The link between the Star Formation History and [alpha/Fe]

(Abridged) The abundance ratios between key elements such as iron and alpha-process elements carry a wealth of information on the star formation history (SFH) of galaxies. So far, simple chemical evolution models have linked [alpha/Fe] with the SFH timescale, correlating large abundance ratios with short-lived SFH. We provide an empirical correlation between [alpha/Fe] (measured from spectral indices) and the SFH (determined via a non-parametric spectral-fitting method). We offer an empirical version of the iconic outline of Thomas et al. (2005), relating star formation timescale with galaxy mass, although our results suggest, in contrast, a significant population of old (>10Gyr) stars even for the lowest mass ellipticals. In addition, the abundance ratio is found to be strongly correlated with the time to build up the stellar component, showing that the highest [alpha/Fe] (>+0.2) are attained by galaxies with the shortest half-mass formation time (<2Gyr), or equivalently, with the smallest (<40%) fraction of populations younger than 10Gyr. These observational results support the standard hypothesis that star formation incorporates the Fe-enriched interstellar medium into stars, lowering the high abundance ratio of the old populations.