Early growth of massive black holes in quasars

Episodic activity of quasars is driving growth of supermassive black holes (SMBHs) via accretion of baryon gas. In this Letter, we develop a simple method to analyze the duty cycle of quasars up to the redshift z similar to 6 universe from luminosity functions (LFs). We find that the duty cycle below redshift z similar to 2 follows the cosmic history of star formation rate ( SFR) density. Beyond z similar to 2, the evolutionary trends of the duty cycle are opposite to that of the cosmic SFR density history, implying the role of feedback from black hole activity. With the duty cycle, we get the net lifetime of quasars (z less than or similar to 5) about similar to 10(9) yr. Based on the local SMBHs, the mean mass of SMBHs is obtained at any redshifts and their seeds are of 10(5) M-circle dot at the reionization epoch (z(re)) of the universe through the conservation of black hole number density in a comoving frame. We find that primordial black holes (similar to 10(3) M-circle dot) are able to grow up to the seeds via a moderate super-Eddington accretion of similar to 30 times the critical rate from z = 24 to z(re). Highly super-Eddington accretion onto the primordial black holes is not necessary.