Interplay between Alfvén and magnetosonic waves in compressible magnetohydrodynamics turbulence

Using spatio-temporal spectra, we show direct evidence of excitation of magnetosonic and Alfven waves in three-dimensional compressible magnetohydrodynamic turbulence at small Mach numbers. For the plasma pressure dominated regime, or the high β regime (with β the ratio between fluid and magnetic pressure), and for the magnetic pressure dominated regime, or the low β regime, we study magnetic field fluctuations parallel and perpendicular to a guide magnetic field B0. In the low β case, we find excitation of compressible and incompressible fluctuations, with a transfer of energy towards Alfvenic modes and to a lesser extent towards magnetosonic modes. In particular, we find signatures of the presence of fast magnetosonic waves in a scenario compatible with that of weak turbulence. In the high β case, fast and slow magnetosonic waves are present, with no clear trace of Alfven waves, and a significant part of the energy is carried by two-dimensional turbulent eddies.