An important question in extragalactic astronomy concerns the distribution of black hole accretion rates of active galactic nuclei (AGN). Based on observations at X-ray wavelengths, the observed Eddington ratio distribution appears as a power law, while optical studies have often yielded a lognormal distribution. There is increasing evidence that these observed discrepancies may be due to contamination by star formation and other selection effects. Using a sample of galaxies from the Sloan Digital Sky Survey Data Release 7, we test if an intrinsic Eddington ratio distribution that takes the form of a Schechter function is consistent with previous work that suggests that young galaxies in optical surveys have an observed lognormal Eddington ratio distribution. We simulate the optical emission line properties of a population of galaxies and AGN using a broad instantaneous luminosity distribution described by a Schechter function near the Eddington limit. This simulated AGN population is then compared to observed galaxies via the positions on an emission line excitation diagram and Eddington ratio distributions. We present an improved method for extracting the AGN distribution using BPT diagnostics that allows us to probe over one order of magnitude lower in Eddington ratio counteracting the effects of dilution by star formation. We conclude that for optically selected AGN in young galaxies, the intrinsic Eddington ratio distribution is consistent with a possibly universal, broad power law with an exponential cutoff, as this distribution is observed in old optically selected galaxies and in X-rays.
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