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 (Qz(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), Qz 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 Qz(s, q, θ). On larger scales (s= 7 and 10 h−1 Mpc), the U-shaped anisotropy in Qz (with θ) is more clearly detected. We compare this shape dependence in Qz(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 Qz(s, q, θ) provides a strong constraint on the allowed HOD parameters (Mmin, M1, α) and breaks key degeneracies between these parameters. For example, our observed Qz(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.