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

We report the measurement of the three-point correlation function (3PCF) ofgalaxies for the Las Campanas Redshift Survey (LCRS). We have not only measuredthe 3PCF in redshift space but also developed a method to measure the projected3PCF which has simple relations to the real space 3PCF. Both quantities havebeen measured as a function of triangle size and shape with only a fractionaluncertainty in each individual bin. Various tests derived from mock catalogshave been carried out to assure that the measurement is stable and that theerrors are estimated reliably. Our results indicate that the 3PCFs both inredshift space and in real space have small but significant deviations from thewell-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 $0.81\mpc$ is noted.The real-space $\Qru$ for $0.2 \ls r_{12} \ls 3\mpc$ and $r_{31}\ls 6\mpc$ canbe well described by half the mean 3PCF predicted by a CDM model with $\Omega_0h=0.2$. Implications for the CDM cosmogonic models are discussed in detail withthe help of mock simulation samples.Comment: minor revisions; accepted for publication in ApJ; 21 pages with 6 figures include