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 ~200,000 galaxies over 2500 deg2. We concentrate our analysis on volume-limited subsamples of specified luminosity ranges, for which we measure the projected correlation function wp(rp), which is directly related to the real-space correlation function ξ(r). The amplitude of wp(rp) rises continuously with luminosity from Mr ≈ -17.5 to Mr ≈ -22.5, with the most rapid increase occurring above the characteristic luminosity L* (Mr ≈ -20.5). Over the scales 0.1 h-1 Mpc < rp < 10 h-1 Mpc, the measurements for samples with Mr > -22 can be approximated, imperfectly, by power-law three-dimensional correlation functions ξ(r) = (r/r0)-γ with γ ≈ 1.8 and r0(L*) ≈ 5.0 h-1 Mpc. The brightest subsample, -23 < Mr < -22, has a significantly steeper ξ(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 rp ~ 1-3 h-1 Mpc as the transition between the one-halo and two-halo regimes of ξ(r). The implied minimum mass for a halo hosting a central galaxy more luminous than L grows steadily, with Mmin ∝ 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 M1 ≈ 23Mmin(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 Mmin 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.