On the Existence of Finite Frequency Fast Modes in the Compressible MHD Turbulence*

Fast modes could play a significant role in turbulent magnetohydrodynamic (MHD) systems, affecting energy dissipation, density fluctuation, and energetic particle transport. We carry out a large number of 3D MHD turbulence simulations with different driving schemes at the injection scale to quantify the fraction of fast modes. We use two approaches to determine the presence of fast modes: mode decomposition based on spatial variations only and spatio-temporal 4D-FFT analysis of all fluctuations. The latter method enables us to distinguish fluctuations that satisfy the dispersion relation of fast modes with finite frequency. Overall, we find that most of the fast mode fluctuations that are identified by the spatial mode decomposition approach is actually at nearly zero frequency (i.e., they do not satisfy the dispersion relationship for fast modes). These results are important for understanding the compressible fluctuations in space and astrophysics plasmas.