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Probing the Galactic Potential Using Optimal Transport Theory

Presentation #405.01 in the session Analysis of equilibrium collisionless systems: power and peril.

Published onApr 25, 2022
Probing the Galactic Potential Using Optimal Transport Theory

We present a novel approach based on optimal transport theory to determine the galactic potential from a single snapshot of the phase-space coordinates of stars in a Milky Way-type galaxy. We push forward the phase-space coordinates of stars with a set of trial potentials and then compute the Wasserstein distance between the input and the pushed-forward phase-space using a discrete-discrete optimal transport algorithm. Wasserstein distance is a powerful measure to define similarities between distribution functions in a non-parametric setting. Consequently, we find the potential that makes the phase-space distribution function stationary by using the Vlasov equation. Furthermore, this approach can be used to quantify the non-equilibrium characteristics of galactic systems. We show that our algorithm performs very successfully on a Plummer sphere model and discuss the prospects for applications to more realistic galaxy simulations and observational data from Gaia.


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