white dwarf?. White Dwarfs. White dwarfs are the remaining cores of dead stars Electron degeneracy pressure supports them against gravity. White dwarfs cool off and grow dimmer with time. Size of a White Dwarf.

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white dwarfs
White Dwarfs
  • White dwarfs are the remaining cores of dead stars
  • Electron degeneracy pressure supports them against gravity
size of a white dwarf
Size of a White Dwarf
  • White dwarfs with same mass as Sun are about same size as Earth
  • Higher mass white dwarfs are smaller
the chandrasekhar limit


The Chandrasekhar Limit

The more massive a white dwarf, the smaller it is.

Pressure becomes larger, until electron degeneracy pressure can no longer hold up against gravity.

WDs with more than ~ 1.4 solar masses can not exist!

the white dwarf limit
The White Dwarf Limit
  • Quantum mechanics says that electrons must move faster as they are squeezed into a very small space
  • As a white dwarf’s mass approaches 1.4MSun, its electrons must move at nearly the speed of light
  • Because nothing can move faster than light, a white dwarf cannot be more massive than 1.4MSun, the white dwarf limit (or Chandrasekhar limit)
accretion disk
Accretion Disk
  • White dwarf in a mass-transfer binary
    • Its gravity pulls matter from the companion star
    • The rotation results in the formation of an accretion disk
    • Temperature of the matter increases as it spirals in
      • Disk can radiate in visible UV and X-ray
accretion disks
Accretion Disks
  • In addition to the heating due to the contraction, friction between orbiting rings of matter in the disk causes the disk to heat up and glow
  • The temperature of accreted matter eventually becomes hot enough for hydrogen fusion
  • Fusion begins suddenly and explosively, causing a nova
nova explosion
Nova Explosion
  • Exploding layer is only about 0.0001 solar masses
  • The spectrum reveals the details
    • Initially, blue-shifted gas with absorption lines – dense gas
    • Then, blue-shifted gas with emission lines – thin gas
  • It can be 100,000 times more luminous than the sun.
  • Fades over a period of weeks or months
  • Mass transfer process begins again
nova explosions


Nova Explosions

Hydrogen accreted through the accretion disk accumulates on the surface of the white dwarf

  • Very hot, dense layer of non-fusing hydrogen on the white dwarf surface

Nova Cygni 1975

  • Explosive onset of H fusion
  • Nova explosion
  • The nova star system temporarily appears much brighter
  • The explosion drives accreted matter out into space
  • The star will “nova” again when the explosive layer accumulates.
    • Many novae take thousands of years to build an explosive layer, but some take only decades.
  • Mass Ejection from Novae
  • (a) Nova Persei
  • (b) Nova Cygni

Our sun will not nova.

It can’t. It’s not part of a binary system.

thought question
Thought Question

What happens to a white dwarf when it accretes enough matter to reach the 1.4 MSun limit?

A. It explodes

B. It collapses into a neutron star

C. It gradually begins fusing carbon in its core

types of supernova
Types of Supernova
  • Massive star supernova (Type II):
  • Core-collapse supernova
  • Iron core of a massive star reaches white dwarf limit and collapses into a neutron star, causing total explosion.
  • If the remaining core is large enough (>2-3 M ) the core will collapse into a black hole, if not it forms a neutron star.
  • They retain their outer hydrogen core prior to the explosion, so their spectra show hydrogen lines.
type i supernovae
Type I Supernovae
  • Type Ia supernovae
    • White dwarf in a binary undergoes a nova, but does not blow away all of the accumulated mass
    • Supported initially by electron degeneracy pressure
    • Mass slowly increases until star reaches the Chandrasekhar limit
      • Electron degeneracy pressure can no longer hold up the star against gravity
    • Core collapses and heats rapidly
    • Carbon fusion occurs everywhere in the star simultaneously
      • Carbon-detonation supernova
    • Massive explosion completely destroys the white dwarf.
    • About 6 times as luminous as a Type II
    • No H in the spectrum because there was none in the white dwarf.
type i supernovae1
Type I Supernovae
  • Type Ib and Ic supernovae
    • Massive star in a binary looses its Hydrogen rich atmosphere to a companion (that is not a white dwarf)
    • Explodes due to core collapse
    • No hydrogen in spectrum because it lost it to the companion
    • Essentially a Type II but without the hydrogen
    • Ib and Ic differ by the presence of the 587.6nm helium line in the spectrum of Ib but not in Ic

One way to tell supernova types apart is with a light curve showing how luminosity changes with time

supernovae light curves
Supernovae Light Curves
  • Maximum luminosity can be more than a billion Suns.
  • Note the characteristic plateau of Type IIs
supernova type massive star or white dwarf
Supernova Type: Massive Star or White Dwarf?
  • Spectra differ also differ (Type I don’t have hydrogen absorption lines)
  • Type Ia spectra become dominated by lines of iron.
  • Type Ib/Ic lack 635.5 nm silicon line and have oxygen, calcium and magnesium.
  • Type Ic lack lines of helium at 587.6 nm which are in Ib
the deaths of massive stars supernovae
The Deaths of Massive Stars: Supernovae

In the multiple shell burning stage of a high mass star:

As each element is burned to depletion at the center, the core contracts, heats up, and starts to fuse the ash of the previous burning stage. A new inner core forms, contracts again, heats again, and so on. Through each period of stability and instability, the star’s central temperature increases, the nuclear reactions speed up, and the newly released energy supports the star for ever-shorter periods of time.

For example, in round numbers, a star 20 times more massive than the Sun burns hydrogen for 10 million years, helium for 1 million years, carbon for 1000 years, oxygen for 1 year, and silicon for a week. Its iron core grows for less than a day.

numerical simulations of supernova explosions


Numerical Simulations of Supernova Explosions

The details of supernova explosions are highly complex and not quite understood yet.

observations of supernovae
Supernovae are rare.

Only a few have been seen with the naked eye in recorded history.

Arab astronomers saw one in AD 1006.

The Chinese saw one in AD 1054.

European astronomers observed two—one in AD 1572 (Tycho’s supernova) and one in AD 1604 (Kepler’s supernova).

In addition, the “guest stars” of AD 185, 386, 393, and 1181 may have been supernovae.

Observations of Supernovae
observations of supernovae1


Observations of Supernovae

They can sometimes be seen in distant galaxies.

observations of supernovae2
Supernova explosions fade in a year or two, but expanding shells of gas, supernova remnants, mark the sites of the explosion.

The gas, originally expelled at 10,000 to 20,000 km/s, may carry away a fifth of the mass of the exploding star.

They last a few tens of thousands of years before they mix with the interstellar medium and disappear

Some can only be seen today in X-rays or radio wavelengths

Some, like Cassiopeia-A, show evidence of jets of matter ejected in opposite directions.

Observations of Supernovae
supernovae remnants
Supernovae Remnants
  • Supernova Remnant: Expanding cloud of material from the explosion of a supernova
  • Crab Nebula (M1)
    • Supernova in 1054 A.D.
    • Angular diameter about one-fifth that of the full Moon.
    • Debris is scattered over a region of “only” 2 pc; Considered to be a youngremnant
    • The blue color is produced by synchrotron radiation
synchrotron radiation
Synchrotron radiation is produced by rapidly moving electrons spiraling through magnetic fields.

Remember – accelerated charged particles emit radiation

In most nebulae

this radiation is in the

radio part of the EM


In the Crab Nebula

it is in the visible


Synchrotron Radiation
supernovae remnant motion
Supernovae Remnant Motion
  • By superimposing positive and negative images taken years apart, we can tell that the Crab Nebula is moving outward
  • We can extrapolate back to the origin of the explosion
  • Corresponds closely

to the date of the

1054 A.D.


vela supernova remnant
Vela Supernova Remnant

Extrapolation shows it exploded about 9000 B.C.

supernova remnants


Supernova Remnants

X rays

The Crab Nebula:

Remnant of a supernova observed in a.d. 1054

The Veil Nebula


Cassiopeia A

The Cygnus Loop

supernova 1987a
Supernova 1987A
  • Stellar evolution theory predicts we should see about 1 supernova in our galaxy about every 100 years.
  • Hasn’t been one in over 400 years
  • Supernova 1987A occurred in the Large Magellanic Cloud
  • Its light curve is

somewhat atypical

SN1987A was produced by the explosion of a hot, blue supergiant rather than a cool, red supergiant.

Evidently, the star was a red supergiant a few thousand years ago but had contracted and heated up slightly becoming smaller, hotter, and bluer before it exploded.

One observation of SN1987A confirmed the theory of core collapse.

At 2:35 AM EST on February 23, 1987, hours before the supernova was first seen, instruments buried in a salt mine under Lake Erie and in a lead mine in Japan, recorded 19 neutrinos in less than 15 seconds.

Trillions must have passed through our bodies

About 1017 neutrinos must have passed through the detectors

They came from the direction of the supernova

  • The glowing ring is gas expelled by SN1987A’s progenitor star while in its red-giant phase.
  • It glows from the UV light pulse from the supernova
neutron stars and black holes
Neutron Stars and Black Holes
  • Gravity always wins. We believe stars end in one of three final states called compact objects.
    • white dwarf
    • neutron star
    • black hole
  • For Type Ia supernovae, the entire star is obliterated, leaving no remnant
  • Type II supernovae end up as a neutron star or a black hole

A neutron star is the ball of neutrons left behind by a massive-star supernova.

Degeneracy pressure of neutrons supports a neutron star against gravity.

theoretical prediction of neutron stars
Theoretical Prediction of Neutron Stars
  • In 1934, two years after the neutron was discovered, Walter Baade and Fritz Zwicky predicted that massive stars would end in an explosion they called a supernova.
    • The core would form a small, tremendously dense sphere of neutrons.
    • Zwicky coined the term

‘neutron star.’

    • The core is supported by

degenerate neutron pressure


Electron degeneracy pressure goes away because electrons combine with protons, making neutrons and neutrinos

Neutrons collapse to the center, forming a neutron star

theoretical prediction of neutron stars1
Theoretical calculations suggest that stars that begin life on the main sequence with 8 to roughly 20 solar masses will leave behind neutron stars.

They have a radius of about 10 km and a density of about 1014 g/cm3

Mass of about 1-3 M

It should spin many times per second – conservation of angular momentum

Surface many times hotter than the sun – energy from gravitational collapse

Magnetic field a trillion times stronger than Earth’s – field squeezed into a small volume

Theoretical Prediction of Neutron Stars
theoretical prediction of neutron stars2
Neutron stars are very hot

Black-body spectrum peaks in X-rays

Couldn’t detect them until x-ray telescopes where put in orbit

Their surface area is very small

Very faint

Theoretical Prediction of Neutron Stars
discovery of neutron stars
Discovery of Neutron Stars
  • Using a radio telescope in 1967, Jocelyn Bell noticed very regular pulses of radio emission coming from a single part of the sky
  • The pulses were coming from a spinning neutron star—a pulsar
the discovery of pulsars
The Discovery of Pulsars
  • Astronomers found other pulsars
    • Periods from 0.033 to 3.75 seconds and were nearly as exact as an atomic clock.
    • Periods were increasing by a few billionths of a second per day.
    • A star or white dwarf could not spin fast enough – it would fly apart
    • Pulses lasted only about 0.001 s.
      • Puts upper limit on the size – 300 km
      • An object cannot change its brightness appreciably in an interval shorter than the time light takes to cross its diameter.
    • The conclusion was that only a neutron star could be a pulsar
the discovery of pulsars1
The Discovery of Pulsars
  • In 1968, astronomers discovered a pulsar at the center of the Crab Nebula.
    • The Crab Nebula is a supernova remnant.
    • Pulses 30 times per second

X-rays Visible

the lighthouse model
The Lighthouse Model
  • Two “hot spots” emit radiation in a “searchlight” pattern along the magnetic axis.
  • The resulting beams sweep through space as the neutron star rotates
  • If the beams happen to intersect Earth, we see a pulsar.
  • Charged particles flow along magnetic field lines and are channeled into an energetic pulsar wind along the equatorial plane.
  • Newly formed pulsars spin rapidly, perhaps 30 - 100 times a second.
  • The energy it radiates into space comes from its energy of rotation.
    • So, its rotation slows over time
  • 99.9 percent of the energy from a pulsar is carried as the pulsar wind.
  • Most have very high speeds – perhaps from asymmetries in the supernova when they were formed.
crab nebula pulsar
Crab Nebula Pulsar
  • The Crab Nebula Pulsar
    • About 950 years old
    • Extremely powerful
      • emits photons of radio, infrared, visible, X-ray, and gamma-ray wavelengths.
    • Note the expanding
    • rings of x-ray-emitting
    • gas driven by the pulsar
    • wind.
    • Also a jet perpendicular
    • to the equatorial plane


Visible light

crab and geminga pulsars
Crab and GemingaPulsars

Observed in gamma radiation, Geminga’s period is seen to be about .24 s.

The Crab’s period is too short to be resolved by the detector.

neutron star binaries
Neutron Star Binaries
  • Over a thousand pulsars are now known, and some are located in binary systems.
    • Enables us to determine the masses of some neutron stars.
      • All are fairly close to 1.4 M
  • The first binary pulsar was discovered in 1974 by Taylor and Hulse.
    • The period grew longer and shorter over a cycle of 7.75 hours.
    • Astronomers recognized it was due to Doppler shift, as in a spectroscopic binary
    • The system has two neutron stars separated by adistance equal to the radius of the Sun
binary pulsars
Einstein’s general theory of relativity predicts that any rapid change in a gravitational field should spread outward at the speed of light as gravitational radiation.

Being so dense and orbiting quickly, the system should be losing energy to gravitational radiation.

They are spiraling toward each other

May give us another test of Einstein’s theory.

Binary Pulsars
double pulsar
A double pulsar was discovered in 2004.

Orbital period of only 2.4 hours.

Beams from both pulsars sweep over Earth.

One spins 44 times per second.

The other spins in 2.8 seconds.

Relativity predicts the system should be emitting gravitational radiation and

decreasing their separation

by 7mm/year

Double Pulsar
hercules x 1
Consider X-ray source Hercules X-1.

It emits pulses of X rays with a period of about 1.2 seconds.

Every 1.7 days, though, the pulses vanish for a few hours.

Contains a 2-solar-mass star and a neutron star

When the neutron star is

eclipsed, the X-rays go off.

Hercules X-1

Matter falling toward a neutron star forms an accretion disk, just as in a white-dwarf binary

x ray burst mechanism
X-Ray Burst Mechanism
  • Process similar to that causing Nova from white dwarfs.
    • Matter falls onto an accretion disk of a neutron star from a companion
    • Inner portions become extremely hot emitting x-rays
    • Temperature may be

hot enough to fuse He.

    • An intense pulse of

x-rays occurs

    • Much more violent

than a Nova because

of the stronger gravity

There may also be jets typical of other objects with accretion disks.

The false-color image below is of SS 433 – called a microquasar

x ray bursters
X-Ray Bursters
  • X-ray bursters produce intense flashes of Xrays followed by long periods of inactivity – perhaps several hours.

Optical and X-ray images of an x-ray source in the globular cluster Terzan 2.

millisecond pulsars
Millisecond Pulsars
  • We expect older pulsars to blink more slowly than younger ones, but sometimes that is not the case
    • The fastest may be quite old – occurring in old globular clusters
    • Angular momentum transferred to the neutron star can increase its spin.
    • Some have periods as low

as 0.001 s. We call them

millisecond pulsars.

    • Related to process creating
    • x-ray bursters.
      • X-ray bursters may be on
      • their way to becoming milli-
      • second pulsars
cluster x ray binaries
Cluster X-Ray Binaries
  • 47 Tucanae has 108 x-ray sources
  • More than half are thought to be binary millisecond pulsars.
pulsar planets
Astronomers found some variation in the pulsation period of PSR1257+12

They determined that it was due to small planets orbiting the pulsar.

Four have been found, from smaller than to moon to 4.3 Earth masses.

It seems likely these

planets are remnants

of long gone companion


Pulsar Planets
gamma ray bursts
Gamma-Ray Bursts
  • In the 1960’s we put satellites in orbit to watch for gamma rays that might signal a nuclear bomb test in violation of the 1963 test-ban treaty.
  • The satellites detected about one gamma-ray burst a day coming from space.
  • At the time the data were classified
gamma ray bursts1
After declassification, astronomers realized these bursts may come from neutron stars or black holes.

Cleverly named: Gamma-ray Bursts

Compton Gamma Ray Observatory, put in orbit in 1991, reported several per day.



> 2 sec

Gamma-Ray Bursts
gamma ray bursts2
Gamma-Ray Bursts
  • Gamma-ray bursts detected by the Compton Gamma Ray Observatory during its nine-year mission.
    • Bursts appear to be distributed isotropically
    • Indicates an origin outside the Milky Way
    • Difficult to measure distances unless we can find an optical counterpart
gamma ray bursts3
Gamma-Ray Bursts
  • We have measured distances to about 2 dozen GRBs.
    • Counterpart spectra reveal large red shifts indicating enormous distances
  • Extremely energetic…
gamma ray bursts4
Long burst may be produced by supernova from stars above 20 solar masses

Such eruptions have been called a hypernovae.

Gamma-Ray Bursts
gamma ray bursts5
Short gamma-ray bursts not associated with hypernovae.

Some bursts repeat

May be produced by neutron stars with magnetic fields 100 times stronger than that in a normal neutron star.

Called magnetars.

Other short bursts may be produced by the merger of two neutron stars

Or even the merger of a neutron star and a black hole

Gamma-Ray Bursts
cause of gamma ray bursts
Cause of Gamma-Ray Bursts
  • Merger of two neutron stars
    • Can produce short-lived bursts
  • Hypernova
    • Can produce long-lived bursts
  • Both models produce a relativistic fireball
neutron star limit
Neutron Star Limit
  • Quantum mechanics says that neutrons in the same place cannot be in the same state
  • Neutron degeneracy pressure can no longer support a neutron star against gravity if its mass exceeds about 3 Msun
  • If the core of a massive star exceeds ~3 solar masses during a supernova then the core will collapse and form a black hole.

A black hole’s mass strongly warps space and time in vicinity of event horizon

Event horizon

black holes
A black hole is an object whose gravity is so powerful, not even light can escape from it.

That definition leads to a discussion of escape velocity – the velocity necessary for an object to completely escape the surface of a celestial body.

Escape velocity depends on two things:

The mass of the celestial body

How far away the object is from the center of mass of the celestial body

Black Holes
surface of a black hole
“Surface” of a Black Hole
  • The “surface” of a black hole is the radius at which the escape velocity equals the speed of light.
  • This spherical surface is known as the event horizon.
  • The radius of the event horizon is

known as the Schwarzschild radius.


Neutron star

3 MSun



The event horizon of a 3 MSun black hole is also about as big as a small city

no escape
No Escape
  • Nothing can escape from within the event horizon because nothing can go faster than light.
  • No escape means there is no more contact with something that falls in. It increases the hole mass, changes the spin or charge, but otherwise loses its identity.
  • Beyond the neutron star limit, no known force can resist the crush of gravity.
  • As far as we know, gravity crushes all the matter into a single point known as a singularity.

If the Sun shrank into a black hole, its gravity would be different only near the event horizon


Tidal forces near the event horizon of a

3 MSun black hole would be lethal to humans

Tidal forces would be gentler near a supermassive black hole because its radius is much bigger

general relativity effects near black holes ii


General Relativity Effects Near Black Holes (II)

Time dilation

Clocks starting at 12:00 at each point.

After 3 hours (for an observer far away from the black hole):

Clocks closer to the black hole run more slowly.

Time dilation becomes infinite at the event horizon.

Event horizon


Light waves take extra time to climb out of a deep hole in spacetime leading to a gravitational redshift

general relativity effects near black holes iii


General Relativity Effects Near Black Holes (III)

gravitational redshift

All wavelengths of emissions from near the event horizon are stretched (redshifted).

 Frequencies are lowered.

Event horizon

black hole verification
Black Hole Verification
  • Need to measure mass
    • Use orbital properties of companion
    • Measure velocity and distance of orbiting gas
  • It’s a black hole if it’s not a star and its mass exceeds the neutron star limit (~3 MSun)

Some X-ray binaries contain compact objects of mass exceeding 3 MSun which are likely to be black holes



Compact object with > 3 Msun must be a black hole!