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General Relativity

The Black Hole at Our Galactic Center

If you look at the constellation Sagittarius, you would see running through it a part of the Milky Way. To our eye this region appears similar to the other parts of the Milky Way, consisting of a broad band of diffuse starlight that is bisected by an empty region that is simply the darkness of a dust lane between us and the more distant stars. Nothing about this region is particularly striking. If you looked at this region with a radio or infrared telescope, however, you would see beyond the shroud of dust, 7.6 kpc away, something very remarkable: gas and stars orbiting a massive black hole at the center of our Galaxy.

With radio telescopes we can map to very high precision the gas at the center of the galaxy. With infrared telescopes we can detect the motions of the bright stars at the galactic center. What we see with these telescopes is a region that is dense in stars and gas. The gas lies in a disk, and filaments of magnetic field flow perpendicularly away from the disk. The stars in this region move with velocities of from several hundred to a thousand km s-1, all much faster than the 208 km s-1 motion of the local stars around the Galaxy. The stars are concentrated in a region, dubbed the Sagittarius A (Sgr A) complex; the stars at the center of this complex moving more rapidly than the stars farther out. At the very center of the Sgr A complex, at a right ascension of 17h 45m 40s and a declination of −29° 00 28 in year 2000 coordinates, is a radio source called Sagittarius A*.[1]

Sgr A* is big. We know this from the motion of Sgr A* and from the motion of stars around Sgr A*. Observers are able to measure the proper motion, which is the motion perpendicular to the line of sight relative to the most distant galaxies, for both Sgr A* and for the stars. This is done by measuring the precise positions of these objects over several years. The proper motion of Sgr A* tells us that the object is much larger than any star that sit at the center of the Galaxy, and the proper motions of the stars combined with the radial motions derived from the Doppler shift of spectral lines tell us very precisely the mass of Sgr A*.

The proper motion of Sgr A* is caused by the Sun's motion around the Galaxy. Take this motion out, and one finds that Sgr A* is motionless at the center of the Sgr A complex. The stars in this region, on the other hand, move with velocities of 100 to 1,000 km s-1. This suggests Sgr A* is much more massive than any nearby star, because the interactions between the stars and Sgr A* should bring them into a kinetic equilibrium, so that the kinetic energy carried by Sgr A* is near the average kinetic energy carried by each star. Under this circumstance, the only way Sgr A* can have as much energy as a star while having a much lower velocity is for Sgr A* to be much more massive that the average star in the region. The lower limit on the mass of Sgr A* derived following this line of reasoning is 4×105 solar masses.[2]

But we can do better. Our lower limit simply makes plausible the idea that the stars in the Sgr A complex are orbiting Sgr A*. Once this assumption is made, we can derive the mass of Sgr A* from the velocities of the stars. The stars within 1 pc of Sgr A* move as though they are in Keplerian orbits around a point mass. By relating the velocity of the stars around Sgr A* to their distance from this object, astronomers derive a mass for Sgr A* of 3.6 million solar masses. This mass is confined to a radius that is less than 0.015 pc (3,000 AU). For this mass and distance, a star can complete an orbit in less than 100 years. Already observations show that the orbital paths of the stars curve towards Sgr A*. The most plausible interpretation of these orbits is that the stars are orbiting a massive black hole candidate, and that candidate is the radio source Sgr A*.

Gas flowing onto Sgr A* is in fact the reason we see radio and x-ray emission this object. As gas from the Sgr A complex flows down onto Sgr A*, gravitational potential energy is converted into electromagnetic. The amount of energy released is small by astronomical standards: only about 1034 ergs s-1 in the x-ray band, which corresponds to twice the Sun's luminosity and about 100 times this amount at radio wavelengths. Sgr A* is therefore no brighter than a star of several solar masses. A black hole can accomplish this amount of energy release by consuming only 10-10 solar masses of gas a year, a tiny amount considering that this corresponds to consuming only one star in the age of the universe. Presumably in the distant past, Sagittarius A* consumed gas at a much higher rate to grow to its current size, perhaps at a rate that made this object as bright as the distant quasars that we see today.

The interesting gravitational effects associated with black holes of several solar masses occur within an area on the sky that is too small to see with modern instruments, but when a black hole's mass is pumped up to millions of solar masses, we have a fighting chance to see some of these effects. For instance, the black disk on the sky defined by the last stable orbit around a 3.6 million solar mass black hole at 7.6 kpc has a projected radius on the sky of about 46 micro-arc-seconds, which translates to an apparent radius of 0.35 AU. This size is just below the resolution that can be achieved in radio astronomy through a method called very long baseline interferometry (VLBI); by combines radio observations of a source from telescopes on opposite sides of the Earth, astronomers can create high-resolution maps of the sky. If the dark disk can be observed through VLBI, we would have a direct test of General Relativity, since that theory gives a direct relationship between the disk's radius and the mass of the black hole. As it stands, radio astronomy can only state that Sgr A* is less than 130 micro-arc-seconds on the sky.[1] We might also see the reflection of the sky into the region inside the Einstein ring for Sgr A*, which is 2.0 arc seconds in radius on the sky. So far these effects have not been seen, and whether or not we ever see them presuppose that the gas flow onto the black hole does not spoil the effects.

[1] Rogers, Alan E. E., Doeleman, Sheperd, Wright, Melvyn C. H., Bower, Geoffrey C., Backer, Donald C., Padin, Stephen, Phillips, J. A., Emerson, Darrel T., Greenhill, Lincoln, Moran, James M., and Kellermann, Kenneth I. “Small-Scale Structure and Position of Sagittarius A* from VLBI at 3 Millimeter Wavelength.” The Astrophysical Journal Letters 434 (20 October 1994): L59–L62.

[2] Reid, M. J., and Brunthaler, A. “The Proper Motion of Sagittarius A. II. The Mass of Sagittarius A.” The Astrophysical Journal 616 (1 December 2004): 872–884.

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