Abundance ratios in red-sequence galaxies over a wide mass range: The
  "X-planes" for magnesium, calcium, carbon and nitrogen
  We analyse the abundance ratios of the light elements Mg, Ca, C and N,
relative to Fe, for 147 red-sequence galaxies in the Coma cluster and the
Shapley Supercluster. The sample covers a six-magnitude range in luminosity,
from giant ellipticals to dwarfs at M^*+4. We exploit the wide mass range to
investigate systematic trends in the abundance ratios Mg/Fe, Ca/Fe, C/Fe and
N/Fe. We find that each of these ratios can be well modelled using
two-parameter relations of the form [X/Fe] = a0 + a1 log sigma + a2 [Fe/H],
where sigma is the velocity dispersion. Analysing these "X-planes" reveals new
structure in the abundance patterns, beyond the traditional one-parameter (e.g.
Mg/Fe-sigma) correlations. The X-planes for the alpha elements, Mg and Ca,
indicate a positive correlation with velocity dispersion, and simultaneously an
anti-correlation with Fe/H (i.e. a1>0 and a2<0). Taking both effects into
account dramatically reduces the scatter, compared to the traditional
X/Fe-sigma relations. For C and N, a similar correlation with velocity
dispersion is recovered, but there is no additional dependence on Fe/H (i.e.
a1>0 and a2~0). The explicit dependence of X/Fe on two parameters is evidence
that at least two physical processes are at work in setting the abundance
patterns. The Fe/H dependence of Mg/Fe and Ca/Fe, at fixed sigma, may result
from different durations of star formation, from galaxy to galaxy. The absence
of corresponding Fe/H dependence for C and N is consistent with these elements
being generated in lower-mass stars. The increase with sigma, at fixed Fe/H, is
similar for elements Mg, C and N, and slightly shallower for Ca. This pattern
of trends cannot be explained solely by a systematic variation of
star-formation time-scale with sigma.
