Statistical Topology and the Random Interstellar Medium

We use topological methods to investigate the small-scale variation and local spatial characteristics of the interstellar medium (ISM) in three regions of the southern sky. We demonstrate that there are circumstances where topological methods can identify differences in distributions when conventional marginal or correlation analyses may not. We propose a nonparametric method for comparing two fields based on the counts of topological features and the geometry of the associated persistence diagrams. We investigate the expected distribution of topological structures quantified through Betti numbers under Gaussian random field (GRF) assumptions, which underlie many astrophysical models of the ISM. When we apply the methods to the astrophysical data, we find strong evidence that one of the three regions is both topologically dissimilar to the other two and not consistent with an underlying GRF model. This region is proximal to a region of recent star formation whereas the others are more distant. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

本研究采用拓扑方法，对南天三个天区的星际介质（interstellar medium, ISM）的小尺度变化与局域空间特性展开探究。研究证实，在部分场景中，相较于传统的边缘分析或相关性分析，拓扑方法能够有效识别分布层面的差异。我们提出一种基于拓扑特征计数与对应持久图几何属性的非参数方法，用于对比两个场域。我们基于高斯随机场（Gaussian random field, GRF）假设，探究了通过贝蒂数量化的拓扑结构的期望分布——该假设是诸多星际介质天体物理模型的核心前提。将该方法应用于天体物理数据后，我们发现有力证据表明：三个天区中的一片不仅与另外两片拓扑结构迥异，且不符合其底层的高斯随机场模型。该天区紧邻近期恒星形成区，而其余两个天区则距离此类恒星形成区更远。本文的补充材料（包含可复现本研究的标准化材料说明）可通过在线补充资源获取。