The mean density and two-point correlation function for the CfA redshift survey slices

In the two complete slices of the extension of the CfA redshift survey, the scale of the largest inhomogeneities is comparable with the extent of the survey. Thus, even though it is among the largest existing redshift surveys in its combination of depth (~ 100h^-1^ Mpc) and large angular coverage (~0.4 sr), this sample is not "fair." The "average" statistical measures used to characterize the galaxy distribution are substantially more uncertain than previously estimated. The mean galaxy number density for the two strips is uncertain by 25%. In the ~3-14h^-1^ Mpc range, the spatial two-point correlation function ζ(s) has a slope γ ~ 1.6 and a correlation length s_0_ ~ 7.5h^-1^ Mpc. This correlation length is larger than the "standard" value matched to the theoretical models. Because of the large uncertainty in the mean density, the ranges in the slope and amplitude are respectively ~1.3-1.9 and ~5-12h^-1^ Mpc. On scales larger than 20h^-1^ Mpc, the correlation function is indeterminate. The correlation function ζ(r_p_, π) shows that the rms peculiar velocities are ~300 km s^-1^, in agreement with analyses of other samples.

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