The ESO Slice Project (ESP) galaxy redshift survey VII. The redshift and real-space correlation functions

We present analyses of the two-point correlation properties of the ESO Slic e Project (ESP) galaxy redshift survey, both in redshift and real space. Fr om the redshift-space correlation function xi(s) we are able to trace posit ive clustering out to separations as large as 50h(-1) Mpc, after which xi(s ) smoothly breaks down, crossing the zero value between 60 and 80 h(-1) Mpc . This is best seen from the whole magnitude-limited redshift catalogue, us ing the J(3) minimum-variance weighting estimator. xi(s) is reasonably well described by a shallow power law with gamma similar to 1.5 between 3 and 5 0 h(-1) Mpc, while on smaller scales (0.2 - 2h(-1) Mpc) it has a shallower slope (gamma similar to 1). This flattening is shown to be mostly due to th e redshift-space damping produced by virialized structures, and is less evi dent when volume-limited samples of the survey are analysed. We examine the full effect of redshift-space distortions by computing the t wo-dimensional correlation function xi(r(p), pi) from which we project out the real-space xi(r) below 10 h(-1) Mpc. This function is well described by a power-law model (r/r(0))(-gamma), with r(o) = 4.15(-0.21)(+0.20) Mpc and gamma = 1.67(-0.09)(+0.07) for the whole magnitude-limited catalogue. Comparison to other redshift surveys shows a consistent picture in which ga laxy clustering remains positive out to separations of 50 h(-1) Mpc or larg er, in substantial agreement with the results obtained from angular surveys like the APM and EDSGC. Also the shape of the two-point correlation functi on is remarkably unanimous among these data sets, in all cases requiring mo re power on scales larger than 5 h(-1) Mpc (a 'shoulder'), with respect to a simple extrapolation of the canonical . The analysis of xi(s) for volume-limited subsamples with different luminosi ty shows evidence of luminosity segregation only for the most luminous samp le with M-bJ, less than or equal to -20.5. For these galaxies, the amplitud e of clustering is on all scales > 4 h(-1) Mpc about a factor of 2 above th at of all other subsamples containing less luminous galaxies. When redshift -space distortions are removed through projection of xi(r(p), pi), however, a weak dependence on luminosity is seen at small separations also at faint er magnitudes, resulting in a growth of r(o) from 3.45(-0.30)(+0.21) h(-1) Mpc to 5.15(-0.44)(+0.39) h(-1) Mpc, when the limiting absolute magnitude o f the sample changes from M = -18.5 to M = -20. This effect is masked in re dshift space, as the mean pairwise velocity dispersion experiences a parall el increase, basically erasing the effect of the clustering growth on xi(s) .