The three-point function in large-scale structure: Redshift distortions and galaxy bias

We study the behaviour of the three-point correlation function ζ of dark matter and mock galaxies, concentrating on the effects of redshift-space distortions and the determination of galaxy bias parameters in current redshift galaxy surveys. On large scales, redshift-space distortions tend to wash out slightly the configuration dependence of the reduced three-point function Q ₃ ∼ ζ/ξ². On smaller scales (≤10h ^-1 Mpc), Q₃ develops a characteristic U-shape anisotropy between elongated and open triangles due to the effects of velocity dispersion. We show that this shape is quite universal, very weakly dependent on scale, initial spectral index or cosmological parameters and should be detectable in current galaxy surveys even if affected by shot noise or galaxy bias. We present a detailed method for obtaining constraints on galaxy bias parameters from measurements of Q₃ in current galaxy redshift surveys, based on the eigenmode analysis similar to that developed for the bispectrum. We show that our method recovers the bias parameters introduced into mock galaxies by a halo occupation distribution prescription and is also able to handle potential systematics in the case when a smaller number than is ideal for mock catalogues is used to estimate the covariance matrix. We find that current redshift surveys (e.g. SDSS or 2dFGRS) are just about large enough to obtain interesting new constraints on bias.