Topological signatures of interstellar magnetic fields – I. Betti numbers and persistence diagrams

Abstract

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.

New Insights in Extragalactic Magnetic Fields

“…The most significant magnetic effects are as follows (Evirgen et al 2018 The multi-phase structure. In agreement with the topological analysis of Makarenko et al (2018), we show that strong local magnetic fields efficiently confine SN remnants, leading to a lower fractional volume of the hot gas (decreasing from 25% to 9% near the mid-plane as magnetic field grows), its lower temperature and higher density (by a factor of 3-10), whereas the total mass of the hot gas varies little. As a result, the density contrast between the warm and hot phases is reduced by almost an order of magnitude.…”

The supernova-regulated ISM – VI. Magnetic effects on the structure of the interstellar medium

“…We find that the fractional volume of the hot gas decreases from 20 to 25 per cent in the Early stage to 1-5 per cent in the Late stage. Makarenko et al (2018) also find differences in the topology of gas density fluctuations, between the Early and Late stages, which suggests that the ISM becomes more homogeneous as the magnetic field grows. As shown in Fig.…”

Persistent topology of the reionisation bubble network. I: Formalism & Phenomenology

“…It has become the preeminent tool of topological data analysis (Zomorodian 2012;Wasserman 2018). In cosmology, persistent homology has previously been applied to the cosmic web Sousbie 2011;Nevenzeel 2013;Pranav et al 2016;Xu et al 2018), to Gaussian random fields (Feldbrugge & van Engelen 2012;Park et al 2013;Cole & Shiu 2018;Feldbrugge et al 2018;Pranav et al 2018), and to interstellar magnetic fields (Makarenko et al 2018). We further discuss the theory of filtrations and homology in section 2.…”