The Three‐Point Correlation Function of Galaxies Determined from the Las Campanas Redshift Survey

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Abstract
We report the measurement of the three-point correlation function (3PCF) of galaxies for the Las Campanas Redshift Survey (LCRS). We have not only measured the 3PCF in redshift space, but we have also developed a method to measure the projected 3PCF that has simple relations to the real-space 3PCF. Both quantities have been measured as a function of triangle size and shape with only a fractional uncertainty in each individual bin. Various tests derived from mock catalogs have been carried out to assure that the measurement is stable and that the errors are estimated reliably. Our results indicate that the 3PCFs both in redshift space and in real space have small but significant deviations from the well-known hierarchical form. The 3PCF in redshift space can be fitted by Qred(s, u, v) = 0.5×10 for 0.8 < s12 < 8 h-1 Mpc and s31 < 16 h-1 Mpc, and the projected 3PCF by Qproj(rp, u, v)=0.7r−0.3p for 0.2 < rp12 < 3 h-1 Mpc and rp31 < 6 h-1 Mpc (s and rp are in units of h-1 Mpc), although a systematic weak increase of Qproj(rp, u, v) with v at rp > 1 h-1 Mpc is noted. The real space Q(r, u, v) for 0.2 r12 3 h-1 Mpc and r31 6 h-1 Mpc can be well described by half the mean 3PCF predicted by a cold dark matter (CDM) model with Ω0h = 0.2. The general dependence of the 3PCF on triangle shape and size is in qualitative agreement with the CDM cosmogonic models. Quantitatively the 3PCF of the models may depend on the biasing parameter and the shape of the power spectrum, in addition to other model parameters. Taking our result together with the constraints imposed by the two-point correlation function and the pairwise velocity dispersion of galaxies also obtained from the LCRS, we find that we have difficulties in producing a simple model that meets all constraints perfectly. Among the CDM models considered, a flat model with Ω = 0.2 meets the 2PCF and PVD constraints, but gives higher values for the 3PCF than observed. This may indicate that more sophisticated bias models or a more sophisticated combination of model parameters must be considered.