Chinese Acad Sci, Key Lab Particle Astrophys, Inst High Energy Phys, Beijing 100049, Peoples R China
; Chinese Acad Sci, Grad Sch, Beijing 100049, Peoples R China
; Observ Carnegie Inst Washington, Pasadena, CA 91101 USA
; Univ Edinburgh, Royal Observ, Inst Astron, Edinburgh EH9 3HJ, Midlothian, Scotland
It has long been believed that accretion onto supermassive black holes powers quasars, but there are still relatively few observational constraints on the spins of the black holes. We address this problem by estimating the average radiative efficiencies of a large sample of quasars selected from the Sloan Digital Sky Survey, by combining their luminosity function and their black hole mass function. Over the redshift interval 0.4 < z < 2.1, we find that quasars have average radiative efficiencies of similar to 30%-35%, strongly suggesting that their black holes are rotating very rapidly, with specific angular momentum a similar to 1, a value that remains roughly constant with redshift. The average radiative efficiency could be reduced by a factor of similar to 2, depending on the adopted zero point for the black hole mass scale. The inferred large spins and their lack of significant evolution are in agreement with the predictions of recent semianalytical models of hierarchical galaxy formation if black holes gain most of their mass through accretion.