  We formulate a model of the conditional colour-magnitude distribution (CCMD)
to describe the distribution of galaxy luminosity and colour as a function of
halo mass. It consists of two populations of different colour distributions,
dubbed pseudo-blue and pseudo-red, respectively, with each further separated
into central and satellite galaxies. We define a global parameterization of
these four colour-magnitude distributions and their dependence on halo mass,
and we infer parameter values by simultaneously fitting the space densities and
auto-correlation functions of 79 galaxy samples from the Sloan Digital Sky
Survey defined by fine bins in the colour-magnitude diagram (CMD). The model
deprojects the overall galaxy CMD, revealing its tomograph along the halo mass
direction. The bimodality of the colour distribution is driven by central
galaxies at most luminosities, though at low luminosities it is driven by the
difference between blue centrals and red satellites. For central galaxies, the
two pseudo-colour components are distinct and orthogonal to each other in the
CCMD: at fixed halo mass, pseudo-blue galaxies have a narrow luminosity range
and broad colour range, while pseudo-red galaxies have a narrow colour range
and broad luminosity range. For pseudo-blue centrals, luminosity correlates
tightly with halo mass, while for pseudo-red galaxies colour correlates more
tightly (redder galaxies in more massive haloes). The satellite fraction is
higher for redder and for fainter galaxies, with colour a stronger indicator
than luminosity. We discuss the implications of the results and further
applications of the CCMD model.
