3.4 Our Galaxy: M_BH (2.9 ± 0.4) x 10⁶ M

Our Galaxy has long been known to contain the exceedingly compact radio source Sgr A*. Interferometry gives its diameter as 63 r_s by less than 17 r_s, where r_s = 0.06 AU = 8.6 x 10¹¹ cm is the Schwarzschild radius of a 2.9 x 10⁶ M BH. It is easy to be impressed by the small size. But as an AGN, Sgr A* is feeble: its radio luminosity is only 10³⁴ erg s^-1 10^0.4 L. The infrared and high-energy luminosities are higher, but there is no compelling need for a BH on energetic grounds. To find out whether the Galaxy contains a BH, we need dynamical evidence.

Getting it has not been easy. Our Galactic disk, which we see in the sky as the Milky Way, contains enough dust to block all but ~ 10^-14 of the optical light from the Galactic center. Measurements of the region around Sgr A* had to await the development of infrared detectors. Much of the infrared radiation is in turn absorbed by the Earth's atmosphere, but there is a useful transmission window at 2.2 µm wavelength. Here the extinction toward the Galactic center is a factor of ~ 20. This is large but manageable. Early infrared measurements showed a rotation velocity of V 100 km s^-1 and a small rise in velocity dispersion to ~ 120 km s^-1 at the center. These were best fit with a BH of mass M_BH ~ 10⁶ M, but the evidence was not very strong. Since then, a series of spectacular technical advances have made it possible to probe closer and closer to the center. As a result, the strongest case for a BH in any galaxy is now our own.

Figure 4. Images of the star cluster surrounding Sgr A* (green cross) at the epochs indicated. The arrows in the left frame show approximately where the stars have moved in the right frame. Star S1 has a total proper motion of ~ 1600 km s-1. [This figure is updated from Eckart & Genzel 1997, M.N.R.A.S., 284, 576 and was kindly provided by A. Eckart.]

Most remarkably, two independent groups led by Reinhard Genzel and Andrea Ghez have used speckle imaging to measure proper motions - the velocity components perpendicular to the line of sight - in a cluster of stars at radii r 0".5 0.02 pc from Sgr A* (Figure 4). When combined with complementary measurements at larger radii, the result is that the one-dimensional velocity dispersion increases smoothly to 420 ± 60 km s^-1 at r 0.01 pc. Stars at this radius revolve around the Galactic center in a human lifetime! The mass M(r) inside radius r is shown in Figure 5. Outside a few pc, the mass distribution is dominated by stars, but as r -> 0, M(r) flattens to a constant, M_BH = (2.9 ± 0.4) x 10⁶ M. Velocity anisotropy is not an uncertainty; it is measured directly and found to be small. The largest dark cluster that is consistent with these data would have a central density of 4 x 10¹² M pc^-3. This is inconsistent with astrophysical constraints (Section 5). Therefore, if the dark object is not a BH, the alternative would have to be comparably exotic. It is prudent to note that rigorous proof of a BH requires that we spatially resolve relativistic velocities near the Schwarzschild radius. This is not yet feasible. But the case for a BH in our own Galaxy is now very compelling.

Figure 5. Mass distribution implied by proper motion and radial velocity measurements (blue points and curve). Long dashes (green) show the mass distribution of stars if the infrared mass-to-light ratio is 2. The red curve represents the stars plus a point mass MBH = 2.9 x 106 M. Short green dashes provide an estimate of how non-pointlike the dark mass could be: its 2 value is 1 worse than the solid curve. This dark cluster has a core radius of 0.0042 pc and a central density of 4 x 1012 M pc-3. [This figure is updapted from Genzel et al. 1997, M.N.R.A.S., 291, 219 and was kindly provided by R. Genzel.]