On Departures from a Power Law in the Galaxy Correlation Function

Abstract

We measure the projected correlation function w_p(r_p) from the Sloan Digital Sky Survey for a flux-limited sample of 118,000 galaxies and for a volume limited subset of 22,000 galaxies with absolute magnitude M_r M_1=4.74 X 10^{13}\msun/h is _M=(M/M_1)^{0.89}, with 75% of the galaxies residing in less massive, single-galaxy halos. This physically motivated model has the same number of free parameters as a power law, and it fits the w_p(r_p) data better, with a \chi^2/d.o.f.=0.93 compared to 6.12 (for 10 degrees of freedom, incorporating the covariance of the correlation function errors). Departures from a power-law correlation function encode information about the relation between galaxies and dark matter halos. Higher precision measurements of these departures for multiple classes of galaxies will constrain galaxy bias and provide new tests of the theory of galaxy formation.