Authors: Riddhi Bandyopadhyay (Princeton University), James R. Beattie (Princeton University), and Amitava Bhattacharjee (Princeton University)

Understanding the nature of compressible fluctuations in a broad range of turbulent plasmas, from the intracluster medium to the solar wind, has been an active eld of research in the past decades. Theoretical frameworks for weakly compressible magnetohydrodynamical turbulence in an inhomogeneous background magnetic eld predict a linear scaling of the normalized mass density fluctuation, as a function of the turbulent Mach number. However, so far, the scaling relation has been tested only using moderate to low plasma beta solar wind observational data, where the compressibility is weak. Here, we combine NASA’s Magnetospheric Multiscale Mission data in Earth’s magnetosheath, where β∼ 10 is high, and β∼ 1/8 highly compressible magnetohydrodynamic turbulence simulations at unprecedented resolutions. Both show that linear scaling holds across a broad range of density fluctuation, turbulent mach number and plasma beta, demonstrating that it is a robust compressible turbulence relation, going beyond the asymptotics of the weakly compressible theory. We discuss the findings in the context of understanding the nature of strongly compressible turbulent fluctuations and the driving parameter in astrophysical and space plasmas.