December 2

We've spent a lot of time talking about black holes from a theoretical
point of view. We've talked about the Chandrasekhar mass limit for
white dwarfs, and a similar limit for neutron stars. Above that limit,
a neutron star cannot support itself against gravity.

What is this mass limit for neutron stars? Well, calculations give us answers
between about 2 and 3 solar masses. Why are the calculations different?
They involve the "equation of state" of neutron star material.

The "equation of state" is just a fancy name for what happens to matter
when you squeeze it or heat it. The problem is that we know the equation
of state quite well up to about nuclear densities (we talked, once again,
about atom bombs in class). But we don't have a good way to MEASURE
the equation of state at higher densities, so for neutron stars
we have to extrapolate from what we can measure. Maybe our extrapolations
are right (assuming no new rules of how matter behaves become active),
or maybe they're wrong. We can't be "too wrong" but we might be "wrong
enough."

So, it's probably correct that any compact object more massive than
about 3 solar masses will be a black hole.

How can we test this?

Well, the first job is to find actual stellar-mass black hole candidates.
The second job is to find distinctions between how these objects emit
light and how neutron stars emilt light. It would also be nice if these
distinctions were in accord with our theoretical expectations.

So, you came up with a number of ways of finding black holes.
The most well-known is to use the laws of gravity to weigh unseen companions
in close binary systems. We use the Doppler Effect combined with the
laws of gravity to derive a minimum mass for the unseen companion.
We gave examples in class of what happens to the speed of the Earth's
orbit as we change the mass of the "Sun."

Using this technique, we have found roughly 20 black hole candidates
(see the table in the figures area).

Note, that when you look at the figures area, that there are errors
associated with the derived masses. A main reason for an error is that
unless the system containing the black hole is exactly edge-on as seen
from Earth, we don't see ALL of the Doppler Effect (some of the motion
is not pointed at us). The most extreme view would be if the system
were perpendicular to ourline of sight; we'd see NONE of the motion
coming towards us or away from us, so we'd derive the minimum-possible
mass.

Normally, thankfully, we can put limits on the angle of inclination
of the system. (we mentioned this only in passing, we didn't give
a particularly concrete example)

Secondly, what we really measure in most cases is the sum of the masses
of the companion star and the unseen star. So we need to know something
about the companion star so we can subtract away its mass. This works
decently well except in the most extreme binaries, where stellar evolution
has been the most affected by mass transfer and mass loss. Again,
we get a "best" answer with an error associated with it.

What other ways are there to find black holes besides finding them
in binary star systems? Well, if they're in a binary, we can find them
by looking at their extreme brightness in the XRay or ultraviolet
part of the spectrum. In fact, we really do things in reverse.
We find candidates that way, and then try to measure the binary properties
in the optical part of the spectrum.

We've talked about how strong gravity bends light. So in principle,
anyway, we can find isolated black holes (not in binary star systems
with accretion disks), if the unseen black hole moves in the line of sight
between us and a distant star. We call this effect "microlensing."

We've already talked about lensing in class, and have shown you gorgeous
pictures of distant objects lensed into long arcs, or even into
a complete circle. In microlensing, the size of the effect is such that all
you can see is that a few extra rays of light, rays that ordinarily would have
missed arriving at earth, So, in microlensing, the dominant effect
is that the source star gets brighter while the Earth and mystery object
and distant star are lined up.

So, people have actually done large microlensing surveys. If you do the
math, it turns out that you need to monitor 1-10 MILLION stars nightly to
see a few microlensing events per year. People have done that and
have seen microlensing (the brightness changes due to microlensing
are different from the brightness changes of an ordinary variable
star, mostly because stars usually vary by changing their temperature,
and thus their color. Gravity doesn't care what color the light ray is,
so it bends/magnifies red and blue light equally).

So far, we haven't found any isolated black holes this way. But we've
been able to observe stars fainter than even big telescopes can observe,
by catching them when they're microlensed!

We haven't talked about this in class, but microlensing does place
useful limits on "dark matter". We know some of what dark matter IS NOT,
by analysing the results of microlensing.


Back to the issue of trying to test whether black holes really exist
in Nature. We'd like stellar-mass black holes to be small in radius
(smaller than neutron stars) and more massive than 3 solar masses. 
As you can see from the table in the figures section, from the reading
of your TWO texts, gravity alone makes us incredibly confident.
But scientists are always worried that we can be fooling ourselves,
so wouldn't it be nice if there were another independent test, and
that all of the black-hole candidates fell on one side of the results of
that test, while all of the neutron stars fell on the other side?

Well, there is!
A major distinction between a black hole and a neutron star is
that a black hole has no hard surface while a neutron star does.
So matter dropped onto the surface of a neutron star should give off energy
differently from matter dropped into a black hole.

There is a class of XRay bursts that recur every few hours. Our best model
for these is that material piles up onto the surface of a neutron star
until it's ignited and flares. Well, do all such flares happen
on objects known to be neutron stars (from their masses measured
from the Laws of Gravity)? Do, NO SUCH flares happen in the systems
containing black hole candidates?

YES, that's exactly what we see. The massive candidates never have xray bursts.

What's the reason? Matter just falls into the black hole and "disappears
from our universe." It doesn't pile up on a hard surface and then
undergo explosive nuclear burning.

So, this is as close as we can be in 2003 to "taking a picture" of
a black hole and a neutron star, and noting that one has a hard surface
and the other doesn't.

If you could take a very high resolution picture of the inner part
of an accretion disk around a black hole (so that we could see the "nothing"
right at the center), and you might be able to do this using
the next generation of xray telescopes (well, the next-next generation),
what would you see? 
Check out the figure in the nov 20 figures page. We described it
at the very end of class on December 2.