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

Abstract

We study the behavior of the three-point correlation function xi_3 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 3-point function Q3 ~ xi_3/xi_2^2. On smaller scales (< 10 Mpc/h), 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 the one developed for the bispectrum. We show that our method recovers the bias parameters introduced into mock galaxies by a HOD prescription and is also able to handle potential systematics in the case when a smaller number than ideal of mock catalogs is used to estimate the covariance matrix. We find that current redshift surveys (e.g. SDSS or 2dFGRS) are just about large enough to get interesting new constraints on bias.