The techniques that allow us to detect supermassive black holes in quiescent galaxies are rarely applicable to the hosts of bright AGNs. In the Seyfert 1 galaxies and in the handful of QSOs that are close enough that the black hole's sphere of influence has some chance of being resolved, the presence of the bright non-thermal nucleus (e.g. Malkan, Gorjian & Tam 1998) severely dilutes the very features which are necessary for dynamical studies. The only bright AGN in which a supermassive black hole has been detected by spatially-resolved kinematics is the nearby (Herrnstein et al. 1999; Newman et al. 2001) Seyfert 2 galaxy NGC 4258, which is blessed with the presence of an orderly water maser disk (Watson & Wallin 1994; Greenhill et al. 1995; Miyoshi et al. 1995). The radius of influence of the black hole at its center, ~ 0 ".15, can barely be resolved by HST but can be fully sampled by the VLBA at 22.2 GHz. Unfortunately, water masers are rare and of the handful that are known, only in NGC 4258 are the maser clouds distributed in a simple geometrical configuration that exhibits clear Keplerian motion around the central source (Braatz et al. 1996; Greenhill et al. 1996, 1997; Greenhill, Moran & Herrnstein 1997; Trotter et al. 1998). Black hole demographics in AGNs must therefore proceed via alternate routes.
Dynamical modeling of the broad emission line region (BLR) constitutes a viable alternative to spatially-resolved kinematical studies. According to the standard model, the BLR consists of many (107 - 8, Arav et al. 1997, 1998; Dietrich et al. 1999), small, dense (Ne ~ 109 - 11 cm-3), cold (Te ~ 2 × 104 K) photoionized clouds (Ferland et al. 1992), localized within a volume of a few light days to several tens of light weeks in diameter around the central ionization source (but see also Smith & Raine 1985, 1988; Pelletier & Pudritz 1992; Murray et al. 1995; Murray & Chiang 1997; Collin-Souffrin et al. 1988). As such, the BLR is, and will likely remain, spatially unresolved. In the presence of a variable non-thermal nuclear continuum, however, the responsivity-weighted radius RBLR of the BLR is measured by the light-travel time delay between emission and continuum variations (Blandford & McKee 1982; Peterson 1993; Netzer & Peterson 1997; Koratkar & Gaskell 1991). If the BLR is gravitationally bound, the central mass is given by the virial theorem as Mvirial = vBLR2RBLR / G, where the FWHM of the emission lines (generally H) is taken as being representative of the rms velocity vBLR, once assumptions are made about the BLR geometry. In a few cases, independent measurements of RBLR and vBLR have been derived from different emission lines: it is found that the two quantities define a "virial relation" in the sense vBLR ~ r-1/2 (Koratkar & Gaskell 1991; Wandel, Peterson & Malkan 1999; Peterson & Wandel 2000), suggesting a simple picture of a stratified BLR in Keplerian motion.
On the downside, mapping the BLR response to continuum variations requires many (~ 101 - 2) repeated observations taken at closely spaced time intervals, t 0.1RBLR/c. Moreover, the observations can be translated into black hole masses only if a series of reasonable, but untested, assumptions are made regarding the geometry, stability and velocity structure of the BLR, the radial emissivity function of the gas, and the geometry and location (relative to the BLR) of the ionizing continuum source. If a wrong assumption is made, systematic errors of a factor ~ 3 can result (Krolik 2001). The uncertainties surrounding reverberation mapping has made the derived black hole masses an easy target for critics (e.g. Richstone et al. 1998; Ho et al. 1999). On the other hand, because the BLR gas samples a spatial region very near to the black hole, there is almost no possibility of making the much larger errors in M that have plagued the ground-based stellar kinematical studies (Magorrian et al. 1998). Thanks to the efforts of international collaborations, reverberation mapping masses are now available for 17 Seyfert 1 galaxies and 19 QSOs (Wandel, Peterson & Malkan 1999; Kaspi et al. 2000).
Taken at face value, reverberation mapping radii are found to correlate with the non-thermal optical luminosity of the nuclear source. While the exact functional form of the dependence is debated (Koratkar & Gaskell 1991; Kaspi et al. 1996, 2000; Wandel, Peterson & Malkan 1999), the RBLR - L relation can potentially provide an inexpensive way of bypassing reverberation mapping measurements on the way to determining black hole masses.
3.1. AGN Black Hole Demographics from the M - Mbulge Relation
With one exception (Ferrarese et al. 2001), black hole demographic studies for AGNs have been based on the M - MB, rather than on the M - , relation for the simple reason that few accurate measurements exist in AGN hosts (e.g. Nelson & Whittle 1995). Lbulge, on the other hand, is more easily measured than (though not necessarily more accurately measured, as discussed below). The modest sample of AGNs with reverberation mapping black hole masses is often augmented using masses derived from the RBLR - L relation (Wandel 1999; Laor 1998, 2001; McLure & Dunlop 2000). For a sample of 14 PG quasars, Laor (1998) reported reasonable agreement with the M - MB relation derived by Magorrian et al. (1998) for quiescent galaxies, finding <M / Mbulge> = 0.006. Seyfert 1 galaxies define a significantly different correlation according to Wandel (1999): <M / Mbulge> = 0.0003. Most recently, McLure & Dunlop (2000) have reanalyzed the QSO sample of Laor and the Seyfert sample of Wandel (the first augmented with almost as many new objects and both with new spectroscopic and/or photometric data for the existing objects). McLure & Dunlop split the difference of the two ealier studies by obtaining <M / Mbulge> = 0.0025. They find no statistical difference between Seyfert 1s and QSOs.
The different conclusions reached by these authors can be traced to a number of factors.
We have recomputed the data from the Wandel (1999) and McLure & Dunlop (2000) studies under a uniform set of assumptions, as follows:
Figure 8. The M / Mbulge relation for quiescent galaxies (solid black dots, with best fit given by the green line), Seyfert 1 galaxies (blue triangles) and nearby QSOs (red circles). The data are taken from Ferrarese & Merritt (2000), McLure & Dunlop (2000) and Wandel, Peterson & Malkan (1999). When necessary, bulge magnitudes are converted to Johnsons B by adopting V - R = 0.59 and B - V = 0.93. The size of the symbols for the AGNs is proportional to the H FWHM: the nominal distinction between narrow and broad line AGNs occurs at the FWHM represented by the symbol size used in the legend. The yellow line represents the best fit to the nearby quiescent galaxies derived by Magorrian et al. (1998); the green line is fit to the black hole masses from Merritt & Ferrarese (2001a) (shown as filled circles). The dotted black lines are the loci for which the black hole mass is a fixed percentage of the bulge mass. The arrows in the upper left corner represent the change in M or Mbulge produced under assumptions different from the ones detailed in the text.
The results are shown in Figure 8. We draw the following conclusions.
3.2. AGN Black Hole Demographics from the M - Relation
Because of its large intrinsic scatter, there is little more that can be learned about black hole demographics from the M - MB relation. An alternative route is suggested by the M - relation for quiescent galaxies, which exhibits much less scatter. Very few accurate measurements of are available in AGNs, due to the difficulty of separating the bright nucleus from the faint underlying stellar population. The first program to map AGNs onto the M - relation was undertaken by Ferrarese et al. (2001). Velocity dispersions in the bulges of six galaxies with reverberation mapping masses were obtained, thus producing the first sample of AGNs for which both the black hole mass and the stellar velocity dispersion are accurately known (with formal uncertainties of 30% and 15% respectively).
Figure 9 shows the relation between black hole mass and bulge velocity dispersion for the six reverberation-mapped AGNs observed by Ferrarese et al. (2001), plus an additional object with a high-quality from the literature (Nelson & Whittle 1995). The quiescent galaxies (Sample A from Ferrarese & Merritt 2000) are shown by the black dots. The consistency between black hole masses in active and quiescent galaxies is even more striking here than in the M - Mbulge plot. The only noticeable difference between the two samples is a slightly greater scatter in the reverberation mapping masses (in spite of similar, formal error bars). Narrow line Seyfert 1 galaxies do not stand out in any way from the rest of the AGN sample.
Figure 9. Black hole mass versus central velocity dispersion for seven reverberation-mapped AGNs with accurately measured velocity dispersions, compared with the nearby quiescent galaxy sample of Ferrarese & Merritt (2000) (plot adapted from Ferrarese et al. 2001).
We conclude that there is no longer any prima facie reason to believe that reverberation-based masses are less reliable than those based on the kinematics of stars or gas disks. This is important since the resolution of stellar kinematical studies will remain fixed at ~ 0".1 for the forseeable future, whereas reverberation mapping samples a region which is per se unresolvable and is the only technique that can yield accurate masses for very small ( 106 M) or very distant black holes.