Cosmological Evolution of the Accretion Rate in Quasars

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  • 27 October 1998
Abstract
We derive the mass accretion rate dM/dt onto quasar black holes (BHs), and its redshift evolution between 0<z<4, using the observed optical and X-ray quasar luminosity functions (LFs). We make the following assumptions: (i) the mass-function of dark matter halos follows the Press-Schechter theory, (ii) the BH mass scales linearly with the halo mass, (iii) quasars have a constant universal lifetime, and (iv) the optical luminosity is modeled as a thin disk, and the X-ray/optical flux ratio is calibrated from a sample of observed quasars. We show that the accretion rate in Eddington units, dm/dt, inferred from either the optical or X-ray data under these assumptions generically decreases as a function of time from z=4 to z=0. For a typical quasar lifetime of 10^7 yr, the value of dm/dt inferred is independent of halo mass and, near z=0, drops to substantially sub-Eddington values at which advection - dominated accretion flows (ADAFs) exist. This decline of dm/dt, possibly followed by a transition to low radiative efficiency ADAFs near z=0, could be the origin of the absence of bright quasars in the local universe and the faintness of accreting BHs at the centers of nearby galaxies. We argue that a decline of the accretion rate of the quasar population is indeed expected in cosmological structure formation models.

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