The three-point correlation function of luminous red galaxies in the Sloan Digital Sky Survey

Abstract

We present measurements of the redshift-space three-point correlation function of 50 967 luminous red galaxies (LRGs) from Data Release 3 (DR3) of the Sloan Digital Sky Survey (SDSS). We have studied the shape dependence of the reduced three-point correlation function (Q z (s, q, θ )) on three different scales, s = 4, 7 and 10 h −1 Mpc, and over the range of 1 < q < 3 and 0 • < θ < 180 • . On small scales (s = 4 h −1 Mpc), Q z is nearly constant, with little change as a function of q and θ. However, there is evidence for a shallow U-shaped behaviour (with θ ) which is expected from theoretical modelling of Q z (s, q, θ). On larger scales (s = 7 and 10 h −1 Mpc), the U-shaped anisotropy in Q z (with θ ) is more clearly detected. We compare this shape dependence in Q z (s, q, θ ) with that seen in mock galaxy catalogues which were generated by populating the dark matter haloes in large N-body simulations with mock galaxies using various halo occupation distributions (HOD). We find that the combination of the observed number density of LRGs, the (redshift-space) two-point correlation function and Q z (s, q, θ ) provides a strong constraint on the allowed HOD parameters (M min , M 1 , α) and breaks key degeneracies between these parameters. For example, our observed Q z (s, q, θ) disfavours mock catalogues that overpopulate massive dark matter haloes with many LRG satellites. We also estimate the linear bias of LRGs to be b = 1.87 ± 0.07 in excellent agreement with other measurements.

Modeling the Galaxy Three‐Point Correlation Function

“…The main results from these recent SDSS and 2dFGRS analyses of the 3PCF are (1) on large scales, the observed 3PCF is in qualitative agreement with expectations for the growth of structure from Gaussian initial conditions; (2) on smaller scales (i.e., in the nonlinear and weakly nonlinear regimes), the 3PCF measured in redshift space scales with the redshift-space two-point correlation function (2PCF, or ) as $ 2 , consistent with the ''hierarchical clustering'' Ansatz (Peebles 1980); (3) the shape dependence of the reduced 3PCF depends at most weakly on galaxy luminosity; and (4) the amplitude of the 3PCF is larger for elongated triangle configurations than for more symmetric triangle shapes (Gaztañaga & Scoccimarro 2005;Nichol et al 2006;Kulkarni et al 2007), again consistent with expectations from nonlinear clustering theory.…”

“…This is in contrast to the results of x 4 above and to the 2dFGRS results of on similar scales, where a significantly stronger shape dependence of Q( ) is evident. As noted by Gaztañaga & Scoccimarro (2005) and Kulkarni et al (2007) the differences can be traced to the binning scheme; the relatively wide binning scheme used here results in smearing and therefore suppression of the U shape of Q over most scales of interest. This effect is not due primarily to the binning in : small bins in both r and u are necessary to see the effects of shape-dependent clustering.…”

“…These surveys now provide both the volume and the number of galaxies required to make robust measurements of the 3PCF over a range of scales. For example, recent papers by Kayo et al (2004), Hikage et al (2005), Nichol et al (2006), Nishimichi et al (2006), and Kulkarni et al (2007) have presented measurements of the 3PCF from the Sloan Digital Sky Survey (SDSS; York et al 2000) as a function of scale, galaxy luminosity, and color. Nichol et al (2006) also quantified the effect of large-scale structures on the shape dependence of the 3PCF.…”

Covariance matrices for halo number counts and correlation functions

“…More complex models and exact computations at lowest order of perturbation theory would introduce homogeneous kernels Q N (x 1 , .., x N ) (in place of the numbers S N ) that also depend on the angles between the vectors x i and x j (Scoccimarro et al 1999). Observations of galaxy clustering show, for instance, that Q 3 displays a weak dependence on the triangle shape, while remaining close to unity (Gaztanaga et al 2005;Kulkarni et al 2007). Here we simply take the constant value Q 3 = S 3 /3.…”

Analytic model for the bispectrum of galaxies in redshift space

“…The current state of the art galaxy redshift surveys [21][22][23][24] have provided large samples of the Universe, and investigators have already carried out some of the tests noted above: 3-point correlation functions have been estimated by [25][26][27][28][29][30] and bispectra by [31][32][33][34].…”