A new method to determine solar energetic particle anisotropies and their associated uncertainties demonstrated for STEREO/SEPT

Context. The shape of the pitch-angle distribution (PAD) of solar energetic particles (SEPs) can be used to infer information about their source and interplanetary transport. In modeling and observational studies of SEP events, these PADs are frequently applied to determine the anisotropy which is a proxy for the strength of the pitch-angle scattering during transport. For the determination of the PAD, derivation of the pitch angle of SEPs takes on a crucial role. For most instrument-sampled PADs, the particle's pitch angle cannot be resolved directly but is usually approximated by considering the time-averaged in situ magnetic field direction, and the center viewing direction of the telescope. However, variations of the magnetic field, and the extent of the physical opening of the instrument lead to uncertainty on the determination of the pitch angle and therefore to uncertainty on the anisotropy and its interpretation. Aims. In this work, we present a new method to determine a distribution of anisotropy values which allows us to estimate the corresponding uncertainty ranges. We apply our method to electron measurements by the Solar Electron and Proton Telescope on board each STEREO spacecraft. Methods. We determined a distribution of anisotropy values by solving an inversion problem that takes into account the directional response of the instrument, the variation of the in situ magnetic field, and the stochastic nature of particle detection. Using 95% confidence intervals, we estimate the uncertainty on the anisotropy. Results. The application of our method to a solar electron event observed by STEREO B on 14 August 2010 yields a maximum anisotropy of 1.9 with an uncertainty on the order of +/- 0.1. During the background period, the anisotropy shows strong fluctuations, and absolute uncertainties on the order of +/- 0.5 that are attributable to low counting statistics.

Automated summary

This study presents a new method to determine the distribution of anisotropy values and estimate uncertainty ranges. The method is applied to electron measurements by the Solar Electron and Proton Telescope on board the STEREO spacecraft. By considering the directional response of the instrument, variation of the in situ magnetic field, and stochastic nature of particle detection, an inversion problem is solved to determine the distribution of anisotropy. The results show a maximum anisotropy of 1.9 with an uncertainty on the order of +/- 0.1 in a solar electron event observed by STEREO.