Variations in $\alpha$-element ratios trace the chemical evolution of
  the disk
  It is well established that the chemical structure of the Milky Way exhibits
a bimodality with respect to the $\alpha$-enhancement of stars at a given
[Fe/H]. This has been studied largely based on a bulk $\alpha$ abundance,
computed as a summary of several individual $\alpha$-elements. Inspired by the
expected subtle differences in their nucleosynthetic origins, here we probe the
higher level of granularity encoded in the inter-family [Mg/Si] abundance
ratio. Using a large sample of stars with APOGEE abundance measurements, we
first demonstrate that there is additional information in this ratio beyond
what is already apparent in [$\alpha$/Fe] and [Fe/H] alone. We then consider
Gaia astrometry and stellar age estimates to empirically characterize the
relationships between [Mg/Si] and various stellar properties. We find small but
significant trends between this ratio and $\alpha$-enhancement, age, [Fe/H],
location in the Galaxy, and orbital actions. To connect these observed [Mg/Si]
variations to a physical origin, we attempt to predict the Mg and Si abundances
of stars with the galactic chemical evolution model Chempy. We find that we are
unable to reproduce abundances for the stars that we fit, which highlights
tensions between the yield tables, the chemical evolution model, and the data.
We conclude that a more data-driven approach to nucleosynthetic yield tables
and chemical evolution modeling is necessary to maximize insights from large
spectroscopic surveys.
