Topological data analysis and diagnostics of compressible MHD turbulence

TL;DR

This paper explores the use of topological data analysis techniques, such as Betti numbers and persistence diagrams, to compare and validate MHD turbulence simulations with astrophysical observations, ensuring robust quantitative analysis.

Contribution

It introduces topological data analysis methods for assessing MHD turbulence simulations and observations, demonstrating their insensitivity to data trends and resolution, and applying them to astrophysical data.

Findings

Topological measures are robust against large-scale trends.

These techniques are insensitive to data resolution.

Applied successfully to interstellar medium observations and simulations.

Abstract

The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with observations. One of the main challenges in this area is to identify robust \it{quantitative} measures to compare structures found in simulations with those inferred from astrophysical observations. A similar challenge is to compare quantitatively results from different simulations. Topological data analysis offers a range of techniques, including the Betti numbers and persistence diagrams, that can be used to facilitate such a comparison. After describing these tools, we first apply them to synthetic random fields and demonstrate that, when the data are standardized in a straightforward manner, some topological measures are insensitive to either large-scale trends or the resolution of the data. Focusing upon one particular astrophysical example, we apply topological data analysis to HI observations of the turbulent interstellar medium (ISM) in the Milky Way and to recent MHD simulations of the random, strongly compressible ISM. We stress that these topological techniques are generic and could be applied to any complex, multi-dimensional random field.