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 6 mag range in luminosity, from giant ellipticals to dwarfs at M-star + 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] = a(0) + a(1) log Sigma + a(2) [Fe/H], where Sigma is the velocity dispersion. Analysing these 'X-planes' reveals new structure in the abundance patterns, beyond the traditional one-parameter correlations (Mg/Fe-Sigma, etc.). The X-planes for the alpha elements, Mg and Ca, indicate a positive correlation with velocity dispersion, and simultaneously an anticorrelation with Fe/H (i.e. a(1) > 0 and a(2) < 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. a(1) > 0 and a(2) approximate to 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, leading to a range in the degree of Type Ia supernova contribution to the chemical enrichment. The absence of corresponding Fe/H dependence for C and N is consistent with these elements being generated in intermediate- and low-mass stars, on time-scales similar to the Fe production. The Sigma dependence, at fixed Fe/H, is similar for elements Mg, C and N, despite their likely origin in stars of very different masses and lifetimes. Ca/Fe is positively correlated with Sigma, at fixed Fe/H, but its dependence is significantly less steep than that of Mg, C and N. We discuss possible origins for this pattern of trends and find no simple prescription that reproduces the observations. In particular, if C and N are produced on time-scales comparable to that of Fe, then the X/Fe-Sigma trends cannot be explained solely by a systematic variation of star formation time-scale with Sigma.