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 MBH given some set of observables. Special attention is given to the case where one uses the AGN continuum luminosity and emission line widths to estimateMBH, and we outline how to set up the conditional probability distribution of MBH given the observed luminosity, line width, and redshift. We show how to combine the broad-line estimates of MBH with information from an intrinsic correlation betweenMBH and L, and from the intrinsic distribution of MBH, in a manner that improves the estimates ofMBH. Simulation was used to assess how the distribution of MBH inferred from the broad-line mass estimates differs from the intrinsic distri-bution, andwe 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 effective-ness of using the C iv emission line to estimateMBH and to indirectly probe the C iv region sizeYluminosity (R-L) re-lationship. A linear regression of log Lk (15498) on logMBH found that L1549 / M 1:170:22BH. A linear regression also found that MBH / L0:410:071549 FWHM2C iv, implying a C iv R-L relationship of the form RC iv / L0:410:071549. Including the C iv line FWHM resulted in a reduction of a factor of 1/3 in the error in the estimates of MBH over simply using the continuum luminosity, statistically justifying its use. We estimated MBH from both C iv and H 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 / L1/2UV for both lines