On Departures from a Power Law in the Galaxy Correlation Function
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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 a volume-limited subset of 22,000 galaxies with absolute magnitude M-r < - 21. Both correlation functions show subtle but systematic departures from the best-fit power law, in particular a change in slope at r(p) similar to 1-2 h(-1) Mpc. These departures are stronger for the volume-limited sample, which is restricted to relatively luminous galaxies. We show that the inflection point in w(p)(r(p)) can be naturally explained by contemporary models of galaxy clustering, according to which it marks the transition from a large-scale regime dominated by galaxy pairs in separate dark matter halos to a small-scale regime dominated by galaxy pairs in the same dark matter halo. For example, given the dark halo population predicted by an inflationary cold dark matter scenario, the projected correlation function of the volume-limited sample can be well reproduced by a model in which the mean number of M-r < - 21 galaxies in a halo of mass M > M-1 = 4.74 x 10(13) h(-1) M-. is [N](M)=(M/M-1)(0.89), with 75% of the galaxies residing in less massive, single-galaxy halos and simple auxiliary assumptions about the spatial distribution of galaxies within halos and the fluctuations about the mean occupation. 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)/dof = 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.