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

Abstract

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 Hb 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., Hb-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.

Toward Precision Measurement of Central Black Hole Masses

“…Shen et al (2008), using a large collection of SDSS spectra, find that log ([FWHM(Hβ)] / [FWHM(Mg ii)]) = 0.0062, with scatter of only ∼ 0.11 dex. Onken & Kollmeier (2008) find that the masses derived from Hβ and Mg ii differ as a function of Eddington ratio, although they argue that it is possible to correct for this bias.…”

Planets, Stars and Stellar Systems

“…This link has been strengthened by gas dynamical measurements of black hole masses for a number of other AGN (Wang et al 2009;Onken and Kollmeier 2008;Zhang et al 2008;Vestergaard et al 2008;McGill et al 2008;Hicks and Malkan 2008;Onken et al 2007;Greene and Ho 2007;Kelly and Bechtold 2007). For a solar-type star, this radius is smaller than the Schwarzschild radius when the black hole's mass is less than 10  M ⊙ -so that it is entirely conceivable that a star could accrete onto the black hole without being disrupted first.…”

XMM-NEWTON , SWIFT , AND ROSAT OBSERVATIONS OF LBQS 0102-2713

“…Following Equation (10) Onken & Kollmeier (2008) found Eddington ratios for SDSS quasars ranging between 0.01 and 1. Shemmer et al (2004) derive values for the Eddington ratio ranging between 0.14 and 1.71 (their Table 2).…”