星际磁场的拓扑特征I。贝蒂数和持久性图
Topological signatures of interstellar magnetic fields - I. Betti numbers and persistence diagrams
摘要：
星际介质（ISM）是一个磁化系统，其中的跨音速或超音速湍流是由超新星爆炸驱动的。这导致在ISM气体密度中产生间歇性的非连续结构，同时相关的发电机作用也产生间歇性的磁场。传统的随机函数理论，仅限于二阶统计矩（或功率谱），不能充分描述这样的系统。我们应用拓扑数据分析（TDA），敏感的所有统计矩和独立的假设高斯统计，气体密度波动的磁流体动力学（MHD）模拟的多相ISM。这种模拟允许发电机动作，因此产生物理上真实的磁场。气体分布的拓扑结构，有和没有磁场，量化的贝蒂数和持久性图。与更标准的相关分析一样，TDA表明ISM气体密度对磁场的存在敏感。然而，TDA给了我们重要的附加信息，不能从关联函数中获得。特别是，每个相关单元的贝蒂数被示出为物理信息。磁场使ISM更加均匀，减少了孤立气体云和空洞的丰度，对空洞的影响更大。值得注意的是，气体分布的修改由磁场捕获的贝蒂数，即使在区域超过300 pc的中平面，其中的磁场是较弱的相关分析未能检测到任何签名的磁效应。
英文摘要：
The interstellar medium (ISM) is a magnetised system in which transonic or supersonic turbulence is driven by supernova explosions. This leads to the production of intermittent, filamentary structures in the ISM gas density, whilst the associated dynamo action also produces intermittent magnetic fields. The traditional theory of random functions, restricted to second-order statistical moments (or power spectra), does not adequately describe such systems. We apply topological data analysis (TDA), sensitive to all statistical moments and independent of the assumption of Gaussian statistics, to the gas density fluctuations in a magnetohydrodynamic (MHD) simulation of the multi-phase ISM. This simulation admits dynamo action, so produces physically realistic magnetic fields. The topology of the gas distribution, with and without magnetic fields, is quantified in terms of Betti numbers and persistence diagrams. Like the more standard correlation analysis, TDA shows that the ISM gas density is sensitive to the presence of magnetic fields. However, TDA gives us important additional information that cannot be obtained from correlation functions. In particular, the Betti numbers per correlation cell are shown to be physically informative. Magnetic fields make the ISM more homogeneous, reducing the abundance of both isolated gas clouds and cavities, with a stronger effect on the cavities. Remarkably, the modification of the gas distribution by magnetic fields is captured by the Betti numbers even in regions more than 300 pc from the midplane, where the magnetic field is weaker and correlation analysis fails to detect any signatures of magnetic effects.
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