An Improved Black Hole Mass - Bulge Luminosity Relationship for AGNs
  Two effects have substantially increased the scatter in the AGN black hole
mass - host galaxy bulge luminosity relationship derived from SDSS spectra. The
first is that at a fixed black hole mass, the SDSS spectrum depends strongly on
redshift because an SDSS fiber sees a larger fraction of the total light of
more distant galaxies. The second is that at a given redshift, the fraction of
host-galaxy light in the fiber increases with decreasing galaxy luminosity. We
illustrate the latter effect using the Kormendy et al. (2009) light profiles of
Virgo ellipticals. With allowance for the two effects, we obtain a black hole
mass - bulge luminosity relationship for AGNs which has a scatter of only +/-
0.23 dex in mass. This is less than the scatter found for inactive galaxies,
and is consistent with the measuring errors. We show that there is a
correspondingly tight linear relationship between the fraction of host galaxy
light in AGN spectra and the Eddington ratio. This linearity implies that at a
given black hole mass, the host luminosities of high-accretion-rate AGNs
(NLS1s) and low-accretion-rate AGNs are similar. The relationship between the
fraction of host galaxy light and the Eddington ratio provides a simple means
of estimating the fraction of host galaxy light in AGN spectra. This means that
the real amplitude of variability of low-accretion-rate AGNs is increased
relative to NLS1s.
