It is traditional to plot things like the mean iron abundances of stars (or ratios of magnesium to iron, or other ratios) as a function of position in the Galaxy. However, stars change their positions over time, so the gradients (the features in any abundance–position plots) will be smeared out over cosmic time by their motions.
At the same time, stars have approximately invariant actions or integrals of motion, which don't change (much) as they orbit. These invariants are only approximate, both because the Galaxy isn't exactly integrable, and also because we don't know or measure everything we need to compute them precisely for any observed star.
Putting these two ideas together, the abundance–action features, or really abundance–invariant features should be much clearer and more informative than the abundance–position features. Awesome, let's go! The only problem is: Selection effects are often simple in the position space, but are almost never simple in the dynamical-invariant-space. So any plots are harder to interpret generally.
These are issues that I have discussed over many years with Hans-Walter Rix (MPIA). Today I discussed them with Danny Horta (Flatiron) and Adrian Price-Whelan (Flatiron), in preparation for an exploratory study by Horta.
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