An Improved [O III] Line Width to Stellar Velocity Dispersion
  Calibration: Curvature, Scatter, and Lack of Evolution in the Black-Hole Mass
  Versus Stellar Velocity Dispersion Relationship
  An improved transformation of the full width at half maxima (FWHM) of the [O
III] 5007 line in AGNs to the stellar velocity dispersion, sigma, of the host
galaxy is given. This significantly reduces the systematic errors in using the
[O III] FWHM as a proxy for sigma. AGN black hole masses, M, estimated using
the Dibai single epoch spectrum method, are combined with the new estimates of
sigma to give a revised AGN M-sigma relationship extending up to high masses.
This shows that the masses of the most massive black holes are systematically
higher than predicted by extrapolation of M \propto sigma^4 to high masses.
This supports recent suggestions that stellar dynamical masses of the most
massive black holes have been systematically underestimated. The steepening of
the M-sigma relationship is consistent with the absence of very high sigma
galaxies in the local universe and with the curvature of the Faber-Jackson
relationship. There appears to be significantly less intrinsic scatter in the
M-sigma relationship for galaxies with black hole masses > 10^9 solar masses.
It is speculated that this is connected with the core elliptical versus
extra-light elliptical dichotomy. The low scatter in the high end of the
M-sigma relationship implies that the transformation proposed here and the
Dibai method are good indicators of stellar velocity dispersion and mass
respectively. There is no evidence for evolution of the M-sigma relationship
over time.
