  We present a simple semi-numerical model designed to explore black hole
growth and galaxy evolution. This method builds on a previous model for black
hole accretion that uses a semi-numerical galaxy formation model and universal
Eddington ratio distribution to describe the full AGN population by
independently connecting galaxy and AGN growth to the evolution of the host
dark matter halos. We fit observed X-ray luminosity functions up to a redshift
of z ~ 4, as well as investigate the evolution of the Eddington ratio
distributions. We find that the Eddington ratio distribution evolves with
redshift such that the slope of the low-Eddington accretion rate distribution
increases with cosmic time, consistent with the behavior predicted in
hydrodynamical simulations for galaxies with different gas fractions. We also
find that the evolution of our average Eddington ratio is correlated with
observed star formation histories, supporting a picture in which black holes
and galaxies evolve together in a global sense. We further confirm the impact
of luminosity limits on observed galaxy and halo properties by applying
selection criteria to our fiducial model and comparing to surveys across a wide
range of redshifts.
