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 } < -21 .
Both correlation functions show subtle but systematic departures from the best-fit power law , in particular a change in slope at r _ { p } \sim 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 \times 10 ^ { 13 } h ^ { -1 } M _ { \odot } is \langle N \rangle _ { 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 } / \hbox { 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 .