用流模型无假设地分析矮星系动力学，精准推断暗物质分布。
JFlow: Model-Independent Spherical Jeans Analysis using Equivariant Continuous Normalizing Flows
- 用等变连续归一化流建模星体相空间密度，无需预设模型
- 仅需少量追踪星即可准确估计速度弥散与暗物质质量密度
- 适用于小样本数据，适合研究暗物质结构的模型无关分析
矮椭圆星系中恒星的动力学特性被用于探究暗物质晕的结构。然而，这些恒星的运动信息通常仅限于天球位置和视线速度，导致全相空间分析困难。传统方法依赖带多个参数的投影解析相空间密度模型，并通过求解球对称的詹斯方程来推断暗物质晕结构。本文提出一种无监督机器学习方法，以模型无关方式求解球对称詹斯方程，作为迈向无假设分析矮星系的第一步。利用等变连续归一化流，我们展示了可在无模型假设下估计球对称星体相空间密度和速度弥散。作为概念验证，我们将该方法应用于Gaia挑战数据集中的球对称模型，针对给定的速度各向异性剖面测量了暗物质质量密度。结果表明，即使在追踪星数量较少的情况下，该方法仍能准确识别暗物质晕结构。
原文摘要 · Abstract (English)
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 for given velocity anisotropy profiles. Our method can identify halo structures accurately, even with a small number of tracer stars.
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