On Departures from a Power Law in the Galaxy Correlation Function

By Idit Zehavi, D. Weinberg, Zheng Zheng, A. Berlind, Joshua A. Frieman, R. Scoccimarro, R. Sheth, M. Blanton, Max Tegmark, H. Mo and 18 more. 2003

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We measure the projected correlation function wp from the Sloan Digital Sky Survey for a flux-limited sample of 118,000 galaxies and a volume-limited subset of 22,000 galaxies with absolute magnitude Mr < -21. Both correlation functions show subtle but systematic departures from the best-fit power law, in particular a change in slope at rp ~ 1-2 h-1 Mpc. These departures are stronger for the volume-limited sample, which is restricted to relatively luminous galaxies. We show that the inflection point in wp can be naturally explained by contemporary models of galaxy clustering, according to which it marks the transition from a large-scale regime dominated by galaxy pairs in separate dark matter halos to a small-scale regime dominated by galaxy pairs in the same dark matter halo. For example, given the dark halo population predicted by an inflationary cold dark matter scenario, the projected correlation function of the volume-limited sample can be well reproduced by a model in which the mean number of Mr < -21 galaxies in a halo of mass M > M1 = 4.74 × 1013 h-1 M☉ is M = 0.89, with 75% of the galaxies residing in less massive, single-galaxy halos and simple auxiliary assumptions about the spatial distribution of galaxies within halos and the fluctuations about the mean occupation. This physically motivated model has the same number of free parameters as a power law, and it fits the wp data better, with a χ2/dof = 0.93, compared to 6.12 (for 10 degrees of freedom, incorporating the covariance of the correlation function errors). Departures from a power-law correlation function encode information about the relation between galaxies and dark matter halos. Higher precision measurements of these departures for multiple classes of galaxies will constrain galaxy bias and provide new tests of the theory of galaxy formation.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/70d0920739673d345832c81bf6dbf4e68b99cb78

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Citations in the corpus

Cosmic evolution of quasar clustering: implications for the host haloes (2004, background): “…et al. 2001; Berlind & Weinberg 2002; Marinoni & Hudson 2002; Magliocchetti & Porciani 2003; van den Bosch, Mo & Yang 2003; Yang, Mo & van den Bosch 2003; Zehavi et al. 2004) and high (Bullock, Wechsler & Somerville 2002; Moustakas & Somerville 2002; Hamana et al. 2004; Zheng 2004) redshift.”
GALAXY CLUSTERING IN THE NEWFIRM MEDIUM BAND SURVEY: THE RELATIONSHIP BETWEEN STELLAR MASS AND DARK MATTER HALO MASS AT 1 < z < 2 (2010, methodology): “This transition is well established in measurements of the correlation function (e.g. Zehavi et al. 2004) and can be seen in the correlation functions shown in Figure 3.”
Clustering of High-Redshift (z ≥ 2.9) Quasars from the Sloan Digital Sky Survey (2007, background): “Groth & Peebles 1977; Davis & Peebles 1983; Hawkins et al. 2003), although there is an excess above the power law below 2h−1 Mpc, thought to be due to halo occupation effects (Zehavi et al. 2004, 2005).”
K-Band Properties of Galaxy Clusters and Groups: Luminosity Function, Radial Distribution, and Halo Occupation Number (2004, background): “Most of these come from matching the observed galaxy two-point correlation function or power spectrum (e.g., Seljak 2000; Peacock & Smith 2000; Yang et al. 2003; Zehavi et al. 2004; Magliocchetti & Porciani 2003).”
What Aspects of Galaxy Environment Matter? (2006, methodology): “For example, we can measure as a function of galaxy properties the mean environments around galaxies (Hogg et al. 2003; Blanton et al. 2005a) or their correlation functions (Davis & Geller 1976; Santiago & Strauss 1992; Hermit et al. 1996; Norberg et al. 2002; Zehavi et al. 2004).”
Towards a concordant model of halo occupation statistics (2006, background): “To make our predictions regarding the occupation numbers somewhat more quantitative, we use our WMAP3 MCMC to compute the slope of 〈Nsat〉M at the high-mass end.”
The distribution of stellar mass in the low‐redshift Universe (2009, methodology): “The near power-law behaviour of galaxy correlations was emphasised in early work (e.g. Davis & Peebles 1983) and has been examined in some detail in previous studies with Sloan Digital Sky Survey data (e.g. Zehavi et al. 2004, 2005; Masjedi et al. 2006).”
First Measurement of the Clustering Evolution of Photometrically Classified Quasars (2005, background): “A small-scale break is worth investigating, as Zehavi et al. (2004) find powerlaw departures on 1–2 h 1 Mpc scales for the projected galaxy autocorrelation.”
The DEEP2 Galaxy Redshift Survey: Color and Luminosity Dependence of Galaxy Clustering at z ∼ 1 (2007, background): “These trends are confirmed by Budavari et al. (2003) and Zehavi et al. (2004) using SDSS data.”
Galaxy Groups in the SDSS DR4. II. Halo Occupation Statistics (2007, background): “…1998, 2002; Peacock & Smith 2000; Seljak 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002; Bullock et al. 2002; Scranton 2002; Kang et al. 2002; Marinoni & Hudson 2002; Zheng et al. 2002, 2005; Magliocchetti & Porciani 2003; Berlind et al. 2003; Zehavi et al. 2004, 2005; Tinker et al. 2005).”
Satellite kinematics – III. Halo masses of central galaxies in SDSS (2010, unknown): “Such methods include the modelling of the clustering of galaxies (e.g., Yang, Mo, & van den Bosch 2003; Zehavi et al. 2004, 2005; Tinker et al. 2005; Collister & Lahav 2005; Skibba et al. 2006; van den Bosch et al. 2007; Brown et al. 2008; Skibba & Sheth 2009), galaxy-galaxy weak lensing (e.g.,…”
A MaxBCG Catalog of 13,823 Galaxy Clusters from the Sloan Digital Sky Survey (2007, methodology): “Galaxies down to 0.4 L∗ in r are then assigned to particular dark matter particles according to a scheme which matches the observed luminosity-dependent two-point clustering of SDSS galaxies as measured by Zehavi et al. (2004).”
The Large-Scale and Small-Scale Clustering of Lyman Break Galaxies at 3.5 ⩽ z ⩽ 5.5 from the GOODS Survey (2005, methodology): “The HOD formalism has been successfully applied to various local galaxy samples (e.g., different luminosities, colors, spectral types, etc.; Zehavi et al. 2004b;Magliocchetti et al. 2003) and also at intermediate redshift (QSOs; Porciani et al. 2004).”
HALO OCCUPATION DISTRIBUTION MODELING OF CLUSTERING OF LUMINOUS RED GALAXIES (2008, background): “…FROM A POWER LAW IN THE GALAXY TWO-POINT CORRELATION FUNCTION Departures of the galaxy two-point correlation function from a pure power law have been observed for both low- and highredshift galaxies (Hawkins et al. 2003; Zehavi et al. 2004; Ouchi et al. 2005; Coil et al. 2006; Lee et al. 2006).”
The Luminosity and Color Dependence of the Galaxy Correlation Function (2004, methodology): “…sample and for volume-limited subsets with different luminosity and color cuts, and we fit the measurements with power laws, which generally provide a good but not perfect description at rpP 20 h 1 Mpc (Zehavi et al. 2004, hereafter Z04; see also Hawkins et al. 2003; Gaztañaga & Juszkiewicz 2001).”