The real space and redshift space correlation functions at redshift z=1/3

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 less than or equal to r less than or equal to 21.7 and redshifts 0.21 less than or equal to z less than or equal to 0.53. The median redshift of the sample is 0.37. We fit the real space correlation function to a power law xi(r)=(r/r(0))(-1.7) finding r(0)=1.9(-0.4)(+0.4) h(-1) Mpc (Omega(0)=1), or r(0)=2.2(-0.4)(+0.5) h(-1) Mpc (Omega(0)=0.2); uncertainties are estimated using the bias-corrected boot-strap 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 xi(r, z)=xi(r, 0) (1+z)(-(3+epsilon)) with xi(r, 0)=(r/5.1 h(-1) Mpc)(-1.7), then epsilon approximate to 1.5. Comparison of the redshift space and real space correlation functions indicates that the one-dimensional pairwise peculiar velocity dispersion cr at z approximate to 0.37 is weakly inconsistent with 720 km s(-1), the value predicted by the cosmic virial theorem if Omega(0)=1. The observed correlation functions are, however, consistent with sigma approximate to 360 km s(-1), the value expected if Omega(0)=0.2.