Deep Potential: Recovering the gravitational potential from a snapshot of phase space

Abstract

One of the major goals of the field of Milky Way dynamics is to recover the gravitational potential field. Mapping the potential would allow us to determine the spatial distribution of matter - both baryonic and dark - throughout the Galaxy. We present a novel method for determining the gravitational field from a snapshot of the phase-space positions of stars, based only on minimal physical assumptions, which makes use of recently developed tools from the field of deep learning. We first train a normalizing flow on a sample of observed six-dimensional phase-space coordinates of stars, obtaining a smooth, differentiable approximation of the distribution function. Using the Collisionless Boltzmann Equation, we then find the gravitational potential - represented by a feed-forward neural network - that renders this distribution function stationary. This method, which we term "Deep Potential," is more flexible than previous parametric methods, which fit restricted classes of analytic models of the distribution function and potential to the data. We demonstrate Deep Potential on mock datasets, and demonstrate its robustness under various non-ideal conditions. Deep Potential is a promising approach to mapping the density of the Milky Way and other stellar systems, using rich datasets of stellar positions and kinematics now being provided by Gaia and ground-based spectroscopic surveys.

21 pages, 13 figures. Much more detailed exposition of the method originally presented in the short conference workshop paper arXiv:2011.04673

References in corpus (9)

• The Gaia mission
• galpy: A Python Library for Galactic Dynamics
• The Radial Velocity Experiment (RAVE): first data release
• The GALAH Survey: Scientific Motivation
• Constraining the Galaxy's dark halo with RAVE stars
• The Mass Profile of the Galaxy to 80 kpc
• Orbital Torus Imaging: Using Element Abundances to Map Orbits and Mass in the Milky Way
• Eclipse timing the Milky Way's gravitational potential
• Charting Galactic Accelerations: When and How to Extract a Unique Potential from the Distribution Function

Cited by in corpus (6)

• PopSED: Population-Level Inference for Galaxy Properties from Broadband Photometry with Neural Density Estimation
• GalaxyFlow: Upsampling Hydrodynamical Simulations for Realistic Mock Stellar Catalogs
• Modelling the selection of galaxy groups with end to end simulations
• Dynamics of tidal spiral arms: Machine learning-assisted identification of equations and application to the Milky Way
• Uncover 3D Dark Matter Distribution of the Milky Way by an Empirical Triaxial Orbit-Superposition Model: Method Validation
• Minimum-entropy constraints on galactic potentials