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For refcode 2007AJ....133.2222S:
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2007AJ....133.2222S Clustering of High-Redshift (z >= 2.9) Quasars from the Sloan Digital Sky Survey Yue Shen, Michael A. Strauss, Masamune Oguri, Joseph F. Hennawi, Xiaohui Fan, Gordon T. Richards, Patrick B. Hall, James E. Gunn, Donald P. Schneider, Alexander S. Szalay, Anirudda R. Thakar, Daniel E. Vanden Berk, Scott F. Anderson, Neta A. Bahcall, Andrew J. Connolly, and Gillian R. Knapp Abstract. 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 deg^2^ 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 {xi}(r)=(r/r_0_)^-{gamma}^, the fitted parameters in comoving coordinates are r_0_=15.2+/-2.7h^-1^ Mpc and {gamma}=2.0+/-0.3, over a scale range 4h^-1^Mpc<=r_p_<=150h^-1^Mpc. Thus high-redshift quasars are appreciably more strongly clustered than their z~1.5 counterparts, which have a comoving clustering length r_0_~6.5h^-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 r_0_=16.9+/-1.7h^-1^ Mpc for the former and r_0_=24.3+/-2.4h^-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)x10^12^h^-1^ M_sun_ for quasars with 2.9<=z<=3.5 and (4 -- 6)x10^12^h^-1^ M_sun_ 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. Key words: Cosmology: Observations, Cosmology: Large-Scale Structure of Universe, Galaxies: Quasars: General, Surveys
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