The luminosity and color dependence of the galaxy correlation function

We study the luminosity and color dependence of the galaxy two- point correlation function in the Sloan Digital Sky Survey, starting from a sample of similar to 200,000 galaxies over 2500 deg(2). We concentrate our analysis on volume- limited subsamples of specified luminosity ranges, for which we measure the projected correlation function w(p)( r(p)), which is directly related to the real- space correlation function xi( r). The amplitude of wp( rp) rises continuously with luminosity from M-r approximate to 17.5 to M-r approximate to 22. 5, with the most rapid increase occurring above the characteristic luminosity L-* ( M-r approximate to 20: 5). Over the scales 0: 1 h (-1) Mpc < r(p) < 10 h (-1) Mpc, the measurements for samples with M-r > 22 can be approximated, imperfectly, by power- law three- dimensional correlation functions xi( r) ( r/r(0))(-gamma) with gamma approximate to 1: 8 and r(0)( L-*) approximate to 5: 0 h (-1) Mpc. The brightest subsample, - 23 < M-r < - 22, has a significantly steeper xi( r). When we divide samples by color, redder galaxies exhibit a higher amplitude and steeper correlation function at all luminosities. The correlation amplitude of blue galaxies increases continuously with luminosity, but the luminosity dependence for red galaxies is less regular, with bright red galaxies exhibiting the strongest clustering at large scales and faint red galaxies exhibiting the strongest clustering at small scales. We interpret these results using halo occupation distribution ( HOD) models assuming concordance cosmological parameters. For most samples, an HOD model with two adjustable parameters fits the wp( rp) data better than a power law, explaining inflections at r(p) similar to 1 -3 h (-1) Mpc as the transition between the one- halo and two- halo regimes of xi( r). The implied minimum mass for a halo hosting a central galaxy more luminous than L grows steadily, with M-min proportional to L at low luminosities and a steeper dependence above L-*. The mass at which a halo has, on average, one satellite galaxy brighter than L is M-1 approximate to 23M(min)( L), at all luminosities. These results imply a conditional luminosity function ( at fixed halo mass) in which central galaxies lie far above a Schechter function extrapolation of the satellite population. The HOD model fits nicely explain the color dependence of wp( rp) and the cross correlation between red and blue galaxies. For galaxies with Mr < -21, halos slightly above M-min have blue central galaxies, while more massive halos have red central galaxies and predominantly red satellite populations. The fraction of blue central galaxies increases steadily with decreasing luminosity and host halo mass. The strong clustering of faint red galaxies follows from the fact that nearly all of them are satellite systems in high- mass halos. The HOD fitting results are in good qualitative agreement with the predictions of numerical and semianalytic models of galaxy formation.