The Luminosity and Color Dependence of the Galaxy Correlation Function

Abstract

We study the luminosity and color dependence of the galaxy 2-point correlation function in the Sloan Digital Sky Survey, starting from a sample of 200,000 galaxies over 2500 deg^2. We concentrate on the projected correlation function w(r_p), which is directly related to the real space ξ(r). The amplitude of w(r_p) grows continuously with luminosity, rising more steeply above the characteristic luminosity L_*. 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 more strongly clustered at large scales and faint red galaxies more strongly clustered 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 w(r_p) data better than a power-law, explaining inflections at r_p ~ 1-3 Mpc/h as the transition between the 1-halo and 2-halo regimes of ξ(r). The implied minimum mass for a halo hosting a central galaxy above a luminosity threshold L grows as M_min ~ L at low luminosities and more steeply above L_*. The mass at which an average halo has one satellite galaxy brighter than L is M_1 ~ 23 M_min(L). 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. HOD models nicely explain the joint luminosity-color dependence of w(r_p) in terms of the color fractions of central and satellite populations as a function of halo mass. The inferred HOD properties are in good qualitative agreement with theoretical predictions.