Chapter 16: The Expanding Universe

This artist's concept illustrates a supermassive black hole with millions to billions times the mass of our sun.

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 supermassive 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 supermassive black holes in nearby galaxies are relatively common, and in fact, it is believed that all but perhaps the smallest of galaxies possess central supermassive black holes.

Andrea Ghez Astrophysicist

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

The Core of Galaxy M87

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 supermassive 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 is 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.

A simulated Black Hole of ten solar masses as seen from a distance of 600km with the Milky Way in the background (horizontal camera opening angle: 90°)

The physics of these supermassive 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 Schwarzschild radius, R_S = 2GM/c² (For the Sun, the Schwarzschild 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, with optical telescopes, we are restricted to looking on scales that are thousands of times the Schwarzschild radius. Recently, the Event Horizon Telescope has used its extraordinary angular resolution at radio wavelengths to make images of the black holes in the Milky Way's galactic center and in the center of M 87. However, it will only be able to do this for a handful of massive black holes. Our evidence for most supermassive black holes is indirect. We must infer the existence of a compact object from its effect on the stars and gas that surround it.

Simulated view of a black hole in front of the Large Magellanic Cloud. The ratio between the black hole Schwarzschild radius and the observer distance to it is 1:9. Of note is the gravitational lensing effect known as an Einstein ring, which produces a set of two fairly bright and large but highly distorted images of the Cloud as compared to its actual angular size.

It seems extraordinary to hypothesize supermassive 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 is squashed into a region 3 km in radius, the density is a phenomenal 10¹⁹km/m³. Density is proportional to mass over radius cubed, r ∝ M/R³, and we have seen that the Schwarzschild 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, supermassive 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 10¹⁹ kg/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! Supermassive black holes are a hundred times less dense than water! Admittedly, this assumes that the mass is evenly distributed within the Schwarzschild radius and we have no reason to believe this is true. Nonetheless, the properties of black holes are counter-intuitive and fascinating to think about.