Black hole mass and Eddington ratio distribution functions of X-ray selected broad-line AGNs at z~1.4 in the Subaru XMM-Newton Deep Field

In order to investigate the growth of super-massive black holes (SMBHs), we construct the black hole mass function (BHMF) and Eddington ratio distribution function (ERDF) of X-ray-selected broad-line AGNs at z~1.4 in the Subaru XMM-Newton Deep Survey field. In this redshift range, a significant part of the accretion growth of SMBHs is thought to be taking place. Black hole masses of X-ray-selected broad-line AGNs are estimated using the width of the broad MgII line and the 3000A monochromatic luminosity. We supplement the MgII FWHM values with the Ha FWHM obtained from our NIR spectroscopic survey. Using the black hole masses of broad-line AGNs at redshifts between 1.18 and 1.68, the binned broad-line AGN BHMF and ERDF are calculated using the Vmax method. To properly account for selection effects that impact the binned estimates, we derive the corrected broad-line AGN BHMF and ERDF by applying the Maximum Likelihood method, assuming that the ERDF is constant regardless of the black hole mass. We do not correct for the non-negligible uncertainties in virial BH mass estimates. If we compare the corrected broad-line AGN BHMF with that in the local Universe, the corrected BHMF at z~1.4 has a higher number density above 10^8 Msolar but a lower number density below that mass range. The evolution may be indicative of a down-sizing trend of accretion activity among the SMBH population. The evolution of broad-line AGN ERDF from z=1.4 to 0 indicates that the fraction of broad-line AGNs with accretion rate close to the Eddington-limit is higher at higher redshifts.