Clustering of High-Redshift (z ≥ 2.9) Quasars from the Sloan Digital Sky Survey

By Yue Shen, M. Strauss, M. Oguri, J. Hennawi, Xiaohui Fan, Gordon Richards, P. Hall, James E. Gunn, D. Schneider, A. Szalay and 6 more. 2007

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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 ξ(r) = (r/r0)-γ, 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 & 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) × 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 beff increases with redshift, e.g., beff ∼ 8 at z = 3.0 and beff ∼ 16 at z = 4.5.

Subfields: Astronomy and Astrophysics, Instrumentation

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THE BULK OF THE BLACK HOLE GROWTH SINCE z ∼ 1 OCCURS IN A SECULAR UNIVERSE: NO MAJOR MERGER–AGN CONNECTION (2010, background): “Even so, the timescales involved for such a process can be as much as an order of magnitude larger than the typical quasar lifetime of 1-100 Myr (e.g., Porciani et al. 2004; Hopkins et al. 2005b; Shen et al. 2007).”
THINK OUTSIDE THE COLOR BOX: PROBABILISTIC TARGET SELECTION AND THE SDSS-XDQSO QUASAR TARGETING CATALOG (2010, background): “…quasars and their co-evolution with galaxies, e.g., through measurements of quasar clustering (e.g., Arp 1970; Hawkins & Reddish 1975; Osmer 1981; Shen et al. 2007; Ross et al. 2009), or they can be used to study the intervening intergalactic medium (e.g., Chelouche et al. 2007; Ménard et al.…”
Accretion-driven evolution of black holes: Eddington ratios, duty cycles and active galaxy fractions (2011, methodology): “Reproducing the strong observed clustering of z = 4 quasars (Shen et al. 2007) requires duty cycles close to one and minimal scatter between luminosity and halo mass (White, Martini & Cohn 2008; Shankar et al. 2010b).”
Clustering of intermediate redshift quasars using the final SDSS III-BOSS sample (2015, methodology): “The high biases found by Shen et al. (2007) imply that the quasars they use are in far rarer halos than those we study, by a factor of∼ 70×.”
A SURVEY OF z ∼ 6 QUASARS IN THE SLOAN DIGITAL SKY SURVEY DEEP STRIPE. II. DISCOVERY OF SIX QUASARS AT zAB>21 (2009, background): “The mean shift with respect to the systemic redshift at z > 3 is about 600 km s−1 (Shen et al. 2007), corresponding to δz ∼ 0.015 at z ∼ 6.”
The Sloan Digital Sky Survey Quasar Catalog: Fourteenth data release (2017, background): “The main science driver was studies of the quasar population through the measurement of their luminosity function (e.g. Richards et al. 2006) and clustering properties (e.g. Hennawi et al. 2006; Shen et al. 2007).”
The Giant Gemini GMOS survey of zem > 4.4 quasars – I. Measuring the mean free path across cosmic time (2014, methodology): “Gemini/GMOS R400 spectra of four quasars which have large differences in zem from our analysis (which sets the rest wavelength here) and from using the Shen et al. (2007) algorithm.”
SELF-CONSISTENT MODELS OF THE AGN AND BLACK HOLE POPULATIONS: DUTY CYCLES, ACCRETION RATES, AND THE MEAN RADIATIVE EFFICIENCY (2007, background): “…and accretion modes, including the addition of modest log-normal scatter inṁ0(M,z) (e.g., Kollmeier et al. 2005; Netzer et al. 2007; Shen et al. 2007b) and sharper revisions in which some black holes accrete at super-Eddington or highly sub-Eddington rates, perhaps with reduced…”
A Cosmological Framework for the Co-Evolution of Quasars, Supermassive Black Holes, and Elliptical Galaxies. I. Galaxy Mergers and Quasar Activity (2007, background): “…(Porciani et al. 2004; Porciani & Norberg 2006; Wake et al. 2004; Croom et al. 2005; Coil et al. 2007; Myers et al. 2007a; da Angela et al. 2007; Shen et al. 2007) and investigations of the quasar proximity effect (Faucher-Giguere et al. 2008; Kim & Croft 2007; Nascimento Guimaraes et al. 2007).”
THE z = 5 QUASAR LUMINOSITY FUNCTION FROM SDSS STRIPE 82 (2012, background): “23 The Lyα line can also have systematic offsets, in particular a ∼ 500 km s−1 redshift due to absorption of the blue wing by the Lyα forest (e.g., Shen et al. 2007).”
The realm of the galaxy protoclusters (2016, background): “However, Shen et al. (2007) found that the most luminous QSOs at 3 < z < 4.5 have a much larger correlation length that is comparable to that of massive clusters today (Postman et al., 1992).”
EDDINGTON-LIMITED ACCRETION AND THE BLACK HOLE MASS FUNCTION AT REDSHIFT 6 (2010, background): “A similar conclusion was reached by Shankar et al. (2010) who showed that the strong clustering at z > 4 measured by Shen et al. (2007) means quasars reside in high mass dark matter halos and (assuming a tight MBH −Mhalo relation) must have a high duty cycle of ≈ 95% at z = 6.”
Black Hole Masses and Enrichment of z ~ 6 SDSS Quasars (2007, methodology): “…spectrum of an individual quasar are correlated, one can obtain a better redshift correction if the peak wavelengths of several lines are measured (see Shen et al. 2007), but we do not apply this method as we do not have enough suitable lines with a high enough signal–to–noise ratio in our spectra.”
A SURVEY OF z ∼ 6 QUASARS IN THE SLOAN DIGITAL SKY SURVEY DEEP STRIPE. I. A FLUX-LIMITED SAMPLE AT zAB < 21 (2007, background): “For the redshifts measured from Lyα, their real errors could be much larger due to the scatter in the relation between Lyα redshifts and systemic redshifts (Shen et al. 2007).”
A physical model for z∼ 2 dust-obscured galaxies (2009, background): “Moreover, the halo masses are consistent with the inferred halo masses of high-redshift galaxies of a comparable luminosity – that is, SMGs (Blain et al. 2004), and quasars (Croom et al. 2005; Lidz et al. 2006; Hopkins et al. 2007b; Shen et al. 2007).”
Reionization and Cosmology with 21-cm Fluctuations (2009, background): “On the other hand, high-redshift quasars have a large clustering bias (Shen et al. 2007), implying that the effect of their ionising contribution on the ionization PS may be significant during the latter part of the pre-overlap era.”
QUASAR CLUSTERING FROM SDSS DR5: DEPENDENCES ON PHYSICAL PROPERTIES (2008, methodology): “…et al. 2008; Ross et al. 2008) owing to the uncertainties in the clustering measurements for individual redshift bins, high redshift (z& 3) SDSS quasars have much stronger clustering than their low redshift (z. 2.2) counterparts (Shen et al. 2007a), reflecting the large bias of their host halos.”
The Sloan Digital Sky Survey Quasar Catalog. IV. Fifth Data Release (2007, methodology): “An independent determination of the redshifts of 5865 quasars with redshifts larger than 2.9 in the catalog was performed by Shen et al. (2007).”
The Sloan Digital Sky Survey quasar catalog: ninth data release (2012, background): “These measurements can be useful to understand the relative shifts between different emission lines and discuss the structure of the broad line region (see Shen et al. 2007; Shang et al. 2007).”