At the bottom of this entry, I give the Weekly Pondering 11 assignment, for those of you in ASTR 1/2. Any text that you need to read is on Blackboard or linked to here.

Recent observations have suggested that most galaxies contain supermassive black holes in their centers [3]. A supermassive black hole, as its names suggests, is a really big black hole. They often have masses millions or billions of times that of our Sun. For instance, there is a black hole in the center of the galaxy we inhabit, the Milky Way galaxy, dubbed Sagittarius A*. By studying the orbits of stars in its vicinity [4], astronomers deduce that its mass is around 2.6 million times the mass of the Sun and its radius is around 7.5 million km. These numbers are a bit baffling—and so let’s see if we can understand them more intuitively.

The radius of Sagittarius A* is about 5% of the radius of Earth’s orbit around the Sun. Thus, its 2.6 million solar masses are squeezed into a volume far smaller than the region inside of Earth’s orbit. Its radius is also about 1160 times as large as Earth’s radius—that is, the distance from the center of the Earth to Earth’s surface. This means that about 1160 Earths would have to be placed end-to-end to connect via a straight line one part of the black hole’s surface to the opposite side. This seems to be an impressive number—but, let’s remember that Sagittarius A* has the mass of about 2.6 million Suns, which is about 870 billion Earths. Thus, Sagittarius A* has the equivalent of almost a trillion Earths, squeezed into a volume circumscribed by a radius equal to only about 1000 Earths. This radius is also about 19 times the radius of the Moon’s orbit around Earth. Imagine, for instance, we move the Moon 19 times farther away than it is now. Inside of the Moon’s orbit, we then jam almost 1 trillion Earths.

This analysis is a bit misleading, however, because the “surface” of a black hole is not a physical surface. We are referring here to the boundary between the part of space from which you can escape, and the part from which you cannot escape. This region is not a physical surface, and is not labeled with a sign post. You wouldn’t know when you crossed this boundary, but, once you crossed it, you will never leave. Where, then, is the matter of the black hole?

The short answer is that we don’t know. According to Einstein’s theory of gravity (also called the general theory of relativity), all of the mass would be forced into a single point of infinite density at the center of the black hole. When we get infinities in physics and astronomy, however, we start to think we’re doing something wrong—and it is partially for this reason that few physicists take this conclusion seriously. We also know that when we try to combine general relativity with the physics of tiny particles (called quantum mechanics, which generally describes physics on small scales), we get nonsensical results. Thus, we likely need an updated theory of gravity, and perhaps quantum mechanics, before we will be able to understand what is happening in the center of a black hole.

Watch the two linked videos. In a paragraph or two, try to come up with and explain at least two questions you have about black holes. We will discuss these questions during the WP this week.

Bibliography

1. Schwarzschild, Karl. "Über das gravitationsfeld eines massenpunktes nach der einsteinschentheorie." Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin (1916): 189-196.

2. Bregman, J., et al. "Colors, magnitudes, spectral types and distances for stars in the field of the X-ray source CYG X-1." Lick Observatory Bulletin 24 (1973): 1.

3. Rees, Martin J., and Marta Volonteri. "Massive black holes: formation and evolution." Proceedings of the International Astronomical Union 2.S238 (2006): 51-58.

4. Ghez, A. M., et al. "The first measurement of spectral lines in a short-period star bound to the galaxy’s central black hole: a paradox of youth." The Astrophysical Journal Letters 586.2 (2003): L127.