QSO Host Galaxy Luminosity and [O III] Line Width as a Surrogate for Stellar Velocity Distribution

Supermassive black holes in galactic nuclei show a close relationship between the black hole mass MBH and the luminosity L and stellar velocity dispersion σ∗ of the host galaxy bulge. Probing these relationships at high redshift may shed light on the link between the formation of the galactic bulge and central black hole, but direct measurements of σ∗ at high redshift are difficult. We show that [O III] line widths provide a useful surrogate for σ∗ by comparing σ[O III] with the value of σ∗ predicted by the Faber-Jackson relation for QSOs with measured host galaxy luminosity. Over a wide range of AGN luminosity, σ[O III] tracks σ∗, albeit with considerable scatter. [O III] line widths are narrower by 0.1 dex in radio-loud QSOs than in radio-quiet QSOs of similar Lhost. In low redshift QSOs, the ratio of star formation rate to black hole growth rate is much smaller than the typical ratio of bulge mass to black hole mass. Nelson & Whittle (1995, 1996) made a comparison of bulge magnitudes, [O III] line widths, and σ∗ in Seyfert galaxies, finding on average good agreement between σ∗ and σ[O III] ≡ FWHM([O III])/2.35. However, direct comparisons of σ[O III] with σ∗ have generally been limited to lower luminosity AGN, and it is important to evaluate the substitution of σ[O III] for σ∗ at higher QSO luminosities. Here we do this by studying the Faber-Jackson relation (Forbes & Ponman 1999; Kormendy & Illingworth 1983) for a sample of quasars for which host galaxy luminosities are available. Host galaxy magnitudes for ellipticals, and bulge magnitudes for spiral hosts were taken from the literature and from our own unpublished measurements (see Bonning et al. 2005 for details). The [O III] line