The Real Space and Redshift Space Correlation Functions at Redshiftz= 1/3

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Abstract
We present the results of a study of the two-point correlation function for a sample of field galaxies taken from the Canadian Network for Observational Cosmology cluster survey. The sample consists of 183 galaxies within a contiguous region of sky covering 216 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 0.37. We fit the real space correlation function to a power law ξ(r) = (r/r0)-1.7, finding r0=1.9−0.4+0.4 h-1 Mpc (Ω0 = 1), or r0=2.2−0.4+0.5 h−1 Mpc (Ω0 = 0.2); uncertainties are estimated using the bias-corrected bootstrap resampling method, with 300 resamplings. This low correlation length implies strong evolution has occurred in the correlation function; if the observed correlation function is modeled as ξ(r, z) = ξ(r, 0)(1 + z)-(3+ε) with ξ(r, 0) = (r/5.1 h-1 Mpc)-1.7, then ε ≈ 1.5. Comparison of the redshift space and real space correlation functions indicates that the one-dimensional pairwise peculiar velocity dispersion σ at z ≈ 0.37 is weakly inconsistent with 720 km s-1, the value predicted by the cosmic virial theorem if Ω0 = 1. The observed correlation functions are, however, consistent with σ ≈ 360 km s-1, the value expected if Ω0 = 0.2.

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