Determining central black hole masses in distant active galaxies

An empirical relationship, of particular interest for studies of high-redshift active galactic nuclei (AGNs) and quasars, between the masses of their central black holes and rest-frame ultraviolet (UV) parameters measured in single-epoch AGN spectra is presented. This relationship is calibrated to recently measured reverberation masses of low-redshift AGNs and quasars. An empirical relationship between single-epoch rest-frame optical spectrophotometric measurements and the central masses is also presented. The UV relationship allows reasonable estimates of the central masses to be made for high-redshift AGNs and quasars for which these masses cannot be directly or easily measured by the techniques applicable to the lower luminosity, nearby AGNs. The central mass obtained by this method can be estimated to within a factor of 3 for most objects. This is reasonable given the intrinsic uncertainty of a factor of less than 2 in the primary methods used to measure the central masses of nearby inactive and active galaxies, namely, resolved gas and stellar kinematics in the underlying host galaxy and reverberation-mapping techniques. The UV relationship holds good potential for being a powerful tool for studying black hole demographics at high redshift as well as statistically studying the fundamental properties of AGNs. The broad-line region size-luminosity relationship is key to the calibrations presented here. The fact that its intrinsic scatter is also the main source of uncertainty in the calibrations stresses the need for better observational constraints to be placed on this relationship. The empirically calibrated relationships presented here will be applied to quasar samples in forthcoming work.