The Sloan Digital Sky Survey Reverberation Mapping Project: Estimating Masses of Black Holes in Quasars with Single-Epoch Spectroscopy

It is well known that reverberation mapping of active galactic nuclei (AGN) reveals a relationship between AGN luminosity and the size of the broad-line region, and that use of this relationship, combined with the Doppler width of the broad emission line, enables an estimate of the mass of the black hole at the center of the active nucleus based on a single spectrum. This has been discussed in numerous papers over the last two decades. An unresolved key issue is the choice of parameter used to characterize the line width; generally, most researchers use FWHM in favor of line dispersion (the square root of the second moment of the line profile) because the former is easier to measure, less sensitive to blending with other features, and usually can be measured with greater precision. However, use of FWHM introduces a bias, stretching the mass scale such that high masses are overestimated and low masses are underestimated. Here we investigate estimation of black hole masses in AGN based on individual or "single epoch" observations, with a particular emphasis in comparing mass estimates based on line dispersion and FWHM. We confirm the recent findings that, in addition to luminosity and line width, a third parameter is required to obtain accurate masses and that parameter seems to be Eddington ratio. We present simplified empirical formulae for estimating black hole masses from the Hbeta (4861 A) and C IV (1549 A) emission lines.