What drives the ultra-violet colours of passive galaxies?
  We present and analyse optical and ultra-violet colours for passive and
optically-red Coma cluster galaxies for which we have spectroscopic age and
element abundance estimates. Our sample of 150 objects covers a wide range in
mass, from giant ellipticals to the bright end of the dwarf-galaxy regime. We
focus on the colours FUV-i, NUV-i, FUV-NUV, u*-g and g-i. We find that all of
these colours are correlated with both luminosity and velocity dispersion at
the >5 sigma level, with FUV-i and FUV-NUV becoming bluer with increasing
`mass' while the other colours become redder. We perform an empirical analysis
to assess what fraction of the variation in each colour can be accounted for by
variations in the average stellar populations, as traced by the optical
spectra. For u*-g and g-i, most of the observed scatter (~80% after allowing
for measurement errors and for systematic errors in u*-g) is attributable to
stellar population variations, with colours becoming redder with increasing age
and metallicity (Mg/H). The FUV-i colour becomes bluer with increasing age and
with increasing Mg/H, favouring a `metal-rich single-star' origin for the UV
upturn. However, correlations with the optically-dominant stellar populations
account for only about half of the large observed scatter. We propose that the
excess scatter in FUV-i may be due to a varying proportion of ancient stars in
galaxies with younger average ages. The NUV-i colour is sensitive to age and
Mg/H, but exhibits excess scatter that can be attributed to `leakage' of the
FUV upturn. Applying a correction based on the FUV-i colour we account for ~80%
of the variance in NUV-i, as for the optical colours. The FUV-NUV colour shows
strong correlations with age and Mg/H, and little residual scatter.
Interpreting this colour is complicated however, since it mixes the effects
from the main-sequence turn-off with those from the hot evolved stars.
