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.
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