### 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 ξ(r) = (r/r_{0})^{-γ}, the fitted parameters in comoving coordinates are r_{0} = 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 r_{0} ≈ 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 r_{0} = 16.9 ± 1.7 h^{-1} Mpc for the former and r_{0} = 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) × 10^{12} h^{-1} M_{⊙} for quasars with 2.9 ≤ z ≤ 3.5 and (4-6) × 10^{12} 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.

Original language | English (US) |
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Pages (from-to) | 2222-2241 |

Number of pages | 20 |

Journal | Astronomical Journal |

Volume | 133 |

Issue number | 5 |

DOIs | |

State | Published - May 2007 |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Keywords

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

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## Cite this

*Astronomical Journal*,

*133*(5), 2222-2241. https://doi.org/10.1086/513517