Star-forming galaxies are predicted to lie on a fundamental plane of
  mass, star formation rate and \alpha-enhancement
  Observations show that star-forming galaxies reside on a tight
three-dimensional plane between mass, gas-phase metallicity and star formation
rate (SFR), which can be explained by the interplay between metal-poor gas
inflows, SFR and outflows. However, different metals are released on different
time-scales, which may affect the slope of this relation. Here, we use central,
star-forming galaxies with M$_{\rm star}=10^{9.0-10.5}$ M$_{\odot}$ from the
EAGLE hydrodynamical simulation to examine three-dimensional relations between
mass, SFR and chemical enrichment using absolute and relative C, N, O and Fe
abundances. We show that the scatter is smaller when gas-phase
$\alpha$-enhancement is used rather than metallicity. A similar plane also
exists for stellar $\alpha$-enhancement, implying that present-day specific
SFRs are correlated with long time-scale star formation histories. Between
$z=0$ and 1, the $\alpha$-enhancement plane is even more insensitive to
redshift than the plane using metallicity. However, it evolves at $z>1$ due to
lagging iron yields. At fixed mass, galaxies with higher SFRs have star
formation histories shifted toward late times, are more $\alpha$-enhanced and
this $\alpha$-enhancement increases with redshift as observed. These findings
suggest that relations between physical properties inferred from observations
may be affected by systematic variations in $\alpha$-enhancements.
