Eddington ratio Distribution of X-ray selected broad-line AGNs at 1.0<z<2.2

We investigate the Eddington ratio distribution of X-ray selected broad-line active galactic nuclei (AGN) in the redshift range 1.0<z<2.2, where the number density of AGNs peaks. Combining the optical and Subaru/FMOS near-infrared spectroscopy, we estimate black hole masses for broad-line AGNs in the Chandra Deep Field-South (CDF-S), Extended Chandra Deep Field-South (E-CDF-S), and the XMM-Newton Lockman Hole (XMM-LH) surveys. AGNs with similar black hole masses show a broad range of AGN bolometric luminosities, which are calculated from X-ray luminosities, indicating that the accretion rate of black holes is widely distributed. We find that a substantial fraction of massive black holes accreting significantly below the Eddington limit at z~2, in contrast to what is generally found for luminous AGNs at high redshift. Our analysis of observational selection biases indicates that the "AGN cosmic downsizing" phenomenon can be simply explained by the strong evolution of the co-moving number density at the bright end of the AGN luminosity function, together with the corresponding selection effects. However, it might need to consider a correlation between the AGN luminosity and the accretion rate of black holes that luminous AGNs have higher Eddington ratios than low-luminosity AGNs in order to understand the relatively small fraction of low-luminosity AGNs with high accretion rates in this epoch. Therefore, the observed downsizing trend could be interpreted as massive black holes with low accretion rates, which are relatively fainter than less massive black holes with efficient accretion.