Do all QSOs have the same black hole mass?
  QSOs from SDSS, 2QZ and 2SLAQ covering an order of magnitude in luminosity at
fixed redshift exhibit similar amplitudes of clustering. In addition, QSO
clustering evolution at z>0.5 is well fitted by a model that assumes a fixed
host halo mass, implying that QSOs may occur in a relatively narrow range of
halo and BH mass. We argue that the slow evolution of early-type galaxies out
to z~1-2 may also provide support for a slow evolution of QSO host BH masses.
The result would mean that if high-z QSOs radiate at Eddington rates then low-z
SyI must radiate at ~100x less than Eddington. We conclude that models where
QSOs radiate at L_Edd require M_BH and M_halo to be decoupled to circumvent the
clustering results. While single BH mass and flickering models fit the z>0.5
clustering results, they appear to be rejected by the z~0, M_BH-L relation from
reverberation mapping. We find that the inclusion of z<0.5 QSO clustering data
improves the fit of a long-lived QSO model and suggest that the predictions of
a PLE model for QSO BH masses agree reasonably with UV-bump and reverberation
estimates (abridged).
