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 4, 428 optically selected luminous quasars with redshift 2. 9 le z le 5. 4 selected over 4041 degsup 2 from the Fifth Data Release of the Sloan Digital Sky Survey. We fit a power-law to the projected correlation function wsub p (rsub p) to marginalize over redshift space distortions and redshift errors. For a real-space correlation function of the form zeta (r) = (r/rsub 0) sup -{gamma}, the fitted parameters in comoving coordinates are rsub 0 = 15. 2 +- 2. 7 hsup -1 Mpc and gamma = 2. 0 +- 0. 3, over a scale range 4 le rsub p le 150 hsup -1 Mpc. Thus high-redshift quasars are appreciably more strongly clustered than their z approx 1. 5 counterparts, which have a comoving clustering length rsub 0 approx 6. 5 hsup -1 Mpc. Dividing our sample into two redshift bins: 2. 9 le z le 3. 5 and z ge 3. 5, and assuming a power-law index gamma = 2. 0, we find a correlation length of rsub 0 = 16. 9 +- 1. 7 hsup -1 Mpc for the former, and rsub 0 = 24. 3 +- 2. 4 hsup -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 and 30 approx 600 Myr for quasars with z ge 3. 5. The corresponding duty cycles are 0. 004 approx 0. 05 for the lower redshift bin and 0. 03 approx 0. 6 for the higher redshift bin. The minimum mass of halos in which these quasars reside is 2-3 x 10sup 12 hsup -1 Msub {circledot} for quasars with 2. 9 le z le 3. 5 and 4-6 x 10sup 12 hsup -1 Msub {circledot} for quasars with z ge 3. 5; the effective bias factor bsub eff increases with redshift, e. g. , bsub eff approx 8 at z = 3. 0 and bsub eff approx 16 at z = 4. 5.