An optimized identification method for radiation belt electron butterfly pitch angle distributions based on the chi-square distribution function

Due to different physical mechanisms, radiation belt electrons exhibit types of pitch angle distribution. Recently, the characterful butterfly pitch angle distribution has received extensive attentions with the flux minimum around 90 degrees pitch angles and the flux peak at lower pitch angles. To identify the butterfly pitch angle distributions, previous studies usually set the threshold for the electron flux ratio between several specific pitch angles. However, such criterion will bring some uncertainties to distinguish butterfly-distribution profile. Therefore, it was difficult to accurately investigate the phenomenological law and physical mechanisms of the butterfly distribution. In this study, we develop an identification method based on the chi-square distribution function to identify butterfly distribution, by comparing the similarity between the observed flux profile and the ideal butterfly distribution profiles simulated by the model. Using two sets of electron flux data with different pitch-angle resolutions measured by Van Allen Probes REPT instrument at L-shell > 3, we find that our method can significantly improve the identification on butterfly distributions. By using two flux datasets with 17 pitch angles and 36 pitch angles, our method can reduce the false identification rates by 12. 6% and 27. 5%, respectively. Our results demonstrate that increasing the pitch-angle resolutions is effective to accurately identify the radiation belt electron distributions. Moreover, the developed method is of great importance for further statistical research on electron butterfly distribution in the Earth and planetary magnetospheres.