A multiscale approach to environment and its influence on the colour distribution of galaxies

We present a multiscale approach to measurements of galaxy density, applied to a volume-limited sample constructed from SDSS DR5. We populate a rich parameter space by obtaining independent measurements of density on different scales for each galaxy, avoiding the implicit assumptions involved, e.g., in the construction of group catalogues. As the first application of this method, we study how the bimodality in galaxy colour distribution (u-r) depends on multiscale density. The u-r galaxy colour distribution is described as the sum of two gaussians (red and blue) with five parameters: the fraction of red galaxies (f_r) and the position and width of the red and blue peaks (mu_r, mu_b, sigma_r and sigma_b). Galaxies mostly react to their smallest scale (< 0.5 Mpc) environments: in denser environments red galaxies are more common (larger f_r), redder (larger mu_r) and with a narrower distribution (smaller sigma_r), while blue galaxies are redder (larger mu_b) but with a broader distribution (larger sigma_b). There are residual correlations of f_r and mu_b with 0.5 - 1 Mpc scale density, which imply that total or partial truncation of star formation can relate to a galaxys environment on these scales. Beyond 1 Mpc (0.5 Mpc for mu_r) there are no positive correlations with density. However f_r (mu_r) anti-correlates with density on >2 (1) Mpc scales at fixed density on smaller scales. We examine these trends qualitatively in the context of the halo model, utilizing the properties of haloes within which the galaxies are embedded, derived by Yang et al, 2007 and applied to a group catalogue. This yields an excellent description of the trends with multiscale density, including the anti-correlations on large scales, which map the region of accretion onto massive haloes. Thus we conclude that galaxies become red only once they have been accreted onto haloes of a certain mass.