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] λ5007 line in AGNs to the stellar velocity dispersion, σ∗, of the host galaxy is given. This significantly reduces the systematic errors in using FWHM([O III]) as a proxy for σ∗. AGN black hole masses, M•, estimated using the Dibai single epoch spectrum method, are combined with the new estimates of σ∗ to give a revised AGN M• –σ∗ relationship extending up to high masses. This shows that for the most massive black holes, M• is systematically higher than predicted by extrapolation of M• ∝ σ 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• – σ∗ relationship is consistent with the absence of very high σ∗ 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• – σ∗ relationship for galaxies with M• > 10 M⊙. 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• –σ∗ relationship implies that the transformation proposed here and the Dibai method are good indicators of σ∗ and M• respectively. There is no evidence for evolution of the M• –σ∗ relationship over time. Subject headings: galaxies:active — galaxies:bulges — galaxies: evolution – galaxies: fundamental parameters — galaxies: nuclei — quasars:emission lines