April 17

FALLING INTO A BLACK HOLE

In order to figure out what a black hole will look like, we need to
think about what we'll see if we watch someone fall into a black hole:

 - First, they accelerate towards the black hole (it's a source of
     gravity!)
 - Then light from them becomes redshifted due to gravity. When I throw
     chalk up in the air, it loses energy by slowing down. Light can't
     slow down (it always moves at the speed of light!), so the only way
     it can lose energy is to become redshifted. This is above and beyond
     the Doppler redshift.
 - They then appear to *decelerate* (slow down). Time runs slower deep
     in a strong gravitational field than it does far away from any
     sources of gravity. So when we look at their clock, it will run
     slower than our clock.
 - They will experience very strong tides. These tides both stretch them
     out vertically (because their feet are closer to the black hole,
     so they are being pulled down faster) and compressed sideways (because
     both sides of them are being drawn towards the same point)
 - As they get closer and closer to the event horizon, they move slower
     and slower, get more and more redshifted, and eventually appear to
     fade away just above the event horizon.

What if we switch perspectives and ask what we'd see if we fell in?

 - We'd accelerate towards the black hole
 - We'd feel very strong tides
 - The rest of the universe would appear blue-shifted because of gravity
 - The rest of the universe would speed up
 - We'd pass through the event horizon
 - We'd keep being accelerated towards the center of the black hole

The event horizon is a mathematical abstract point, beyond which you can't
return, but it's not an especially weird physical point - you can pass
through it perfectly fine!

We also made the point that the strange effects of a black hole only happen
very near the event horizon. A one solar mass black hole is only 6m
across (R_S=3km). So if we replaced the sun with a one solar mass black hole,
the Earth's orbit wouldn't change at all! (93 million miles is very far away
compared to 3km).


OBSERVATIONS: How would we find a stellar-mass black hole in the universe?

If it's on its own:

 The black hole itself isn't giving off any light (this is a bit of a lie,
 as we'll see on Friday, but it's very close to the truth), so we can't
 directly detect it.

 There's nothing around the black hole to give off light (we just said it's
 on its own!), so we can't directly detect its effect on other matter.

 The only way we can detect it is through GRAVITATIONAL LENSING of
 the light from background stars. There are a few projects (MACHO
 and OGLE are the biggest) dedicated to looking for this sort of lensing.
 While they've found lots, most of them seem to be low-mass stars,
 not black holes.


Half the star systems in our Galaxy are multiple systems (mostly
binaries), and the multiple systems have more stars than the single
systems (by definition!), so more than half the stars in our Galaxy are
in multiple systems. How could we observe a black hole in a binary
system?

 1. When the companion orbits, we will see its lines get Doppler blue-shifted
 and red-shifted as it goes around the orbit (sometimes it's moving towards
 us, sometimes away). Using the laws of gravity, we can figure out the
 mass of the dark object. We get a MINIMUM mass from this - the orbit could
 be mostly in the plane of the sky, in which case the motion towards and
 away from us is a tiny fraction of the real motion! If the mass we get
 is too large to be a WD or NS, and yet the object is too faint to be
 seen, that's awfully suggestive... we don't know of any other 10 solar mass
 objects that don't give off much light!

 2. If the companion is close enough, material from the outer parts of
 the companion will get pulled off by the black hole's gravity and form an
 accretion disk (a disk of material that's falling onto the black hole)
 around the black hole. As the material gets compressed due to tides, it
 heats up and gives off very high energy light (mainly X-rays). So we can
 look for X-ray sources as possible black hole candidates.

 3. Some X-ray sources fluctuate very fast (on timescales of milliseconds).
 From the same argument that we used to get the sizes of pulsars, we can
 deduce that the region producing the X-rays couldn't be much bigger than
 a neutron star.

 4. The X-rays are coming from deep in the gravitational field, so they
 will be red-shifted. We can see some lines in the X-ray due to highly
 ionized metals (eg. iron) in some of these sources that are red-shifted
 as much as you'd expect if they were coming from the inner regions of
 an accretion disk around a black hole.

So far, none of these are definitive pieces of evidence that the object
is a black hole. However, if we see an X-ray source that's fluctuating
on millisecond timescales with redshifted lines at the same point
as a star that's orbiting an object that's at least 4 solar masses but
doesn't give off any optical light, the most plausible explanation is
that it is a black hole. Most of the dozen or so black hole candidates
fulfill some number of these conditions, and are most likely black holes...
but we've never definitely proved that we've seen a black hole.

A definitive piece of evidence would be if we could get direct high-resolution
X-ray images of the accretion disk. As shown in class, the accretion
disk around a black hole has some notable features:
 - it is black in the middle! (no great shock)
 - one edge of the disk is blue-shifted (by the Doppler effect), while
    the rest is red-shifted (because of gravity)
 - the far side of the disk appears tilted up above the black hole
    because of gravitational lensing

If we could get an image like this, it would be hard to accept any other
explanation than that it is a black hole. We can't make these images yet,
but there is a planned mission called MAXIM that hopes to be launched in
about 10 years that would be able to.