The Three-point Correlation Function of Galaxies Determined from the Las Campanas Redshift Survey

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 also developed a method to measure the projected 3PCF which 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 $\Qsu=0.5\cdot 10^{[0.2+0.1({s\over s+1})^2]v^2}$ for $0.8<s_{12}<8 \mpc$ and $s_{31}<16\mpc$, and the projected 3PCF by $\Qrpu=0.7r_p^{-0.3}$ for $0.2<r_{p12}<3\mpc$ and $r_{p31}<6\mpc$ ($s$ and $r_p$ are in unit of $\mpc$), though a systematic weak increase of $\Qrpu$ with $v$ at $r_p>1\mpc$ is noted. The real-space $\Qru$ for $0.2 \ls r_{12} \ls 3\mpc$ and $r_{31}\ls 6\mpc$ can be well described by half the mean 3PCF predicted by a CDM model with $\Omega_0 h=0.2$. Implications for the CDM cosmogonic models are discussed in detail with the help of mock simulation samples.