A halo model of galaxy colours and clustering in the Sloan Digital Sky Survey

Successful halo-model descriptions of the luminosity dependence of clustering distinguish between the central galaxy in a halo and all the others (satellites). To include colours, we provide a prescription for how the colour-magnitude relation of centrals and satellites depends on halo mass. This follows from two assumptions: (i) the bimodality of the colour distribution at a fixed luminosity is independent of halo mass and (ii) the fraction of satellite galaxies which populate the red sequence increases with luminosity. We show that these two assumptions allow one to build a model of how galaxy clustering depends on colour without any additional free parameters than those required to model the luminosity dependence of galaxy clustering. We then show that the resulting model is in good agreement with the distribution and clustering of colours in the Sloan Digital Sky Survey, both by comparing the predicted correlation functions of red and blue galaxies with measurements and by comparing the predicted colour-mark correlation function with the measured one. Mark correlation functions are powerful tools for identifying and quantifying correlations between galaxy properties and their environments: our results indicate that the correlation between halo mass and environment is the primary driver for correlations between galaxy colours and the environment; additional correlations associated with halo 'assembly bias' are relatively small. Our approach shows explicitly how to construct mock catalogues which include both luminosities and colours - thus providing realistic training sets for, e. g., galaxy cluster-finding algorithms. Our prescription is the first step towards incorporating the entire spectral energy distribution into the halo model approach.