The Cross-correlation between Galaxies of Different Luminosities and Colors

We study the cross-correlation between galaxies of different luminosities and colors, using a sample of 284489 galaxies selected from the Sloan Digital Sky Survey, Data Release 4. Galaxies are divided into 6 samples according to luminosity, and each of these samples is further divided into red and blue subsamples according to their (g − r) colors. Projected auto-correlation is estimated for each subsample, and projected cross-correlation is estimated for each pair of subsamples. At projected separations rp & 1 h Mpc, all correlation functions are roughly parallel, although the correlation amplitude depends systematically on both luminosity and color. On rp . 1 h Mpc, the autoand cross-correlation functions of red galaxies are significantly enhanced relative to the corresponding power laws obtained on larger scales. Such enhancement is absent for blue galaxies and in the crosscorrelation between red and blue galaxies. We esimate the relative bias factor on scales r & 1hMpc for each subsample using its auto-correlation function as well as its cross-correlation functions with other subsamples. The relative bias factors obtained from different methods are similar. For blue galaxies the luminosity-dependence of the relative bias is strong over the entire luminosity range probed (−23.0 < Mr ≤ −18.0), while for red galaxies the dependence is weaker and becomes insignificant for luminosities below L. In order to examine whether a significant stochastic/nonlinear component exists in the bias relation, we study the ratioRij ≡ WiiWjj/W 2 ij , whereWij is the projected correlation between subsample ‘i’ and ‘j’. We find that the values of Rij are all consistent with 1 for all-all, redred and blue-blue samples, however significantly larger than 1 for red-blue samples. For faint red faint blue samples the values of Rij are as high as ∼ 2 on small scales (rp . 1 h Mpc) and decrease with increasing rp. These results suggest that a significant stochastic/nonlinear component exists in the relationship between red and blue galaxies, particularly on small scales. Subject headings: large-scale structure of the universe galaxies: halos methods: statistical