[No posts for a few days because vacation.]
Great day today! I met up with Eilers (MPIA) early to discuss our project to constrain the dynamics of the Milky Way disk using the statistics of the actions and conjugate angles. During our conversation, I finally was able to articulate the point of the project, which I have been working on but not really understanding. Or I should say perhaps that I had an intuition that we were going down a good path, but I couldn't articulate it. Now I think I can:
The radial action of a star in the Milky Way disk is a measure of how much it deviates in velocity from the circular velocity. The radial action is (more or less) the amplitude of that deviation and the radial angle is (more or less) the phase of that deviation. Thus the radial action and angle are functions (mostly though not perfectly) of the stellar velocity. So as long as the selection function of the survey we are working with (APOGEE cross Gaia in this case) is a function only (or primarily) of position and not velocity, the selection function doesn't really come in to the expected distribution of radial actions and angles!
That's cool! We talked about how true these assumptions are, and how to structure the inference.