Cosmological Evolution of Quasars

We present a model for the cosmological evolution of quasars (QSOs) under the assumption that they are powered by massive accreting black holes. Accretion flows around massive black holes make a transition from high radiative efficiency (∼ 10%) to low efficiency, advection-dominated flows when Ṁ/ṀEdd falls below the critical rate ∼ 0.3α2 ∼ 10−2 where Ṁ is the mass accretion rate, ṀEdd ∝ M is the usual Eddington rate with the nominal 10% efficiency, and α(≤ 1) is the dimensionless viscosity parameter. We identify this transition with the observed break at a redshift ∼ 2 in the QSOs’ X-ray luminosity evolution. Growth of black holes through accretion could naturally lead to such a transition at a critical redshift zc ∼ 1− 3, provided that most of high redshift QSOs appear with near Eddington luminosities at z ∼ 3 − 4 and the accretion rates decline over the Hubble time in a roughly synchronous manner. Before the transition, the QSOs’ luminosities (with a high efficiency) slowly decrease and after the transition at zc, the QSO luminosities evolve approximately as ∝ (1 + z) K(z) where K(z) gradually varies from z = zc to z ∼ 0 around K ∼ 3. The results depend on the details of the QSO X-ray emission mechanism. We discuss some further implications. Subject headings: accretion, accretion disks − cosmology: theory − quasars: general