Dissecting the Red Sequence: The Bulge and Disc Colours of Early-Type
  Galaxies in the Coma Cluster
  We explore the internal structure of red sequence galaxies in the Coma
cluster across a wide range of luminosities ($-17>M_g>-22$) and cluster-centric
radii ($0<r_{\rm{cluster}}<1.3 r_{200}$). We present the 2D bulge-disc
decomposition of galaxies in deep Canada-France-Hawaii Telescope $u,g,i$
imaging using GALFIT. Rigorous filtering is applied to identify an analysis
sample of 200 galaxies which are well described by an `archetypal' S0 structure
(central bulge + outer disc). We consider internal bulge and/or disc colour
gradients by allowing component sizes to vary between bands. Gradients are
required for $30\%$ of analysis sample galaxies. Bulge half-light radii are
found to be uncorrelated with galaxy luminosity ($R_e \sim 1$ kpc, $n\sim2$)
for all but the brightest galaxies ($M_g<-20.5$). The S0 discs are brighter (at
fixed size, or smaller at fixed luminosity) than those of star-forming spirals.
A similar colour-magnitude relation is found for both bulges and discs. The
global red sequence for S0s in Coma hence results from a combination of both
component trends. We measure an average bulge $-$ disc colour difference of
$0.09\pm0.01$ mag in $g-i$, and $0.16\pm0.01$ mag in $u-g$. Using simple
stellar population models, bulges are either $\sim2$-$3\times$ older, or
$\sim2\times$ more metal-rich than discs. The trend towards bluer global S0
colours observed further from Coma's core is driven by a significant
correlation in disc colour with cluster-centric radius. An equivalent trend is
detected in bulge colours at a marginal significance level. Our results
therefore favour environment-mediated mechanisms of disc fading as the dominant
factor in S0 formation.
