A Statistical Study of the Solar Wind Dependence of Multi-Harmonic Toroidal ULF Waves Observed by the Arase Satellite

Toroidal standing Alfvén wave is one of the ultra-low frequency waves that are frequently observed in the terrestrial magnetosphere. They sometimes exhibit multi-harmonic frequency spectra, indicating wide energy range input in the magnetosphere. However, their energy source has not been fully understood due to the lack of statistical studies. Here we used the data of the Arase satellite observations for ∼3.5 years and conducted a statistical analysis of the solar wind dependence of the occurrence rate, wave power, and frequency of the multi-harmonic toroidal waves. We automatically detected the multi-harmonic waves and categorized them into four groups according to the solar wind velocity and the cone angle of the interplanetary magnetic field. We found that the occurrence rate and wave power of the multi-harmonic waves increase with the solar wind velocity on the flank sides. In the noon sector, the occurrence rate of the multi-harmonic waves increases with the decrease of the cone angle. The median frequency of the multi-harmonic waves on the dayside is positively correlated with the upstream wave frequency predicted by the theory of the ion beam instability for a small cone angle. The occurrence rate also increases with the solar wind dynamic pressure fluctuations. Therefore, we suggest that the Kelvin-Helmholtz instability, the upstream waves, and the dynamic pressure fluctuations are possible sources of the multi-harmonic waves. This study sheds light on the activity of the multi-harmonic waves which can affect radiation belt electrons under various solar wind conditions.