Astrophysicist Scott Tremaine on glowing gas spiraling towards the fringe of the event horison, quasars, and guideposts in finding massive black holes
Why are black holes difficult to discover? What are the super-bright light sources in the centers of some galaxies? What is the energy source for quasars? These and other questions are answered by Richard Black Professor of Astrophysics at Princeton University Scott Tremaine.
Black holes are among the strangest predictions of Einstein’s theory of general relativity – the regions from which nothing, not even light, can escape. More precisely, there are singularities in space-time surrounded by an event horizon – this region from which nothing can get out once it’s got inside the event horizon. Although Einstein’s theory of relativity dates back to around 1917, the properties of black holes were only fully understood in the 1960’s. And one of the most remarkable properties is that at equilibrium a stationary black hole is described in practice by only two parameters – its mass and its angular momentum, or a spin.
This extreme simplicity led the Indian astrophysicist Chandra Shekhar to say very elegantly that black holes are the most perfect macroscopic objects of the universe.
Obviously you can’t study black holes in the laboratory. The only way you can hope to study black holes is to find them in the sky, in astrophysical systems. Obvious this is tough to do, because black holes are black and in edition they are very small. The typical black holes I’m talking about are black holes that may be up to a thousand million times the mass of the sun – would fit more or less the size of the Earth’s orbit. And although that may seem very large to us, by astrophysical standards it’s extremely small. An isolated black hole would be almost impossible to discover in astrophysics. The chance you do have is to find black holes that are in gas-rich environments, because the gas surrounding the black hole will form a disk, a spinning disk around the black hole, and then stresses inside the rotating disk will heat up the gas, remove orbital energy from the gaseous material, and will gradually spiral into the black hole until it disappears behind the event horizon. But at the same time it will heat up until it starts to glow. Typically it’ll glow in ultraviolet or maybe even in x-rays. And there is some hope that you can detect that characteristic glow from the gas spiraling into the black hole. This whole process can be thought of as a furnace. And any furnace can be characterized by an efficiency which is the ratio of the light and energy that it’s put out to the fuel that it consumes. The natural measure for efficiency is based on an Einstein’s famous formula – e=mc^2. So a furnace with an efficiency of unity would release an energy of mc^2 for every mass m that it consumed.
Typical furnaces are much less efficient than that. So for example, when you burn fossil fuel you are only getting out of the fossil fuel an energy that’s about one billionth of its rest mass energy mc^2. Nuclear reactors are more efficient. They have an efficiency of about 1/1000. The sun, which produces energy by fusion, has an efficiency of about 1/100. The remarkable thing about black holes surrounded by a disk of gas is that they have far higher efficiency than any other system we know. They have efficiency somewhere between 10% and 30%.
Black holes are so much more efficient than fossil fuels that you could supply the entire energy requirement, say, of the United States by letting a few kilograms of mass spiral into a black hole.
The problem, of course, is controlling the black hole, but at least in principle the efficiency is many orders of magnitude better than any other furnace that we know of.
Despite the relatively low efficiency of stars like the Sun in burning fuel compared to black holes stars do provide most of the light in the Universe. The stars that we see are almost all concentrated in galaxies – assemblies of up to million millions of stars. The Milky Way is one such assembly. It’s the galaxy in which we live. But there are billions of galaxies outside the Milky Way. A very small fraction of these galaxies were discovered to have unusual bright point-like sources of light in the middle. The spectrum of that light showed that it wasn’t coming from stars.
It had been coming from some hot glowing defused gas. In the most extreme cases the light from the small source in the middle of the galaxy outshone all the light from all the stars in the galaxy. Sometimes by the factor of a hundred or more. These extremely bright sources came to be called ‘quasars’. The problem in discovering quasars, in studying them, in understanding them was different from the problem with most astronomical sources. Most astronomical sources are hard to study because they are so faint. The problem with quasars was that they were so bright that they outshone all the galaxies around them. So for many decades after their discovery no one was sure that the quasars were associated with galaxies – they just looked like bright points, because the glare from the quasar obscured the galaxy behind them. The trouble with that is that if they look like bright points, then they look just like stars and you couldn’t tell the difference between a quasar and a star.
This problem was resolved fortunately because some quasars are also very strong sources of radio emission which stars are not. And in 1963 Martin Schmidt, at California Institute of Technology, was able to identify a previously unknown very strong radio source with a particular object that up until then had been confused with an ordinary star. He was able to take a spectrum of the star and because of the cosmological expansion he was able to detect the high velocity that this apparent star had and to deduce that it was something like 10 million times as far away as it would’ve been if it was a normal star. This is the origin of the term ‘quasar’ – it’s an abbreviation for ‘quasi-stellar object’.
Once Schmidt had made this identification it was realized that the quasars were typically very distant and extremely luminous objects. By now something like over a hundred thousand quasars are known. Almost as soon as Schmidt discovered the first quasar, people began to worry about what the possible source of energy would be. Quite properly most astronomers concentrated on relatively conventional sources like dense clusters of stars. But very soon after the original discovery two astrophysicists, Edwin Sapleter in the United States and Yakov Zeldovich in Russia, proposed that the energy source for quasars might be accretion of material onto a black hole – this furnace in which the gas is heated and begins to glow as it spirals in towards the black hole. By now it’s universally accepted that quasars do arise in precisely this way.
There is a wide variety of arguments, direct and indirect, for this. One of the most compelling is that quasars are extremely small. You can tell this not because you can resolve them – even with the best resolution, with the telescopes, like the Hubble telescope – they still appear to be point sources of light. But many quasars vary on short time scales – as short as a few weeks or months. And if you think about it for little it’s very hard to make a source very strongly in brightness of the size of the source is bigger than the time it takes like to travel across it. Because if it is bigger than the time it takes to travel across it there is no way that the two parts of the source can be correlated or connected. And so they should very randomly and the effect should cancel out. That requires that quasars are smaller than a few times the distance they can travel in a month or so. And that in turn requires that they are smaller than maybe a hundred times the size of the solar system, and many orders magnitudes are smaller than galaxies. That size is big enough to contain a black hole of a hundred million or a thousand million solar masses. But there is no other system we can think of that could produce this much energy from that small volume.
The other simple argument is simply one of the efficiency. I said earlier, the quasars are far more efficient than any other engine or furnace that we know of. We know how bright the quasars are. We know how long they last. We can calculate the total amount of energy they put out. We can calculate the total amount of fuel they put out. For sources like stars the amount of fuel required would exceed all the mass in a typical galaxy. For a quasar the amount of fuel is a few hundred million solar masses which we easily acquire in the gas-rich central regions of a galaxy.
By now about a hundred thousand quasars are known. We have a very good idea of the distribution through the history of the universe. Quasars are known as far away or as early in the history of the universe as when it was about 10% of its current age.
But most of the quasars that we see were formed and shone when the universe was maybe half to a third of its current age. In fact, it turns out that the density of quasars after taking account of the expantion of the universe peaked when the universe was about a third of its current age. And earlier on it was much smaller and later it was much smaller, that is, the current density of quasars is now two or three orders of magnitude smaller than it was at their peak – when the universe was about 30% of its current age. These arguments lead to a very simple syllogism that has driven a lot of the research on quasars for the last several decades: if quasars are black holes, if the black holes are located at the centers of galaxies and if the current density of quasars is a hundred or a thousand times smaller than the density at their peak, since the black holes didn’t go away, there must be a large number of galaxies in the local universe that contain black holes that used to be shining as quasars and that they are now dormant, presumably because they don’t have fuel. That suggests that if we go and look at nearby galaxies in many cases we should find massive invisible black holes at their centers.
This argument was made as early as 1970. Since then there have been two important guideposts in trying to look for massive black holes in the centers of galaxies. The first is that they really should be exactly at the center. Partly this is because the quasars that we see, where we can resolve the host galaxy around them, are found to be almost exactly in the center. Second – if a mass of the black hole is not at the center of the galaxy, gravitational drag from the stars that it’s orbiting through will make it spiral in until it sits in the center of the galaxy. Third – black holes to shine as quasars have to have a substantial supply of fuel – that’s much easier if they are sitting at the bottom of the gravitational potential well at the center of the galaxy.
And finally, we are like the drunkard looking under a lamp post for his keys because that’s the only plays we can see them. Black holes are sufficiently hard to find and the only reasonable chance we have locating one is if we know where to look. And the natural place to look is the center of the galaxy.
The second guidepost is very simple argument made by the Polish astronomer Andrei Soltan. He pointed out that because the universe is homogeneous the average density of black holes average over millions of light years small compared with the size of the universe but large compared to individual galaxies – that density should be the same everywhere. If we go into a survey of quasars we know what the density of quasar light is the same volume. Since the universe is homogeneous that density has to be the same in all volumes. We know the efficiency of black holes – they are accreting material from the disk around them. And so since we know the density of quasar light in a particular volume, we know how much fuel had to be burnt to create that light. Since we know how much fuel had to be burnt and that the ash from that fuel composes the black holes, we know the density of black holes that should be in the local universe. We don’t know of this density of black holes means that there should be very massive black holes in a small fraction of galaxies or less massive black holes in almost all galaxies, but we know the target density that we are looking for.
The best way to find these black holes is by their indirect gravitational influence on the galaxy near them. We can’t see individual stars in other galaxies but we can measure the average velocities of the stars in the region of the galaxy by looking at broadening of the spectral lines from the stars due the Doppler shift.
So what you can do to look for black holes is go close to the centers of galaxies and look for increased broadening of the spectral lines of the stars which is due to their more rapid motions is in the deep gravitational field of the black hole. That process was started with ground-based telescopes in the early 1980’s but only really became possible with the Hubble space telescope. The region in which the black hole can influence the motions of the stars is rather small. The Hubble space telescope has spacial resolution – it’s about a factor of ten better than the competitive ground-based telescopes of that time. That meant that it could go closer to the center of the galaxy and had a better chance of seeing this increase in the motions. This has been a major project of the Hubble telescope of the time since it was launched. We now have strong evidence for massive dark objects in the centers of 40-50 galaxies. We don’t know for sure that they are black holes, because the size scales that even the Hubble telescope can resolve are maybe ten thousand times bigger than the event horizon of the black hole. But we do know that these galaxies contain massive objects in their centers. They are dark and they are so compact that we can’t think of any other astrophysical system that they could be other than a black hole.
By now Hubble has looked at essentially all of the near-by galaxies that has a reasonable chance of finding black holes in. It’s turned other tasks. The prospect for the future is that ground-based telescopes will be able to take over that role because of the development of the technology of adaptive optics which, will cancel out the blurring effects of the earth atmosphere. In addition to the galaxies that have been measured with the Hubble space telescope there are two special galaxies where we have strong evidence for black holes from other means.
One is the galaxy with the name NGC-4258 which happens to have a thin rotating disk of gas in its center in which the conditions of temperature and density happen to be right to allow water vapor in the disk to act as a laser, that is, as a microwave laser. Small regions in that disk emit strong coherent radiation. We can detect that radiation, we can measure its velocity. And as a result, we can see that the disk has beautiful rotation curve – rotation is a function of radius, just like the rotation in the solar system is the character with a characteristic shape associated with a massive point in its center. The rotation speed and the geometry of the disk are measured so precisely that we can measure the mass of the central body to within about 1% – it’s around 40 million times the mass of the Sun. Again, it’s so compact that the only system we know of has to be a black hole.
The second special system is our own galaxy. It’s harder in many ways to study our own galaxy than any other galaxies, because we are in the plain of the galactic disk, there are vast amounts of dust and small particles between us in the center of the galaxy. It’s only visible in infrared radiation, and infrared technology has been slower and more difficult to develop than ordinary telescopes in visible light. However that has now been done. We now have exquisitely detailed observations of the center of the galaxy. We can see half a dozen individual stars on orbits with orbital periods as short as 15 years. It’s clear that those stars are orbiting around the massive body which we can’t see but it’s clearly there. You can measure the mass of that body – it’s about 4 million solar masses. You can set an upper limit of its size. This upper limit is maybe a few times the size of the solar system. Once again, the only possible object it can be is a black hole.
There are two profound questions which remain after what we’ve learnt. The first is the relation between black holes and galaxies. We know that black holes are only a small fraction of the mass in galaxies – maybe a few tens of 1%. Nevertheless, the energy that was released in forming that black hole is far larger than the energy that was released in forming the rest of the galaxy. And what we don’t know is whether that energy that was released when material was accreted by the black hole played any role in the formation of the galaxy. That is, does the galaxy determine the properties of the black hole or does the black hole determine the properties of the galaxy? To what extent do this feedback from accretion of material and the release of energy from the black hole affect the properties of the galaxy – its size, its mass, its amount of gas. That’s probably the most profound and the most difficult question in the study of formation of galaxies.
The second major issue is whether we can learn something from these black holes about Einstein’s theory of relativity. The supermassive black holes in the centers of the galaxies are the best hope we have for clean physical systems in which the predictions of Einstein’s theory of relativity will be unique. And they are the best hope that we have for providing high accuracy tests of whether Einstein was right or whether the modifications to this theory are going to be required to describe the strong gravitational fields that you find on your black holes in the centers of galaxies.