Professor Charles
Bailyn: Okay,
this is the last class of the
section on black holes and
relativity.
I should say,
this particular section of the
course has gone in a direction I
didn't quite expect.
We've done a little more--gone
a little more deeply into the
theory.
We haven't done quite as much
on actual observed objects.
That's not such a terrible
thing.
I'm quite happy with that.
I just want to point out a
couple of things that were on
the syllabus that we didn't get
to, because they're very
interesting things.
You can look them up on the
little black hole website and
find out all sorts of things
about them.
And one of them is,
there exists a category of
what's called supermassive black
holes.
I mentioned the black holes
that come from stars,
and I'll talk about that much
more today.
But I don't think I'm going to
have a chance to talk about the
supermassive black holes.
These are black holes that live
in the centers of galaxies and
can have masses of hundreds of
thousands, millions,
sometimes even billions of
times the mass of the Sun.
So, very massive black holes in
the centers of
galaxies--including our own
galaxy, by the way.
And it is gas falling into
these black holes that powers
the quasars.
We saw a gravitationally lensed
quasar the other day.
These are very powerful sources
of emission that are located in
the centers of galaxies,
sometimes called active
galactic nuclei,
and they're caused by these
very massive black holes.
So, that's one thing we're
probably not going to get to.
Another thing is,
I had originally intended to
talk a little bit about
gravitational waves.
I mentioned that in the context
of the fact that the emission of
these waves causes the orbital
periods of things like the
binary pulsar,
and indeed all orbits,
in principle,
to gradually becomes shorter.
The orbital period,
the semi-major axis,
gradually becomes shorter.
But there's also the hope--it
hasn't yet been done--that you
could detect these waves
directly,
that you could make a kind of
telescope that would actually
observe gravitational waves.
This is now in progress.
It hasn't yet succeeded.
So, these can,
in principle,
be directly detected.
That hasn't been done yet,
but it will be soon,
I think.
There's something called the
Laser Interferometer Gravity
Observatory, abbreviated LIGO,
which is basically a
kilometer-long hunk of metal,
the length of which can be
measured to some fraction of the
size of an atom.
And when a gravitational wave
rolls over this,
what you expect to happen is
you should see the thing getting
slightly longer and slightly
shorter as the wave goes over
it.
The problem with this is that
the effect of passing trucks on
highways ten miles away is many,
many times greater than the
effect of passing gravitational
waves.
And so, what they've done is
they've built two of these
things, one in Washington State
and one in Louisiana.
And the plan is to operate them
simultaneously,
so that you can see,
things that happen in both
places might be attributable to
some cosmic source.
There's a whole bunch of other
stuff to talk about this.
It's a fabulous experiment,
and as I say,
we probably won't get a chance
to talk about it in detail.
But you can go to the black
hole website,
and that has links to all sorts
of other things.
And you may--if they succeed in
this, somebody's winning the
Nobel Prize, and so,
you may find out about it by
reading it in the paper five
years from now,
or so.
Yes?
Student: So--I'm
sorry--you mentioned
supermassive black holes.
Have you ever directly observed
them?
Professor Charles
Bailyn: Have we ever
directly observed a supermassive
black hole?
It depends what you mean by
"directly observe."
By definition,
you can't directly observe a
black hole.
We infer their presence in
almost exactly the same way that
we infer the presence of the
small black holes,
which I'm going to talk about
now;
namely, by watching things
orbit around them.
And so, basically what you--for
example, in the center of our
own galaxy, there's a one--I
think 1 million,
3 million, I don't remember,
some number of millions of
solar masses of stuff right at
the center of the galaxy.
You can tell that because the
orbits of the stars closest in,
which emits no radiation at
all.
And so, there's something down
there that's extremely massive
and totally dark.
And we know that that's true by
watching the orbits of nearby
stars.
And we can actually carry out
this same kind of observation in
the centers of other galaxies.
And as far as we can tell,
there's one of these
supermassive black holes in the
middle of every significant
galaxy.
And that's actually been one of
the achievements of this kind of
astronomy over the past dozen
years,
or so--is to demonstrate in
each case, for which we have
enough data, there seems to be
an extremely massive invisible
something,
down in the middle of these
things.
And there are other reasons to
think that they're actually
black holes, rather than,
you know, a hundred million
neutron stars,
or something silly like that.
And so, we're pretty much
convinced, by now,
that these things live in the
centers of galaxies,
and we're quite convinced that
there's one in the middle of our
own galaxy.
Yes?
Student: Why are they in
the middle of all the galaxies?
Professor Charles
Bailyn: Why are they in the
middle of all the galaxies?
This is actually a little bit
of a mystery.
How these things get made is
not clear.
It's pretty clear how the
stellar mass,
the ten solar mass ones,
get made.
It's the collapse of a single
star.
How these things build up,
how they grow,
where they came from in the
first place, is a little less
clear than it is for the stellar
mass thing.
There is recent work which
suggests that the very first
generation of stars was quite
massive,
thousands of solar masses,
rather than stars of one solar
mass, or something like that.
And maybe this first generation
of stars collapsed down into
thousand mass black holes,
and then a whole bunch of them
ran into each other and fell
into the centers of galaxies.
But I would have to say that it
isn't entirely clear where these
supermassive things come from.
In contrast to the situation
with ten solar mass black holes,
where we have,
if not a detailed theory,
at least, a good handle on the
broad story of where they come
from.
Okay.
So, that's what we're not going
to talk about.
So, now, let me talk about what
we are going to talk about.
Sort of a meta-lecture, I guess.
Let's see, last time I talked
about the Binary Pulsar.
And that was an example of a
very detailed test of
post-Newtonian relativity.
And what I want to talk about
now is strong-field relativity.
Relativistic effects that have
nothing to do with Newtonian
theory, that are totally
different,
and then, happen when you're
really, very close to an event
horizon, or in some other kind
of drastic situation.
So, here's the plan,
here's how you would--how would
you go about testing the
predictions of strong-field
relativity?
Well, the first thing you'd
want to do is find a black hole.
Not just talk about them but,
you know, be able to point in
the sky to where one of them is.
And then, you'd like to study
it and find out whether this
thing you think is a black hole
actually behaves as general
relativity would predict for
such an object.
And, in particular,
there's this very strong
prediction from relativity that
such a thing would not have a
surface.
That it would have an event
horizon down which things would
disappear--not a surface of any
kind.
And so, what I want to talk
about today is both of these
steps.
And, the story starts in the
late 1960s, in the middle of the
1960s, when the first x-ray--
astronomical observations of
x-rays were made.
So, it starts with x-ray
astronomy.
One of the features of
astronomy for the past
half-century,
or so, is that,
you know,
by the 1950s,
there had been a lot of
astronomy, but it had all been
done in optical light,
with optical telescopes.
And the story of astronomy for
the past fifty years has
basically been one after another
of different kinds of
electromagnetic radiation,
not optic--other than optical
light, have gradually been
opened up.
The first of these was radio
astronomy.
And so, all of a sudden,
people point radio telescopes
at the sky, and they find out
all sorts of things--one of
which,
for example,
was pulsars,
which we talked about the last
time.
The next part of the
electromagnetic spectrum that
was opened was x-rays.
Now, there's a problem with
doing x-ray observations,
which is that x-rays don't make
it through the atmosphere.
The atmosphere is completely
opaque to x-rays.
This is a good thing.
The Sun emits x-rays,
and you would not want to be in
a place in which you didn't have
an atmosphere to absorb the
x-rays on the way to yourself.
You'd get skin cancer
immediately.
And so, the fact that the
atmosphere absorbs x-rays is
good for everybody,
except for the x-ray
astronomers,
because it makes it difficult
to do these kinds of
observations.
So, this only got started at
the point where you could put
satellites into orbit outside
the atmosphere,
and equip them with x-ray
detectors, basically Geiger
Counters.
There's a lot of talk these
days about going back to the
Moon.
And one of the very few
scientific advantages of a moon
colony is that you could do
ground-based x-ray astronomy.
And so, you know,
you picture a hobbyist in his
backyard, you know,
with a kind of Geiger Counter
in a coffee can,
or something,
going outside and observing
x-rays from the sky.
And I think that would be a
great thing--but I digress.
Let's see, x-ray astronomy,
yes, in the 1960s.
So, they send up Geiger
Counters on satellites,
and increasingly sophisticated
x-ray telescopes over the years.
And they discovered something
that they didn't expect.
Namely--so, this is now in the
1960s also, around the same time
the pulsars were discovered.
They also discover very strong
sources of x-rays;
x-ray sources.
And there's a lot of energy
coming out of these things,
thousands of times,
even hundreds of thousands of
times, the radiation that the
Sun emits.
Radiation--and from these x-ray
sources, essentially all of it
in x-rays.
There's small amounts of
optical, radio,
other kinds of radiation,
but basically these are x-ray
emitting stars.
They're stars that emit huge
amounts of x-ray luminosity,
and not a whole lot else.
And they're very,
very, very powerful.
And so, people wondered what
these were.
These were unexpected.
Nobody had predicted that this
would be there.
And as they started to think
about what these things might
be, they realized,
well, what is x-ray?
An x-ray is a very energetic
photon, very short wavelength
light;
therefore, each one of the
photons carries a big punch.
So, these are energetic photons.
And the more energetic the
radiation that is emitted,
in sort of general terms,
the hotter the material that
emits it has to be,
just in order to crank up the
energy, you need.
That's why ordinary objects at
room temperature glow in the
infrared.
If you heat them up,
they start at thousands of
degrees.
Things start to glow in the red.
You heat them up still further,
you get white light,
blue light.
If you crank things up to
hundreds of thousands of
degrees, you start to get
ultraviolet radiation.
And it turns out,
in order to get x-rays,
you need to have things that
have been heated up to millions
of degrees.
So, energetic photons would
come from--require high
temperature, by which I mean,
you know, a million degrees,
or so.
By contrast,
the Sun and other similar
stars, has a surface temperature
of about 6,000 degrees.
That's hot enough to glow in
the optical, but not hot enough
to generate large numbers of
x-rays.
And you can also go further and
say, you can figure out how much
radiation ought to come from a
given volume of million-degree,
whatever it is.
And you discover--so,
combining the temperature and
the luminosity,
there's a little formula which
I won't write down,
which tells you how big the
thing has to be in order to emit
that much radiation.
If the Sun were five times
bigger, it would emit 5^(2) more
radiation.
And it turns out that if you
combine this stuff,
the emitting region is
small--much smaller than an
ordinary star.
There's another argument,
a completely different
argument, that whatever is
emitting these x-rays has to be
small,
which is the following:
the brightness of these things
varies.
So, also, here's a second
argument.
Brightness varies,
and it varies quickly,
hundreds of times a second.
Hundreds--so,
on time scales of 1/100th of a
second, the brightness of these
things can vary by a factor of
2, or more.
Now, that immediately tells you
that the size of the region that
is emitting the radiation has to
be smaller than 1/100th of a
light second.
Because, imagine--here's a
thing that's emitting radiation.
And so, it's got,
you know, photons coming off in
all directions.
And you're kind of over here
watching the thing.
If it suddenly changes
brightness, you'll see the
brightness change from the front
part of the object before you
see the brightness change from
this part of the object,
because this part of the object
has less of a distance to travel
to get to you.
And so, the amount of time it
takes light to get from one side
of this object to the other is a
kind of minimum amount of time
that you would expect to be able
to see a change in the
brightness.
Now, you can ask,
what if just this little piece
gets brighter?
Well, then, that little piece
had better be emitting
essentially all of the radiation
you see when it--all of the
increased brightness of the
radiation that you see.
And so, then,
you just apply this same
argument to that little piece.
And so, the size of this has to
be less than 0.01 of a light
second.
Now, light is 3 x 10^(8) meters
per second.
So, the size of these things
has to be less than 3 x 10^(6)
meters.
That's less than what?
3,000 kilometers.
This is something that's--so,
all this radiation,
thousands of times the
radiation that you see from the
Sun,
all of it in x-rays has to be
coming from something that's
substantially smaller than the
Earth.
And, in fact,
some of these things vary on
time scales even smaller than
that.
So, lots of energy,
very small object.
This points you,
again, towards neutron stars,
because they can pack a
considerable punch in a
relatively small volume.
And as these objects were
studied more and more,
a picture came up of what they
actually were.
And these are things that are
called x-ray binary stars.
"Binary," meaning a double
star--two stars in orbit around
one another.
And the idea,
here, is that one of these
stars is a kind of ordinary star
like the Sun,
got a slightly weird shape,
which I'll explain in a minute.
So, this is some kind of
relatively ordinary star.
And the other star in the
system that it's orbiting around
is, well, the generic term is,
"compact object," an example of
which would be a neutron star,
or potentially a black hole.
And the deal is that these guys
are orbiting so close to each
other that if you look at the
gravitational force on an atom
of gas at this point of the
star-- Oh, I should say,
the reason that the star is
this weird shape is because of
huge--this is basically a tide.
This pulls one part of the star
towards it and that distorts the
ordinarily spherical shape.
And so, you get this kind of
teardrop thing.
And if you analyze the
gravitational forces on an atom
of gas, here,
it's pulled in two directions.
It's pulled downward by--it's
pulled towards the ordinary star
by the gravity of the ordinary
star.
But it's also pulled in the
other direction by the
gravitational force of this
other thing, whatever it is.
And at this,
sort of, teardrop place,
here, this peak here,
the gravity toward the compact
object is greater.
And that means that the surface
of this particular point on the
surface of the ordinary star,
in fact, that material is
pulled off the star and pulled
onto the compact object.
It kind of--what happens is,
it kind of goes into orbit and
it ends up orbiting around the
compact object.
So, you have a gas stream,
and all this stuff ends up in a
big disk of material,
here, called an accretion disk.
And so, basically,
the gas goes into orbit around
the compact object.
Now, you know something about
orbits.
These are perfectly
ordinary--each atom has its own
little orbit.
The orbits are perfectly
ordinary orbits,
which can be described by the
usual set of equations.
And one thing you know about
that is that the inner orbits go
faster than the outer orbits.
And so, if you imagine two
pieces of gas,
sort of, right next to each
other, one inside the other,
the inside one has to go
faster.
And so, they rub against each
other, the different parts of
the gas.
So, this gas generates
friction, and friction does two
things.
First, it heats the stuff up.
And where does the energy for
that heat come from?
It extracts energy from the
orbit, and that,
in turn, leads to the gas
spiraling in.
So, the gas in this disk
gradually spirals in.
As it does, it creates a lot
heat, generates a lot of
radiation.
And what was demonstrated in
the early 1970s is that the
inner parts of such an accretion
disk can be heated up to
millions of degrees,
which is exactly what you want
to be able to explain the
x-rays.
So, inner accretion disk goes
up to millions of degrees,
and that's where all these
x-rays are coming from.
Okay.
So, that's what these x-ray
sources are supposed,
in principle,
to be.
And there's,
by now, a lot of evidence that
this general picture is
basically true.
Questions?
Yes?
Student: When I was
asking you before if we--you
directly observed a supermassive
black hole that was what I was
referring to,
would they in turn be
the--these like [Inaudible]
Professor Charles
Bailyn: The accretion disks?
Student: Yes.
Professor Charles
Bailyn: Yes,
absolutely.
These are also observed around
supermassive black holes.
That's where the light from
quasars comes from--from
accretion disks around the
supermassive black holes.
They have it, too.
Again, the question of where
that gas comes from is a little
less clear than it is in the
case of the x-ray binaries.
But yes, this is why.
So, there's two ways you know
that the supermassive black
holes exist.
One is from the orbits of stuff
around them, and the other is
from the emission from the
accretion disk.
But there isn't always gas.
The one in the center of our
galaxy, there is no accretion
disk, and so,
we don't see it at all.
And so, in some cases they're
accreting gas,
in other cases not.
Presumably, that's also true of
black holes in binary star
systems – that there are some
of them that aren't close enough
to their companion to pull mass
off,
and we don't see them as bright
x-ray sources.
Student: Does that
necessarily mean that the
objects nearby aren't stable--I
mean, are not getting pulled
apart by them?
Professor Charles
Bailyn: Sorry?
Student: Does that mean
that the--does that necessarily
mean the nearby objects are not
getting pulled apart by these
black holes?
Professor Charles
Bailyn: The nearby objects
are not getting pulled apart.
Well, the companion star is
gradually being stripped of all
its gas by the black hole,
in this case.
But if it were a little further
away it would be a perfectly
stable orbit.
Other questions, yes?
Student: Why should the
inside have a higher velocity
than the outside?
Professor Charles
Bailyn: Oh.
This is smaller.
That's bigger.
Yes?
Student: Yeah,
if your compact object is a
neutron star,
then could it also be a pulsar?
Professor Charles
Bailyn: In principle,
it could.
In practice,
it turns out that all that gas
swirling around does bad things
to the magnetic field and to the
radio emission.
So, in practice,
they tend not to be pulsars,
but in principle,
they could be.
Student: Also,
is pulsar, by definition,
like, one that's oriented in
such a way that we can see the
pulsations or is it [Inaudible]
Professor Charles
Bailyn: Well,
I mean, it depends on exactly
how you define it.
But a pulsar is something that
emits radio from an off-axis
magnetic field.
Presumably, if it doesn't
happen to cross us,
we wouldn't know it's a pulsar,
but somebody else in the galaxy
might.
Student: Okay.
Professor Charles
Bailyn: Other questions at
this point?
All right, so,
having found a bunch of these
x-ray binaries,
the question is,
"Can you tell whether they're
black holes or not?"
And now, let me remind you that
the mass of a neutron star has
to be less than the three times
the mass of the Sun.
So, the plan is,
you observe the orbit of the
companion, and determine the
mass of the compact object.
And there's a derivation you
can do, which I won't show you,
but again, you can look up on
the black hole website,
which shows--remember what
we're doing, here.
Let's observe the radial
velocity of the companion versus
time--goes up,
goes down.
And you determine two things
from this: the orbital period
and the amplitude of this sine
curve, which I'm going to call
K.
And it turns out,
you can prove the following
relationship.
This is actually easy to prove
but it takes three pages to do
it, so, I won't go through the
exercise.
PK^(3) / 2πG is
equal to the mass of the compact
object--the mass of the thing
you don't see,
times sin^(3)i.
I'll explain that in a
second--times 1 plus the mass of
the object that--the ordinary
star,
divided by the mass of the
compact object,
and this is squared.
So now, why would you do this?
So, this is a little
calculation.
You start with Kepler's laws.
You do three pages of algebra.
You come out with this.
It's written down on the
classes server.
Why would you do--why would you
express it in this particular
form?
Here's the deal.
This is called the mass
function, so-called,
and can be observed from the
velocity curve only.
Student: [Inaudible]
Professor Charles
Bailyn: Yes,
the whole term--this only.
That's called the mass function.
And the term on the right,
here, is very interesting,
because it's the mass of the
object you don't see.
Mass of the compact object,
times something that is less
than 1, sine of any angle.
Oh, I should say,
the i here,
this is the inclination of the
object to the line of sight,
if it's coming exactly towards
you and away from,
i is 90 degrees.
If it's going around this way,
it's zero.
That has to be in there because
you're observing radial
velocity.
But it doesn't matter what this
is.
Sine of anything is 1 or less.
Sine cubed of anything is 1 or
less.
So, this term up here has to be
less than 1.
This term on the bottom has to
be greater than 1.
It's 1 plus something squared.
So, on the bottom,
you have a term that's greater
than 1.
That means that this quantity,
which you can easily observe,
is less than the mass of the
compact object.
So, if the mass function--you
measure the mass function,
and it comes out to be greater
than three solar masses,
then the compact object is also
greater than three solar masses.
And if that's true,
it has to be a black hole,
because it has to be smaller,
so small that it could
otherwise only reasonably be a
neutron star.
And yet it's bigger than the
mass of the neutron star itself.
There's a moderate technical
problem with making this
observation.
And the problem is,
this is hard to observe,
because the accretion disk is
too bright.
So, the accretion disk
outshines the star.
Fortunately,
nature solves that problem for
us, because many of these
objects have intermittent
accretion.
So the accretion happens.
You see all these x-rays.
Then the accretion turns off
for various reasons.
And then, when the accretion's
off, all you see is the
companion star,
and so you can--when the
accretion is off,
you can make this measurement.
So, here's how you go about
finding a black hole.
First, suddenly,
there's a new source of x-rays.
The x-rays turn on in one of
these transient systems.
Then, you wait.
Then the x-rays turn off.
This happens after a few
months, typically.
Once the x-rays turn off,
that means the accretion disk
isn't there anymore,
and you measure the mass
function.
And then, if that's greater
than three solar masses,
you win;
namely, you've discovered a
black hole.
And this is a sequence of
events that I'm rather fond of.
This is what got me tenure.
And so, I thought I'd show you
an example of how this works out
in real life.
Let's see, okay.
Here is--oh,
let me turn the lights down
just slightly.
Right, so this is just a,
sort of, artist's conception of
an x-ray binary.
Here's the companion star.
Here's the accretion disk.
Down in the middle,
there is a compact object so
small you can't see it.
This red stuff is supposed to
be radio emission coming out of
the poles.
And you can see the little gas
stream going from one to
another.
This is what it looks like when
it's x-ray active.
When the x-rays turn off,
what happens is,
the stuff just piles up in the
outer part of the accretion
disk.
There's not enough friction to
drive it down in there,
no x-rays, and basically,
all you can see is the
companion star.
So, let me now take you back
fifteen years in time.
This is something that crossed
my desk shortly after I came to
Yale as an assistant professor
in the early 1990s.
This is an astronomical
telegram.
That's an old fashioned word.
Now, of course,
we do it all by email.
And these are a system for
distributing the results of
fast-breaking news in the
heavens.
You know, if you see a
supernova or some exciting--or
comet, or something exciting
going off in the sky,
you can't wait to publish it
for a year and a half,
because, by then,
it will be gone,
and no one else will study it.
So, we have this system for
distributing news of
fast-breaking events,
so that other people can study
them.
In this particular case,
there's a whole bunch of astro
jargon down in here.
The title's the only thing you
have to pay attention to.
"X-ray transient in the
constellation of Musca."
New x-ray source suddenly
appeared in Musca.
These guys found it.
You've probably never heard of
the constellation of
Musca--Musca the Fly.
Yeah.
There's two reasons you haven't
heard of it.
One is it's in the southern
hemisphere.
You can't see it from here.
But the other reason is it's a
pretty pathetic excuse for a
constellation.
It's one, lousy,
fourth magnitude star.
That's why they call it the
Fly, right?
But they had to call that part
of the sky something,
and it's now my favorite
constellation because it has
this object in it.
Anyway, a bright x-ray source
suddenly turned up in Musca.
A month or so later,
the x-ray source was still
bright.
I found myself in this lovely
spot.
This is an observatory in Chile
where you can see the southern
hemisphere, among other things.
And the two telescopes pictured
here--this was,
at the time,
the largest,
most powerful telescope in the
southern hemisphere.
This is the door,
just to give you a sense of
scale.
And this thing here,
in the foreground,
which looms large in this
picture, but is actually much
smaller than that,
I have to tell you,
is one of the more far-flung
outposts of the Yale Empire.
This is Yale's one-meter
telescope.
It was built in Bethany,
Connecticut,
and then in the early 1970s,
somebody said,
well, Connecticut's a really
stupid place to have a research
telescope, it snows all the
time.
And so they,
kind of, picked it up and took
it down to Chile.
And so, it's,
by now, only our second best
research telescope,
and I'm very fond of it.
And so, I found myself
observing at this telescope a
few months after the discovery
of this x-ray source in Musca.
So, I junked the program I
thought I was going to do and
looked at that thing,
instead.
And what I found was that every
10.5 hours it got a little
brighter, and then a little
fainter, and a then a little
brighter.
And this was the--the accretion
disk was still there,
so presumably,
this was some effect,
for example,
of the companion star crossing
in front of the accretion disk,
or something like that.
And so, I fired off my own
telegram.
There's two things you need to
know from this one.
That's me.
And the other one is that I
claimed that there was a
10.5-hour modulation in the
brightness of the source,
which might be the orbital
period.
That's an interesting thing to
know, because if you know the
orbital period,
if you know P in the
mass function,
and you think that this might
turn out to be a black hole,
you can figure out how big
K has to be in order for
this to be a black hole.
And the answer is that if you
were to measure the radial
velocity of this thing,
the difference between the
maximum and the minimum radial
velocity would be--if that were
800 kilometers a second or
greater,
then the compact object in this
system would have to be a black
hole.
Problem was,
I couldn't make that
measurement, because,
first of all,
the Yale telescope wasn't
powerful enough to do it.
Second of all,
the accretion disk was still
too bright to allow observations
of the companion.
So, I teamed up with a couple
people who had done this once
already, before:
Ron Remillard from MIT,
Jeff McClintock from The
Smithsonian.
And we applied to get time on
the big telescope.
The big telescope,
which I showed you,
is from The National
Observatory, and you have to
write a proposal to get time on
it.
Many people want to get time on
it.
It's quite competitive.
But we wrote a good proposal.
And so, the following year,
after the x-rays had turned
off, they gave us three nights
of telescope time on the big
telescope in order to make this
radial velocity curve.
So, just to orient you,
here's Chile.
Here's the capital, Santiago.
Cerro Tololo's up in the Andes,
here.
So, you take this enormous
plane ride and then drive up
to--drive up into here.
And then, what happened
was--let's see.
The first night it rained.
This is kind of an occupational
hazard.
The reason there are all these
telescopes in Chile is because
it's mountains in the desert,
which is an excellent place to
put telescopes.
As it turns out,
even in the desert,
sometimes it's cloudy,
sometimes it rains.
That was the first night,
so that was out.
The second night--oh,
that was interesting,
there was a hailstorm.
I don't know if you've ever
been in a six-story high,
hollow steel building in the
hail.
It's a very interesting
experience, but it's not
productive, scientifically.
And so, you know,
they give you these little
rooms to sleep in,
which are light-tight and
sound-tight, because you have to
sleep in the daytime.
And so, there's this very
dramatic moment.
You wake up at 4:00 in the
afternoon and you raise the
shades to see if there are
clouds.
So, fortunately,
the third of our three nights,
it was all clear.
The storm had passed and we
were able, then--and so,
now, we're sitting somewhere in
this building,
and we were able to make our
observations.
So, let me show you what we did.
Here is a plot of hours,
time and hours,
on the night of the 3rd of
April, 1992, versus radial
velocity.
So, this is going to be a
radial velocity plot.
First thing we observed was
this point, right after sunset.
And you notice that the object
is coming toward us at 250
kilometers a second.
That's already very good news.
Because 250 kilometers a second
is actually a little greater
than the escape velocity of the
galaxy.
And so, the only reason
something would have that kind
of speed is if it was in orbit
around some other nearby
object--or objects in the galaxy
aren't usually that bright.
So, we made a couple more
observations.
And after the third
observation, it was clear that
the basic parameters of this
system were, more or less,
correct.
It had started off coming at us
at 250 kilometers a second.
A couple hours later,
it was going away from us at
200 kilometers a second.
So, in a mere two hours,
it had turned itself around
from coming at us at a high rate
of speed, to going away from us.
So, that's good.
It's in an orbit.
It's in an orbit with a very
short period.
And so, that was very
encouraging.
And then, we collected more
data.
And by about midnight,
we were feeling pretty pleased
with ourselves,
because you can see what's
happening.
It's now coming--going away
from us at 400 kilometers a
second, but clearly it's about
to turn around and go this way.
If you extrapolate 5 1/4 hours
before this turnaround,
you'd get a point down here.
That meant it would have been
going from minus 400 to positive
400.
That's 800 kilometers a second.
If you believe that,
then this probably is a black
hole.
So, we're feeling pretty
pleased with ourselves.
We opened a little bottle of
the local firewater--awful stuff
called Pisco.
You're not supposed to do that,
right?
You're not supposed to operate
heavy machinery.
And nature was not kind.
We were punished for this.
There was a small earthquake.
Chile's in an earthquake zone,
and so, this does bad things
for precision-aligned optics.
So, the next point was a little
skewed for reasons that we never
explained in our paper.
And then, there was a gap
where, for a little while,
we didn't take any data,
while we were straightening
ourselves out again.
And then, here's the next point.
And so, now,
that's encouraging again.
And then, more data was
collected toward the end of the
night.
And so, as dawn was beginning
to come up, we were kind of back
where we started.
The thing was coming towards us
at 250 kilometers a second.
And we really needed one more
point down here,
in order to nail the whole
thing down.
The problem was that the
object, of course,
is now setting in the West.
You know, the Earth turns,
so objects rise in the East and
they set in the West.
And if you can picture a
telescope following an object
down into the West,
it's sort of pointing like
this.
The principle optical element
in this telescope is a huge
mirror, a four-meter wide
mirror.
So, thirteen feet across.
And it's not bolted down,
particularly,
because if you put bolts in the
mirror,
changes in temperature will
change the size of the bolts,
and it'll throw the optics out
of alignment.
So, it's just,
kind of, sitting there,
and it's tipping this way.
And eventually it's going to,
you know, fall out,
fall on the floor.
It is way more than seven
years' bad luck for an
astronomer to break the primary
mirror of the largest telescope
in the southern hemisphere.
And so, they don't let the
astronomers actually move the
telescope themselves.
That would be far too dangerous.
They have trained experts to do
this.
And the trained expert was
saying to us at this point,
you know, "You've got to stop
observing this object.
We're beyond the safety
limits," and so forth.
And we said,
as scientists do,
"No, no, in the interest of
science, we must have one more
point."
This argument went on for a
while, and they were about to,
kind of, pull the plug on us.
And then, we said,
"Okay, fine," you know,
"we understand.
Safety of the telescope is
paramount."
But during the argument,
we'd accumulated one more
point.
And so, this is kind of the
clinching case,
down here, as it's coming
towards us at 400 kilometers a
second.
So, we're very pleased with
ourselves.
Over breakfast,
we did the exercise of finding
the best-fit sine curve.
Here it is.
And if you work out what the
mass function is--the orbital
period is 10.5 hours--the mass
function is 3.1 times the mass
of the Sun.
So, very good, very good news.
You'll notice this plus or
minus 0.05.
The data's not all that great.
We've subsequently gotten a lot
more data on this thing.
It does turn out to be about
3.1.
But it's also true
that--remember that that formula
had this sin i in it.
And we were able,
by other means,
to determine what the
inclination is.
And it's now clear that this
object has a--that this binary
system has a compact object of a
mass of about seven solar masses
in it.
Very, very nice thing.
We published this paper.
Other people have published
other papers.
By now--oh, here's our telegram
from the next morning.
Again, gobbledygook,
except for the fact that the
value of the mass function is
3.1, "providing dynamical
evidence that the primary is a
black hole."
So, we wanted to publish a
paper, you know,
entitled, "Black Hole Found in
the Constellation of Musca."
People were a little cautious
about that.
They said, you know,
you haven't yet proved that
Einstein's relativity is
correct.
If Einstein's wrong,
this doesn't necessarily have
to be a black hole.
We said, come on.
You get to assume that
Einstein's right.
They said, well, maybe not.
So, we get to call these
things, "dynamically confirmed
black hole candidates."
That's the official word.
And here is the current
collection of these things,
scaled to the Sun and Mercury.
The one we were looking at,
it's a very close one.
It's a 10.5-hour orbit.
This thing, much bigger,
thirty-hour [correction:
thirty-day]
orbit, much bigger companion
star.
But all of the black holes in
here are sort of between five
and fifteen times the mass of
the Sun.
And so, now,
fifteen years later,
there's a whole collection of
these things.
There's also a collection of
things that turned out to be
neutron stars.
So now, you can do an
experiment.
And you can do experiment in
general relativity.
Here's the derivation.
I'll skip that for you.
And you can ask yourself
whether event horizons actually
exist.
So, here's the experiment.
You have a dozen or so things
that are neutron stars.
You have another dozen or so
things that are black holes.
You pour gas onto both of them.
And indeed--you know,
that's what the companion stars
are doing.
That's why they have all these
x-rays.
What happens if gas falls on a
neutron star?
It picks up a lot of speed and
starts going at the speed of
light and it hits right into the
surface.
And so, when it hits the
surface, all its kinetic energy,
all its thermal energy,
has to stop.
The kinetic energy stops,
and all that energy goes into
the surface of the neutron star,
somehow--what's called a
boundary layer--and has to,
in some way,
get re-radiated.
It basically heats up the
surface of the neutron star.
You get x-rays from this
surface layer.
Gas falling onto a black hole
doesn't do it.
It falls right through the
event horizon.
And the kinetic energy and the
thermal energy in that gas just
contributes to the mass of the
black hole, and it doesn't get
re-radiated.
So your prediction is,
for the same amount of mass
falling onto a neutron star as
onto a black hole,
you would predict that the
neutron star would be brighter,
because all of this extra
energy brought in by the
accreting material would be
radiated--whereas,
in the case of the black hole,
it would not be.
It would just be captured by
the black hole itself.
So, with the most sophisticated
recent x-ray telescope,
people have tried to measure
black holes and neutron stars in
a situation where they emit
comparable amounts--where the
mass accretion rate,
the amount of mass that's being
accreted, is comparable.
So, the black things here are
the black holes.
The open circles are the
neutron stars.
This is a measure of brightness
and it's logarithmic.
So, this is 10^(-8),
10^(-6) and some silly set of
units.
And so, this,
between here and here,
that's a factor of 100.
This is the orbital period.
The reason they plot the
orbital period is,
there's good reason to think
that the amount of mass
accretion is proportional to the
orbital period.
So, you expect long orbits to
have more mass accretion than
shorter ones.
But the point of this graph is
clear.
There's a gap you can drive a
truck through of about a factor
of 100 in the brightness between
the neutron stars,
the things that we think are
neutron stars,
and the things we think of as
black holes.
And so, the interpretation of
this has been that the black
holes don't have a surface.
Because if they had a surface,
then all of this extra energy
would have to radiate,
as it does in the case of the
neutron stars.
So, this is a first step
towards a test of strong-field
general relativity.
It's only a first step,
because you really have to
understand how much mass is
falling,
and what the geometry of the
mass flow is,
and a whole bunch of very
complicated gas dynamics.
This is sometimes called
"gastrophysics."
And so, that's what we're
working on doing now,
to try and understand exactly
what's going on with these
things.
And if one understood that,
then you might take such a plot
to represent a proof that event
horizons exist.
And so, that kind of brings you
up to 2007, in the study of
strong-field relativity and
black holes.
And that's the end of this
section of the course.
That's the end of this section
of the semester.
Have a good break and we'll
torment you with a test
afterwards.
 
