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

We present measurements of the redshift-space three-point correlation function of 50967 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, theta)) on three different scales, s = 4, 7 and 10 h(-1) Mpc, and over the range of 1 < q < 3 and 0 degrees < theta < 180 degrees. On small scales (s = 4 h(-1) Mpc), Q(z) is nearly constant, with little change as a function of q and theta. However, there is evidence for ($) over circle shallow U-shaped behaviour (with 0) which is expected from theoretical modelling of Q(z)(s, q, theta). On larger scales (s = 7 and 10 h(-1) Mpc), the U-shaped anisotropy in Q(z) (with theta) is more clearly detected. We compare this shape dependence in Q(z) (s, q, theta) 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, theta) provides a strong constraint on the allowed HOD parameters (M-min, M-1, alpha) and breaks key degeneracies between these parameters. For example, our observed Q(z)(s, q, theta) 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.