Cosmological evolution of the duty cycle of quasars

Quasars are powered by accretion onto supermassive black holes, but the problem of the duty cycle related to the episodic activity of the black holes remains one of the major questions of the cosmological evolution of quasars. In this Letter, we obtain quasar duty cycles based on analyses of a large sample composed of 10,979 quasars with redshifts z <= 2.1 from the Sloan Digital Sky Survey (SDSS) Data Release 3 (DR3). We estimate the masses of the quasar black holes and obtain their mass function (MF) in the present sample. We then get the duty cycle (delta) over bar (z) = 10(-3) similar to 1 based on Soltan's argument, implying that black holes are undergoing multiple episodic activity. We find that the duty cycle has a strong evolution. By comparison, we show that the evolution of the duty cycle follows the history of the cosmic star formation rate (SFR) density in the universe, providing intriguing evidence of a natural connection between star formation and the triggering of black hole activity. Feedback on star formation from black hole activity is briefly discussed.