On the variation in stellar $\alpha$-enhancements of star-forming
  galaxies in the EAGLE simulation
  The ratio of $\alpha$-elements to iron in galaxies holds valuable information
about the star formation history since their enrichment occurs on different
timescales. The fossil record of stars in galaxies has mostly been excavated
for passive galaxies, since the light of star-forming galaxies is dominated by
young stars which have much weaker atmospheric absorption features. Here we use
the largest reference cosmological simulation of the EAGLE project to
investigate the origin of variations in stellar $\alpha$-enhancement among
star-forming galaxies at $z=0$, and their impact on integrated spectra. The
definition of $\alpha$-enhancement in a composite stellar population is
ambiguous. We elucidate two definitions - termed `mean' and `galactic'
$\alpha$-enhancement - in more detail. While a star-forming galaxy has a high
`mean' $\alpha$-enhancement when its stars formed rapidly, a galaxy with a
large `galactic' $\alpha$-enhancement generally had a delayed star formation
history. We find that absorption-line strengths of Mg and Fe correlate with
variations in $\alpha$-enhancement. These correlations are strongest for the
`galactic' $\alpha$-enhancement. However, we show that these are mostly caused
by other effects which are cross-correlated with $\alpha$-enhancement, such as
variations in the light-weighted age. This severely complicates the retrieval
of $\alpha$-enhancements in star-forming galaxies. The ambiguity is not severe
for passive galaxies and we confirm that spectral variations in these galaxies
are caused by measurable variations in $\alpha$-enhancements. We suggest that
this more complex coupling between $\alpha$-enhancement and star formation
histories can guide the interpretation of new observations of star-forming
galaxies.
