  We compute new population synthesis models of Lick absorption line indices
with variable alpha/Fe ratios and use them to derive average ages,
metallicities, and alpha/Fe element enhancements for a sample of 126 field and
cluster early-type galaxies. Calibrating the models on galactic globular
clusters, we show that any population synthesis model being based on stellar
libraries of the Milky Way is intrinsically biased towards super-solar alpha/Fe
ratios at metallicities below solar. We correct for this bias, so that the
models presented here reflect constant alpha/Fe ratios at all metallicities.
The use of such unbiased models is essential for studies of stellar systems
with sub-solar metallicities like (extragalactic) globular clusters or dwarf
galaxies.
  For the galaxy sample investigated here, we find a clear correlation between
alpha/Fe and velocity dispersion. Zero-point, slope, and scatter of this
correlation turn out to be independent of the environment. Additionally, the
alpha/Fe ratios and mean ages of elliptical galaxies are well correlated, i.e.
galaxies with high alpha/Fe ratios have also high average ages. This strongly
reinforces the view that the alpha/Fe element enhancement in ellipticals is
produced by short star formation timescales rather than by a flattening of the
initial mass function. The more massive the galaxy, the shorter is its star
formation timescale, and the higher is the redshift of the bulk of star
formation, independent of the environmental density. We show that this finding
is incompatible with the predictions from hierarchical galaxy formation models,
in which star formation is tightly linked to the assembly history of dark
matter halos.
