Mode Energy Partition in Partially Ionized Compressible MHD Turbulence

Abstract

We investigate how neutral-ion collisional damping modifies the spectral properties and energy partition of compressible MHD turbulence using a suite of 3D two-fluid simulations. By systematically varying the neutral-ion coupling strength and decomposing the turbulent velocity field into Alfv\'en, slow, and fast (polarization) modes, we quantify how each mode responds to the transition from strong to weak coupling. In the strong-coupling regime, the Alfv\'en and slow modes follow nearly Kolmogorov $k^{-5/3}$ spectra and dominate the kinetic energy budget, while fast modes exhibit a steeper spectrum and contribute $\sim$10\% of the total energy. As the coupling weakens and neutral-ion damping becomes significant, all mode spectra steepen, approaching a dissipation-dominated $k^{-4}$ spectrum, except that the slope mode's spectrum parallel to the mean magnetic field has a power-law slope shallower than -4. While the total kinetic energy is reduced in the weak coupling regime, the slow-mode energy fraction increases substantially toward small scales, whereas the Alfv\'en-mode fraction decreases correspondingly. In contrast, the fast-mode energy fraction remains largely insensitive to coupling strength. These results demonstrate that partial ionization not only steepens the turbulent spectra but also reshapes the mode energy distribution, enhancing the relative importance of the slow mode while suppressing Alfv\'en mode in the damping regime. Our findings have important implications for turbulence-driven processes in the partially ionized interstellar medium, including cosmic-ray transport and acceleration.