Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications

We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas-pressure-dominated (high beta) and magnetic-pressure-dominated (low beta) plasmas at different Mach numbers. In addition, we present results for super-Alfvenic turbulence and discuss in what way it is similar to sub-Alfvenic turbulence. We describe a technique of separating different magnetohydrodynamic modes (slow, fast and Alfven) and apply it to our simulations. We show that, for both high- and low-beta cases, Alfven and slow modes reveal a Kolmogorov k(-5/3) spectrum and scale-dependent Goldreich-Sridhar anisotropy, while fast modes exhibit a k(-3/2) spectrum and isotropy. We discuss the statistics of density fluctuations arising from MHD turbulence in different regimes. Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation. In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence. In addition, we show that magnetic field enhancements and density enhancements are marginally correlated. Addressing the density structure of partially ionized interstellar gas on astronomical-unit scales, we show that the viscosity-damped regime of MHD turbulence that we reported earlier for incompressible flows persists for compressible turbulence and therefore may provide an explanation for these mysterious structures.