The Mass of Quasars

TL;DR

This paper reviews current methods for estimating quasar black hole masses, discusses their limitations and biases, and emphasizes the need for improved techniques and data to enhance accuracy in quasar studies.

Contribution

It provides an in-depth analysis of single-epoch virial mass estimators, highlighting biases and the impact of errors on quasar black hole mass measurements.

Findings

SE mass estimates are biased by errors and sample selection effects.

Current methods have an accuracy of about 0.5 dex in mass estimation.

Improved reverberation mapping data is needed for better mass estimates.

Abstract

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.