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

We provide a simple theoretical model for the quasar luminosity function athigh redshifts that naturally reproduces the statistical properties of theluminous SDSS quasar sample at redshifts z~4.3 and z>5.7. Our model is based onthe assumptions that quasar emission is triggered by galaxy mergers, and thatthe black hole mass is proportional to a power-law in the circular velocity vof the host galactic halo. We assume that quasars shine at their Eddingtonluminosity over a time proportional to the mass ratio between the small andfinal galaxies in the merger. This simple model fits the quasar luminosityfunction at z~2-3, reproduces the normalization and logarithmic slope (beta-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 thelocal universe, and matches the estimated duty cycle of quasar activity (~10^7years) in Lyman-break galaxies at z~3. Based on the derived luminosity functionwe 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, the limiting quasar luminosity in our best-fitrelation of L proportional to v^5/G, scales as the binding energy of the hostgalaxy divided by its dynamical time, implying that feedback is the mechanismthat regulates black hole growth in galactic potential wells.Comment: 19 pages, 6 figures. Submitted to Ap