An expanded M_bh-sigma diagram, and a new calibration of active galactic
  nuclei masses
  [Abridged] We present an updated and improved M_bh-sigma diagram containing
64 galaxies for which M_bh measurements (not just upper limits) are available.
Due to new and increased black hole masses at the high-mass end, and a better
representation of barred galaxies at the low-mass end, the "classical" (all
morphological type) M_bh-sigma relation for predicting black hole masses is
log(M_bh/M_Sun) = (5.13+/-0.34)log[sigma/200] + (8.13+/-0.05), with an rms
scatter of 0.43 dex. Modifying the regression analysis to correct for a
hitherto over-looked sample bias in which black holes with masses <10^6 M_Sun
are not (yet) detectable, the relation steepens further to give log(M_bh/M_Sun)
= (5.95+/-0.44)log[sigma/200] + (8.15+/-0.06). We have also updated the
"barless" and "elliptical-only" M_bh-sigma relations introduced by Graham and
Hu in 2008 due to the offset nature of barred/disc galaxies. These relations
have a total scatter as low as 0.34 dex and currently define the upper envelope
of points in the M_bh-sigma diagram. These relations also have a slope
consistent with the value 5, in agreement with the prediction by Silk & Rees
based on feedback from massive black holes in bulges built by
monolithic-collapse.
  Using updated virial products and velocity dispersions from 28 active
galactic nuclei, we determine that the optimal scaling factor f - which brings
their virial products in line with the 64 directly measured black hole masses -
is 2.8^{+0.7}_{-0.5}. This is roughly half the value reported by Onken et al.
and Woo et al., and consequently halves the mass estimates of most
high-redshift quasars. We have explored the results after separating the
samples into barred and non-barred galaxies, and we have also developed a
preliminary corrective term to the velocity dispersion based on bar dynamics.
