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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.