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Huge Black Holes Help

By — McGraw-Hill Professional
Updated on Sep 18, 2011

Black-hole Density Versus Mass

In recent years, the idea that black holes exist at the centers of many, if not most, spiral galaxies has been gaining acceptance. This is so in part because of an interesting twist in the formula for the Schwarzchild radius as a function of mass.

The radius that an object must attain in order to become a black hole is directly proportional to the mass. From elementary solid geometry, you will recall that the volume of an object is proportional to the cube of the radius. If an object’s mass is doubled, the size of its Schwarzchild radius doubles too. However, its volume becomes eight times as great. This means that the more massive a black hole happens to be, the less dense it is. In fact, the density of a black hole is inversely proportional to the square of its mass (Fig. 15-4).

Galaxies and Quasars Quasars Black-hole
Density Versus Mass

Figure 15-4. The density of a black hole is inversely proportional to the square of the mass.

Suppose that before there were any stars in the Universe, but only hydrogen and helium gas, vast clouds congealed because of gravitation? Suppose that this took place on a much bigger scale than the process of star formation? If such a cloud were large enough, it could become a black hole before it attained a density anywhere near enough to start nuclear fusion. The black hole would continue to pull matter in, becoming larger still and yet less dense. As the atoms approached the event horizon, they would be accelerated to nearly the speed of light. This would give them tremendous kinetic energy, and the result would be an object of brilliance greater than that of any nuclear fusion engine of comparable size. If the cloud had any spin to begin with, that spin would be exaggerated as the gas atoms fell into the black hole, in much the same way as the air circulation around a hurricane gets faster and faster as the molecules are drawn into the eye of the storm.

Galactic Centers

In the nuclei of spiral galaxies such as ours, the concentration of stars is highest. This is to say, there are the most stars per cubic light-year in and near the center of a galaxy. In the spiral arms, the concentration of stars is lower. The concentration is lower still in regions above and below the plane of the spiral disk and in between the spiral arms. Our Sun is near the plane of the Milky Way’s disk, in one of the spiral arms, and approximately halfway from the center to the edge.

The appearance of spiral galaxies, some of which bear remarkable resemblance to satellite photographs of hurricanes and typhoons, makes it tempting to think that they spin around and around. They do, and all the stars move in the direction intuitively suggested by the sense of the pinwheel. However, some stars stay near the plane of the disk, whereas others dip below it and rise above it during each orbit around the center (Fig. 15-5). Stars in the central bulge, which resembles a gigantic globular cluster or a small elliptical galaxy having low eccentricity, orbit in planes that are tilted every which way. Near the center of the bulge, the density of stars increases. If our Sun were one of the stars in this region, our nighttime sky would be filled with many more stars than we see now. Moonless, clear nights would be as bright as a gloomy day.

Galaxies and Quasars Quasars Galactic
Centers

Figure 15-5. Structure of a spiral galaxy as seen edgewise.

However, what if the Sun were located at or very near the exact center of the galactic core? Many astronomers think that if that were the case, there would be no life on Earth. The Sun and all the stars in its vicinity would have passed through the event horizon of a black hole and would be “on the inside looking out.” This black hole is thought to contain millions, if not billions, of solar masses. If the black hole is big enough, stars can fall through the event horizon and still remain intact. According to this theory, the centers of some, if not most, spiral and elliptical galaxies are “island universes” of a special sort, for they are closed off from the rest of the Cosmos by a one-way gate in time-space. Every time another star falls in, the mass of the black hole increases, and its density goes down a little more. Given sufficient time, measured in trillions of years, is it possible that these black holes might swallow whole galaxies and then clusters of galaxies?

At this point, we enter the realm of pure speculation. This is a good place to shift our attention to the theory that gave rise to notions of spatial curvature, time warps, and other esoteric aspects of latter-day cosmology.

Practice problems of this concept can be found at: Galaxies and Quasars Practice Problems

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