The origins of the bulge and disc components of galaxies are of primary importance to understanding galaxy formation. Here bulge-disc decomposition is performed simultaneously in B- and R-bands for 922 bright galaxies in 8 nearby (z < 0.06) clusters with deep redshift coverage using photometry from the NOAO Fundamental Plane Survey. The total galaxy colours follow a universal colour-magnitude relation (CMR). The discs of L_* galaxies are 0.24 magnitudes bluer in $B-R$ than bulges. Bulges have a significant CMR slope while the CMR slope of discs is flat. Thus the slope of the CMR of the total light is driven primarily (60%) by the bulge-CMR, and to a lesser extent (40%) by the change in the bulge-to-total ratio as a function of magnitude. The colours of the bulge and disc components do not depend on the bulge-to-total ratio, for galaxies with bulge-to-total ratios greater than 0.2. While the colours of the bulge components do not depend significantly on environment, the median colours of discs vary significantly, with discs in the cluster centre redder by 0.10 magnitudes than those at the virial radius. Thus while star formation in bulges appears to be regulated primarily by mass-dependent, and hence presumably internal, processes, that of discs is affected by the cluster environment.
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