basis-function expansions for the MW

Today Kathryn Johnston (Columbia) organized a few-hour meeting at Flatiron to discuss kinematic or dynamical models of the Milky Way that would have far more flexibility than the models we have used up to now. That is, employing function expansions or highly parameterized models of perturbations away from the toy models that are currently used in Galaxy dynamics at the present day. Part of the discussion was about expansions that help with making simulations more accurate, but some (and the part I cared about) was about making data analyses better.

Many good ideas came up for near-term projects, for instance: One was refinement of an idea with Chervin Laporte (UVic) to use his disk simulations to make empirical basis functions from simulation snapshots that would permit us to make flexible but interpretable models of the disk in the Gaia data. Connected to this, the idea of making such basis functions not in 3-d density or potential space but in 6-d phase-space-density space. That could be valuable both for data analysis with Gaia and for theory. Indeed, the things that Martin Weinberg (Amherst) has been thinking about in basis functions might be expandable to 6-d.

There was much discussion about how such basis function expansions might make data or theory descriptions of the Milky Way (or simulations thereof) compact. This is a dimensionality reduction point and issue. There was more-or-less consensus that we should only be thinking about linear dimensionality reduction (which is good, because it can often be made into a convex optimization problem) but non-linear generalizations could be worth thinking about.

In some ways, the most impressive aspect of the day was the community-building activity. Johnston got together groups of people that have not usually collaborated and set up the conditions under which they might actually collaborate. She is not just an extremely insightful and accomplished physicist: She is really thinking about improving the long-term health of the fields in which she works.