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Chapter 14
Neutron Stars and Black Holes
Guidepost
The preceding chapters have traced the story of stars from
their birth as clouds of gas in the interstellar medium to their
final collapse. This chapter finishes the story by discussing
the kinds of objects that remain after a massive star dies.
How strange and wonderful that we humans can talk about
places in the universe where gravity is so strong it bends
space, slows time, and curves light back on itself! To carry on
these discussions, astronomers have learned to use the
language of relativity. Throughout this chapter, remember
that our generalized discussions are made possible by
astronomers studying general relativity in all its mathematical
sophistication. That is, our understanding rests on a rich
foundation of theory.
This chapter ends the story of individual stars. The next three
chapters, however, extend that story to include the giant
communities in which stars live— the galaxies.
Outline
I. Neutron Stars
A. Theoretical Prediction of Neutron Stars
B. The Discovery of Pulsars
C. A Model Pulsar
D. The Evolution of Pulsars
E. Binary Pulsars
F. The Fastest Pulsars
G. Pulsar Planets
II. Black Holes
A. Escape Velocity
B. Schwarzschild Black Holes
C. Black Holes Have No Hair
D. A Leap into a Black Hole
E. The Search for Black Holes
Outline (continued)
III. Compact Objects with Disks and Jets
A. X-Ray Bursters
B. Accretion Disk Observations
C. Jets of Energy from Compact Objects
D. Gamma-Ray Bursts
Neutron Stars
A supernova
explosion of a
M > 8 Msun star
blows away its
outer layers.
The central core will collapse into a
compact object of ~ a few Msun.
Formation of Neutron Stars
Compact objects more massive than the
Chandrasekhar Limit (1.4 Msun) collapse further.
 Pressure
becomes so high
that electrons and
protons combine to
form stable neutrons
throughout the
object:
p + e-  n + ne
 Neutron Star
Properties of Neutron Stars
Typical size: R ~ 10 km
Mass: M ~ 1.4 – 3 Msun
Density: r ~ 1014 g/cm3
 Piece of
neutron star
matter of the
size of a
sugar cube
has a mass
of ~ 100
million tons!!!
Discovery of Pulsars
Angular momentum conservation
=> Collapsing stellar core spins
up to periods of ~ a few
milliseconds.
Magnetic fields are amplified up to
B ~ 109 – 1015 G.
(up to 1012 times the average
magnetic field of the sun)
=> Rapidly pulsed (optical and radio) emission from
some objects interpreted as spin period of neutron stars
Pulsars / Neutron Stars
Neutron star surface has a temperature of
~ 1 million K.
Cas A in X-rays
Wien’s displacement law,
lmax = 3,000,000 nm / T[K]
gives a maximum wavelength of lmax = 3 nm,
which corresponds to X-rays.
Pulsar Periods
Over time, pulsars
lose energy and
angular momentum
=> Pulsar rotation
is gradually
slowing down.
Lighthouse Model of Pulsars
A Pulsar’s
magnetic field
has a dipole
structure, just
like Earth.
Radiation
is emitted
mostly
along the
magnetic
poles.
Neutron Star
(SLIDESHOW MODE ONLY)
Images of Pulsars and Other Neutron Stars
The vela Pulsar moving
through interstellar space
The Crab
nebula and
pulsar
The Crab Pulsar
Pulsar wind + jets
Remnant of a supernova observed in A.D. 1054
The Crab Pulsar (2)
Visual image
X-ray image
Light Curves of the Crab Pulsar
Proper Motion of Neutron Stars
Some
neutron
stars are
moving
rapidly
through
interstellar
space.
This might be a result of anisotropies
during the supernova explosion
forming the neutron star
Binary Pulsars
Some pulsars form binaries with
other neutron stars (or black
holes).
Radial velocities resulting from
the orbital motion lengthen the
pulsar period when the pulsar
is moving away from Earth...
…and shorten the pulsar
period when it is approaching
Earth.
Neutron Stars in Binary Systems: X-ray
Binaries
Example: Her X-1
2 Msun (F-type) star
Neutron star
Orbital period =
1.7 days
Accretion disk material heats to
several million K => X-ray emission
Star eclipses neutron
star and accretion
disk periodically
Pulsar Planets
Some pulsars have
planets orbiting
around them.
Just like in binary pulsars,
this can be discovered
through variations of the
pulsar period.
As the planets orbit
around the pulsar, they
cause it to wobble
around, resulting in
slight changes of the
observed pulsar period.
Black Holes
Just like white dwarfs (Chandrasekhar limit: 1.4 Msun),
there is a mass limit for neutron stars:
Neutron stars can not exist
with masses > 3 Msun
We know of no mechanism to halt the collapse
of a compact object with > 3 Msun.
It will collapse into a single point – a singularity:
=> A Black Hole!
Escape Velocity
Velocity needed to
escape Earth’s
gravity from the
surface: vesc ≈ 11.6
km/s.
Now, gravitational
force decreases
with distance (~
1/d2) => Starting out
high above the
surface => lower
escape velocity.
vesc
vesc
vesc
If you could compress Earth to a smaller radius
=> higher escape velocity from the surface.
The Schwarzschild Radius
=> There is a limiting radius
where the escape velocity
reaches the speed of light, c:
2GM
Rs = ____
c2
G = Universal const. of gravity
M = Mass
Rs is called the
Schwarzschild Radius.
Vesc = c
Schwarzschild Radius and Event Horizon
No object can travel
faster than the
speed of light
=> nothing (not
even light) can
escape from inside
the Schwarzschild
radius
 We have no way
of finding out what’s
happening inside
the Schwarzschild
radius.
 “Event horizon”
Schwarzschild Radius of Black Hole
(SLIDESHOW MODE ONLY)
Black Holes in Supernova Remnants
Some supernova
remnants with no
pulsar / neutron star
in the center may
contain black holes.
Schwarzschild Radii
“Black Holes Have No Hair”
Matter forming a black hole is losing
almost all of its properties.
Black Holes are completely
determined by 3 quantities:
Mass
Angular Momentum
(Electric Charge)
General Relativity Effects Near
Black Holes
An astronaut descending
down towards the event
horizon of the BH will be
stretched vertically (tidal
effects) and squeezed
laterally.
General Relativity Effects Near Black
Holes (2)
Time dilation
Clocks starting at
12:00 at each point.
After 3 hours (for an
observer far away
from the BH):
Clocks closer to the
BH run more slowly.
Time dilation
becomes infinite at
the event horizon.
Event Horizon
General Relativity Effects Near Black
Holes (3)
Gravitational Red Shift
All wavelengths of emissions
from near the event horizon
are stretched (red shifted).
 Frequencies are lowered.
Event Horizon
Observing Black Holes
No light can escape a black hole
=> Black holes can not be observed directly.
If an invisible
compact object is
part of a binary, we
can estimate its
mass from the
orbital period and
radial velocity.
Mass > 3 Msun
=> Black hole!
End States of Stars
(SLIDESHOW MODE ONLY)
Candidates for Black Hole
Compact object with
> 3 Msun must be a
black hole!
Compact Objects with Disks and Jets
Black holes and neutron stars can be
part of a binary system.
Matter gets
pulled off from
the companion
star, forming
an accretion
disk.
=> Strong X-ray source!
Heats up to a few million K.
X-Ray Bursters
Several bursting
X-ray sources
have been
observed:
Rapid outburst
followed by
gradual decay
Repeated
outbursts: The
longer the
interval, the
stronger the burst
The X-Ray Burster 4U 1820-30
In the cluster NGC 6624
Optical
Ultraviolet
Black-Hole vs. Neutron-Star Binaries
Black Holes: Accreted matter
disappears beyond the event
horizon without a trace.
Neutron Stars: Accreted
matter produces an X-ray
flash as it impacts on the
neutron star surface.
Black Hole X-Ray Binaries
Accretion disks around black holes
Strong X-ray sources
Rapidly, erratically variable (with flickering on
time scales of less than a second)
Sometimes: Quasi-periodic oscillations (QPOs)
Sometimes: Radio-emitting jets
Radio Jet Signatures
The radio jets of
the Galactic blackhole candidate
GRS 1915+105
Model of the X-Ray Binary SS 433
Optical spectrum shows
spectral lines from material
in the jet.
Two sets of lines:
one blue-shifted,
one red-shifted
Line systems shift
back and forth across
each other due to jet
precession
Gamma-Ray Bursts (GRBs)
Short (~ a
few s), bright
bursts of
gamma-rays
GRB of May 10, 1999:
1 day after the GRB
2 days after the GRB
Later discovered with X-ray and optical
afterglows lasting several hours – a few days
Many have now been associated with host
galaxies at large (cosmological) distances.
Probably related to the deaths of very
massive (> 25 Msun) stars.
New Terms
neutron star
pulsar
lighthouse model
pulsar wind
glitch
magnetar
gravitational radiation
millisecond pulsar
singularity
black hole
event horizon
Schwarzschild radius
(RS)
Kerr black hole
ergosphere
time dilation
gravitational red shift
X-ray burster
quasi-periodic oscillations
(QPOs)
gamma-ray burster
soft gamma-ray repeater
(SGR)
hypernova
collapsar