The evolution of host mass and black hole mass in QSOs from the 2dF QSO Redshift Survey

We investigate the relation between the mass of super-massive black holes (Mbh) in QSOs and the mass of the dark matter halos hosting them (Mdh). We measure the widths of broad emission lines (Mgii lambda 2798, Civ lambda 1549) from QSO composite spectra as a function of redshift. These widths are then used to determine virial black hole mass estimates. We compare our virial black hole mass estimates to dark matter halo masses for QSO hosts derived by Croom et al. (2005) based on measurements of QSO clustering. This enables us to trace the Mbh-Mdh relation over the redshift range z=0.5 to 2.5. We calculate the mean zero-point of the Mbh-Mdh relation to be Mbh=10^(8.4+/-0.2)Msun for an Mdh=10^(12.5)Msun. These data are then compared with several models connecting Mbh and Mdh as well as recent hydrodynamical simulations of galaxy evolution. We note that the flux limited nature of QSO samples can cause a Malmquist-type bias in the measured zero-point of the Mbh-Mdh relation. The magnitude of this bias depends on the scatter in the Mbh-Mdh relation, and we reevaluate the zero-point assuming three published values for this scatter. (abridged)