The Two - Point Correlation Function at Redshift

We present the results of a study of the two-point correlation function for a sample of field galaxies taken from the CNOC cluster survey. The sample consists of 144 galaxies within a contiguous region of space subtending 225 square arcminutes. The objects have r-band magnitudes 17.0 ≤ r ≤ 21.7 and redshifts 0.21 ≤ z ≤ 0.53. The median redshift of the sample is z̄ = 0.36. The real space correlation function is found to be consistent with a power law ξ(r) = ( /r0) −1.7 with r0 = 2.1 +0.6 −0.3 h −1Mpc (Ω0 = 1), or r0 = 2.5 +0.7 −0.4 h −1Mpc (Ω0 = 0.2). Uncertainties are estimated using the bias-corrected bootstrap resampling method, with 300 resamplings. This low correlation length implies strong evolution since z∼ 0.36 has occurred in either the correlation function or the luminosity function; if the observed correlation function is modeled as ξ(r, z) = ξ(r, 0)(1 + z)−(3+ε) with ξ(r, 0) = ( /5.1 h−1Mpc) −1.7, then ε = 0.8 −1.3. Comparison of the redshift space and real space correlation function indicates that the one-dimensional pairwise peculiar velocity dispersion σ at z ≈ 0.36 is weakly inconsistent with 770 km s−1, the value predicted by the Cosmic Virial Theorem if Ω0 = 1. The observed correlation function is, however, consistent with σ = 400 km s−1, the value expected if Ω0 = 0.2. Subject headings: large-scale structure of the universe — galaxies: clustering — galaxies: evolution Department of Astronomy, University of Toronto, Toronto, Ont., Canada M5S 3H8 Guest observer, Canada-France-Hawaii Telescope, operated jointly by NRC of Canada, CNRS of France, and the University of Hawaii C.A.S.A., University of Colorado, Campus Box 389, Boulder, CO 80309-0389