Determining Masses
in Galactic Centers

One thing that makes us rather certain that massive black holes can exist in the center of active galaxies is that there is strong experimental evidence for enormous amounts of unseen mass in the centers of some galaxies (whether active or not).

The Virial Theorem and Masses

There are some simple ideas concerning gravitational energy in astronomy constituting what is called the Virial Theorem that allow us to estimate the amount of mass contained in a region. The basic idea is that a large concentration of mass (whether we can see it or not) causes a very large gravitational field, and that by observing the velocity of objects in that region we can infer the magnitude of the gravitational field and therefore the mass. If we know the distance to the object, then from simple trigonometry we can determine the spatial extent in which this mass is distributed from its angular diameter.

Example: The Velocities and Masses in the Center of M87

We may illustrate these ideas using the previously considered example of the active galaxy M87. The analysis is outlined in the following figure.

Estimate of the central mass in M87. The best fit to the observed velocities for matter swirling around the central region indicates that more than 3 billion solar masses are contained here within a radius of 3.5 parsecs. See the Source for a detailed discussion.

By using Doppler methods to determine the rotational velocity for matter moving around the central region, we may use basically Kepler's Laws to determine the amount of mass that must be contained there.

The Case for Supermassive Black Holes

In this case, and in other examples, one finds that the centers of galaxies often contain billions of solar masses in very compact regions. Since there is far less luminosity in such regions than would be expected if this mass were in the usual distribution of gas, dust, and stars, a supermassive black hole is considered by most astronomers to be the simplest explanation that fits the observations.

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