neutron stars and black holes please press “1” to test your transmitter
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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.
The Chandrasekhar LimitCan 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.
Formation of Neutron Stars
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 + e
→ Neutron Star
Properties of Neutron Stars
Typical size: R ~ 10 km
Mass: M ~ 1.4 – 3 Msun
Density: ~ 1014 g/cm3
→ Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!
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
Pulsars
=> Collapsing stellar core spins up to periods of ~ a few milliseconds.
Angular momentum conservation
=> Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars
Magnetic fields are amplified up to B ~ 109 – 1015 G.
(up to 1012 times the average magnetic field of the sun)
The Lighthouse Model of Pulsars
A Pulsar’s magnetic field has a dipole
structure, just like Earth.
Radiation is emitted
mostly along the magnetic
poles.
Images of Pulsars and other Neutron Stars
The vela Pulsar moving through interstellar space
The Crab nebula and
pulsar
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.
Neutron Stars in Binary Systems: X-ray binaries
Accretion disk material heats to several million K => X-ray emission
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!
The Concept of Black HolesEscape Velocity
Velocity needed to escape Earth’s gravity from the surface: vesc ≈ 11.6 km/s.
vesc
Ggravitational force decreases with distance (~ 1/d2) => lower escape velocity when starting at larger distance.
vesc
vesc
Compress Earth to a smaller radius => higher escape
velocity from the surface.
The Concept of Black HolesSchwarzschild Radius
=> limiting radius where the escape velocity reaches the speed of light:
Ves
c =
c
The Schwarzschild Radius, Rs
(Event Horizon)
Rs = 2GM ____ c2
G = Universal const. of gravity
M = Mass
Schwarzschild Radius and Event Horizon
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”
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
“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
Time dilation
Event Horizon
Clocks closer to the BH run more slowly.
Time dilation becomes infinite at the event horizon.
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.
Event Horizon
c) 1 hr
b) More than 0, but less than 1 hr
d) Several hours
e) Forever
a) No time at all.
Falling into the Black Hole
Event Horizon
=> You will never actually see something “falling into the Black Hole”
(i.e., crossing the Event Horizon)!
The Distant Observer’s View
General Relativity Effects Near Black HolesGravitational Red Shift
Event Horizon
Wavelengths of light emitted from near the event horizon are stretched (red shifted).
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.
A Myth about Black Holes
Far away from the black hole, gravity is exactly the same as for the uncollapsed mass!
Getting Too Close to a Black Hole
Rs
3 Rs
There is no stable orbit within 3 Schwarzschild radii from the black hole.
Rs = Schwarzschild Radius
Observing Black HolesNo light can escape a black hole
=> Black holes can not be observed directly.
Black hole or Neutron Star in a binary system
Wobbling motion
Mass estimate
Mass > 3 Msun
=> Black hole!