Abstract
We provide a simple theoretical model for the quasar luminosity function at high redshifts that naturally reproduces the statistical properties of the luminous Sloan Digital Sky Survey (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 inferred duty cycle of quasar activity (~107 yr) in Lyman break galaxies at z ~ 3. An acceptable fit to all of these constraints requires 0.7 σ8 1.0. 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 ~8% at z 5.7. It is interesting to note that the limiting quasar luminosity in our best-fit relation L ∝ v/G scales as the binding energy of the host galaxy divided by its dynamical time, implying that feedback is the mechanism that regulates black hole growth in galactic potential wells.
Highlights
While the quasar luminosity function has been studied extensively at redshifts below z $ 3 (e.g., Boyle, Shanks, & Peterson 1988; Hartwick & Schade 1990; Pei 1995; Boyle et al 2000), the Sloan Digital Sky Survey (SDSS; Fukugita et al 1996; Gunn et al 1998; York et al 2001) has, in recent years, substantially increased the number of quasars known at ze3:5 (Fan et al 2001a, 2001b; Schneider et al 2001)
We provide a simple theoretical model for the quasar luminosity function at high redshifts that naturally reproduces the statistical properties of the luminous Sloan Digital Sky Survey (SDSS) quasar sample at redshifts z $ 4:3 and ze5:7
We predict the quasar luminosity function under the hypothesis that quasar activity is associated with galaxy mergers
Summary
While the quasar luminosity function has been studied extensively at redshifts below z $ 3 (e.g., Boyle, Shanks, & Peterson 1988; Hartwick & Schade 1990; Pei 1995; Boyle et al 2000), the Sloan Digital Sky Survey (SDSS; Fukugita et al 1996; Gunn et al 1998; York et al 2001) has, in recent years, substantially increased the number of quasars known at ze3:5 (Fan et al 2001a, 2001b; Schneider et al 2001). The density of bright quasars is observed to decline rapidly with redshift below z $ 2 (Boyle, Shanks, & Peterson 1988; Hartwick & Schade 1990) This decline has been explained (Kauffman & Haehnelt 2000; see Cavaliere & Vittorini 2000) in terms of decreases in the merger rate and the availability of cold gas to fuel the black holes. Our model for the evolution of the quasar luminosity function is based on the Press-Schechter (1974) mass function and halo merger rates computed with the excursion set formalism (Bond et al 1991; Lacy & Cole 1993).
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