Compressible MHD Turbulence in the interstellar medium and the solar wind: spectrum and scale-dependent alignment

Compressible magnetohydrodynamic (MHD) turbulence is a ubiquitous state for many astrophysical plasmas, including the solar wind and the interstellar medium of our galaxy. Yet, basic statistics describing compressible, magnetized turbulence remain uncertain. Utilizing unprecedented grid resolutions of up to 10,080 cube cells, we have simulated magnetized compressible turbulence in the world's largest MHD simulation (Nature Astronomy https://doi.org/10.1038/s41550-025-02551-5) . We measure two coexisting kinetic energy cascades in the turbulence separating the plasma into scales that are non-locally interacting, supersonic and weakly magnetized (with the power-law exponent n ~ 2) and locally interacting, subsonic and highly magnetized (n ~ 3/2), in wave number space. The 3/2 spectrum can be explained with both scale-dependent energy fluxes and velocity-magnetic field alignment. The magnetic energy spectrum forms a local cascade (n ~ 9/5), deviating from any known ab initio theory. Within the 3/2 cascade, the plasma becomes aligned in a scale-dependent manner, with all primitive variables and their curls tending towards parallel and anti-parallel states in localized regions, Beltramizing, Taylorizing, and Alfvenizing the plasma on these scales (arXiv:2502.08883). We associates this with the tendency of turbulence to deplete its nonlinearities, which has significant implications for the asymptotic state of MHD turbulence, challenging existing theories. Predictions regarding the scaling of density fluctuations with the turbulent mach number are strongly supporterd by data from Parker Solar Probe and MMS data.