It has long been believed that accretion onto supermassive black holes powers quasars , but there has been 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 \sim 30 \% - 35 \% , strongly suggesting that their black holes are rotating very fast , with specific angular momentum a \approx 1 , which stays roughly constant with redshift .
The average radiative efficiency could be reduced by a factor of \sim 2 , depending on the adopted zeropoint for the black hole mass scale .
The inferred large spins and their lack of significant evolution are in agreement with the predictions of recent semi-analytical models of hierarchical galaxy formation if black holes gain most of their mass through accretion .