Jan Rybizki (MPIA) is in town this week, to sprint on nucleosynthetic models of the APOGEE chemical abundances that Andy Casey, Melissa Ness, and I generated with The Cannon. Rybizki has a nucleosynthesis model that takes an IMF, a SFR, infall, outflow, and so on, and computes the detailed abundances of all stars, using the latest and greatest knowledge about supernovae and AGB yields. His model is single-zone, and always homogeneously mixed, so it produces (always) a one-dimensional track through chemical-abundance space. Yesterday, while I was swanning around, he was showing that he can use the APOGEE abundances and his model to learn adjustments to the supernovae yield tables, or adjustments to the data zeropoints, and that he can get pretty good fits to the bulk (or really I should say mean trends) of the APOGEE red-clump-star data, with this very simple one-zone model.
We called Andy Casey in the morning, to discuss the projects available to us and get his feedback. During this conversation, we discussed the following point: Because there are only a few types of supernovae (and AGB) and because Rybizki's models are deterministic and well-mixed, in fact no set of one-zone models (not even a large mixture of them) can span much of abundance space. That is, if the one-zone models with deterministic yields and good mixing are close to true, then all stars should live in a low-dimensional subspace of the abundance space (convolved with noise deviations). If the stars live in a fairly high-dimensional subspace (and they appear to, and most of the literature says they do), then either there must be stochasticity to the yields, or else there must be separation of elements or bad mixing. You can't solve the problem (just) by going to the low-number-of-supernovae limit, because of the deterministic nature of the yields and the small number of supernovae types: You need real diversity to explain an interesting abundance space. This might be our low-hanging fruit, although we have got a lot of ideas now!
In related news, I wrote code today, for my project of building a data-driven nucleosynthesis model.