Clustering of high-redshift (z≥2.9) quasars from the sloan digital sky survey

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 wp (rp) to marginalize over redshift-space distortions and redshift errors. For a real-space correlation function of the form xi(r) = (r/r0)(-gamma), the fitted parameters in comoving coordinates are r0 = 15: 2 +/- 2: 7 h(-1) Mpc and gamma = 2.0 +/- 0.3, over a scale range 4 h(-1) Mpc <= rp <= 150 h(-1) Mpc. Thus high-redshift quasars are appreciably more strongly clustered than their z approximate to 1.5 counterparts, which have a comoving clustering length r0 approximate to 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 gamma = 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 similar to 4-50 Myr for quasars with 2.9 <= z <= 3.5, and similar to 30-600 Myr for quasars with z >= 3.5. The corresponding duty cycles are similar to 0.004-0.05 for the lower redshift bin and similar to 0.03-0.6 for the higher redshift bin. The minimum mass of halos in which these quasars reside is (2-3) x 10(12) h(-1) M circle dot for quasars with 2.9 <= z <= 3.5 and (4Y6) x 10(12) h(-1) M circle dot for quasars with z >= 3.5; the effective bias factor b(eff) increases with redshift, e. g., b(eff) similar to 8 at z = 3.0 and b(eff) similar to 16 at z = 4: 5.