Today was a day of applied math. In one instance, Rodrigo Luger (Flatiron) reformulated all of Doppler Imaging (and the Rossiter–McLaughlin effect) into a simpler form using a model that is (essentially) the outer product of spherical harmonics on the surface of the star and a Fourier-transform basis in the spectral domain. This permits him to do the operations of Doppler imaging extremely fast and with no explicit numerical integrals on the surface of the star. We'd like to implement this in some mash up of Starry and wobble.
In another instance, Kathryn Johnston (Columbia) realized (or really this kind of thing is obvious to her) that my project with Suroor Gandhi (NYU) to model The Snail (the vertical phase spiral in the local Milky Way disk) can be implemented in a potential expansion, expanding in powers away from a simple harmonic oscillator potential. That is much more general than what we were doing, and contains what we were doing within it as a special case. That led to all sorts of talk about what kinds of expansions we might be able to do. Like can we expand a non-equilibrium galaxy in small terms away from an equilibrium galaxy? That's something that Johnston was talking about on Friday in her weekly Dynamics Group meeting.
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