Virial masses of black holes from single epoch spectra of active galactic nuclei

We describe the general problem of estimating black hole masses of active galactic nuclei (AGNs) by calculating the conditional probability distribution of M-BH given some set of observables. Special attention is given to the case where one uses the AGN continuum luminosity and emission line widths to estimate M-BH, and we outline how to set up the conditional probability distribution of M-BH given the observed luminosity, line width, and redshift. We show how to combine the broad-line estimates of M-BH with information from an intrinsic correlation between M-BH and L, and from the intrinsic distribution of M-BH, in a manner that improves the estimates of M-BH. Simulation was used to assess how the distribution of M-BH inferred from the broad-line mass estimates differs from the intrinsic distribution, and we find that this can lead to an inferred distribution that is too broad. We use these results and a sample of 25 sources that have recent reverberation mapping estimates of AGN black hole masses to investigate the effectiveness of using the C IV emission line to estimate M-BH and to indirectly probe the C IV region size-luminosity (R-L) relationship. A linear regression of log L-lambda (1549 angstrom) on log M-BH found that L-1549 proportional to M-BH(1.17 +/- 0.22) A linear regression also found that M-BH proportional to L-1549(0.41 +/- 0.07) FWHMC IV2, implying a C IV R-L relationship of the form R-C IV proportional to L-1549(0.41 +/- 0.07) Including the C IV line FWHM resulted in a reduction of a factor of similar to 1/3 in the error in the estimates of M-BH over simply using the continuum luminosity, statistically justifying its use. We estimated M-BH from both C IV and H beta for a sample of 100 sources, including new spectra of 29 quasars. We find that the two emission lines give consistent estimates if one assumes R proportional to L-UV(1/2) for both lines.