Spatial variations in the Milky Way disc metallicity-age relation
  Stellar ages are a crucial component to studying the evolution of the Milky
Way. Using Gaia DR2 distance estimates, it is now possible to estimate stellar
ages for a larger volume of evolved stars through isochrone matching. This work
presents [M/H]-age and [$\alpha$/M]-age relations derived for different spatial
locations in the Milky Way disc. These relations are derived by hierarchically
modelling the star formation history of stars within a given chemical abundance
bin. For the first time, we directly observe that significant variation is
apparent in the [M/H]-age relation as a function of both Galactocentric radius
and distance from the disc mid-plane. The [M/H]-age relations support claims
that radial migration has a significant effect in the plane of the disc. Using
the [M/H] bin with the youngest mean age at each radial zone in the plane of
the disc, the present-day metallicity gradient is measured to be $-0.059 \pm
0.010$ dex kpc$^{-1}$, in agreement with Cepheids and young field stars. We
find a vertically flared distribution of young stars in the outer disc,
confirming predictions of models and previous observations. The mean age of the
[M/H]-[$\alpha$/M] distribution of the solar neighborhood suggests that the
high-[M/H] stars are not an evolutionary extension of the low-$\alpha$
sequence. Our observational results are important constraints to Galactic
simulations and models of chemical evolution.
