Solar wind control of upstream wave frequency

In the region upstream from the Earth's bow shock, large-amplitude ULF waves are generated by ions backstreaming along the magnetic field and subsequently convected downstream across the bow shock. Early observations showed that the frequency of these waves is proportional to the magnitude of the interplanetary magnetic field (IMF). The large scatter in this relationship implied that there are parameters other than IMF strength that significantly affect the frequencies of these waves. In this study, we examine the frequency of upstream ULF waves observed by ISEE spacecraft under various solar wind conditions. We find that the wave frequency in the spacecraft frame depends on both the IMF strength and cone angle. The IMF strength is the most important parameter that controls the wave frequency in the spacecraft frame, consistent with previous results. However, the IMF cone angle also plays a role in determining the frequency. Increasing the cone angle lowers the wave frequency in the spacecraft frame. The effect of Alfvenic Mach number is minimal. Increasing Alfvenic Mach number tends to enhance the wave frequency in the spacecraft frame. The results are consistent qualitatively with the prediction of linear theory based on the resonant interaction between the right-handed magnetosonic wave and backstreaming ions, suggesting that this instability is responsible for the majority of waves. However, there is still a subgroup of wave events that are not consistent with this instability. The strength of the bow shock as measured by the magnetosonic Mach number appears to have little effect on the ratio of the backstreaming ions velocity to the solar wind velocity as inferred from the resonant condition.