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