  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.
