Other kinematic studies of SMBHs, and the SMBH census

Kinematic studies of stars around the SMBH in the center of our own Galaxy have only been possible in recent years with the development of diffraction limited near infra-red imaging on large ground-based telescopes. Before that, studies of the central regions of other galaxies (where the obscuration problem is much less severe) were crucial for establishing the existence of SMBHs. In particular, there were two studies published in the mid-1990s that were pivotal in providing compelling evidence for SMBHs -- the Hubble Space Telescope (HST) observations of M87 and the radio observations of the H$_2$O MASERs in NGC 4258.

The center of M87 was an important target for HST since a central SMBH had long been suspected based upon previous ground-based optical observations of the galaxy's central regions [86,87], as well as due to the presence of a prominent synchrotron emitting jet of plasma that flows away from the galaxy's core at relativistic speeds. HST imaged a disk of ionized gas, with a radius of $\sim 50{\rm\thinspace pc}$ centered on the galactic core [88]. The high resolution of HST allowed the spectrum of this ionized gas to be measured as a function of position across the gas disk, thereby allowing the kinematics of the disk to be determined [89]. It was found that the velocity profile of the central $20{\rm\thinspace pc}$ of the gas disk possessed a Keplerian profile (i.e., $v\propto r^{-1/2}$) as expected if the gas was orbiting in the gravitational potential of a point-like mass [89,90]. From the measured velocities of this disk ($\sim 1000\hbox{${\rm\thinspace km}{\rm\thinspace s}^{-1}\,$}$), the central mass was determined to be $3\times 10^9\hbox{$\rm\thinspace M_{\odot}$}$. The only known and long-lived object to possess such a large mass in a small region of space, and be as under-luminous as observed, is a SMBH.

Similar conclusions were drawn for the center of the galaxy NGC 4258, albeit using very different observational techniques [91,92]. The center of this galaxy contains molecular gas which is subjected to heating by a central X-ray source. Collisional pumping of water within the molecular gas leads to a population inversion thereby driving a naturally occurring maser. Both the spatial position and line-of-sight velocity of the masing blobs can be measured very accurately using radio observations (in particular, the Very Long Baseline Array; VLBA). It is found that the masers lie in a very thin disk (oriented almost edge-on to us) that is orbiting a central object of mass $3.6\times 10^7\hbox{$\rm\thinspace M_{\odot}$}$ with an almost perfect Keplerian velocity profile (with the velocity of the inner masing region being $\sim 1000\hbox{${\rm\thinspace km}{\rm\thinspace s}^{-1}\,$}$). The accuracy with which the velocity profile follows a Keplerian law tightly constrains the spatial extent of the central mass, again rendering any explanation other than a SMBH very problematic. The direct detection of centripetal accelerations within the masing regions provides a powerful consistency check [93].

While the Galactic Center, M87 and NGC 4258 are important cases in the argument for the existence of SMBHs, it is difficult to generalize these observational techniques to all galaxies. A more generally applicable technique is to examine the ensemble velocity distribution of stars in the central region of a galaxy via observations of stellar absorption lines in galactic spectra. By carefully comparing detailed galactic models (that include the distribution of stars across the possible phase space of orbits within a given gravitational potential) with high quality imaging and spectral data, one can constrain the mass of any central black hole. Using these techniques, several authors have performed relatively large surveys of nearby galaxies in order to examine the demographics of SMBHs. There are two exciting results from these studies. Firstly, it appears that every galaxy that possesses a well defined bulge contains a SMBH. Secondly, there is a good correlation between the mass of the central black hole $M$ and the mass of the galactic bulge ($M_{\rm bulge}$), with $M/M_{\rm bulge}\sim 0.003$ [94,95]. In fact, it has been shown that the more fundamental (and better) correlation is between the mass of the central SMBH and the velocity dispersion $\sigma$ (or ``temperature'', considering an analogy between stellar kinematics in a galaxy and particle kinematics in a gas) of the stellar population; $M\propto \sigma^{b}$, with $b=4-5$ [96,97]. The underlying cause for this correlation is still the subject of intense work and much debate, since these stars are far enough from the center of the galaxy to have negligible direct influence from the gravitational field of the SMBH. It is widely regarded that this correlation argues for a connection between the formation of the SMBH and the galaxy itself.