  We present a fully analytical halo model of colour-dependent clustering that
incorporates the effects of galactic conformity in a halo occupation
distribution (HOD) framework. The model, based on our previous numerical work,
describes conformity through a correlation between the colour of a galaxy and
the concentration of its parent halo, leading to a correlation between central
and satellite galaxy colours at fixed halo mass. The strength of the
correlation is set by a tunable `group quenching efficiency', and the model can
separately describe group-level correlations between galaxy colour (1-halo
conformity) and large scale correlations induced by assembly bias (2-halo
conformity). We validate our analytical results using clustering measurements
in mock galaxy catalogs, finding that the model is accurate at the 10-20
percent level for a wide range of luminosities and length scales. We apply the
formalism to interpret the colour-dependent clustering of galaxies in the Sloan
Digital Sky Survey (SDSS). We find good overall agreement between the data and
a model that has 1-halo conformity at a level consistent with previous results
based on an SDSS group catalog, although the clustering data require satellites
to be redder than suggested by the group catalog. Within our modelling
uncertainties, however, we do not find strong evidence of 2-halo conformity
driven by assembly bias in SDSS clustering.
