A Physical Model for the Luminosity Function of High‐Redshift Quasars

We provide a simple theoretical model for the quasar luminosity function at high redshifts that naturally reproduces the statistical properties of the luminous SDSS quasar sample at redshifts z ∼ 4.3 and z � 5.7. Our model is based on the assumptions that quasar emission is triggered by galaxy mergers, and that the black hole mass is proportional to a power-law in the circular velocity of the host galactic halo, vc. We assume that quasars shine at their Eddington luminosity over a time proportional to the mass ratio between the small and final galaxies in the merger. This simple model fits the quasar luminosity function at z ∼ 2–3, reproduces the normalization and logarithmic slope (β ∼ −2.58) at z ∼ 4.3, explains the space density of bright SDSS quasars at z ∼ 6.0, reproduces the black hole – halo mass relation for dormant black holes in the local universe, and matches the estimated duty cycle of quasar activity ( ∼ 10 7 years) in Lyman-break galaxies at z ∼ 3. Based on the derived luminosity function we predict the resulting gravitational lensing rates for high redshift quasars. The lens fractions in the SDSS samples are predicted to be ∼ 2 % at z ∼ 4.3 and ∼ 10 % at z � 5.7. Interestingly,