In the supermassive black hole business, the masses which are most
challenging to
measure are those of the black holes powering local AGNs. Compared to QSOs,
lower-luminosity AGNs have a small ratio between nuclear non-thermal and
stellar
luminosity, making it difficult to assess what fraction of the total
luminosity is due to
accretion onto the central black hole. Furthermore, the history of past
activity is not
known, so it is not obvious what fraction of the SBH mass,
M
,
predated the onset of
the present nuclear activity (and the assumption that AGNs radiate at the
Eddington limit is not justifiable). In other words, Soltan's arguments,
which hold
rather nicely for high redshift powerful QSOs, are not applicable to
their less flamboyant, nearby cousins.
To make matters worse, the techniques that allow us to detect supermassive black holes in quiescent galaxies are seldom applicable to the hosts of AGNs. In Seyfert 1 galaxies, and in the handful of QSOs for which traditional dynamical studies of the gas or stellar kinematics can be performed, the presence of the bright non-thermal nucleus (e.g. Malkan, Gorjian & Tam 1998) overwhelms the very spectral features which are necessary for dynamical studies. The only Seyfert galaxy in which a SBH has been detected by spatially-resolved kinematics is 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 the Hubble Space Telescope (HST) but is fully sampled by the VLBA at 22.2 GHz. Unfortunately, water masers are rare (Greenhill et al. 2002) 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. 1997, 1996; Greenhill, Moran & Hernquist 1997; Trotter et al. 1998). A study of black hole demographics in AGNs must therefore proceed through alternative techniques.
To my knowledge, the only attempt at deriving a mass function for local
(z < 0.1) AGNs was published by
Padovani et al. (1990)
using the CfA magnitude limited
sample of Seyfert 1 galaxies. For each galaxy, the mass of the central
SBH was
derived from the dynamics of the broad line region (BLR) under the virial
approximation,
M =
v2 r/G. The radius rof the BLR was
calculated by assuming
that the ionization parameter U (or more precisely, its product
with the electron
density) is known and invariant from object to object. U depends
on the inverse
square of r, and linearly on the number of ionizing photons; the
latter quantity can
be derived if the spectral energy distribution of each object is
known. As noted by
Padovani et al. , however, the ionization parameter is likely not
invariant. More recently,
Wandel, Peterson & Malkan
(1999)
have calibrated the "photoionization
method" against the more sophisticated technique which has become known as
"reverberation mapping"
(Blandford & McKee 1892;
Peterson 1993;
Netzer & Peterson 1997;
Koraktar & Gaskell 1991).
The latter method relies on
the fact that if the non-thermal nuclear continuum is variable, then the
responsivity-weighted radius r of the BLR is measured by the
light-travel time
delay between emission and continuum variations. As in the case of the
photoionization method, the mass of the central black hole follows from
the virial
approximation, if the BLR is gravitationally bound. The latter
assumption has now received strong support in a few well-studied cases
(Koratkar & Gaskell
1991;
Wandel, Peterson & Malkan
1999;
Peterson & Wandel 2000,
but see also
Krolik 2001).
Wandel, Peterson & Malkan
(1999)
concluded that photoionization techniques
and reverberation-mapping estimates of the BLR sizes (or central masses)
compare well, but only in a statistical sense. In other words,
M
estimates from the two methods can differ by up to an order of magnitude
for individual objects, yet there
does exist a reasonably good linear correlation between the two quantities
when large samples are investigated, which bodes well for the Padovani
et al. analysis. Eight of the Seyfert 1 galaxies in the Padovani et
al. sample also have reverberation-mapping masses
(Wandel et al. 1999;
Kaspi et al. 2000).
For these galaxies, the reverberation masses are a factor 3.6 ± 3.4
larger (in the mean) than the
photoionization masses. In Fig. 1, the
cumulative mass function in local Seyfert 1
galaxies derived by Padovani et al. , once corrected for this factor and
scaled to
H0 = 75 km s-1 Mpc-1, is
compared to the mass function in QSO black holes.
The total density of SBHs in Seyfert 1 galaxies is ~ 5000
M
Mpc-3. Despite the
upward revision by a factor ~ eight compared to the original estimate,
the main
conclusion reached by Padovani et al. still holds: "the bulk of the mass
related to the accretion processes connected with past QSO activity does
not reside in Seyfert 1 nuclei. Instead, the remnants of past activity
must be present in a much larger number of galaxies". In the local
universe, the ratio of Seyfert 2 to Seyfert 1 galaxies is ~ four
(Maiolino & Rieke 1995),
while LINERs are a factor of a few more numerous than Seyferts
(Vila-Vilaro 2000).
Yet even after correcting
the mass density given above to include these classes of AGNs, the total
cumulative mass density in local AGNs falls a factor of several below that
estimated for high redshift QSOs. Thus, in the search for SBHs, powerful
QSOs and completely quiescent galaxies appear to be equally promising
targets.