how to model the empirical abundance space

I got in some great research time late today working with Adrian Price-Whelan (Flatiron) to understand the morphology of the distribution of stars in APOGEE–Gaia in elements-energy space. The element abundances we are looking at are [Fe/H] and [alpha/Fe]. The energy we are looking at is vertical energy (as in something like the vertical action in the Milky Way disk). We are trying to execute our project called Chemical Tangents, in which we use the element abundances to find the orbit structure of the Galaxy. We have arguments that this will be more informative than doing Jeans models or other equilibrium models. But we want to demonstrate that this semester.

There are many issues! The issue we worked on today is how to model the abundance space. In principle we can construct a model that uses any statistics we like of the abundances. But we want to choose our form and parameterization with the distribution (and its dependence on energy of course) in mind. We ended our session leaning towards some kind of mixture model, where the dominant information will come from the mixture amplitudes. But going against all this is that we would like to be doing a project that is simple! When Price-Whelan and I get together, things tend to get a little baroque if you know what I mean?