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 284,489 galaxies selected from SDSS DR4. Galaxies are divided into six samples according to luminosity, and each of these samples is further divided into red and blue subsamples according to their (g-r) colors. Projected autocorrelation is estimated for each subsample, and projected cross-correlation is estimated for each pair of subsamples. At projected separations r(p) greater than or similar to 1 h(-1) Mpc, all correlation functions are roughly parallel, although the correlation amplitude depends systematically on both luminosity and color. On r(p) less than or similar to 1 h(-1) Mpc, the autocorrelation and 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 cross- correlation between red and blue galaxies. We estimate the relative bias factor on scales r(p) greater than or similar to 1 h(-1) Mpc for each subsample using its autocorrelation 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 < M-r <= -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 ratio R-ij equivalent to WiiWjj/W-ij(2), where W-ij is the projected correlation between subsample i and j. Results suggest that a significant stochastic/nonlinear component exists in the relationship between red and blue galaxies, particularly on small scales.