Realistic simulated galaxies form [$\alpha$/Fe]-[Fe/H] knees due to a sustained decline in their star formation rates

We examine the stellar [$\alpha$/Fe]-[Fe/H] distribution of $\simeq1000$ present-day galaxies in a high-resolution EAGLE simulation. A slight majority of galaxies exhibit the canonical distribution, characterised by a sequence of low-metallicity stars with high [$\alpha$/Fe] that transitions at a "knee" to a sequence of declining [$\alpha$/Fe] with increasing metallicity. This population yields a knee metallicity - galaxy-mass relation similar to that observed in Local Group galaxies, both in slope and scatter. However, many simulated galaxies lack a knee or exhibit more complicated distributions. Knees are found only in galaxies with star formation histories (SFHs) featuring a sustained decline from an early peak ($t\simeq7~{\rm Gyr}$), which enables enrichment by Type Ia supernovae to dominate that due to Type II supernovae (SN II), reducing [$\alpha$/Fe] in the interstellar gas. The simulation thus indicates that, contrary to the common interpretation implied by analytic galactic chemical evolution (GCE) models, knee formation is not a consequence of the onset of enrichment by SN Ia. We use the SFH of a simulated galaxy exhibiting a knee as input to the VICE GCE model, finding it yields an $\alpha$-rich plateau enriched only by SN II, but the plateau comprises little stellar mass and the galaxy forms few metal-poor ([Fe/H]$\lesssim - 1$) stars. This follows from the short, constant gas consumption timescale typically assumed by GCEs, which implies the presence of a readily-enriched, low-mass gas reservoir. When an initially longer, evolving consumption timescale is adopted, VICE reproduces the simulated galaxy's track through the [$\alpha$/Fe]-[Fe/H] plane and its metallicity distribution function.