Black Hole Masses and Eddington Ratios at 0.3 <z< 4

We study the distribution of Eddington luminosity ratios, L_bol/L_edd, ofactive galactic nuclei (AGNs) discovered in the AGN and Galaxy Evolution Survey(AGES). We combine H-beta, MgII, and CIV line widths with continuumluminosities to estimate black hole (BH) masses in 407 AGNs, covering theredshift range z~0.3-4 and the bolometric luminosity range L_bol~10^45-10^47erg/s. The sample consists of X-ray or mid-infrared (24 micron) point sourceswith optical magnitude R<=21.5 mag and optical emission line spectracharacteristic of AGNs. For the range of luminosity and redshift probed byAGES, the distribution of estimated Eddington ratios is well described aslog-normal with a peak at L_bol/L_edd ~ 1/4 and a dispersion of 0.3 dex. Sinceadditional sources of scatter are minimal, this dispersion must account forcontributions from the scatter between estimated and true BH mass and thescatter between estimated and true bolometric luminosity. Therefore, weconclude 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 areeven more sharply peaked. Because the mass estimation errors must be smallerthan ~0.3 dex, we can also investigate the distribution of Eddington ratios atfixed BH mass. We show for the first time that the distribution of Eddingtonratios at fixed BH mass is peaked, and that the dearth of AGNs at a factor ~10below Eddington is real and not an artifact of sample selection. These resultsprovide strong evidence that supermassive BHs gain most of their mass whileradiating close to the Eddington limit, and they suggest that the fueling ratesin luminous AGNs are ultimately determined by BH self-regulation of theaccretion flow rather than galactic scale dynamical disturbances.Comment: 34 pages including 12 figures. Incorporates referee's comments. Accepted for publication in Ap