  (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.
