An Improved Method for Using Mg II to Estimate Black Hole Masses in Active Galactic Nuclei

We present a method for obtaining accurate black hole (BH) mass estimates from the Mg II emission line in active galactic nuclei (AGNs). Employing the large database of AGN measurements from the Sloan Digital Sky Survey (SDSS) presented by Shen et al., we find that AGNs in the redshift range 0.3-0.9, for which a given object can have both Hβ and Mg II line widths measured, display a modest but correctable discrepancy in Mg II-based masses that correlates with the Eddington ratio. We use the SDSS database to estimate the probability distribution of the true (i.e., Hβ-based) mass given a measured Mg II line width. These probability distributions are then applied to the SDSS measurements from Shen et al. across the entire Mg II-accessible redshift range (0.3-2.2). We find that accounting for this residual correlation generally increases the dispersion of Eddington ratios by a small factor (~0.09 dex for the redshift and luminosity bins we consider). We continue to find that the intrinsic distribution of Eddington ratios for luminous AGNs is extremely narrow, 0.3-0.4 dex, as demonstrated by Kollmeier et al. Using the method we describe, Mg II emission lines can be used with confidence to obtain BH mass estimates.