A black hole is a region of space that has so much mass concentrated in it that there is no way for a nearby object to escape its gravitational pull. In other words, a black hole is any region of space-time where the local acceleration due to gravity exceeds the speed of light, c.

The idea of a mass concentration so dense that even light would be trapped goes all the way back to Laplace in the 18th century. Almost immediately after Einstein developed general relativity, Karl Schwarzschild discovered a mathematical solution to the equations of the theory that described such an object. It was only much later, with the work of such people as Oppenheimer, Volkoff, and Snyder in the 1930's, that people thought seriously about the possibility that such objects might actually exist in the Universe. These researchers showed that when a sufficiently massive star runs out of fuel, it is unable to support itself against its own gravitational pull, and it should collapse into a black hole.

In general relativity, gravity is a manifestation of the curvature of spacetime. Massive objects distort space and time, so that the usual rules of geometry don't apply anymore. Near a black hole, this distortion of space is extremely severe and causes black holes to have some very strange properties. In particular, a black hole has something called an 'event horizon.' This is a spherical surface that marks the boundary of the black hole. You can pass in through the horizon, but you can't get back out. In fact, once you've crossed the horizon, you're doomed to move inexorably closer and closer to the 'singularity' at the center of the black hole.

You can think of the horizon as the place where the escape velocity equals the velocity of light. Outside of the horizon, the escape velocity is less than the speed of light, so if you fire your rockets hard enough, you can give yourself enough energy to get away. But if you find yourself inside the horizon, then no matter how powerful your rockets are, you can't escape.

The horizon has some very strange geometrical properties. To an observer who is sitting still somewhere far away from the black hole, the horizon seems to be a nice, static, unmoving spherical surface. But once you get close to the horizon, you realize that it has a very large velocity. In fact, it is moving outward at the speed of light! That explains why it is easy to cross the horizon in the inward direction, but impossible to get back out. Since the horizon is moving out at the speed of light, in order to escape back across it, you would have to travel faster than light. You can't go faster than light, and so you can't escape from the black hole. (If all of this sounds very strange, don't worry. It is strange. The horizon is in a certain sense sitting still, but in another sense it is flying out at the speed of light.)

Once you're inside of the horizon, space-time is distorted so much that the coordinates describing radial distance and time switch roles. That is, "r", the coordinate that describes how far away you are from the center, is a time-like coordinate, and "t" is a space-like one. One consequence of this is that you can't stop yourself from moving to smaller and smaller values of r, just as under ordinary circumstances you can't avoid moving towards the future (that is, towards larger and larger values of t). Eventually, you're bound to hit the singularity at r = 0. You might try to avoid it by firing your rockets, but it's futile: no matter which direction you run, you can't avoid your future. Trying to avoid the center of a black hole once you've crossed the horizon is just like trying to avoid next Thursday.

Incidentally, the name 'black hole' was invented by John Archibald Wheeler, and seems to have stuck because it was much catchier than previous names. Before Wheeler came along, these objects were often referred to as 'frozen stars.' I'll explain why below.

Before thinking about a black hole's actual appearance, let's first think about what a black hole is: the black hole is an object of our imagination, driven by the mathematics of general relativity, our current best theory of gravity. To this point, there is no evidence that they exist. On the observational side, we know that very massive and compact objects exist. Many compact objects of several times the Sun's mass are found in binary star systems, where the compact object generates tremendous power by pulling onto itself the atmosphere from an orbiting star. The orbits of stars at the center of our Galaxy suggest that an extremely massive compact object sits there. Black holes are thought to power the active galactic nuclei found in some distant galaxies. Where we falter is in evidence that proves these compact objects are black holes. Under our theories, they can only be black holes, but if general relativity is not valid, then these compact objects may be something else. In this absence of evidence, astrophysicists assume the existence of black holes, which allows them to model the effect of a massive compact object on its surroundings.

We can ask of general relativity the question that we ask of Newtonian gravity: what is the gravitational field in the vacuum surrounding a point of mass? In Newtonian gravity, the answer is the inverse-square law; in general relativity, the answer is the black-hole. As with Newtonian gravity, where the inverse-square law describes the gravitational field outside of all spherically-symmetric masses such as the Sun, the stars, and the planets, the black-hole solution describes the gravitational field around a spherically-symmetric mass under general relativity. This solution is used to calculate both the bending of light as it passes by the Sun and the deviation of Mercury's orbit from a closed ellipse. For very weak gravitational fields, the equation for the black hole's gravitational field becomes identical to the inverse-square law of Newtonian gravity. For very strong gravitational fields, such as those found around neutron stars, the black hole solution of the gravitational field strongly Doppler shifts to lower frequencies the radiation from the star's surface, and it bends the path of the light from the star so strongly that a large fraction of the star's back side is visible to us.

The most peculiar properties of strong gravitational fields appear in the black hole. The best known property is the black hole's event horizon. It is a spherical boundary that completely surrounds the point mass that generates the black hole. An object that fall through the event horizon become dark to those remaining outside; once it has fallen inside, neither the object nor light from it can ever escape back to the outside. This effect is the reason that the black hole has its name. But the event horizon is not the only peculiar effect seen in black holes. Circular orbits are not possible close to the black hole's event horizon. The circular orbit closest to the event horizon is called the last stable orbit of the black hole, and at this orbit light can orbit the black hole in a circle indefinitely. Related to the last stable orbit is the ability of a black hole to create an infinite number of images of a background star.

While the Newtonian gravitational field is proportional to a single constant—the mass of the gravitating body—the black hole's gravitational field is set by two constants—a mass and an angular momentum. A black hole with zero angular momentum, called a Schwarzschild black hole, is spherically symmetric. A black hole with non-zero angular momentum, called a Kerr black hole, is axisymmetric about the axis of rotation. All objects in space carry some angular momentum, and if we are seeing black holes in our universe, they are inevitably Kerr black holes. But the Schwarzschild black hole is simpler than the Kerr black hole, and its principal features are shared with the Kerr black hole, so it is described next.

The gravitational field of a Schwarzschild black hole depends on only one constant: a mass. Around this central mass, which is assumed to exist at a single point in space, the gravitational field is isotropic, so it varies only with the distance from the central mass.

The principal features of a Schwarzschild black hole—time dilation, a gravitational Doppler shift, the bending of light, and the presence of an event horizon—arise because ofthe equivalence principle. All of these effects are seen under special relativity bya traveler accelerating at a constant rate; the difference is that around a black hole, an accelerating observer can remain motionless relative to the black hole. Over distances much smaller than the observer's distance from the black hole, the observer sees physics that is identical to that seen by an accelerating traveler in special relativity. An observer hovering over a black hole sees the radiation arriving from above Doppler shifted to higher frequencies, and he sees the radiation arriving from below Doppler shifted to lower frequencies. He sees the clocks of observers hovering farther way from the black hole's center as moving more quickly than his own, and he sees the clock of those closer the the black hole's center as moving more slowly. He sees the path followed by light bend, so that objects at the same distance from the black hole as himself appear to be above him. The only thing missing is the event horizon.

In special relativity, the distance from an accelerating traveler to the event horizon is inversely proportional to the strength of the observer's acceleration. Far from a black hole, the acceleration of an hovering observer is inversely proportional to the square of the distance to the center of the black hole. We expect the event horizon for a black hole to appear at approximately the place where the acceleration experienced by the hovering observer produces under special relativity an event horizon distance equal to the distance from the black hole center. This approximation in fact holds, for the precise radius of a black hole's event horizon is r = 2GM/c2, where the radius r is defined by the circumference of the event horizon, G is the gravitational constant, M is the black hole's mass, and c is the speed of light. This radius is called the Schwarzschild radius. For a solar mass black hole, the event horizon has a radius of only 3 km. For a one billion solar mass black hole, which is about the maximum mass expected for a black hole at the center of a galaxy, the radius is 20 AU, or about the distance of Uranus from the Sun. In other words, black holes are small.

You must have noted the strange phrasing for the radius of the black hole's event horizon. In general relativity, space ceases to obey Euclidean geometry. This means that if I took a ruler, measured out a radius, and then measured the circumference of a circle having that radius, I would not get the Euclidean relationship C = 2 π r, but some other relationship that depends both on my acceleration and on the variation of the local gravitational field. The value of the radius from the black hole's center is normally defined from the circumference of a circle centered on the black hole. With this definition of radius, if one moves from one radius to another, one cannot derive the distance traveled by simply taking the difference of the two numbers. The actual formula for the distance traveled depends on the mass of the black hole.

In nature, objects orbit black holes; they don't hover over them. When an object orbits a star in a circular orbit, its speed increases as the radius of the orbit decreases. Where does this speed equal the speed of light? For a black hole, it equals the speed of light at a radius of 1.5 times the Schwarzschild radius. The circular orbit at this radius is called the last stable orbit of the black hole. Outside this orbit, matter orbits the black hole at a speed less than speed of light. At this orbit, only light can orbit the black hole; matter place in this orbit falls into the black hole. Inside this orbit, even light falls to the event horizon.

The existence of the last stable orbit implies something very unusual about black holes: light passing by a black hole can orbit it several times before escaping to a distant observer. This is a much more dramatic effect than the gravitational lens associated with stars and galaxies. The bending of light by a star can only produce two images of a more distant star, but a black hole can produce an infinite number of images. These images are created in pairs, with the first pair corresponding to the images produced by a star. The next pair of images is created when the light passing on either side of the black hole completes a single orbit around the black hole before traveling to the observer. A third pair is created when the light completes two orbits of the black hole. This progression continues to infinity, with each image pair smaller on the sky than the previous pair. Because the pairs of images become smaller with each orbit, the amount of light reaching the observer from a star becomes smaller with each image, which keeps finite the total amount of light contained in this infinity of images. Perhaps, rather than as “black holes,” these objects should be known as “black crystals,” for their effect on distant stars is similar to the multitude of images created by a piece of cut crystal.

In astrophysics, everything within the universe—planet, star, and galaxy—spins. This is true of the black hole as well. A star that collapses to form a black hole gives part of its angular momentum to the black hole. A black hole in a binary star system acquires angular momentum as it pulls the atmosphere from its companion star onto itself. The massive black hole candidates we see at the centers of galaxies are surrounded by accretion disks that dump both matter and angular momentum onto the black holes.

A “spinning” black hole is called a Kerr black hole; it is described by only two physical properties: mass and angular momentum. The Schwarzschild black hole, which has zero angular momentum, is a special case of the Kerr black hole. The amount of angular momentum a black hole may carry is limited by the black hole's mass; the maximum magnitude of the angular momentum is proportional to the mass.

A Kerr black hole's gravitational field has an axis of symmetry that can be thought of as an axis of rotation. The angular momentum vector is in the direction of this axis. The gravitational field is also mirror-symmetric about an equatorial plane that contains the black hole's center. The angular momentum vector is perpendicular to the equatorial plane. As the angular momentum goes to zero, the gravitational field becomes spherically-symmetric.

Like the Schwarzschild black hole, the Kerr black hole has an event horizon. The radius of the event horizon is dependent both on the mass and the angular momentum of the black hole. For a given mass, the circumference of the event horizon is at its maximum for zero angular momentum. The circumference falls as the magnitude of the angular momentum rises. At the maximum angular momentum, a minimum circumference of half the maximum circumference is found.

The striking feature of a spinning black hole is that the gravitational field pulls objects around the black hole's axis of rotation. This effect, called frame dragging in the jargon of general relativity, prevents an accelerating observer close to the black hole's event horizon from holding a fixed position relative to the stars. Regardless how much he accelerates, the observer is incapable of stopping his motion around the black hole, although he can keep a fixed distance above the event horizon. The boundary surrounding the black hole that separates the space where an accelerating observer can remain static with the distant stars from the space where no amount of acceleration can keep an observer at a static location is called the static limit. This boundary touches the event horizon at the poles, but it extends much farther out than the event horizon away from the poles, reaching its maximum radius at the black hole's equatorial plane. The volume enclosed between the event horizon and the static limit is called the ergosphere.

In astrophysics the effect of a black hole's angular momentum would be seen on an object falling onto the black hole or in orbit around the black hole. If we drop an object onto a Kerr black hole, it would spiral around the black hole's spin axis as it falls. The only way to fall in a straight line into the black hole is to fall along the axis of rotation. Traveling along any other line, an object spirals down a cone whose apex is at the black hole's center and whose axis is the black hole's axis of rotation. The direction of motion is set by the direction of the angular momentum vector; a dropped object always travels counter-clockwise around the angular momentum vector. As an object approaches the event horizon, its radial motion slows to a crawl, but its orbital motion goes to a constant rate, so that the object appears to be stuck to a rotating event horizon.

The counterclockwise rotation of an object free-falling from rest at infinity onto a Kerr black hole is matched by the same counterclockwise rotation of an object thrown way from the black hole is such a way that it comes to rest at infinity. This counterclockwise spiral for both infalling and outgoing objects means that when an object falls onto a Kerr black hole, we see it spiral inward, because the light that escapes from the object back to us spirals outward with the same handedness.

Orbits around Kerr black holes are generally complex. As with the Schwarzschild black hole, an orbit around a Kerr black hole is not closed. Unlike an orbit around the Schwarzschild black hole, a Kerr black hole orbit is not generally confined to a plane. The only orbits confined to a plane are those on the equatorial plane. Orbits out of the equatorial plane move in three dimensions. These orbits are confined to a volume that is limited by a maximum and minimum radius and by a maximum angle away from the equatorial plane.

Circular orbits exist around Kerr black holes, but they are confined to the equatorial plane. These orbits are very different from the circular orbits around a Schwarzschild black hole, because, while there are an infinite number of circular orbits around a Schwarzschild black hole of a given radius, all with the same orbital period, there are only two circular orbits of a given radius around a Kerr black hole, one clockwise and the other counterclockwise around the black hole's axis of rotation, with the period of the counterclockwise orbit shorter than that of the clockwise orbit.

One consequence of the split in clockwise and counterclockwise orbital periods is that the radii of the last stable orbit is different for the clockwise and counterclockwise orbits. As with the Schwarzschild black holes, the last stable orbits for a Kerr black hole are the circular orbits closest to the event horizon. Objects in orbit inside of the last stable orbit fall onto the event horizon. The last stable counterclockwise orbit is closer to the event horizon than the last stable clockwise orbit.

As with the Schwarzschild black hole, the Kerr black hole is the vacuum gravitational field far from a spinning body. This means that the frame dragging that is so striking close to the black hole should also appear around any body that rotates, such as Earth. The effect can in principle be seen with a gyroscope, because the frame dragging causes the orientation of a gyroscope to change. As with measurements of the deflection of light passing the Sun, measurements of frame dragging around the Earth or Sun only test general relativity in the limit of weak gravitational fields. The effect, however, is so small that it is extremely difficult to measure. So far no instrument has measured the effect. A NASA satellite called Gravity Probe B, which is designed to measure the effect, just completed gathering data in the first quarter of 2006 after more than 17 months in space. Project scientists expect to know if they have successfully measured the frame dragging caused by Earth's rotation in a year's time.

There are at least two different ways to describe how big something is. We can say how much mass it has, or we can say how much space it takes up. Let's talk first about the masses of black holes.

There is no limit in principle to how much or how little mass a black hole can have. Any amount of mass at all can in principle be made to form a black hole if you compress it to a high enough density. We suspect that most of the black holes that are actually out there were produced in the deaths of massive stars, and so we expect those black holes to weigh about as much as a massive star. A typical mass for such a stellar black hole would be about 10 times the mass of the Sun, or about 10^31 kilograms. Astronomers also suspect that many galaxies harbor extremely massive black holes at their centers. These are thought to weigh about a million times as much as the Sun, or 10^36 kilograms.

The more massive a black hole is, the more space it takes up. In fact, the Schwarzschild radius (which means the radius of the horizon) and the mass are directly proportional to one another: if one black hole weighs ten times as much as another, its radius is ten times as large. A black hole with a mass equal to that of the Sun would have a radius of 3 kilometers. So a typical 10-solar-mass black hole would have a radius of 30 kilometers, and a million-solar-mass black hole at the center of a galaxy would have a radius of 3 million kilometers. Three million kilometers may sound like a lot, but it's actually not so big by astronomical standards. The Sun, for example, has a radius of about 700,000 kilometers, and so that supermassive black hole has a radius only about four times bigger than the Sun.

Yes. You can't see a black hole directly, of course, since light can't get past the horizon. That means that we have to rely on indirect evidence that black holes exist.

Suppose you have found a region of space where you think there might be a black hole. How can you check whether there is one or not? The first thing you'd like to do is measure how much mass there is in that region. If you've found a large mass concentrated in a small volume, and if the mass is dark, then it's a good guess that there's a black hole there. There are two kinds of systems in which astronomers have found such compact, massive, dark objects: the centers of galaxies (including perhaps our own Milky Way Galaxy), and X-ray-emitting binary systems in our own Galaxy.

According to a recent review by Kormendy and Richstone (to appear in the 1995 edition of "Annual Reviews of Astronomy and Astrophysics"), eight galaxies have been observed to contain such massive dark objects in their centers. The masses of the cores of these galaxies range from one million to several billion times the mass of the Sun. The mass is measured by observing the speed with which stars and gas orbit around the center of the galaxy: the faster the orbital speeds, the stronger the gravitational force required to hold the stars and gas in their orbits. (This is the most common way to measure masses in astronomy. For example, we measure the mass of the Sun by observing how fast the planets orbit it, and we measure the amount of dark matter in galaxies by measuring how fast things orbit at the edge of the galaxy.)

These massive dark objects in galactic centers are thought to be black holes for at least two reasons. First, it is hard to think of anything else they could be: they are too dense and dark to be stars or clusters of stars. Second, the only promising theory to explain the enigmatic objects known as quasars and active galaxies postulates that such galaxies have supermassive black holes at their cores. If this theory is correct, then a large fraction of galaxies -- all the ones that are now or used to be active galaxies -- must have supermassive black holes at the center. Taken together, these arguments strongly suggest that the cores of these galaxies contain black holes, but they do not constitute absolute proof.

Two very recent discoveries has been made that strongly support the hypothesis that these systems do indeed contain black holes. First, a nearby active galaxy was found to have a "water maser" system (a very powerful source of microwave radiation) near its nucleus. Using the technique of very-long-baseline interferometry, a group of researchers was able to map the velocity distribution of the gas with very fine resolution. In fact, they were able to measure the velocity within less than half a light-year of the center of the galaxy. From this measurement they can conclude that the massive object at the center of this galaxy is less than half a light-year in radius. It is hard to imagine anything other than a black hole that could have so much mass concentrated in such a small volume.

A second discovery provides even more compelling evidence. X-ray astronomers have detected a spectral line from one galactic nucleus that indicates the presence of atoms near the nucleus that are moving extremely fast (about 1/3 the speed of light). Furthermore, the radiation from these atoms has been redshifted in just the manner one would expect for radiation coming from near the horizon of a black hole. These observations would be very difficult to explain in any other way besides a black hole, and if they are verified, then the hypothesis that some galaxies contain supermassive black holes at their centers would be fairly secure.

A completely different class of black-hole candidates may be found in our own Galaxy. These are much lighter, stellar-mass black holes, which are thought to form when a massive star ends its life in a supernova explosion. If such a stellar black hole were to be off somewhere by itself, we wouldn't have much hope of finding it. However, many stars come in binary systems -- pairs of stars in orbit around each other. If one of the stars in such a binary system becomes a black hole, we might be able to detect it. In particular, in some binary systems containing a compact object such as a black hole, matter is sucked off of the other object and forms an "accretion disk" of stuff swirling into the black hole. The matter in the accretion disk gets very hot as it falls closer and closer to the black hole, and it emits copious amounts of radiation, mostly in the X-ray part of the spectrum. Many such "X-ray binary systems" are known, and some of them are thought to be likely black-hole candidates.

Suppose you've found an X-ray binary system. How can you tell whether the unseen compact object is a black hole? Well, one thing you'd certainly like to do is to estimate its mass. By measuring the orbital speed of visible star (together with a few other things), you can figure out the mass of the invisible companion. (The technique is quite similar to the one we described above for supermassive black holes in galactic centers: the faster the star is moving, the stronger the gravitational force required to keep it in place, and so the more massive the invisible companion.) If the mass of the compact object is found to be very large very large, then there is no kind of object we know about that it could be other than a black hole. (An ordinary star of that mass would be visible. A stellar remnant such as a neutron star would be unable to support itself against gravity, and would collapse to a black hole.) The combination of such mass estimates and detailed studies of the radiation from the accretion disk can supply powerful circumstantial evidence that the object in question is indeed a black hole.

Many of these "X-ray binary" systems are known, and in some cases the evidence in support of the black-hole hypothesis is quite strong. In a review article in the 1992 issue of Annual Reviews of Astronomy and Astrophysics, Anne Cowley summarized the situation by saying that there were three such systems known (two in our galaxy and one in the nearby Large Megallanic Cloud) for which very strong evidence exists that the mass of the invisible object is too large to be anything but a black hole. There are many more such objects that are thought to be likely black holes on the basis of slightly less evidence. Furthermore, this field of research has been very active since 1992, and the number of strong candidates by now is larger than three.

Back in the 1970's, Stephen Hawking came up with theoretical arguments showing that black holes are not really entirely black: due to quantum-mechanical effects, they emit radiation. The energy that produces the radiation comes from the mass of the black hole. Consequently, the black hole gradually shrinks. It turns out that the rate of radiation increases as the mass decreases, so the black hole continues to radiate more and more intensely and to shrink more and more rapidly until it presumably vanishes entirely.

Actually, nobody is really sure what happens at the last stages of black hole evaporation: some researchers think that a tiny, stable remnant is left behind. Our current theories simply aren't good enough to let us tell for sure one way or the other. As long as I'm disclaiming, let me add that the entire subject of black hole evaporation is extremely speculative. It involves figuring out how to perform quantum-mechanical (or rather quantum-field-theoretic) calculations in curved space-time, which is a very difficult task, and which gives results that are essentially impossible to test with experiments. Physicists *think* that we have the correct theories to make predictions about black hole evaporation, but without experimental tests it's impossible to be sure.

Now why do black holes evaporate? Here's one way to look at it, which is only moderately inaccurate. (I don't think it's possible to do much better than this, unless you want to spend a few years learning about quantum field theory in curved space.) One of the consequences of the uncertainty principle of quantum mechanics is that it's possible for the law of energy conservation to be violated, but only for very short durations. The Universe is able to produce mass and energy out of nowhere, but only if that mass and energy disappear again very quickly. One particular way in which this strange phenomenon manifests itself goes by the name of vacuum fluctuations. Pairs consisting of a particle and antiparticle can appear out of nowhere, exist for a very short time, and then annihilate each other. Energy conservation is violated when the particles are created, but all of that energy is restored when they annihilate again. As weird as all of this sounds, we have actually confirmed experimentally that these vacuum fluctuations are real.

Now, suppose one of these vacuum fluctuations happens near the horizon of a black hole. It may happen that one of the two particles falls across the horizon, while the other one escapes. The one that escapes carries energy away from the black hole and may be detected by some observer far away. To that observer, it will look like the black hole has just emitted a particle. This process happens repeatedly, and the observer sees a continuous stream of radiation from the black hole.

Remember what we said before: Penelope is the victim of an optical illusion. The light that you emit when you're very near the horizon (but still on the outside) takes a very long time to climb out and reach her. If the black hole lasts forever, then the light may take arbitrarily long to get out, and that's why she doesn't see you cross the horizon for a very long (even an infinite) time. But once the black hole has evaporated, there's nothing to stop the light that carries the news that you're about to cross the horizon from reaching her. In fact, it reaches her at the same moment as that last burst of Hawking radiation. Of course, none of that will matter to you: you've long since crossed the horizon and been crushed at the singularity. Sorry about that, but you should have thought about it before you jumped in.

A black hole by itself is invisible, detectable only through its mild effect on passing starlight, but place it where it can pull massive amounts of gas onto itself, and the black hole lights up as brilliantly as any object in the galaxy at all wavelength, extending from the radio into the gamma-ray. Nature provides a black hole with just this environment when the black hole is a member of a compact binary star system. When a black hole is in close orbit with a fusion-powered star, so that the center of gravity of the system lies within the atmosphere of the star, gas flows from the star onto the black hole, forming a hot disk orbiting and lighting up the black hole. We believe we are seeing this process in the x-ray binary star systems.

X-ray binary stars are among the most brilliant objects in the x-ray sky. They can release up to 1038 ergs s-1 of power, which is 5,000 times the power output of the Sun. They are visible across the galaxy, because x-rays can penetrate the clouds of gas and dust in the galactic plane, and some are visible in nearby galaxies such as the Megallanic clouds. They are highly variable, with low-luminosity states that generate a tenth of a percent of the power generated in the high-luminosity state. Many of these systems are composed of a neutron star in orbit with a fusion-powered star, but a handful of systems appear to be a black hole in orbit with a fusion-powered star. It has been estimated that the Galaxy contains about 108 black holes, but only several hundred to several thousand are currently in x-ray binary systems.

The best evidence for the presence of a black-hole candidate in some of these systems is the mass measure for the compact object in the system. This is not a simple undertaking, because the system cannot be resolved in a telescope. Under the best circumstances, the surface of a giant star can be resolved through interferometry; smaller stars remain points of light in the best optical telescopes. With a compact binary system, we have two objects separated by the diameter of a star, with a distance of at least a kiloparsec, and more often tens or hundreds of kiloparsecs. Such systems cannot be resolved, so our only information about the orbit of a compact binary system comes from measuring the Doppler shift of light from each object.

The problem is that the Doppler shift does not contain enough information to precisely derive a mass for each object in a close binary. We can derive a period for the system, and we can derive the velocity along the line of sight for each object in the system, but we cannot derive a velocity perpendicular to our line of sight. For instance, if we were looking along a system's rotation axis, we would see no Doppler shift, but if were looking perpendicular to the rotation axis, we would see maximum and minimum Doppler shifts equal to the absolute velocity of each object in the system. At any other angle, the maximum velocity we measure would be less than the absolute velocity. The effect is that we cannot derive a mass, but we can derive a minimum value for the mass. Because we believe a compact object larger than about 3 solar masses must be a black hole, this spectroscopic measure of mass is sufficient for showing that an x-ray binary cannot contain a neutron star.

Some x-ray binary systems show eclipses of the accretion disk by the fusion-powered star. This effect enables us to refine estimates of a compact object's mass by giving us an estimate of the angle between our line of sight and the rotation axis of the system.

From spectroscopic measurements of mass, we know of several systems that contain black-hole candidates. Two sources in the Small Megallanic Cloud, SMC X-1 and SMC X-3, contain black-hole candidates with masses of about 6 solar masses for the former and greater than 7 solar masses for the latter. Within our own galaxy, the binary Cygnus X-1, which is about 2.5 kiloparsecs away, had a mass greater than 7 solar masses, with a most likely value of 16 solar masses. Two other Galactic binaries with the position-based names of 0620-003, and 2023+338 have masses greater than 7 and 8 solar masses. Under current theory, the compact object in each of these systems should be a black hole.

The interesting question, however, is can we prove that the large, compact objects in these systems are in fact black holes? Does the light emitted by these systems contain unambiguous signatures of general relativity?

The hurdle confronting astronomers who want to answer these questions is the similarity between neutron stars and black holes. A neutron star is not much larger than the last stable orbit of a black hole of the same mass, so the amount of energy released by an accretion disk around a neutron star is not dramatically different from that release by an accretion disk around a black hole of the same mass. The only difference in the accretion disk between the two types of compact object is that the inner edge of the disk around a neutron star interacts with the surface of the neutron star, while the inner edge of the disk around a black hole goes into free-fall to the event horizon.

Under this circumstance, the evidence is largely negative; one can observe the effects of a surface, but not of a last stable orbit. The strongest signature of a surface is a thermonuclear explosion of hydrogen and helium. Such events have been seen in many x-ray binaries containing neutron stars. Hydrogen and helium from the accretion disk flows onto the surface of the neutron star. If the gas flows at a high rate, the atmosphere of the neutron star will be hot enough to sustain continuous thermonuclear fusion of hydrogen and helium to heavier elements, but if the gas flow is at a low rate, hydrogen and helium build up in the atmosphere until a thermonuclear detonation occurs. This sudden outburst is easily identified as a thermonuclear event, and its observation is clear evidence that the compact object has a surface. If one of our large black-hole candidates would exhibit a thermonuclear flash, we would have evidence of a compact object larger than 3 solar masses that is not a black hole. So far, no such event has been seen.

Other signatures are more ambiguous. Both the energy liberated through steady thermonuclear fusion and the energy liberated as the gas from the accretion disk mixes with the atmosphere of a neutron star are converted to thermal radiation deep in the atmosphere. This radiation should escape the star as black-body radiation, which should be apparent in the spectrum of these systems. Many, although not all, x-ray binaries with neutron stars do show such emission, and none of the binaries with black-hole candidates show such thermal emission. Again, this provides an absence of evidence for a surface, which does not necessarily mean that no surface is present.

The x-ray binary provides us with the best opportunity to find black-hole candidates. Whether we can prove that these candidates are in fact black holes is yet to be seen. Certainly if one of our candidates suddenly produces thermonuclear bursts, we will have evidence against some piece of our physics that says black holes are larger than 3 solar masses. To this point, however, these systems tell us more about the physics of accretion disks and the evolution of stars in compact binaries than it does about black holes and general relativity.

If you look at the constellation Sagittarius, you would see running through it a part of the Milky Way. To our eye this region appears similar to the other parts of the Milky Way, consisting of a broad band of diffuse starlight that is bisected by an empty region that is simply the darkness of a dust lane between us and the more distant stars. Nothing about this region is particularly striking. If you looked at this region with a radio or infrared telescope, however, you would see beyond the shroud of dust, 7.6 kpc away, something very remarkable: gas and stars orbiting a massive black hole at the center of our Galaxy.

With radio telescopes we can map to very high precision the gas at the center of the galaxy. With infrared telescopes we can detect the motions of the bright stars at the galactic center. What we see with these telescopes is a region that is dense in stars and gas. The gas lies in a disk, and filaments of magnetic field flow perpendicularly away from the disk. The stars in this region move with velocities of from several hundred to a thousand km s-1, all much faster than the 208 km s-1 motion of the local stars around the Galaxy. The stars are concentrated in a region, dubbed the Sagittarius A (Sgr A) complex; the stars at the center of this complex moving more rapidly than the stars farther out. At the very center of the Sgr A complex, at a right ascension of17h 45m 40s and a declination of−29° 00′ 28″in year 2000 coordinates, is a radio source called Sagittarius A*.

Sgr A* is big. We know this from the motion of Sgr A*and from the motion of stars around Sgr A*. Observers are able to measure the proper motion, which is the motion perpendicular to the line of sight relative to the most distant galaxies, for both Sgr A* and for the stars. This is done by measuring the precise positions of these objects over several years. The proper motion of Sgr A* tells us that the object is much larger than any star that sit at the center of the Galaxy, and the proper motions of the stars combined with the radial motions derived from the Doppler shift of spectral lines tell us very precisely the mass of Sgr A*.

The proper motion of Sgr A* is caused by the Sun's motion around the Galaxy. Take this motion out, and one finds that Sgr A*is motionless at the center of the Sgr A complex. The stars in this region, on the other hand, move with velocities of 100 to 1,000 km s-1. This suggests Sgr A* is much more massive than any nearby star, because the interactions between the stars and Sgr A* should bring them into a kinetic equilibrium, so that the kinetic energy carried by Sgr A* is near the average kinetic energy carried by each star. Under this circumstance, the only way Sgr A* can have as much energy as a star while having a much lower velocity is for Sgr A*to be much more massive that the average star in the region. The lower limit on the mass of Sgr A* derived following this line of reasoning is 4×105 solar masses.

But we can do better. Our lower limit simply makes plausible the idea that the stars in the Sgr A complex are orbiting Sgr A*. Once this assumption is made, we can derive the mass of Sgr A* from the velocities of the stars. The stars within 1 pc of Sgr A* move as though they are in Keplerian orbits around a point mass. By relating the velocity of the stars around Sgr A* to their distance from this object, astronomers derive a mass for Sgr A* of 3.6 million solar masses. This mass is confined to a radius that is less than 0.015 pc (3,000AU). For this mass and distance, a star can complete an orbit in less than 100 years. Already observations show that the orbital paths of the stars curve towards Sgr A*. The most plausible interpretation of these orbits is that the stars are orbiting a massive black hole candidate, and that candidate is the radio source Sgr A*. Gas flowing onto Sgr A* is in fact the reason we see radio and x-ray emission this object. As gas from the Sgr A complex flows down onto Sgr A*, gravitational potential energy is converted into electromagnetic. The amount of energy released is small by astronomical standards: only about 1034 ergs s-1in the x-ray band, which corresponds to twice the Sun's luminosity and about 100 times this amount at radio wavelengths. Sgr A* is therefore no brighter than a star of several solar masses. A black hole can accomplish this amount of energy release by consuming only 10-10 solar masses of gas a year, a tiny amount considering that this corresponds to consuming only one star in the age of the universe. Presumably in the distant past, Sagittarius A* consumed gas at a much higher rate to grow to its current size, perhaps at a rate that made this object as bright as the distant quasars that we see today.

The interesting gravitational effects associated with black holes of several solar masses occur within an area on the sky that is too small to see with modern instruments, but when a black hole's mass is pumped up to millions of solar masses, we have a fighting chance to see some of these effects. For instance, the black disk on the sky defined by the last stable orbit around a 3.6 million solar mass black hole at 7.6 kpc has a projected radius on the sky of about 46 micro-arc-seconds, which translates to an apparent radius of 0.35 AU. This size is just below the resolution that can be achieved in radio astronomy through a method called very long baseline interferometry (VLBI); by combines radio observations of a source from telescopes on opposite sides of the Earth, astronomers can create high-resolution maps of the sky. If the dark disk can be observed through VLBI, we would have a direct test of General Relativity, since that theory gives a direct relationship between the disk's radius and the mass of the black hole. As it stands, radio astronomy can only state that Sgr A* is less than 130 micro-arc-seconds on the sky. We might also see the reflection of the sky into the region inside the Einstein ring for Sgr A*, which is 2.0 arc seconds in radius on the sky. So far these effects have not been seen, and whether or not we ever see them presuppose that the gas flow onto the black hole does not spoil the effects.

Many distant galaxies have extremely bright centers. These Active Galactic Nuclei (AGN) can outshine their host galaxies. Some bright AGNs are so distant that the host galaxy is invisible, and only the bright, star-like nucleus is seen; such objects are call quasars, which is derived from the term “quasi-stellar object.” Less brilliant and closer AGNs appear as galaxies with unusually bright nuclei; these galaxies are called Seyfert galaxies. Some galaxies with active nuclei shoot out jets of matter moving at close to the speed of light. These jets, which can extends tens of kiloparsecs from their origin, are seen by their radio emission. We are apparently looking directly into the jet of some of these galaxies; these AGNs, called blazars, and they vary violently and rapidly in brightness.

Despite this wide variety of appearance, the dominant theory is that all of these objects are a manifestations of a single object: a massive black hole at the center of a galaxy. This theory preceded the evidence that our own Galaxy harbors a massive black hole candidate in the Sagitarii A complex. In fact, the black hole theory for AGNs prompted the suggestion that our own galaxy harbors a massive black hole long before evidence for it appeared. The postulate that a black hole is the engine of a AGN is motivated by the rapidly changes in brightness of these objects: an AGN can change its power output in less than a day, which suggests that the source of the power is less than 200AU across.

The basic AGN theory is that a massive black hole sitting at the center of a galaxy pulls gas onto itself, releasing gravitational potential energy that is either radiated away as light or converted into the kinetic energy of a jet. The light comes from a large accretion disk orbiting the black hole. This disk of gas orbiting the black hole slowly converts its gravitational potential energy into thermal energy, causing the gas to slowly drop into lower orbits, until eventually it falls inside the last stable orbit and onto the black hole. The energy released is radiated away from the disk's photosphere with electromagnetic frequencies spanning from the visible to the gamma-ray. The outer regions of the accretion disk generate optical and ultraviolet radiation, while the inner regions generate x-rays and gamma-rays. Some of this radiation drives a wind from the disk's photosphere, providing the mass for the jet. The jet itself may acquire energy directly from the radiation from the disk, or from magnetic fields generated and expelled by the accretion disk. Around this system orbits clouds of gas. This gas is absorbs and reradiates light from the accretion disk. These clouds produce strong emission lines at optical and ultraviolet frequencies.

The accretion disk of a bright AGN can radiate 100 trillion times the power of the Sun. Only 107 solar masses of gas per year need pass through the accretion disk onto the black hole to create this amount of energy.

How massive is the black hole driving all of this? It can be from one million to one billion times the mass of the Sun. A rough estimated of the mass can be derived from the fact that many AGNs drive a wind away from the black hole. If this wind is driven by radiation, then the force of the radiation, which is proportional to the energy released by the AGN, is larger than the force of gravity, which is proportional to the mass of the black hole. Setting these forces in equilibrium gives us an estimate of the mass of the black hole candidate. For an AGN radiating 100 trillion times the power of the Sun, the mass estimate is one billion solar masses.

A better measure of the mass of the black hole candidate is derived by combining measurements of variability of the radiation with measurements of the width of spectral lines. The idea is simple enough: if we can measure both the velocity and the distance of something orbiting the black hole, we can directly derive the mass of the black hole. With Sagittarii A*of our own Galaxy, the stars of the Sagittarii A complex are the orbiting objects. With AGNs, the orbiting objects are the clouds that create the line radiation.

A velocity for the clouds is found by measuring the shape of the emission lines from an AGN. The motion of the clouds Doppler shifts the radiation, with clouds moving towards us creating blue-shifted lines, and clouds moving away creating red-shifted lines. Seen together, all of these Doppler-shifted lines blend together to create a single broad line. The width of the line therefore gives a measure of velocity. The measure of distance comes from a characteristic of our theory. The light emitted by the accretion disk smoothly spans a broad range of frequencies. For this reason, this light is called continuum radiation. In the theory, this light is responsible for heating the orbiting clouds. If the accretion disk becomes brighter, the clouds should become hotter, and the line radiation they produce should become brighter. But because the clouds are far from the accretion disk, there is a time delay between the brightening of the accretion disk and the brightening of the line radiation. This delay is observed, and it gives us a measure of the distance from the black hole to the clouds.

Astronomers have been able to use this method to derive masses for several black holes candidates. For instance, the galaxy NGC 4151 is found to contain a black hole candidates of 10 million solar masses. The galaxy NGC 5548 is found to contain a black hole candidate of between 20 and 80 million solar masses. These are typical of the masses being derived. The black hole candidates in AGNs have so far been larger than our own Galaxy's Sgr A*, with its mass of 2.6 million solar masses.

The black hole in the AGN theory is the engine that lights the accretion disk and drives the relativistic jets, but otherwise it is invisible to us. None of the unusual effects of a black hole are necessary to produce what we see. The theory does not depend on general relativity being the correct theory of gravity. The theory only depends on the existence of a compact object of millions to billions of solar masses. This means that the most brilliant and common manifestation of the black hole tells us nothing about black holes, and everything about how energy is released by massive amounts of gas falling into a deep gravitational potential.

Supermassive Black Holes Preceed Galaxy Growth

Astronomers may have solved a cosmic chicken-and-egg problem: the question of which formed first in the early universe, galaxies or the supermassive black holes seen at their cores.

"It looks like the black holes came first. The evidence is piling up," said Chris Carilli of the National Radio Astronomy Observatory (NRAO). Carilli outlined the conclusions from recent research done by an international team studying conditions in the first billion years of the universe's history in a lecture presented during the American Astronomical Society's 2009 meeting in Long Beach, California.

Earlier studies of galaxies and their central black holes in the nearby universe revealed an intriguing linkage between the masses of the black holes and of the central "bulges" of stars and gas in the galaxies. The ratio of the black hole and the bulge mass is nearly the same for a wide range of galactic sizes and ages. For central black holes from a few million to many billions of times the mass of our Sun, the black hole's mass is about 1 one-thousandth of the mass of the surrounding galactic bulge.

"This constant ratio indicates that the black hole and the bulge affect each others' growth in some sort of interactive relationship," said Dominik Riechers of Caltech. "The big question has been whether one grows before the other or if they grow together, maintaining their mass ratio throughout the entire process."

In the past few years, scientists have used the National Science Foundation's Very Large Array radio telescope and the Plateau de Bure Interferometer in France to peer far back in the 13.7-billion-year history of the universe, to the dawn of the first galaxies.

"We finally have been able to measure black-hole and bulge masses in several galaxies seen as they were in the first billion years after the Big Bang, and the evidence suggests that the constant ratio seen nearby may not hold in the early universe. The black holes in these young galaxies are much more massive compared to the bulges than those seen in the nearby universe," said Fabian Walter of the Max-Planck-Institute for Radioastronomy (MPIfR) in Germany.

"The implication is that the black holes started growing first."

The next challenge is to figure out how the black hole and the bulge affect each other's growth. "We don't know what mechanism is at work here, and why, at some point in the process, the 'standard' ratio between the masses is established," Riechers said.

New telescopes now under construction will be key tools for unraveling this mystery, Carilli explained. "The Expanded Very Large Array (EVLA) and the Atacama Large Millimeter/submillimeter Array (ALMA) will give us dramatic improvements in sensitivity and the resolving power to image the gas in these galaxies on the small scales required to make detailed studies of their dynamics," he said.

"To understand how the universe got to be the way it is today, we must understand how the first stars and galaxies were formed when the universe was young," Carilli said. "With the new observatories we'll have in the next few years, we'll have the opportunity to learn important details from the era when the universe was only a toddler compared to today's adult."

Strange, Explosive Supernova is the Missing Link in Gamma-Ray Burst Connection

"A new finding reveal a strange supernova is actually the missing link between supernova explosions that generate gamma-ray bursts (GRBs) and those that don’t.

"Sayan Chakraborti in a news release said, “This is a striking result that provides a key insight about the mechanism underlying these explosions,” “This object fills in a gap between GRBs and other supernovae of this type, showing us that wide range of activity is possible in such blasts.”

"The researchers spotted the supernova for the first time in 2012. The supernova is what is known as a core-collapse supernova. This type of blast occurs when the nuclear fusion reactions at the core of a very massive star can no longer provide the energy needed to hold up the core against the weight of the outer parts of the star. The core then collapses in a super­-dense neutron star or a black hole, while the rest of the star’s material is blasted into space.

"The most common type of these supernova produce no burst of gamma rays. In a very small percentage of cases, though, the in falling material is drawn into a short-lived swirling disk surrounding the new neutron star or black hole. This disk generates jets of material that move outward from the disk’s poles, and produce gamma-ray bursts.

"In this case, though, researchers have found that not all “engine-driven” supernova explosions produce gamma-ray bursts.

"Chakrabortiin a news release said what we see is that there is a wide diversity in the engines in this type of supernova explosion,” “Those with strong engines and lighter particles produce gamma-ray bursts, and those with weaker engines and heavier particles don’t.”

"The discovery reveals that the nature of the engine plays a major role in determinng what type of supernova explosion will occur. This, in turn, reveals why some supernovae produce gamma-ray bursts and others don’t.


Images of SN 2012ap and its host galaxy, NGC 1729.