Dependence of the oblique propagation of ULF foreshock waves on solar wind parameters

According to theory, foreshock ultra-low frequency (ULF) waves are allowed to propagate mainly along the ambient magnetic field; however, waves obliquely propagating at a noticeably large angle can be easily observed. Although the mechanism of wave refraction was proposed to resolve the disagreement, doubts on the application of wave refraction to oblique propagation still remain. With the Time History of Events and Macroscale Interactions during Substorms (THEMIS) data, we examine the dependence of the oblique propagation of the ULF waves on solar wind parameters. The distributions of the oblique propagation angle θ_kB2 are spread out over a wide range of the solar wind parameters. From the mechanism of wave refraction, we derive the θ_kB2 as a function of the upstream propagation angle θ_kB1, the ratio of solar wind speed to upstream and downstream wave phase speed |V→_sw|:Vph1:Vph2, and the angle between the interplanetary magnetic field (IMF) and solar wind velocity θ _BV. Both of the prediction and the observation show the irrelevance of the wave frequency, the sense of polarization, the strength of the IMF, and solar wind speed to the oblique propagation. We find that the prediction from wave refraction is in good agreement with the observation, especially along the track of prediction lines with the same θ_kB1 and |V→_sw|:Vph1:Vph2.