7. THE BLACK-HOLE MASS/BULGE MASS RELATION

Does M depend at all on other properties of the host galaxies? A much-discussed possibility is that M scales with the mass of the spheroidal component of the host (Kormendy 1993; KR; Faber et al. 1997; Magorrian et al. 1998; Richstone 1998; Ford et al. 1998; van der Marel 1999). The significance of the scatter in the correlation, or whether any correlation exists at all, is not yet certain. It is somewhat disconcerting that different authors plotting the same objects do not always arrive at the same conclusion. The discrepancies can often be traced to different assumptions about distances, source of bulge-to-disk decomposition, and even apparent magnitudes adopted for the host galaxies (e.g., extinction is not always corrected). The set of host galaxy parameters I adopt is compiled in Table 1.

Figure 8 a illustrates that there indeed appears to be a trend of M increasing with bulge mass (luminosity). It is encouraging to note that the central masses derived from gas and stellar kinematics do not show any obvious systematic offsets relative to one another. No obvious differentiation by Hubble type is evident either. As has been noted by others, the scatter of M at a given luminosity is considerable, at least a factor of 10, perhaps up to 100. The scatter may have been exacerbated slightly by four possibly anomalous points. NGC 4486B is a companion to M87, and it appears to have been tidally truncated; its original luminosity was probably higher. On the other hand, the bulge luminosity of NGC 4945 could very well have been overestimated. Its bulge-to-disk ratio was found using the relation of Simien & de Vaucouleurs (1986), which may be inappropriate for a galaxy of such late Hubble type (Scd). Finally, the masses of M81 and NGC 3079 are quite uncertain and probably have been underestimated.

Figure 8. ( a) Log M versus log LB(bulge) for the objects listed in Table 1. The typical uncertainty of M is probably about a factor of 2. Open symbols denote points that may have an exceptionally large uncertainty in either of the two variables (see text). Masses derived from stellar kinematics are plotted as circles, those from gas kinematics as squares, the unconventional case of Arp 102B as a triangle, and five upper limits as crosses. Lines of constant mass to luminosity ratio are also shown. ( b) Same as in ( a), but for the Seyfert galaxies listed in Table 2 (except Mrk 110).

The trend is much more significant when five upper limits are included. NGC 205, a dwarf elliptical companion of M31, contains a blue, compact nucleus with characteristics resembling an intermediate-age globular cluster. Its core radius, determined from HST photometry, combined with a ground-based measurement of its velocity dispersion yields an upper limit of 9 × 10⁴ M for any dark mass (Jones et al. 1996). The bulgeless, late-type (Scd) spiral M33 also has a stringent upper limit on its central mass. Its nuclear cluster is extremely tiny (core radius 0.39 pc), and its central velocity dispersion is 21 km s^-1; Kormendy & McClure (1993) put an upper limit of M 5 × 10⁴ M. NGC 4395 in some ways resembles M33, but it is even more extreme. The nucleus is optically classified as a type 1.8 Seyfert (broad H and H present), emits a largely nonstellar featureless continuum that extends into the UV (Filippenko, Ho, & Sargent 1993), and displays variable soft X-ray emission and a compact flat-spectrum radio core (Moran et al. 1999). These properties alone would be unremarkable were it not for the fact that the nucleus has an absolute blue magnitude of only -9.8 and lives in a Magellanic spiral 2.6 Mpc away! Filippenko & Ho (1998) detected the Ca II infrared triplet lines in absorption from echelle spectra taken with the Keck telescope, from which they were able to estimate the strength of the stellar component contributing to the nuclear light (M_B = -7.3 mag) and the central stellar velocity dispersion ( 30 km s^-1). Combining the velocity dispersion with a cluster size (r 0.7 pc) obtained from HST images, Filippenko & Ho limit the central mass to 8 × 10⁴ M. The Circinus galaxy is thought to house a Seyfert nucleus, and if it contains a SMBH, its mass within r 10 pc has been constrained to be 4 × 10⁶ M (Maiolino et al. 1998). The last upper limit shown in the figure pertains to the globular cluster M15; following KR, I adopt an upper limit of M = 1 × 10³ M.

However, before reading too much into this diagram, we should ask whether the apparent correlation might arise from selection effects. The absence of points on the upper left-hand corner is probably real; there is nothing preventing us from detecting a massive BH in a small galaxy. Yet, we should be cautious, because very few low-mass galaxies have been studied so far, most of the effort having been focused on luminous, early-type systems. On the other hand, the empty region on the lower right-hand corner could be an artifact. Small masses are difficult to detect at large distances, and most luminous galaxies are far away. So the apparent correlation could be an upper envelope. Future observations are needed to settle this issue.

The median value of M / L_B(bul) for the 20 detected objects is 0.012, which translates into a mass ratio of 0.002 for M / L_B 6 typical for old stellar populations (van der Marel 1991). That is, on average about 0.2% of the bulge mass is locked up in the form of a SMBH. Magorrian et al. (1998) constructed axisymmetric f (E, L_z) models for a sample of 32 early-type (mostly E and S0) galaxies having both HST photometry and ground-based stellar kinematics data, and they concluded that the data are consistent with nearly all of the galaxies having SMBHs. The 29 detected objects have a median M / M_bul 0.005, higher than found here. However, as Magorrian et al. realize, the assumption of a two-integral distribution function may have caused them to overestimate M (cf. van der Marel 1999). Interestingly, quasars possibly also obey a similar M-M_bul relation. McLeod (1998) finds that, for the most luminous quasars, there exists a minimum host luminosity that increases with nuclear power. Assuming that the quasar luminosities correspond to energy generation at the Eddington rate, M / M_bul is again ~ 0.002 (McLeod 1998).

With regard to the dead quasar prediction discussed in Section 1, recall that we expect to find on average a 10⁷ M BH for every L_B 10¹⁰ L galaxy, or M / L_B(bul) 3.3 × 10^-3 M / L since bulges contribute typical 30% of the galaxy light in B (Schechter & Dressler 1987). Evidently, if = 0.1, we have already found about three times that value. This implies that either is smaller than 0.1, or that quasars do not make up all of the AGN population.