Decoding the age-chemical structure of the Milky Way disc: an application of copulas and elicitable maps

In the Milky Way, the distribution of stars in the [alpha/Fe] versus [Fe/H] and [Fe/H] versus age planes holds essential information about the history of star formation, accretion, and dynamical evolution of the Galactic disc. We investigate these planes by applying novel statistical methods called copulas and elicitable maps to the ages and abundances of red giants in the Apache Point Observatory Galactic Evolution Experiment survey. We find that the high- and low-alpha disc stars have a clean separation in copula space and use this to provide an automated separation of the alpha sequences using a purely statistical approach. This separation reveals that the high-alpha disc ends at the same [alpha/Fe] and age at high [Fe/H] as the low-[Fe/H] start of the low-alpha disc, thus supporting a sequential formation scenario for the high- and low-alpha discs. We then combine copulas with elicitable maps to precisely obtain the correlation between stellar age tau and metallicity [Fe/H] conditional on Galactocentric radius R and height z in the range 0 < R < 20 kpc and vertical bar z vertical bar < 2 kpc. The resulting trends in the age-metallicity correlation with radius, height, and [alpha/Fe] demonstrate a approximate to 0 correlation wherever kinematically cold orbits dominate, while the naively expected negative correlation is present where kinematically hot orbits dominate. This is consistent with the effects of spiral-driven radial migration, which must be strong enough to completely flatten the age-metallicity structure of the low-alpha disc.