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. An unresolved key issue is the choice of parameter used to characterize the line width, either FWHM or line dispersion (the square root of the second moment of the line profile). We argue here that 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 AGNs 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. While the AGN continuum luminosity at 5100 A is usually used to predict the Hbeta reverberation lag, we show that the luminosity of the Hbeta broad component can be used instead without any loss of precision, thus eliminating the difficulty of accurately accounting for the host-galaxy contribution to the observed luminosity.