Lecture 23: Black Holes
Readings: Sections 24-3, 24-5
through 24-8
Key
Ideas
Black
Holes are totally collapsed objects
Gravity
so strong not even light can escape
Predicted
by General Relativity
Schwarzschild
Radius & Event Horizon
Find
them by their Gravity
X-ray Binary Stars
Black
Hole Evaporation via Hawking Radiation
GravityÕs
Final Victory
A
star more massive than 18 MSun would leave behind a core with M >
2-3 MSun
Neutron degeneracy pressure would fail and nothing can
stop gravitational collapse
Core
would collapse into a singularity,
an object with
Zero
radius
Infinite
density
Black
Holes
The
ultimate extreme object
Gravity
so strong not even light escapes
Infalling matter gets shredded by powerful tides &
crushed into infinite density
Vesc
exceeds the speed of light.
According to General Relativity, there is no form of
pressure that can stop its collapse to a singularity. E=mc2 strikes
again.
Black:
It neither emits nor reflects light
Hole:
Nothing
entering can ever escape
Schwarzschild
Radius
Light
cannot escape from a Black Hole if it comes from a radius less than the Schwarzschild
Radius:
M=Mass
of the Black Hole
For
M=1 MSun, RS~ 3km
(if the entire mass of the Sun was squished to a ball
with R~3km, it would be a black hole.)
Neutron
Star vs. Black Hole
Neutron
Star
M=1.5 MSun
R=10 km
Black
Hole
M=1.5 MSun
RS= 4.5 km
Rcore= infinitely small
The
Event Horizon
RS
defines the Event Horizon
Events
that happen inside RS are invisible to the outside Universe
Thngs
that get inside RS can never leave the black hole
The
ÒPoint of No ReturnÓ for a Black Hole
Gravity
around Black Holes
Far
away from a black hole:
Gravity
is the same as for a star of the
same mass
If the Sun were replace by a black hole with M=1 MSun,
the planets would all orbit the same as before
Close
to a black hole:
R < 3 RS, no stable orbits – all
matter gets sucked in (not true for NewtonÕs Law of Gravity)
At R=1.5 RS, photons orbit in a circle!
Journey
to a Black Hole: A Thought Experiment
Jack:
in a spacesuit, is falling into a black hole, carrying a blue laser beacon
Jill:
orbiting the black hole in a starship at a safe distance in a stable circular
orbit
JackÕs
point of view: sees the ship getting further away, flashes his blue laser once
a second by his watch
JillÕs
point of view: Each flash takes longer to arrive (because it has farther to
go), as is redder and fainter than the one before it.
Near
the Event Horizon
Jack
Sees:
His
blue laser flash every second by his watch
The
outside world look distorted as light is bent by the black hole
Jill
Sees:
JackÕs
laser flashes come ~1 hour apart
Flashes
are redshifted to radio wavelengths
Flashes
are getting fainter with each flach
Down
the holeÉ..
Jill
Sees:
Sees
one last laser flash after a long delay
Flash
is faint and at long radio wavelengths
She
never sees another flash from JackÉ.
Jack
Sees:
Universe
vanish as he crosses the Event horizon
Gets shredded by strong tides near the singularity and
crushed to infinite density
JillÕs
Conclusions:
The
powerful gravity of a black hole warps space and time around it:
Time
appears to stand still at the event horizon as seen by a distant observer
Time
flows as it always does as seen by an infalling astronaut
Light emerging from near the black hole is Gravitationally
Redshifted to longer (redder)
wavelengths (not the same thing as the Doppler shift or WienÕs Law).
JackÕs
Conclusions are considerably less coherent as he is shredded by the black hole.
Seeing
what cannot be seenÉ
Q:
If black holes are black, how can we see them?
A:
By the effects of their gravity on their surroundings
A
star orbiting around an unseen massive object
X-rays
emitted by gas superheated as it falls into the black hole.
X-Ray
Binaries
Bright,
variable X-ray sources identified by X-ray observatory satellites (remember
that X-rays cannot penetrate EarthÕs atmosphere, so these observations must be
done from space).
Spectroscopic binary with only one set of spectral
lines = the companion is invisible
Gas from the visible star is dumped on the companion,
heats up as its gravitational energy is converted into heat, and emits X-rays
Estimate
the mass of the unseen companion from the orbit
Black
hole candidates will have M > 4 MSun
Black
Hole Candidates
X-ray
binaries with unseen companions of mass > 4 MSun too big for a
Neutron Star
Candidates:
Cygnus
X-1: M=6-10 MSun
V404
Cygni: M > 6 MSun
LMC
X-3: M=7-10 MSun
None
are as yet iron-clad cases
Work
continues to refine our mass estimates
Example:
Cygnus X-1
There is no sign of the companion at any wavelength
(but X-rays emission high for a ÒnormalÓ binary)
1)
A red giant would be easily seen
2)
A main sequence star would be seen with a little effort
3)
CanÕt be a WD because M > 1.4 MSun
4)
CanÕt be an neutron star because M > 3 MSun
Process
of elimination says itÕs a black hole. Not as good a case as seeing the event
horizon!
Black
Holes are not totally Black!
ÒClassicalÓ
General Relativity says:
Black
Holes are totally black
Can
only grow in mass and size as more matter falls into them
Last
forever (nothing gets out once inside)
But:
General
Relativity does NOT include the effects of Quantum Mechanics
Evaporating
Black Holes
Black
Holes evaporate very slowly by emitting Hawking Radiation
Vacuum fluctuations produce a
particle–antiparticle pair near the event horizon, one particle falls
into the hole, the other is radiated.
Very
cold thermal radiation (T~10 nK)
Bigger
black holes are colder (evaporate more slowly)
Takes
a very long timeÉ
5
MSun black hole takes 1073 years
1063
times the present age of the Universe
Not
important today, but could be important in the distant future as all other
sources of radiation die off.