Equatorial electron pitch angle distributions in Earth's outer radiation belt: Storm-time evolution and empirical modeling

Pitch angle distributions (PADs) of trapped particles play an important role in understanding the processes driving the dynamics of Earth’s radiation belts and ring current. The Van Allen Probes mission has provided electron observations of PADs with an unprecedented coverage in energy (from tens of keV to several MeV) and pitch angles during the mission’s lifespan. We approximate the equatorial electron PADs using the Fourier sine series expansion up to degree 5. The corresponding coefficients can be directly related to the main PAD shapes (pancake, butterfly, flat-top and cap), and the approximated PADs can be easily integrated and converted to omnidirectional flux. Using the entire Van Allen Probes MagEIS data set in 2012-2019, we analyze the response of the equatorial electron PAD shapes to 129 geomagnetic storms with minimum Dst< -50nT. At lower energies (<100 keV), the PADs are stable throughout geomagnetic storms and mainly exhibit a pancake shape. At higher energies, the storm-time PAD evolution depends on the magnetic local time (MLT). At dayside, the pancake distributions become steeper during the main phase and then recover to their original broader form during recovery phase, likely due to the inward radial diffusion. At nightside MLT, the butterfly distributions become more pronounced during the main phase due to the combination of drift-shell splitting and magnetopause shadowing. We present a simple polynomial regression model of PAD shapes driven by the solar wind dynamic pressure. The model allows reconstructions of the full equatorial PADs based on uni-directional measurements at low equatorial pitch angles (applicable to LEO satellite data), as well as from omnidirectional electron flux observations and significantly outperforms the standard sin(alpha) approximation.