ASTR 160: Frontiers and Controversies in Astrophysics

Lecture 15

 - Supermassive Black Holes


The lecture begins with a question-and-answer session about black holes. Topics include the extent to which we are sure black holes exist in the center of all galaxies, how massive they are, and how we can observe them. The lecture then turns to strong-field relativity: relativistic effects that are unrelated to Newtonian theory. The possibility of testing predictions of the existence of black holes is discussed in the context of strong-field relativity. One way we might learn about black holes is through observation of the orbit of the companion star in an X-ray binary star system. Through this we can estimate the mass of the compact object. The lecture ends with an explanation of how astronomers find black holes, and how Professor Bailyn was able to discover one himself.

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Frontiers and Controversies in Astrophysics

ASTR 160 - Lecture 15 - Supermassive Black Holes

Chapter 1. Supermassive Black Holes and Gravitational Waves [00:00:00]

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.

Chapter 2. Strong-Field Relativity [00:07:15]

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 52 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.

Chapter 3. X-Rays of Binary Stars [00:17:01]

Now, light is 3 x 108 meters per second. So, the size of these things has to be less than 3 x 106 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.PK3 / 2πG is equal to the mass of the compact object–the mass of the thing you don’t see, times sin3i. 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.

Chapter 4. Finding Black Holes with X-Rays [00:30:08]

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 ¼ 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.

Chapter 5. Conclusion [00:46:43]

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.

[end of transcript]

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