The Mass of Quasars

I review the current status of quasar black hole (BH) mass estimations. Spectroscopic methods have been developed to estimate BH mass in broad line quasars to an accuracy of ~0.5 dex. Despite their popularity, significant issues and confusion remain regarding these mass estimators. I provide an in-depth discussion on the merits and caveats of the single-epoch (SE) virial BH mass estimators, and a detailed derivation of the statistical biases of these SE mass estimates resulting from their errors. I show that error-induced sample biases on the order of a factor of several are likely present in the SE mass estimates for flux-limited, statistical quasar samples, and the distribution of SE masses in finite luminosity bins can be narrower than the nominal uncertainty of these mass estimates. I then discuss the latest applications of SE virial masses in quasar studies, including the early growth of supermassive black holes, quasar demography in the mass-luminosity plane, and the evolution of the BH-host scaling relations, with specific emphases on selection effects and sample biases in the SE masses. I conclude that there is a pressing need to understand and deal with the errors in these BH mass estimates, and to improve these BH weighing methods with substantially more and better reverberation mapping data.