Neutron Stars
and
Black Holes
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The Death of a Massive Star
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 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.
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 + 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!!!
Pulsars / Neutron stars
Neutron star surface has a
temperature of ~ 1 million K.
Cassiopeia A
Considering the typical surface temperature of
a neutron star, they should be observable
preferentially in which wavelength range?
1.
2.
3.
4.
5.
radio
infrared
optical
ultraviolet
X-ray
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
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
The Crab Pulsar
Pulsar wind + jets
Remnant of a supernova observed in A.D. 1054
The Crab Pulsar
X-rays
Visible light
Which one of the following is a
phenomenon through which white
dwarfs could be (indirectly) observed?
1.
2.
3.
4.
5.
Supernova remnants
Globules
Pulsars.
X-ray binaries.
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 Holes
Escape Velocity
vesc
Velocity needed to escape Earth’s gravity from the
surface: vesc ≈ 11.6 km/s.
Ggravitational force decreases with distance (~ 1/d2) =>
lower escape velocity when starting at larger distance.
Compress Earth to a smaller
radius => higher escape
velocity from the surface.
vesc
vesc
The Concept of Black Holes
Schwarzschild Radius
=> limiting radius where the escape
velocity reaches the speed of light:
(Event Horizon)
2GM
Rs = ____
c2
G = Universal const. of gravity
M = Mass
Vesc = c
The Schwarzschild Radius, Rs
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)
1.
2.
3.
4.
5.
1.35 million km
6380 km
250 m
0.9 cm
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
Clocks closer to the
BH run more slowly.
Time dilation
becomes infinite at
the event horizon.
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.
a) No time at all.
b) More than 0, but less than 1 hr
c) 1 hr
d) Several hours
e) Forever
Event Horizon
Falling into the
Black Hole
=> You will never actually see
something “falling into the Black Hole”
(i.e., crossing the Event Horizon)!
The Distant
Observer’s View
Event Horizon
Falling into the
Black Hole
The Falling
Observer’s View
“Spaghettification”
Event Horizon
General Relativity Effects
Near Black Holes
Spatial distortion of light → gravitational lensing
Deflection of Light by the Sun
Deflection of Light by the Sun
Einstein Cross
General Relativity Effects
Near Black Holes
Gravitational Red Shift
Wavelengths of light emitted from near the
event horizon are stretched (red shifted).
Event Horizon
What would happen to the Earth if the sun
suddenly turned into a black hole (of the
same mass as the sun has now)
1.
2.
3.
It would be sucked into the black hole.
Its orbit around the black hole would be
exactly the same as around the sun now.
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 = Schwarzschild Radius
3 Rs
Rs
There is no stable orbit within 3
Schwarzschild radii from the black hole.
Observing Black Holes
No 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!
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: Radio-emitting jets