Ultrarelativistic electron butterfly distributions created by parallel acceleration due to magnetosonic waves

The Van Allen Probe observations during the recovery phase of a large storm that occurred on 17 March 2015 showed that the ultrarelativistic electrons at the inner boundary of the outer radiation belt (L* = 2.6\textendash3.7) exhibited butterfly pitch angle distributions, while the inner belt and the slot region also showed evidence of sub-MeV electron butterfly distributions. Strong magnetosonic waves were observed in the same regions and at the same time periods as these butterfly distributions. Moreover, when these magnetosonic waves extended to higher altitudes (L* = 4.1), the butterfly distributions also extended to the same region. Combining test particle calculations and Fokker-Planck diffusion simulations, we successfully reproduced the formation of the ultrarelativistic electron butterfly distributions, which primarily result from parallel acceleration caused by Landau resonance with magnetosonic waves. The coexistence of ultrarelativistic electron butterfly distributions with magnetosonic waves was also observed in the 24 June 2015 storm, providing further support that the magnetosonic waves play a key role in forming butterfly distributions.