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1. Neutron Stars
and
Black Holes
Why do we expect neutron stars exist?
How do we know neutron stars exist?
What theoretical arguments predict the existence of black
holes?
What evidence is there that black holes indeed exist?

2. Neutron stars: how do
they form?

3. Neutron Stars:
If we pack electrons
close enough together
 white dwarf
(electron degenerate)
If we pack neutrons
close enough together
 neutron star
(neutron degenerate)
Q: Recall the Chandrasekhar limit (1.4 solar
masses), what happens if the collapsing core
is greater than this?

4. Properties of neutron stars:
~ 10 km in radius
Density ~1014g/cm3
Between 1.4 and 3 Msun
Q: What happens when a
NS becomes more
massive than 3 Msun?
Spin rapidly
Hot
Strong magnetic field
Pressure becomes so high that
electrons and protons combine
to form stable neutrons
throughout the object.
Q: Why would we expect neutron
stars to spin rapidly, be hot, and
have strong magnetic fields?

5. Internal structure of a neutron star:

6. Pulsars:
1967 Jocelyn Bell noticed
pulses which repeated
regularly in the sight line of a
distant galaxy  first pulsar
that was detected.
Periods range from ~ 0.030
to 3.75 seconds
Gradually slow down
Pulses last ~ 0.001 s
This places an upper
limit on the size of the
object emitting the
pulse…
Suppose it was a white dwarf of 12,000 km
diameter emitting the pulse…
Since the near side is 12,000 km closer than
the far side, the light from the near side would
arrive ~0.04 s sooner than the light from the
far side…
 The pulse would be smeared out over a
longer interval.
An object cannot change its brightness in an interval
shorter than the time it takes light to travel its diameter.
 For a 0.001 s pulse interval, the diameter must be smaller than
300 km.
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t d c
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7. The link between neutron stars
and pulsars:
In 1968, astronomers discovered
a pulsar in the Crab nebula.
The Crab
Pulsar is
roughly 25
km (~16 mi.)
in diameter
and rotates
~ 30
times/second!
It’s slowing in its
rotation by 38
nanoseconds/day
due to energy
loss by the pulsar
wind.

9. Theoretical model of a pulsar:
Pulsars do not pulse, but
rather emit beams of
radiation that sweep around
the sky as the neutron star
rotates
Strong magnetic and electric
fields are likely the cause of
the intense beams of
radiation
Note that we only
can see the
pulsars whose
beams sweep
over Earth.

10. The evolution of pulsars:
Q: the Crab pulsar is
slowing down in its
rotation by 38
nanoseconds/day…
why?
Pulsars lose energy
as they emit beams of
radiation and the
pulsar wind (high-
speed atomic
particles)
Q: Where, ultimately,
does this energy come
from?
 The energy of
rotation! (That’s why
they slow down)

11. pulsar B1508+55 path
1000km/s
Q: What could explain these strange
motions of pulsars that are observed?
Roaming pulsars: Some pulsars appear
to be moving at a high speed through
space…

12. Compact Objects with Disks and Jets – x-rays:
Black holes and neutron stars can
be part of a binary system.
=> Strong X-ray source!
Matter gets pulled off from
the companion star, forming
an accretion disk.
Heats up to a few million K.
Binary pulsars allow us to measure the mass
and all the other good things we get from
binaries…
 Looking for x-ray sources is one way to
detect neutron stars (and black holes…).

13. Binary pulsars:
In 1974, Taylor and Hulse detected
the first binary pulsar
(PSR1913+16);
The pulses were changing, growing
longer, and then shorter over a
period of 7.75 hours
From Doppler shifts, the orbital
velocities and masses were
calculated…
and it turned out that this system
was two neutron stars orbiting each
other with a separation of roughly
the radius of our sun!
PSR1913+16 held another surprise…
In 1916 Einstein predicted that a rapid
change in a gravitational field should
spread out like waves (gravitational
radiation)
Taylor and Hulse were able to show
that the orbital period was decreasing
because the stars were spiraling
toward each other.
They won the Nobel prize in 1993.

14. Neutron Stars in Binary Systems: X-ray binaries – Her X-1:
Her X-1
2 Msun (F-type) star
Accretion disk material heats to several million K
=> X-ray emission
Star eclipses the
neutron star and
accretion disk every
1.7 days hiding the
x-ray pulses for a
few hours
Orbital period =
1.7 days
Pulses every
1.2 seconds

15. Masses of pulsars:
From Doppler shifts, astronomers
have estimated the masses of
dozens of binary pulsars.
Typical masses are ~ 1.35 solar
masses.
Q: If the core must be at least 1.4
solar masses to form a NS, then how
could the typical mass of a NS be
1.35?
A: A NS of slightly less than 1.4 solar
masses can exist if the NS loses
mass. Also, a 1.4 solar mass WD
produces a 1.2 solar mass NS.
Some of the mass is converted into
binding energy.
The gravitational fields near neutron
stars are so strong, that a
marshmallow dropped onto a
neutron star from a distance of 1AU
would release the equivalent energy
of a 3 Mt nuclear bomb! (~231
Hiroshima-sized bombs!)

16. X-ray bursters:
Matter flows onto the NS where it
accumulates until it becomes hot and
dense enough to ignite
The result is a burst of x-rays
“x-ray burster”
Notice the similarity between this and
the mechanism which generates
novae….

17. The X-Ray Burster 4U 1820-30
Optical Ultraviolet
This is a neutron star orbiting a white
dwarf
The period is only 11 minutes!
 The separation is only about a
third of the Earth/moon distance!
This is possibly the result of a collision
of a neutron star and a giant…
the NS then went into orbit inside the
giant!

18. The fastest pulsars:
Q: Would you expect a pulsar that
pulses rapidly to be young or old?
Due to the gradual slowing of the
rotation, one would expect young
pulsars to blink rapidly and old
pulsars to blink slowly, but…
A few that blink the fastest may be
quite old….
One of the fastest (PSR1937+21)
pulses 642 times a second!
The energy contained in the rotation
of this pulsar is comparable to the
total energy of a supernovae
explosion!
Q: How could this be?
To explain this, it appears that this
pulsar was sped up by accreting
matter from a binary companion.
The fastest pulsars go by the name
“millisecond pulsars.”
Why are they so fast?
What happens to them when they
rotate so fast?
Since the pulse period of the pulsar is
the rotation period, these fast pulsars
are probably flattened like pancakes!
Take PSR1937+21;
Assume it is 10 km in radius…
Spinning at 642 times a second, the
period is 0.0016 seconds and the
equatorial velocity is about 40,000
km/s!
2 /
r t
 


19. Pulsar Planets:
Small Doppler shifts were observed in the
spectra of PSR1257+12
Analysis revealed that this pulsar was orbited
by at least two planets with masses roughly
4.3 and 3.9 Earth masses!
Further analysis revealed a third planet with a
mass of about that of our moon!
And there is evidence that a fourth planet
about 100 Earth masses orbits this pulsar with
a much larger separation.
Q: How can a NS have planets?!?
(Recall that NS are created by supernovae,
and a giant star about to explode would
envelop any planets within an AU or two…)
As a planet orbits around a
pulsar, the planet causes it to
wobble around, resulting in
slight changes of the
observed pulsar period.
These planets are probably the remains
of a stellar companion that was
devoured by the NS.

20. 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!

21. Escape Velocity:
Escape velocity depends
on two things;
1. Mass
2. Distance from CoM
vesc
Gravitational force decreases with
distance (~ 1/r2)
Starting out high above the surface
lower escape velocity.
vesc
vesc
If you could compress Earth to a smaller
radius => higher escape velocity from the
surface.
Velocity needed to escape Earth’s
gravity from the surface: ≈ 11.6 km/s
(~25,000 mph).

22. The Schwarzschild Radius:
There is a limiting radius where the
escape velocity reaches the speed of
light, c:
Vesc = c
Rs =
2GM
____
c2
Rs is called the Schwarzschild radius.
G = gravitational constant
M = mass

23. Schwarzschild Radius and Event Horizon:
No object can travel faster than
the speed of light
 We have no way of finding
out what’s happening inside
the Schwarzschild radius.
=> nothing (not even light) can
escape from inside the
Schwarzschild radius
 “Event horizon”

25. “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)

26. General Relativity Effects Near Black Holes:
An astronaut descending down
towards the event horizon of the black
hole will be stretched vertically (tidal
effects) and squeezed laterally.

27. General Relativity Effects Near Black Holes (II):
2 2 1 2
' (1 )
t t c
 
 
Time dilation
Event horizon
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.
In SR:
2 1 2
' (1 2 )
t t c 
  
In GR:

28. General Relativity Effects Near Black Holes (III):
gravitational redshift
Event horizon
All wavelengths of emissions from
near the event horizon are stretched
(redshifted).
 Frequencies are lowered.

29. Observing Black Holes:
No light can escape a black hole
=> Black holes can not be observed directly.
We can estimate its mass
from the orbital period and
radial velocity.
Mass > 3 Msun
=> Black hole!
2 3
2
4
total
a
M
G P


But… if an invisible compact object is part of a binary…

30. A compact object
with > 3 Msun must
be black hole!

32. Jets of Energy from Compact Objects:
Some X-ray binaries show
jets perpendicular to the
accretion disk.
These bipolar flows are
formed the same way as
they do for protostars.
(Bipolar flow - angular
momentum  hot accretion
disk  high-energy photons
emitted  shot out via
thermal & magnetic
processes.
Your impression of a black
hole might suggest that it’s
impossible to get energy out
of such an object.

33. Opposing jets of gas are
streaming away from a
supermassive black hole at
Centaurus A´s galactic nucleus
- remnants of a giant explosion.

34. 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 to near ¼ c
(it’s receding and
approaching!)
Lines shift back and forth
across each other every
164 days due to jet
precession
SS 433 is most likely a
black hole!

35. In 1963, a nuclear test ban treaty was signed – nuclear weapons tests
were off limits…
In 1968, the U.S. had satellites designed to detect gamma rays – signs of
a nuclear detonation…
Those satellites started detecting bursts of gamma rays at a rate of about
one burst a day…
That data became declassified in 1973.
The bursts usually lasted only a matter of seconds…
They came from all directions of the sky and not from any particular
region…
They occur without warning…
And they have more power than the most violent supernovae
explosions….

36. Gamma-Ray Bursts (GRBs):
GRB of May 10, 1999:
1 day after the GRB
2 days after the GRB
Some of these GRBs repeat – known as “soft gamma-ray repeaters,”
“soft” = low energy gamma rays.
We suspect that these originate from neutron stars with really strong
magnetic fields (“magnetars”).
When shifts in the magnetic field breaks through the crust of a magnetar,
bursts of gamma rays are emitted.
On August 27, 1998, one of these ionized Earth’s atmosphere and
disrupted radio communications worldwide.

37. Gamma-Ray Bursts (GRBs) II:
Possible origins:
Could be the result of the merger of two neutron
stars (recall the binary pulsar PSR1913+16 detected by
Taylor and Hulse.)
and/or from the collapse of really massive stars
(>25 solar masses) - “hypernovae”
March 29, 2003 GRB in
Leo…
Left behind a spectrum
which resembled that of
a SN
Hypernovae are
indeed responsible for
some GRBs
But the NS merger is not
ruled out….

38. GRBs III:
If a GRB occurred only 1,600 ly from Earth, we would be showered with the
radiation equivalent to a 10,000 Mt nuclear blast!
Possibly every few hundred million years one could occur near enough to Earth
for us to be affected.
Possibly one of these caused one of the mass extinctions that show up in the
fossil record…
Q: How could something which seems so rare as a neutron star merger, be so
common that we detect at least one of these GRBs every day?

39. Over 800 GRBs
detected by the
BATSE instrument
onboard the CGRO