2007ApJS..168....1K

We describe the general problem of estimating black hole masses of active galactic nuclei (AGNs) by calculating the conditional probability distribution of M_BHgiven 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_BHgiven the observed luminosity, line width, and redshift. We show how to combine the broad-line estimates of M_BHwith information from an intrinsic correlation between M_BHand 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_BHinferred 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_BHand to indirectly probe the C IV region size-luminosity (R-L) relationship. A linear regression of logL_λ(1549 Å) on logM_BHfound that L₁₅₄₉∝M^1.17±0.22_BH. A linear regression also found that M_BH∝L^0.41±0.07₁₅₄₉FWHM²_CIV_, implying a C IV R-L relationship of the form R_CIV_∝L0.41±0.07^₁₅₄₉. Including the C IV line FWHM resulted in a reduction of a factor of ∼1/3 in the error in the estimates of M_BHover simply using the continuum luminosity, statistically justifying its use. We estimated M_BHfrom both C IV and Hβ 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∝L^1/2_UV for both lines.