On Departures from a Power Law in the Galaxy Correlation Function

We measure the projected correlation function w_p(r_p) from the Sloan DigitalSky Survey for a flux-limited sample of 118,000 galaxies and for a volumelimited subset of 22,000 galaxies with absolute magnitude M_r<-21. Bothcorrelation functions show subtle but systematic departures from the best-fitpower law, in particular a change in slope at r_p~1-2 Mpc/h. These departuresare stronger for the volume-limited sample, which is restricted to relativelyluminous galaxies. We show that the inflection point in w_p(r_p) can benaturally explained by contemporary models of galaxy clustering, according towhich it marks the transition from a large scale regime dominated by galaxypairs in separate dark matter halos to a small scale regime dominated by galaxypairs in the same dark matter halo. For example, given the dark halo populationpredicted by an inflationary cold dark matter scenario, the projectedcorrelation function of the volume-limited sample can be well reproduced by amodel in which the mean number of M_r<-21 galaxies in a halo of mass M>M_1=4.74X 10^{13}\msun/h is _M=(M/M_1)^{0.89}, with 75% of the galaxies residing inless massive, single-galaxy halos. This physically motivated model has the samenumber 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). Departuresfrom a power-law correlation function encode information about the relationbetween galaxies and dark matter halos. Higher precision measurements of thesedepartures for multiple classes of galaxies will constrain galaxy bias andprovide new tests of the theory of galaxy formation.