Neutron Stars and Black Holes

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Neutron Stars and Black Holes
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The Death of a Massive Star
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Neutron Stars
A supernova explosion of a M gt 8 Msun star blows
away its outer layers. The central core will
collapse into a compact object of a few Msun.
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The Chandrasekhar Limit
Can such a remnant of a few Msun be a white dwarf?
The more massive a white dwarf is, the smaller it
is (radius decreases as mass increases)!
There is a limit of 1.4 Msun, beyond which white
dwarfs can not exist Chandrasekhar Limit.
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Formation of Neutron Stars
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Compact objects more massive than the
Chandrasekhar Limit (1.4 Msun) collapse beyond
the degenerate (white dwarf) state.
? Pressure becomes so high that electrons and
protons combine to form stable neutrons
throughout the object
p e- ? n ne
? Neutron Star
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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!!!
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Pulsars / Neutron stars
Neutron star surface has a temperature of 1
million K.
Cassiopeia A
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Considering the typical surface temperature of a
neutron star, they should be observable
preferentially in which wavelength range?

1. radio
2. infrared
3. optical
4. ultraviolet
5. X-ray

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Pulsars
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Angular momentum conservation
gt 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)
gt Rapidly pulsed (optical and radio) emission
from some objects interpreted as spin period of
neutron stars
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The Lighthouse Model of Pulsars
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A Pulsars magnetic field has a dipole structure,
just like Earth.
Radiation is emitted mostly along the magnetic
poles.
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Images of Pulsars and other Neutron Stars
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The vela Pulsar moving through interstellar space
The Crab nebula and pulsar
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The Crab Pulsar
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Pulsar wind jets
Remnant of a supernova observed in A.D. 1054
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The Crab Pulsar
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X-rays
Visible light
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Which one of the following is a phenomenon
through which white dwarfs could be (indirectly)
observed?

1. Supernova remnants
2. Globules
3. Pulsars.
4. X-ray binaries.
5. Solar eclipses.

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Neutron Stars in Binary Systems X-ray binaries
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Accretion disk material heats to several million
K gt X-ray emission
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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 gt 3 Msun
We know of no mechanism to halt the collapse of a
compact object with gt 3 Msun.
It will collapse into a single point a
singularity
gt A Black Hole!
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The Concept of Black HolesEscape Velocity
vesc
Velocity needed to escape Earths gravity from
the surface vesc 11.6 km/s.
Ggravitational force decreases with distance (
1/d2) gt lower escape velocity when starting at
larger distance.
vesc
Compress Earth to a smaller radius gt higher
escape velocity from the surface.
vesc
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The Concept of Black HolesSchwarzschild Radius
gt limiting radius where the escape velocity
reaches the speed of light
The Schwarzschild Radius, Rs (Event Horizon)
Vesc c
2GM
____
Rs
c2
G Universal const. of gravity
M Mass
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Schwarzschild Radius and Event Horizon
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Nothing (not even light) can escape from inside
the Schwarzschild radius

• We have no way of finding out whats happening
  inside the Schwarzschild radius
• Event horizon

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Take a guess How large is the Schwarzschild
radius of the Earth?(The actual radius of the
Earth is 6380 km)

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1. 1.35 million km
2. 6380 km
3. 250 m
4. 0.9 cm
5. 12 nm

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0
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Black Holes Have No Hair
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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)
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General Relativity Effects Near Black Holes
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Time dilation
Clocks closer to the BH run more slowly.
Time dilation becomes infinite at the event
horizon.
Event Horizon
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For how long would we in principle receive
signals from a space probe that we are sending
into a black hole (if there were no limit to how
faint the signals are that it is sending back to
us)? Assume that the free-fall time to reach the
event horizon (without GR effects) is 1 hr.
a) No time at all.
b) More than 0, but less than 1 hr
c) 1 hr
d) Several hours
e) Forever
Event Horizon
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Falling into the Black Hole
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gt You will never actually see something falling
into the Black Hole (i.e., crossing the Event
Horizon)!
The Distant Observers View
Event Horizon
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Falling into the Black Hole
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The Falling Observers View
Spaghettification
Event Horizon
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General Relativity Effects Near Black Holes
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Spatial distortion of light ? gravitational
lensing
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Deflection of Light by the Sun
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Deflection of Light by the Sun
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Einstein Cross
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General Relativity Effects Near Black Holes
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Gravitational Red Shift
Wavelengths of light emitted from near the event
horizon are stretched (red shifted).
Event Horizon
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What would happen to the Earth if the sun
suddenly turned into a black hole (of the same
mass as the sun has now)

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1. It would be sucked into the black hole.
2. Its orbit around the black hole would be exactly
   the same as around the sun now.
3. It would be ejected from the solar system.

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A Myth about Black Holes
Far away from the black hole, gravity is exactly
the same as for the uncollapsed mass!
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Getting Too Close to a Black Hole
Rs Schwarzschild Radius
3 Rs
Rs
There is no stable orbit within 3 Schwarzschild
radii from the black hole.
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Observing Black Holes
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No light can escape a black hole
gt Black holes can not be observed directly.

• Black hole or Neutron Star in a binary system
• Wobbling motion
• Mass estimate

Mass gt 3 Msun gt Black hole!
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Black Hole X-Ray Binaries
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Accretion disks around black holes
Strong X-ray sources
Rapidly, erratically variable (with flickering on
time scales of less than a second)
Sometimes Radio-emitting jets