  The observed correlation between star-formation in central galaxies and in
their neighbours (a phenomenon dubbed galactic conformity) is in need of a
convincing physical explanation. We use a volume-limited sample of galaxies
with redshifts less than 0.03 drawn from the SDSS DR7 to investigate the scale
dependence of the effect and how it changes as a function of the mass of the
central galaxy. Conformity extends over a central galaxy stellar mass range
spanning two orders of magnitude. In central galaxies with masses less than
10^10 M_sun, conformity extends out to scales in excess of 4 Mpc, well beyond
the virial radii of their dark matter halos. For low mass central galaxies,
large-scale conformity with neighbours is only seen when the centrals have low
star formation rate or gas content. In contrast, at high stellar masses,
conformity with neighbours applies in the gas-rich regime and is clearly
confined to scales comparable to the virial radius of the dark matter halo of
the central galaxy. Our analysis of a mock catalogue from the Guo et al (2011)
models shows that conformity-like effects are much weaker than observed, and
apply only to the low SFR/M* tail of neighbouring galaxies. In the models, the
median and the upper percentiles of the SFR/M* distribution remain almost
unchanged, which is in contradiction with the data. Conformity between
low-mass, gas-poor central galaxies and their distant neighbours cannot be
explained within the framework of halo occupation distribution (HOD) models. It
is likely a signature of pre-heating of the intergalactic gas at an earlier
epoch. The smaller-scale conformity between high-mass, gas-rich central
galaxies and their close neighbours may be a signature of ongoing gas accretion
onto central galaxies in a minority of massive dark matter halos.
