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 open as one of the major questions of 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 $z\le2.1$ from the Sloan Digital Sky Survey (SDSS) Data Release Three. We estimate masses of quasar black holes and obtain their mass function (MF) of the present sample. We then get the duty cycle $\bar{\delta}(z)=10^{-3}\sim 1$ based on the So{\l}tan'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 evolution of the duty cycle follows the history of cosmic star formation rate (SFR) density in the Universe, providing intriguing evidence for a natural connection between star formation and triggering of black hole activity. Feedback on star formation from black hole activity is briefly discussed.