Interstellar sonic and Alfvénic Mach numbers and the Tsallis distribution

Abstract

In an effort to characterize the Mach numbers of interstellar medium (ISM) magnetohydrodynamic (MHD) turbulence, we study the probability distribution functions (PDFs) of spatial increments of density, velocity, and magnetic field for 14 ideal isothermal MHD simulations at a resolution of 5123. In particular, we fit the PDFs using the Tsallis function and study the dependency of the 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 Alfvén Mach numbers. For three-dimensional density, column density, and Position-Position-Velocity data, we find that the amplitude and width of the PDFs show a dependency on the sonic Mach number. We also find that the width of the PDF is sensitive to the global Alfvénic 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 the sonic and Alfvénic Mach numbers of simulated ISM turbulence points to it being a useful tool in the analysis of the observed ISM, especially when used simultaneously with other statistical techniques. © 2011. The American Astronomical Society. All rights reserved.