This paper explores several simple model variations for the connections among
quasars, galaxies, and dark matter halos for redshifts 1 < z < 6. A key
component of these models is that we enforce a self-consistent black hole (BH)
history by tracking both BH mass and BH growth rate at all redshifts. We
connect objects across redshift with a simple constant-number-density
procedure, and choose a fiducial model with a relationship between BH and
galaxy growth rates that is linear and evolves in a simple way with redshift.
Within this fiducial model, we find the quasar luminosity function (QLF) by
calculating an "intrinsic" luminosity based on either the BH mass or BH growth
rate, and then choosing a model of quasar variability with either a lognormal
or truncated power-law distribution of instantaneous luminosities. This gives
four model variations, which we fit to the observed QLF at each redshift. With
the best-fit models in hand, we undertake a detailed comparison of the four
fiducial models, and explore changes to our fiducial model of the BH-galaxy
relationship. Each model variation can successfully fit the observed QLF, the
shape of which is generally set by the "intrinsic" luminosity at the faint end
and by the scatter due to variability at the bright end. We focus on accounting
for the reasons that physically different models can make such similar
predictions, and on identifying what observational data or physical arguments
are most essential in breaking the degeneracies among models.Comment: 14 pages, 8 figures, 1 tabl
