We study the luminosity and color dependence of the galaxy two-point correlation function in the Sloan Digital Sky Survey ( SDSS ) , starting from a sample of \sim 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 { w _ { p } ( r _ { p } ) } rises continuously with luminosity from M _ { r } \approx - 17.5 to M _ { r } \approx - 22.5 , with the most rapid increase occurring above the characteristic luminosity L _ { * } ( M _ { r } \approx - 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 \approx 1.8 and r _ { 0 } ( L _ { * } ) \approx 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 { w _ { p } ( r _ { p } ) } data better than a power-law , explaining inflections at r _ { p } \sim 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 } \propto 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 } \approx 23 M _ { 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 { w _ { p } ( r _ { p } ) } and the cross correlation between red and blue galaxies .
For galaxies with M _ { r } < -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 semi-analytic models of galaxy formation .