We study the distribution of Eddington luminosity ratios, L_bol/L_edd, of active galactic nuclei (AGNs) discovered in the AGN and Galaxy Evolution Survey (AGES). We combine H-beta, MgII, and CIV line widths with continuum luminosities to estimate black hole (BH) masses in 407 AGNs, covering the redshift range z~0.3-4 and the bolometric luminosity range L_bol~10^45-10^47 erg/s. The sample consists of X-ray or mid-infrared (24 micron) point sources with optical magnitude R<=21.5 mag and optical emission line spectra characteristic of AGNs. For the range of luminosity and redshift probed by AGES, the distribution of estimated Eddington ratios is well described as log-normal with a peak at L_bol/L_edd ~ 1/4 and a dispersion of 0.3 dex. Since additional sources of scatter are minimal, this dispersion must account for contributions from the scatter between estimated and true BH mass and the scatter between estimated and true bolometric luminosity. Therefore, we conclude that: (1) neither of these sources of error can contribute more than ~0.3 dex rms; and (2) the true Eddington ratios of optically luminous AGNs are even more sharply peaked. Because the mass estimation errors must be smaller than ~0.3 dex, we can also investigate the distribution of Eddington ratios at fixed BH mass. We show for the first time that the distribution of Eddington ratios at fixed BH mass is peaked, and that the dearth of AGNs at a factor ~10 below Eddington is real and not an artifact of sample selection. These results provide strong evidence that supermassive BHs gain most of their mass while radiating close to the Eddington limit, and they suggest that the fueling rates in luminous AGNs are ultimately determined by BH self-regulation of the accretion flow rather than galactic scale dynamical disturbances.
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