The Black Hole Mass–Galaxy Bulge Relationship for QSOs in the Sloan Digital Sky Survey Data Release 3

We investigate the relationship between black hole mass and host galaxy velocity dispersion for QSOs in Data Release 3 of the Sloan Digital Sky Survey. We derive black hole mass from the broad Hbeta line width and continuum luminosity, and the bulge stellar velocity dispersion from the [OIII] narrow line width. At higher redshifts, we use MgII and [OII] in place of Hbeta and [OIII]. For redshifts z < 0.5, our results agree with the black hole mass - bulge velocity dispersion relationship for nearby galaxies. For 0.5 < z < 1.2, this relationship appears to show evolution with redshift in the sense that the bulges are too small for their black holes. However, we find that part of this apparent trend can be attributed to observational biases, including a Malmquist bias involving the QSO luminosity. Accounting for these biases, we find ~0.2 dex evolution in the black hole mass-bulge velocity dispersion relationship between now and redshift z ~ 1