The Care and Feeding of Black Holes

The most plausible explanation for these most implausible objects appears to be, oddly enough, similar to models that exist for binary X-ray stars in our own galaxy. The idea is that matter under the influence of an intense gravitational field loses energy and releases enormous quantities of radiation in the process. Just as water goes over Niagara Falls, losing its potential energy while providing us with power to drive electric generators, so can material fall into a stellar gravitational field and emit light.

Currently, the most popular model is that material near the quasar falls into a black hole. But doesn’t a black hole swallow everything around it? This is a very common misconception, and the answer is no. Only material very close would inevitably be sucked into this type of object. In fact, if the Sun were suddenly to become a black hole, the orbit of the Earth would not change at all.

How much energy is released depends on the strength of the gravitational field, and how much mass is fed into the hole. (The black hole really doesn’t have a surface, but the material continues to yield energy to the outside world until it passes a place known as the Schwarzschild radius, named after the German astronomer who worked out its properties nearly a century ago.

Project 5: How can we get the vast quasar energy from a black hole?

(5.1) We can estimate the energy output by the classical result E_G = GMm/R, where G is the gravitational constant, M is the mass of the black hole, m is the mass of the object “fed” into it, and R is the Schwarzschild radius. Take M to be 10⁹ solar masses, and imagine m to be one solar mass. R (calculated below) turns out to be about 3 x 10¹⁴ cm. Find E_G.

[E_G = 6.7 x 10^-8 x 2 x 10³³ x 10⁹ x 2 x 10³³ / 3 x 10¹⁴ = 10⁵⁴ ergs. If this mass is fed to the black hole over a time of one year (about 3 x 10⁷ sec), the output of the system will be 10⁵⁴/ 3 x 10⁷ ergs/sec or about 3 x 10⁴⁶ ergs/sec, more than enough to power 3C273 as observed!]

(5.2) The Schwarzschild radius is given by R_s = 2GM/c², where G is the

gravitational constant, M is the mass of the black hole, and c is the velocity of light. It represents the position near the black hole where the escape velocity is equal to “c”. Calculate this radius for an object that has the mass of 10⁹ solar masses. [R_s = 2 x 6.7 x 10^-8 x 2 x 10³³ x 10⁹/ 10²¹ = 3 x 10¹⁴ cm. This is about the size of our solar system. So we can get this energy out of a relatively small package, just as we require.]

Thus, our picture becomes this: an intense gravitational field provides the pull that sweeps about one star the size of our Sun each year into its confines. The energy released provides the x-rays, radio waves, and optical light that we see coming from the quasar. The variability is explained by the small size of the object; even though it shines more brightly than hundreds of entire galaxies, it occupies a volume no larger than our solar system. But lest we rest on our laurels, 3C273 had yet one more trick up its sleeve, one that threatened to wreck our entire model….