potential expansions

Late in the day I zoomed up to Columbia to discuss streams with Bonaca, Johnston, Küpper, and Price-Whelan. We discussed things related to our upcoming NSF proposal. One idea in the proposal is too look at models of the Milky Way gravitational potential that make use of expansions. In these kinds of problems, issues arise regarding what expansion to use, and what order to go to. On the former, choices include expansions that are orthogonal in something you care about, like the potential or density, or expansions that are orthogonal in the context of the data you have. That is, the data constrain the potential incompletely, so an expansion that is orthogonal in the potential basis will not have coefficients that are independently constrained by the data; there will be data-induced covariances in the uncertainties. On the latter (what order), choices include, at one extreme, just making a heuristic or educated guess, and on the other extreme, going fully non-parametric and inferring an infinity of parameters. You can guess what I want to try! But we will probably put more modest goals in the proposal, somewhere in-between. Amusingly, both of these problems (orthogonal expansions for incomplete observations, and choices about expansion order) come up in cosmology and have been well studied there.

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