SIMBAD references

We study the two-point correlation function of a uniformly selected sample of 4426 luminous optical quasars with redshift 2.9≤z≤5.4 selected over 4041 deg² from the Fifth Data Release of the Sloan Digital Sky Survey. We fit a power-law to the projected correlation function w_p(r_p) to marginalize over redshift-space distortions and redshift errors. For a real-space correlation function of the form ξ(r)=(r/r₀)^–γ, the fitted parameters in comoving coordinates are r₀=15.2±2.7 h^–1 Mpc and γ=2.0±0.3, over a scale range 4 h^–1 Mpc≤r_p≤150 h^–1 Mpc. Thus high-redshift quasars are appreciably more strongly clustered than their z~1.5 counterparts, which have a comoving clustering length r₀~6.5 h^–1 Mpc. Dividing our sample into two redshift bins, 2.9≤z≤3.5 and z≥3.5, and assuming a power-law index γ=2.0, we find a correlation length of r₀=16.9±1.7 h^–1 Mpc for the former and r₀=24.3±2.4 h^–1 Mpc for the latter. Strong clustering at high redshift indicates that quasars are found in very massive, and therefore highly biased, halos. Following Martini & Weinberg, we relate the clustering strength and quasar number density to the quasar lifetimes and duty cycle. Using the Sheth & Tormen halo mass function, the quasar lifetime is estimated to lie in the range ∼4-50 Myr for quasars with 2.9≤z≤3.5, and ∼30-600 Myr for quasars with z≥3.5. The corresponding duty cycles are ∼0.004-0.05 for the lower redshift bin and ∼0.03-0.6 for the higher redshift bin. The minimum mass of halos in which these quasars reside is (2-3)x10¹² h^–1 M_☉ for quasars with 2.9≤z≤3.5 and (4-6)x10¹² h^–1 M_☉ for quasars with z≥3.5; the effective bias factor b_eff increases with redshift, e.g., b_eff∼8 at z=3.0 and b_eff∼16 at z=4.5.