We present an observationally motivated model to connect the AGN and galaxy populations at 0.2<z<1.0 and predict the AGN X-ray luminosity function (XLF). We start with measurements of the stellar mass function of galaxies (from the Prism Multi-object Survey) and populate galaxies with AGNs using models for the probability of a galaxy hosting an AGN as a function of specific accretion rate. Our model is based on measurements indicating that the specific accretion rate distribution is a universal function across a wide range of host stellar mass with slope gamma_1 = -0.65 and an overall normalization that evolves with redshift. We test several simple assumptions to extend this model to high specific accretion rates (beyond the measurements) and compare the predictions for the XLF with the observed data. We find good agreement with a model that allows for a break in the specific accretion rate distribution at a point corresponding to the Eddington limit, a steep power-law tail to super-Eddington ratios with slope gamma_2 = -2.1 +0.3 -0.5, and a scatter of 0.38 dex in the scaling between black hole and host stellar mass. Our results show that samples of low luminosity AGNs are dominated by moderately massive galaxies (M* ~ 10^{10-11} M_sun) growing with a wide range of accretion rates due to the shape of the galaxy stellar mass function rather than a preference for AGN activity at a particular stellar mass. Luminous AGNs may be a severely skewed population with elevated black hole masses relative to their host galaxies and in rare phases of rapid accretion.
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