基于组合得分建模的恒星流分层贝叶斯推断
Hierarchical Bayesian inference with compositional score modeling for stellar streams
AI总结：
该研究旨在通过分层框架，结合多个恒星流与银河系圆周速度曲线约束推断银河系势。采用分层建模，训练神经后验估计器并通过组合得分建模组合信息。结果显示该方法有效，能降低参数不确定性，且可适应新数据集，计算成本低。
AI中文摘要：
背景：恒星流追踪银河系在广泛银心半径范围内的引力势。不同流采样银河系不同区域，结合多个流比单独建模单个流能更严格地约束全局质量分布。现有多流分析大多依赖基于似然的方法，每次有额外流或运动学测量时都需重新进行推断。目的：旨在通过单个分层框架，结合多个恒星流与银河系圆周速度曲线的额外约束来推断银河系势。方法：对问题进行分层建模，将所有流共有的参数与每个前身特定的参数分开。在模拟流库上训练基于得分的神经后验估计器，并在训练后通过组合得分建模组合来自不同流的信息。结果：对独立模拟的测试表明，推断的后验分布校准良好且准确。与单流分析相比，结合多个流可降低全局势参数的不确定性。应用于盖亚数据时，该模型支持一个轻度扁率的暗物质晕，轴比$q_{NFW}=0.77$，尺度半径$a_{NFW}=9.3$千秒差距，盘质量为$4.3\times10^{10}M_\odot$，局部暗物质密度$\rho_{NFW,\odot}=0.01153M_\odot pc^{-3}$，与近期基于流的研究一致。结论：此分层框架提供了一种实用方法，可在不针对每个新数据集重复完整推断过程的情况下组合多个恒星流的信息。该方法能以最小计算成本适应新数据集，如未来的盖亚DR4或新的光谱调查。
英文摘要：
Context: Stellar streams trace the gravitational potential of the Milky Way over a wide range of Galactocentric radii. Since different streams sample different regions of the Galaxy, combining several of them can constrain the global mass distribution more tightly than modeling any single stream in isolation. Most of the existing multi-stream analyses rely on likelihood-based methods that require a new inference run whenever additional streams or kinematic measurements become available. Aims: We aim to infer the Milky Way potential from multiple stellar streams combined with an additional constraint through the Galactic circular velocity curve within a single hierarchical framework. Methods: We model the problem hierarchically, separating parameters that are common to all streams from parameters that are specific to each progenitor. We train score-based neural posterior estimators on a library of simulated streams and combine information from different streams through compositional score modeling as a post-training step. Results: Tests on independent simulations show that the inferred posteriors are well calibrated and accurate. Combining several streams reduces the uncertainties on the global potential parameters relative to single-stream analyses. Applied to Gaia data, the model favours a mildly oblate dark matter halo with axis ratio $q_{NFW} = 0.77$, scale radius $a_{NFW} = 9.3$ kpc, a disk mass of $4.3 \times 10^{10} M_\odot$, and a local dark matter density $ρ_{NFW,\odot} = 0.01153 M_\odot pc^{-3}$ consistent with recent stream-based studies. Conclusions: This hierarchical framework provides a practical way to combine information from multiple stellar streams without repeating the full inference procedure for each new dataset. The method is adaptable to new datasets, like future Gaia DR4, or new spectroscopic surveys, with minimal computational cost.
