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