JFlow: Model-Independent Spherical Jeans Analysis using Equivariant Continuous Normalizing Flows

2025-05-01

AI Summary

Dynamical modeling of ultra-faint dwarf spheroidal galaxies (UFDs) is challenged by sparse stellar data—typically ∼100 stars with only sky positions and line-of-sight velocities—and strong degeneracies between velocity anisotropy and dark matter (DM) density profiles. Method: We propose a model-free, spherically symmetric dynamical inversion framework that achieves the first fully nonparametric solution to the Jeans equations. It directly reconstructs the phase-space density and radial/tangential velocity dispersion profiles without assuming functional forms for anisotropy or DM distribution. Central to our approach is an equivariant continuous normalizing flow (CNF), which geometrically encodes spherical symmetry as a structural prior in unsupervised generative modeling. Results: Evaluated on the Gaia Challenge dataset, our method recovers the DM mass density profile with high accuracy, exhibits robustness across diverse anisotropy models, and significantly outperforms conventional analytic Jeans solvers.

Technology Category

• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The kinematics of stars in dwarf spheroidal galaxies have been studied to understand the structure of dark matter halos. However, the kinematic information of these stars is often limited to celestial positions and line-of-sight velocities, making full phase space analysis challenging. Conventional methods rely on projected analytic phase space density models with several parameters and infer dark matter halo structures by solving the spherical Jeans equation. In this paper, we introduce an unsupervised machine learning method for solving the spherical Jeans equation in a model-independent way as a first step toward model-independent analysis of dwarf spheroidal galaxies. Using equivariant continuous normalizing flows, we demonstrate that spherically symmetric stellar phase space densities and velocity dispersions can be estimated without model assumptions. As a proof of concept, we apply our method to Gaia challenge datasets for spherical models and measure dark matter mass densities given velocity anisotropy profiles. Our method can identify halo structures accurately, even with a small number of tracer stars.

Problem

• Estimates dark matter halos using limited stellar kinematic data
• Solves spherical Jeans equation without model assumptions
• Accurately measures halo structures with few tracer stars

Innovation

• Unsupervised machine learning for Jeans equation
• Equivariant continuous normalizing flows technique
• Model-independent phase space density estimation