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 β) and magnetic pressure dominated (low β) plasmas at different Mach numbers. In addition, we present results for superAlfvenic turbulence and discuss in what way it is similar to the subAlfvenic turbulence. We describe a technique of separating different magnetohydrodynamic (MHD) modes (slow, fast and Alfven) and apply it to our simulations. We show that, for both high and low β cases, Alfven and slow modes reveal the Kolmogorov k spectrum and scale-dependent GoldreichSridhar anisotropy, while fast modes exhibit k spectrum and isotropy. We discuss the statistics of density fluctuations arising from MHD turbulence at 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 AU scales, we show that the viscositydamped regime of MHD turbulence that we earlier reported for incompressible flows persists for compressible turbulence and therefore may provide an explanation for those mysterious structures.