Properties of Magnetohydrodynamic Modes in Compressively Driven Plasma Turbulence

We study properties of magnetohydrodynamic (MHD) eigenmodes by decomposing the data of MHD simulations into linear MHD modes—namely, the Alfvén, slow magnetosonic, and fast magnetosonic modes. We drive turbulence with a mixture of solenoidal and compressive driving while varying the Alfvén Mach number ($M_A$), plasma β, and the sonic Mach number from subsonic to transsonic. We find that the proportion of fast and slow modes in the mode mixture increases with increasing compressive forcing. This proportion of the magnetosonic modes can also become the dominant fraction in the mode mixture. The anisotropy of the modes is analyzed by means of their structure functions. The Alfvén-mode anisotropy is consistent with the Goldreich-Sridhar theory. We find a transition from weak to strong Alfvénic turbulence as we go from low to high $M_A$. The slow-mode properties are similar to the Alfvén mode. On the other hand, the isotropic nature of fast modes is verified in the cases where the fast mode is a significant fraction of the mode mixture. The fast-mode behavior does not show any transition in going from low to high $M_A$. We find indications that there is some interaction between the different modes, and the properties of the dominant mode can affect the properties of the weaker modes. This work identifies the conditions under which magnetosonic modes can be a major fraction of turbulent astrophysical plasmas, including the regime of weak turbulence. Important astrophysical implications for cosmic-ray transport and magnetic reconnection are discussed