Interstellar Sonic and Alfv\'enic Mach Numbers and the Tsallis Distribution

TL;DR

This study demonstrates that Tsallis distribution fitting effectively characterizes the Mach numbers in MHD turbulence simulations of the interstellar medium, showing sensitivity to sonic and Alfvénic Mach numbers and potential for observational analysis.

Contribution

It introduces the use of Tsallis distribution functions to analyze PDFs of MHD turbulence, revealing their dependence on Mach numbers and applicability to observational data.

Findings

Tsallis fits accurately model PDFs of MHD turbulence.

Fit parameters are sensitive to sonic and Alfvénic Mach numbers.

Method remains effective with observational effects like noise and smoothing.

Abstract

In an effort to characterize the Mach numbers of ISM magnetohydrodynamic (MHD) turbulence, we study the probability distribution functions (PDFs) of patial increments of density, velocity, and magnetic field for fourteen ideal isothermal MHD simulations at resolution 512^3. In particular, we fit the PDFs using the Tsallis function and study the dependency of fit parameters on the compressibility and magnetization of the gas. We find that the Tsallis function fits PDFs of MHD turbulence well, with fit parameters showing sensitivities to the sonic and Alfven Mach numbers. For 3D density, column density, and position-position-velocity (PPV) data we find that the amplitude and width of the PDFs shows a dependency on the sonic Mach number. We also find the width of the PDF is sensitive to global Alfvenic Mach number especially in cases where the sonic number is high. These dependencies are also found for mock observational cases, where cloud-like boundary conditions, smoothing, and noise are introduced. The ability of Tsallis statistics to characterize sonic and Alfvenic Mach numbers of simulated ISM turbulence point to it being a useful tool in the analysis of the observed ISM, especially when used simultaneously with other statistical techniques.