  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 cosmological EAGLE simulation to investigate the origin of variations in
$\alpha$-enhancement among star-forming galaxies at $z=0$. 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.
