The (black hole mass)-(host spheroid luminosity) relation at high and
  low masses, the quadratic growth of black holes, and intermediate-mass black
  hole candidates
  From a sample of 72 galaxies with reliable supermassive black hole masses
M_(bh), we derive the M_(bh)-(host spheroid luminosity, L) relation for (i) the
subsample of 24 core-Sersic galaxies with partially depleted cores, and (ii)
the remaining subsample of 48 Sersic galaxies. Using (K_s)-band 2MASS data, we
find the near-linear relation M_(bh) ~ L_(K_s)^(1.10+/-0.20) for the
core-Sersic spheroids thought to be built in additive dry merger events, while
M_(bh) ~ L_(K_s)^(2.73+/-0.55) for the Sersic spheroids built from gas-rich
processes. After converting literature B-band disk galaxy magnitudes into
inclination- and dust-corrected bulge magnitudes, via a useful new equation
presented herein, we obtain a similar result. Unlike with the M_(bh)-sigma
diagram, which is also updated here using the same galaxy sample, it remains
unknown whether barred and non-barred Sersic galaxies are offset from each
other in the M_(bh)-L diagram.
  While black hole feedback has typically been invoked to explain what was
previously thought to be a nearly constant M_bh/M_sph mass ratio of ~0.2%, we
advocate that the near-linear M_bh-L and M_bh-M_sph relations observed at high
masses may have instead largely arisen from the additive dry merging of
galaxies. We argue that feedback results in a dramatically different scaling
relation, such that black hole mass scales roughly quadratically with the
spheroid mass in Sersic galaxies. We therefore introduce a revised cold-gas
'quasar' mode feeding equation for semi-analytical models to reflect what we
dub the "quadratic growth" of black holes in Sersic galaxies built amidst
gas-rich processes. Finally, we use our new Sersic M_bh-L equations to predict
the masses of candidate `intermediate mass' black holes in almost 50 low
luminosity spheroids containing AGN, finding many masses between that of
stellar mass black holes and supermassive black holes.
