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
•
•
White dwarfs with same mass as Sun are
about same size as Earth
Higher mass white dwarfs are smaller
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
• 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)
What can happen to a white
dwarf in a close binary system?
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
• 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
Nova
• The temperature of
accreted matter
eventually becomes
hot enough for
hydrogen fusion
• Fusion begins
suddenly and
explosively, causing
a nova
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
Hydrogen accreted through
the accretion disk
accumulates on the surface
of the white dwarf
Nova Cygni 1975
 Very hot, dense layer of
non-fusing hydrogen on the
white dwarf surface
 Explosive onset of H
fusion
 Nova explosion
Nova
• The nova star
system temporarily
appears much
brighter
• The explosion
drives accreted
matter out into
space
Novae
• 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
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
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 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 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
• Maximum luminosity can be more than a
billion Suns.
• Note the characteristic plateau of Type IIs
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
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
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
They can sometimes be seen in distant galaxies.
Observations of Supernovae
• 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.
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 young
remnant
• 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
spectrum
• In the Crab Nebula
it is in the visible
spectrum.
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.
supernova
Vela Supernova Remnant
Extrapolation shows it exploded about 9000 B.C.
Supernova Remnants
X rays
The Crab Nebula:
Remnant of a supernova
observed in a.d. 1054
Optical
The Cygnus Loop
The Veil
Cassiopeia
A Nebula
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
• 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.
SN1987A
• 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
SN1987A
• 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
• 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
• 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
A neutron star is about the same size as a small city ~15mi
Neutron Stars
Theoretical Prediction of Neutron
Stars
• 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
• 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
How were neutron stars
discovered? “LGM”
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
• 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 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
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.
Pulsars
• 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
• 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
X-rays
Visible light
Crab and Geminga Pulsars
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.
Start here today
What can happen to a neutron
star in a close binary system?
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 a distance
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.
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
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.
Matter falling toward a neutron star forms an
accretion disk, just as in a white-dwarf binary
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 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
• 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 millisecond pulsars
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
stars.
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 Bursts
• 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.
– Short-lived
– Long-lived
• > 2 sec
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 Bursts
• We have measured distances to about 2 dozen
GRBs.
– Counterpart spectra reveal large red shifts
indicating enormous distances
• Extremely energetic…
Gamma-Ray Bursts
• Long burst may be produced by
supernova from stars above 20
solar masses
• Such eruptions have been called
a hypernovae.
Gamma-Ray Bursts
• 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
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
What is a black hole?
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
2GM
ve 
r
“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.
2𝐺𝑀
𝑅𝑠 = 2
𝑐
Neutron star
3 MSun
Black
Hole
The event horizon of a 3 MSun black hole is also about
as big as a small city
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.
Singularity
• 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.
What would it be like to visit a
black hole?
If the Sun shrank
into a black hole, its
gravity would be
different only near
the event horizon
Time passes more slowly 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)
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)
gravitational redshift
All wavelengths of emissions
from near the event horizon are
stretched (redshifted).
 Frequencies are lowered.
Event horizon
Do black holes really exist?
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
One famous X-ray binary with a likely black hole is in
the constellation Cygnus
Compact object with >
3 Msun must be a black
hole!