Correlating galaxy colour and halo concentration: A tunable Halo Model
  of galactic conformity
  We extend the Halo Occupation Distribution (HOD) framework to generate mock
galaxy catalogs exhibiting varying levels of "galactic conformity", which has
emerged as a potentially powerful probe of environmental effects in galaxy
evolution. Our model correlates galaxy colours in a group with the
concentration of the common parent dark halo through a "group quenching
efficiency" $\rho$ which makes older, more concentrated halos $\textit{at fixed
mass}$ preferentially host redder galaxies. We find that, for a specific value
of $\rho$, this 1-halo conformity matches corresponding measurements in a group
catalog based on the Sloan Digital Sky Survey. Our mocks also display
conformity at large separations from isolated objects, potentially an imprint
of halo assembly bias. A detailed study - using mocks with assembly bias erased
while keeping 1-halo conformity intact - reveals a rather nuanced situation,
however. At separations $\lesssim 4$Mpc, conformity is mainly a 1-halo effect
dominated by the largest halos and is $\textit{not}$ a robust indicator of
assembly bias. Only at very large separations ($\gtrsim 8$Mpc) does genuine
2-halo conformity, driven by the assembly bias of small halos, manifest
distinctly. We explain all these trends in standard Halo Model terms. Our model
opens the door to parametrized HOD analyses that self-consistently account for
galactic conformity at all scales.
