A first step toward constraining supermassive black-hole growth

Updated scaling relations, useful for estimating black hole masses MBH of large samples of distant AGNs and quasars using a single spectrum, are presented. This is timely given the recent improvements made to the reverberation mapping mass determinations and the empirical radius–luminosity relationships on which the scaling relations rely. The redshift distribution of mass estimates of different quasar samples, based on these scaling relations, shows that luminous, distant quasars have very massive black holes MBH ≳ 109M⊙, even at z ≳ 4. Also, there is a limit to how massive and luminous black holes can become: MBH ≲ 1010M⊙ and Lbol < 1048 erg s−1. Preliminary mass functions of active black holes out to z ≈ 4 are presented.