Black holes are thought not to be observable directly, since any light that might be shone upon them would not be reflected, but swallowed up inside the black hole's event horizon (the imaginary surface around the black hole inside of which gravity is so strong that light cannot escape). A black hole is thought to be completely describable by three numbers: (1) mass, (2) charge and (3) rotation rate. Of these, the one most likely to offer the possibility of observation at a distance is mass, because it is associated with gravity. If the black hole is a member of a binary star system and the other star is "normal" (i.e. we can see it), then we should see the normal star move in orbit around the black hole. The speed of the normal star in its orbit is determined by the mass of its companion (the suspected black hole). The more massive the companion, the faster the orbit. We also know from theoretical calculations that a non-luminous body greater than a certain mass cannot support itself against its own gravity, and must collapse to a black hole. ==>> Certain stars have been observed to orbit unseen companions, and the orbital speed suggests that the mass of the unseen companions could exceed the lower limit for a black hole. ==>> Also, stars near the centers of certain galaxies have orbits suggesting that they revolve around a very large mass, but the brightness of the galaxy center is not as great as would be expected from a collection of stars with such a mass. The inference is that these systems include a black hole. +++>>>
Here's a similar problem: Suppose I show you a length of garden hose with a string coming out of one end. On the end of the string is a small weight, and I tell you that the other end of the string is tied to a piece of lead. The piece of lead inside the hose is hidden from view. I show you that if I hold the hose vertically, and move the string up and down, it remains taught, indicating that the
concealed piece of lead is not caught in the hose. I then hold the upper end of the vertical hose, pinch the string with the same hand, and move it in a circle horizontally, causing the visible weight to spin around. I spin the visible weight at just the right speed to balance the concealed lead weight, and release the string, showing you that the centripetal force of the visible weight just balances the weight of the concealed lead. You measure the speed of the rotation. I stop spinning it, and you measure the mass of the visible weight. From your measurements you are able to calculate the mass of the concealed lead. However, a lead sphere of that mass would have a diameter greater than the inside diameter of the hose. What shape is the concealed lead? [If you try this, make sure that you're in a place where the visible weight can't hit
someone or some thing if the string breaks!! Actually it might be fun for your students to stand at a distance on the playground and use binoculars to watch one of them (the star) do this while they measure the number of orbits over a given time.] <<<+++

Let's say you are observing what seems to be a binary star system through a telescope.Perhaps you see only one star but it seems to be orbiting around something else that you can't see. What could it be orbiting around? Well, if you observe the star you can see for a long enough time period, you can get a good idea of the orbital motion and get an estimate of the masses of the stars in the binary. You can also look for x-ray radiation that would be emitted if gas from the star you can see is swirling in towards the object you can't see.


If, from your observations, the object is very massive, about three solar masses or larger, and very small, then it is hard to understand how it could be anything but a black hole. There is a limit to how much matter the known forces (electromagnetic and nuclear) can support in very small volumes.


So, you might argue that the evidence is quite indirect and you would be right. This is why the objects that we think might be black holes are actually called "black hole candidates." It's still a bit controversial.

There are basically 2 ways: one is by its gravitational attraction to something else that is orbiting it. We can tell by the radius of the orbit and the period (the time it takes to go once around the black hole) what the mass of the central body is. If we can't see it, and its mass must be greater than a certain size within a certain radius, we know that it must be a black hole because nothing can withstand that much of its own gravity.
The other way is by the accretion disk of hot gas that swirls into a black hole. It emits so much energy, that nothing else could produce that much energy.

Other more exotic ways, which are predicted but have not been actually found yet, are by the types of gravitational waves that black holes which interact with other matter should emit.

There are several different ways that astronomers have "seen" black holes (of course, you can't actually see the black hole, it is black and also very compact) because there are different sizes of black holes.


The first size is the smallest we know about, which have roughly the same mass as our sun or a few times as big. These have been detected in what are called "X-ray binaries." X-ray binaries consist of a black hole (or perhaps a neutron star, which is also very small and dense but not as much as a black hole) and another star orbiting the black hole. Matter falls off the other star and heats up, due to turbulence, as it falls toward the black hole. This hot matter emits the X-rays, which we see.
Astronomers believe a many of these have black holes because the star orbiting the black hole is close in.

Then there are large black holes, anywhere from a million to a billion times the mass of the sun. These usually live at the centers of galaxies.
In fact, UCLA astronomers have found (by looking at the orbits of stars very, very close to the center of the galaxy) that there is something very small and very massive at the center of our own Milky Way galaxy. It is hard to imagine what else it could be except a black hole. These large black holes are also believed to be in other galaxies, and they also emit lots of energy, like X-rays. Essentially, they are like monster versions of the X-ray binaries, eating up lots of matter. These are thought to be the power sources of objects known as quasars, which are very energetic but also generally very far away from our galaxy.


There has also been talk recently of the discovery of "medium" black holes, but I don't know much about those.