Rapidly Spinning Black Holes in Quasars: An Open Question

Wang et al. (2006) estimated an average radiative efficiency of 30% -- 35% for quasars at moderate redshift. We find that their method is not independent of quasar lifetimes and thus that quasars do not necessarily have such high efficiencies. Nonetheless, it is possible to derive interrelated constraints on quasar lifetimes, Eddington ratios, and radiative efficiencies of supermassive black holes. We derive such constraints using a statistically complete sample of quasars with black hole mass estimates from broad Mg II, made both with and without the radiation pressure correction of Marconi et al. (2008). We conclude that for quasars with L/LEdd > 0.02, lifetimes can range from 140 to 750 Myr for Schwarzschild black holes. Coupled with observed black hole masses, quasar lifetimes of < 140 Myr would imply that radiatively inefficient accretion or BH mergers must be important in the accretion history of quasars. Given reasonable assumptions about the quasar population, if the average quasar lifetime is < 1 Gyr, and if radiatively inefficient accretion is unimportant, then not many BHs with Eddington ratio < 0.2 can be rapidly spinning.