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

Yue Shen, Michael A. Strauss, Masamune Oguri, Joseph F. Hennawi, Fan Xiaohui, 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, Gillian R. Knapp

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316 Scopus citations


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(rp) to marginalize over redshift-space distortions and redshift errors. For a real-space correlation function of the form ξ(r) = (r/r0), 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 ≤ rp ≤ 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 & Tonnen halo mass function, the quasar lifetime is estimated to lie in the range ∼4-50Myr 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) × 1012 h-1 M for quasars with 2.9 ≤ z ≤ 3.5 and (4-6) × 1012 h-1 M for quasars with z ≥ 3.5; the effective bias factor b eff increases with redshift, e.g., beff ∼ 8 at z = 3.0 and beff ∼ 16 at z = 4.5.

Original languageEnglish (US)
Pages (from-to)2222-2241
Number of pages20
JournalAstronomical Journal
Issue number5
StatePublished - May 2007

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Cosmology: observations
  • Large-scale structure of universe
  • Quasars: general
  • Surveys


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