The evolution of host mass and black hole mass in quasi-stellar objects from the 2dF QSO Redshift Survey

We investigate the relation between the mass of supermassive black holes (M-BH) in quasi-stellar objects (QSOs) and the mass of the dark matter haloes hosting them (M-DH). We measure the widths of broad emission lines (Mg (II)lambda 2798, C (IV)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. based on measurements of QSO clustering. This enables us to trace the M-BH-M-DH relation over the redshift range z = 0.5-2.5. We calculate the mean zero-point of the M-BH-M-DH relation to be M-BH = 10(8.4 +/- 0.2) M-circle dot for an M-DH = 10(12.5) M-circle dot. These data are then compared with several models connecting M-BH and M-DH 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 M-BH-M-DH relation. The magnitude of this bias depends on the scatter in the M-BH-M-DH relation, and we re-evaluate the zero-point assuming three published values for this scatter. We create a subsample of our data defined by a constant magnitude interval around L* and find (1 + z)(3.3 +/- 1.3) evolution in M-BH between z similar to 0.5 and 2.5 for typical, L* QSOs. We also determine the Eddington ratios (L/L-Edd) for the same subsample and find no significant evolution: (1 + z)(-0.4 +/- 1.1). Taken at face value, our data suggest that a decrease in active black hole mass since z similar to 2.5 is the driving force behind luminosity evolution of typical, L*, optically selected QSOs. However, we note that our data are also consistent with a picture in which reductions in both black hole mass and accretion rate contribute equally to luminosity evolution. In addition, we find that these evolution results are strongly affected by the virial black hole mass estimators used. Changes to the calibration of these have a significant effect on the evolution results.