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# 16.15 Black Holes in Nearby Galaxies

All evidence points to the existence of a supermassive black hole in the center of the Milky Way Galaxy. In fact, the evidence for the black hole in our galaxy is better than the evidence for any black hole because it's based on dozens of stellar orbits and an excellent model of the central mass distribution. Based on the mediocrity principle, astronomers have assumed we should be able to find  super massive black holes in other galaxies. Astronomers have searched hard for these compact objects and in recent years, they have had great success. Careful study of the nuclei of some nearby galaxies reveals extreme concentrations of matter within the central few parsecs. What's more, the orbital velocities of these objects require a highly dense central object. There is growing evidence that super massive black holes in nearby galaxies are relatively common, and in fact, it is believed that all but perhaps the smallest of galaxies possess central super massive black holes.

The best evidence for large black holes uses spectroscopy to measure the mean velocities of stars near the centers of galaxies. If the motions are too rapid to be accounted for by the stellar populations known to inhabit the nuclear regions, a case can be made for a compact object like a black hole. A steadily increasing number of galaxies have been found to show sharp increases in stellar velocities near their nuclei. Stellar velocities can be used to "weigh" a galaxy within a certain radius. This method is most effective on relatively nearby galaxies where a small central region can be isolated with a spectrograph. The Hubble Space Telescope has been used fo much of this research.

In our own Milky Way galaxy, it is possible to directly image the motions of stars in the inner most parts of the galaxy and measure their orbits. This work was first done by Andrea Ghez and Rein hart Genzel. This technique allows us to directly determine the mass of of our galaxy's central super massive black hole. It is estimated to be a bit more than 4 million solar masses.

Astronomers can identify galaxies for which they can combine measurements of light "cusps" or central concentrations and rapid nuclear motions. The combination provides good evidence for super massive black holes. The velocity dispersion shows how the enclosed mass near the center of a galaxy varies with radius. An image shows how the light varies with radius. The ratio of the two quantities gives the variation in mass-to-light ratio with radius. Certain galaxies show a sharp rise in the mass-to-light ratio within the central parsec. Normal stellar populations have mass-to-light ratios of 2 to 30, so any values higher than this range must indicate a dark mass concentration. This mass in extremely compact, so it is quite different from the dark matter that is distributed over large volumes in the halos of galaxies (although there is dark matter in the centers of galaxies as well as distributed at larger scales). Astronomers have seen evidence of black holes that range in mass from a few million solar masses in our galaxy and in M 32, to a few billion solar masses in M 87, a giant elliptical galaxy in the Virgo cluster.

While we can't directly measure stellar motions in the cores of other galaxies, high-resolution imaging can still add additional evidence for the presence of central super massive black holes. This type of imaging can be done at a level of 0.1 second of arc using the Hubble Space Telescope, or at a level of 0.3 to 0.4 second of arc using ground-based telescopes on excellent sites (and in the infrared with adaptive optics even higher resolutions can be achieved). The Local Group galaxy M 32 has a sharp spike of light within the central parsec. Alongside it is M 31, which also shows a central concentration of light. The density of stars in the center of M 32 is over 100 million times the density of stars in the Sun’s neighborhood. Models of this light distribution indicate a black hole of 3 million solar masses. M 31 is believed to harbor a black hole of 10 million solar masses. However, a central light peak does not point uniquely to a black hole; it might also give evidence of a very dense star cluster.

The physics of these super massive black holes is fundamentally no different than the physics of stellar massive black holes that are produced through the evolution of the largest stars. The radial size of a black hole is given by the Schwarzs child radius, RS = 2GM/c2 (For the Sun, the Schwarzs child radius is 3 km). Therefore a 106 solar mass black hole has a radius of 3 × 106 km and a 109 solar mass black hole has a radius of 3 × 109 km. The diameter of the more massive black hole is therefore 40 A.U., or only 0.0002 pc. Imagine the mass of a billion suns packed into a volume the size of the Solar System! We can use the small angle equation to show how difficult it would be to resolve a supermassive black hole in a nearby galaxy. The smallest angle that can be resolved by the Hubble Space Telescope is about 0.05 arc seconds. At a distance of D = 106 pc, in the Local Group, the size of the smallest feature that can be resolved is d = Da / 206,265 = 106 x 0.05 / 206,265 = 0.2 pc. At the distance of the Virgo cluster, the minimum resolvable feature is 1.5 times larger, or 3 pc. Even for the nearest galaxies, we are restricted to looking on scales that are thousands of times the Schwarzschild radius. Our evidence for super massive black holes is therefore indirect. We must infer the existence of a compact object from its effect on the stars and gas that surround it.

Just as a crime can be solved without actually having a reliable witness, the case for a black hole can be made without directly "seeing" the black hole. Putting all our lines of indirect evidence together, astronomers believe that we can say with certainty that super massive black holes are a standard feature in all but perhaps the smallest galaxies. A survey by John Kormendy and others in Hawaii and Texas finds evidence for black holes in about 25% of nearby galaxies. It also appears that the mass of a super massive black hole depends on the mass of the spherical component of a galaxy. In spiral galaxies, the bulge mass dictates the mass of the black hole. In elliptical galaxies, the entire stellar mass dictates the mass of the black hole. For galaxies of all type, the black hole is massive but still only a small fraction of the overall mass of the galaxy, only 0.1%. Dark forces are at work in the hearts of many galaxies.

It seems extraordinary to hypothesize super massive black holes when the evidence for stellar-mass black holes is strong but not overwhelming. Yet the state of matter in such a compact object is not that unusual. Let us start with a black hole the mass of the Sun. If 2 × 1030 kg are squashed into a region 3 km in radius, the density is a phenomenal 1019km/m3Density is proportional to mass over radius cubed, r ∝ M/R3, and we have seen that the Schwarzs child radius is proportional to mass. Combining these relationships gives the result that the density of a black hole is inversely proportional to the square of the mass, r ∝ M-2. In other words, super massive black holes are far less dense than puny stellar mass black holes. This means that if a one solar mass black hole has a density of 1019kg/m3, then a million solar mass black hole has a density of 1019/(106)2 = 107 kg/m3, and a billion solar mass black hole has a density of 1019/(109)2 = 10 kg/m3. This last number is only ten times the density of the air you are breathing! Super massive black holes are a hundred times less dense than water! Admittedly, this assumes that the mass is evenly distributed within the Schwarts child radius and we have no reason to believe this is true. Nonetheless, the physics of black holes are counter-intuitive and fascinating to think about.