The Center for Astrophysics Redshift Survey: Luminosity Function and Two-Point Correlation Function

Abstract

We compare the luminosity function and the two-point spatial correlation function for the two slices of the CfA redshift survey extension to mB(0) ≤ 15.5 [8h ≤ RA. ≤ 17h and 26.5° ≤ DEC. ≤ 38.5°], with those for the early survey limited to mB(0) ≤ 14.5 [bII ≥ 40°, and DEC. ≥ 0°]. The derived properties of the two samples agree within the errors. The parameters of the luminosity function are M* = −19.1±0.1 and α = −1.2±0.1 for the 15.5 sample, and M* = −19.3±0.1 and α = −1.1 ± 0.1 for the 14.5 sample. We use an inhomogeneity-independent method to calculate the luminosity function. The slopes of the correlation functions for the two samples are −1.5 ± 0.35, shallower than the canonical slope of −1.8. The correlation lengths are 7.5 ± 5h−1 Mpc, larger than the correlation length of 5h−1 Mpc matched to the theoretical models. Because of the 25% uncertainty in the mean density of the 15.5 sample, the correlation function is indeterminate on scales larger than ∼ 20h−1 Mpc.