In the first paper we didn’t analyze in detail why the gas would hold on to its heat. We just pointed out two situations in which it might happen. One is that the gas could be very opaque. So even though the gas is hot, it takes too long for any radiation from it to escape. Meanwhile the gas is flowing in steadily, so if the radiation is not able to escape before the gas falls into the center, the heat energy stays with the gas. That’s one option. The other is that the gas might be terribly dilute. It turns out that, in very dilute gases, radiation processes are not very effective. This is because individual atoms or particles radiate only when they interact with each other. If gas is very dilute, the particles don’t meet each other very often and so don’t have the opportunity to interact and radiate. These are the two extreme situations where it’s plausible that the gas will be able to hold on to its energy, and one could have advection-dominated accretion.

In the first paper, we just said, look, here is this somewhat unusual regime of accretion that might happen in certain situations. If it does, what will the gas flow look like? We worked out the basic properties of the accretion flow. Then in the second paper, we worked out some of the properties in a little bit more detail. In particular, we showed that these advection-dominated flows might have lots of mass ejections or outflows. So, even while gas is flowing in, a good fraction might still get kicked out. The reason is straightforward. Since the gas has difficulty radiating, it gets very hot, and because of the high temperature it evaporates easily. By the time we finished the second paper, advection-dominated accretion was still just a toy model without any obvious application. It was in the third paper that we finally investigated the possible relevance of all this to real astrophysical objects.

The whole thing started very much by chance, as it usually does in research. I had gone to a conference on accretion flows in Sweden—in 1993 I think—and one of the topics discussed there was a mystery that was bothering people. It seemed that there were certain conditions under which none of the regular accretion solutions theorists were familiar with at that time would work. Every solution was either disallowed or unstable and no one was able to figure out what would happen to the gas. It was just a formal little problem, but the sort of thing that theorists love to investigate. My thought after hearing the discussion at the meeting was that the fallacy might be in the implicit assumption everyone was making that all the heat energy in the gas is radiated. So I asked myself what would happen if the gas did not radiate its heat energy but held on to its heat and carried the energy inward with it. Following this train of thought led to our work on advection-dominated accretion.

After finishing the first two papers, we said, "now let’s see whether advection-dominated accretion can actually occur in an accretion flow around a compact star." In that third paper, we considered accretion on black holes and also neutron stars, and we showed that if the gas accretes at a low enough rate, below some critical rate, then advection-dominated accretion is plausible. We couldn’t prove that it is the only kind of accretion that could happen. In fact, at these low rates, another more standard form of accretion is also allowed, one in which the gas radiates its energy efficiently. So all we could show was that, below the critical rate of accretion, advection-dominated accretion is allowed along with other forms of accretion, whereas above the critical rate, advection-dominated accretion is not possible. But we then made a somewhat bold suggestion. We speculated that, whenever advection-dominated accretion is allowed, nature would prefer it over other forms of accretion. Even though other possibilities are available, nature would zero in on this kind of accretion. If our hypothesis turned out to be correct, then it was clear that our new accretion solution would be relevant to a lot of real systems in nature.

I think people were tempted to dismiss the first two papers as just games being played by theorists. But the third paper really got people interested. Now they realized that maybe this new kind of accretion has some relevance to real objects, so they’d better pay attention.

Following the third paper, we wrote a sequence of papers in which we applied our advection-dominated accretion model to a number of specific objects, all famous objects that people had studied and puzzled over before we came on the scene. And we showed how our model explained a lot of facts about these objects.

Well, one was Sagittarius A*, which is the big few-million solar-mass black hole at the center of our Milky Way Galaxy. For many years people had wondered what’s going on with this guy. It’s very, very dim—extremely dim. What was puzzling was that there’s a reasonable amount of gas available to accrete onto the black hole. So why is it so dim? We showed that Sagittarius A* must have an advection-dominated accretion flow, whereby the diffuse accreting gas does not radiate very much. So, instead of radiating the heat energy released by accretion, the gas holds on to most of the energy and carries it into the black hole. That paper was published in Nature in 1995 ("Explaining the spectrum of Sagittarius A* with a model of an accreting black hole," Nature 374[6523]: 623-5, 13 April 1995).

That was the first application of our model to a real object, and it was a very important object. Lots of papers had been published in Nature about Sagittarius A*, many of them puzzling over why the object is so dim. So we thought that our paper really needed to go into Nature.

After that, we applied the model to x-ray binaries. In a paper in 1996 ("A new model for black hole soft x-ray transients in quiescence," Astrophysical Journal 457[1]: 821-33, 1 February 1996), written with Insu Yi and my colleague Jeff McClintock, we proposed a new model for black holes in transient x-ray binaries when they are in a very dim state called "quiescence." Once again, as in the case of Sagittarius A*, we showed that things which had puzzled people earlier could now be understood by invoking advection-dominated accretion.

In 1997/98, my student Ann Esin wrote two really beautiful papers ("Advection-dominated accretion and the spectral states of black hole x-ray binaries: application to Nova Muscae 1991," Astrophysical Journal 489[1]: 865-89, 10 November 1997; and "Spectral transitions in Cygnus X-1 and other black hole x-ray binaries," Astrophysical Journal 505[1]: 854-68, 1 October 1998) applying the model to two x-ray binaries called Nova Muscae 1991 and Cygnus X-1. What she showed was that a lot of different things people had seen in these x-ray binaries—so-called spectral states—could be unified under the umbrella of the advection-dominated accretion model.

Well, when we wrote our first two papers, I had no idea where we were going. At that point we were just curious, and we were having fun. The people who thought we were just a couple of theorists playing games were perfectly correct—that is exactly what we were doing! By the time we wrote the third paper, however, we discovered that there are real physical regimes in which this kind of accretion is possible and furthermore that these regimes are accessible to observation. I began to have a hunch this might be important. Then when we applied the model to the first few objects mentioned above, I became really confident. At that point it became clear, at least to me, that this work would be relevant to a lot of real objects in nature.

There are two important changes from those early days. One is that new insights are being obtained through very detailed computer simulations. When we did our early work, we had to make a lot of approximations. We calculated everything in one dimension, assuming that gas properties vary only as a function of the radius. We had to make this approximation so that the problem would be theoretically tractable. Now people are simulating these flows on computers in all three dimensions, and finding unexpected results.

The most important new result to come out of the computer simulations is the idea that when you have an advection-dominated accretion flow, a lot of gas is ejected from the system. We had anticipated this in our early papers, especially the second paper, but we didn’t quite appreciate how important the effect would be. The computer simulations have made us all appreciate the importance of outflows.

Another thing we’re pursuing quite vigorously comes out of a 1997 paper that I wrote with my colleagues Mike Garcia and Jeff McClintock ("Advection-dominated accretion and black hole event horizons," Astrophysical Journal 478[2]: L79-82, 1 April 1997) in which we compared accretion flows around black holes and neutron stars. What we had predicted already, back in 1995, was that in the presence of advection-dominated accretion black holes would be much dimmer than neutron stars. The idea is very simple: you have all this hot gas accreting onto a compact star, but not radiating along the way; the gas comes down to the center carrying a huge amount of heat energy with it. If the object at the center is a black hole, the gas just falls in carrying its heat energy with it. There is no opportunity for the energy to be radiated, so the energy is lost. If the object at the center is a neutron star, however, the gas sticks to the surface of the star; then, as it cools down, it radiates its heat energy. The energy doesn’t disappear, but comes out ultimately as x-rays from the surface of the neutron star. So we said that, whenever we look at an X-ray binary in quiescence, since the accretion flow is advection-dominated, the binaries with black holes should be quite a bit dimmer than those with neutron stars. And, lo and behold, when we went and looked at the data, we found that quiescent x-ray binaries with black holes are indeed 100 or 1,000 times fainter than those with neutron stars. We first saw this effect in 1997 with a very small amount of data, but we’ve been collecting more data since then. Now the evidence is looking very good. And it’s completely consistent with the idea of black holes swallowing everything and neutron stars not being able to swallow anything.

According to theory, you cannot have a neutron star more massive than a certain limiting mass. The limit is something like two or three solar masses. Certainly beyond three solar masses it is virtually impossible to have a neutron star. So people go and look at x-ray binaries, and they try to measure the mass of the compact star. If the mass is greater than three solar masses, they say it cannot be a neutron star so it must be a black hole. By this means, astronomers have made a catalog of transient X-ray binaries, some of which are identified as black hole systems and some as neutron star systems.

The beautiful thing is that the systems that are identified as black holes, just on the basis of their masses, are also significantly dimmer in quiescence than the other guys that are identified as neutron stars. That’s a very nice confirmation of the advection-dominated accretion model, but more importantly, it is a confirmation of the expected difference between black holes and objects that are not black holes. It’s the first time that anyone has actually shown that those objects we call black holes based on their mass truly do swallow stuff—that things actually disappear through their event horizons and once stuff has gone in you see no sign of it ever again. This is the most important predicted property of a black hole; in fact, it is how a black hole is defined. But it never really had been confirmed experimentally. The difference in brightness of black hole and neutron star X-ray binaries in quiescence was the first time anyone ever tried to test whether black holes have event horizons. And the test was successful! People are still debating whether there is some other explanation for the observations, but our original explanation in terms of the event horizon swallowing hot gas is still the most plausible one.

There is a direction that a lot of people are following right now that is very promising. An obvious fact about accretion models is that the results are very general. It doesn’t matter what the size of a black hole is, whether it’s 10 solar masses, as in an x-ray binary, or a million or even a billion solar masses, as in the center of a galaxy. Even though when we look at the objects, they seem completely different, the underlying physics of the accretion flow is often the same. Now people are thinking, "wouldn’t it be nice to have a unified understanding of the whole range of black holes, with a common set of models, and be able to transfer our understanding from one class of black holes to another?" Say, for instance, that there is some phenomenon we see in an x-ray binary that we are able to model successfully. Couldn’t we apply the same model to a supermassive black hole in a galactic nucleus and explain some data or suggest a new observation? Or, it could be in reverse—something we understand in large black holes in galactic nuclei might be applied to small black holes in x-ray binaries. Or perhaps we could use our black hole models to predict the properties of hypothetical intermediate mass black holes, with masses of a thousand or ten thousand solar masses, and search for these objects.

I would like to make one other comment about why the field of advection-dominated accretion has become so interesting. As I mentioned earlier, this kind of accretion occurs at low mass accretion rates, which means that not much gas flows in. Furthermore, a lot of the gas is ejected from the system, and the rest holds on to its heat and radiates very little. For all these reasons, objects with these flows are extraordinarily dim. This means that, observationally, it is a tremendous challenge to see them or measure their properties. Unless we have superb telescopes, these systems will be below our observational thresholds. Today, we have very sensitive telescopes, and we’re able to observe the advection-dominated regime of accretion. This could not have been done 20 years ago. Moreover, people are realizing that if you look at all the black holes in the universe, only a very tiny fraction are able to accrete gas at a high rate and shine brightly. Most black holes in the universe accrete at a low rate, have advection-dominated accretion flows, and are extremely dim. The dim, advection-dominated state is the natural state of the vast majority of black holes in the universe. That is perhaps one reason why this work has had so much influence.