标题： JFlow：基于等变连续归一化流的模型无关球对称Jean斯分析 显示英文标题

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

摘要： 矮椭球星系中恒星的运动学已被研究以理解暗物质晕的结构。然而，这些恒星的运动学信息通常仅限于天球位置和视线速度，使得完整的相空间分析具有挑战性。传统方法依赖于具有多个参数的投影解析相空间密度模型，并通过求解球对称Jean方程推断暗物质晕的结构。在这篇论文中，我们介绍了一种无监督机器学习方法，用于以模型无关的方式求解球对称Jean方程，作为朝向无模型分析矮椭球星系的第一步。利用等变连续归一化流，我们证明了在没有模型假设的情况下可以估计球对称恒星相空间密度和速度弥散。作为一个概念验证，我们将我们的方法应用于Gaia挑战数据集中的球对称模型，并测量给定速度各向异性剖面的暗物质质量密度。即使只有少量示踪恒星，我们的方法也能准确识别晕的结构。 显示英文摘要

摘要： 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.