
We 'see' them by their gravitational effects upon nearby stars which they are often eating or causing to move at very high velocities just before they enter the black hole. A star cluster that 'weighs' 1 billion times the mass of the Sun, but only has 1 few million stars, and has a very small volume producing lots of energy, is a prime candidate for a black hole. Also, a binary star system where the total mass is 20 solar masses but the only visible star has a mass of 2 solar masses means a dark companion with a mass of 18 solar masses. In other words a black hole.
We can see them, as the Hubble Space Telescope does, by the intense core of light they produce in the centers of galaxies. When astronomers study the speed of the gases in the cores of these galaxies, they find that the gases are orbiting faster than is possible if only the identifiable stars are accounting for the mass. We can never see them directly, but we can see what they do to the gas and stars around them. The above image shows a tilted dusty disk at the center of a galaxy. The bright spot is the den of the supermassive black hole.
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