A Comparative Analysis of Virial Black Hole Mass Estimates of Moderate-luminosity Active Galactic Nuclei Using Subaru/FMOS

{We present an analysis of broad emission lines observed in moderate-luminosity active galactic nuclei (AGNs), typical of those found in X-ray surveys of deep fields, with the goal of testing the validity of single-epoch virial black hole mass estimates. We have acquired near-infrared spectra of AGNs up to z \~{} 1.8 in the COSMOS and Extended Chandra Deep Field-South Survey, with the Fiber Multi-Object Spectrograph mounted on the Subaru telescope. These near-infrared spectra provide a significant detection of the broad H{$\alpha$} line, shown to be a reliable probe of black hole mass at low redshift. Our sample has existing optical spectroscopy that provides a detection of Mg II, typically used for black hole mass estimation at z {\gt}\~{} 1. We carry out a spectral-line fitting procedure using both H{$\alpha$} and Mg II to determine the virial velocity of gas in the broad-line region, the continuum luminosity at 3000 {\AA}, and the total H{$\alpha$} line luminosity. With a sample of 43 AGNs spanning a range of two decades in luminosity, we find a tight correlation between the ultraviolet and emission-line luminosity. There is also a close one-to-one relationship between the full width at half-maximum of H{$\alpha$} and Mg II. Both of these then lead to there being very good agreement between H{$\alpha$}- and Mg II-based masses over a wide range in black hole mass, i.e., M $_{BH}$ \~{} 10$^{7-9}$ M $_{⊙}$. In general, these results demonstrate that local scaling relations, using Mg II or H{$\alpha$}, are applicable for AGNs at moderate luminosities and up to z \~{} 2. }