A Study of Electron Forbush Decreases with a 3D SDE Numerical Model

Abstract

Because of the precise measurements of the cosmic ray electron flux by the PAMELA and AMS02, Electron Forbush decreases (Fds) have recently been observed for the first time. This serves as motivation to perform a numerical study of electron Forbush decreases with an advanced time-dependent, three-dimensional (3D) stochastic differential equation model, developed earlier to study proton Fds. The model includes a realistic interstellar electron spectrum reconstructed from Voyager observations, and diffusion and drift coefficients to reproduce the modulated spectrum observed by PAMELA in 2009. On the basis of this numerical model, electron Fd profiles for a range of rigidities are simulated. In addition, a systematic comparison between electron and proton Fds during different solar polarity epochs is performed. This approach gives insight into the rigidity dependence of the heliospheric diffusion coefficients and of drift effects over two magnetic field polarity cycles. We find that during an A > 0 epoch, the recovery time of a 1 GV proton Fd is remarkably shorter than the 1 GV electrons, whereas the electron Fd display a faster recovery during an A < 0 epoch. This model clear predicts a charge-sign dependent effect in the recovery time of Fds but less so for their magnitude.

A Numerical Study of Cosmic Proton Modulation Using AMS-02 Observations

“…). As the time t is an intrinsic variable in the SDE numerical method, time-dependent problems (transient events) are automatically handled without introducing additional dimensions (Luo et al 2017(Luo et al , 2018. In our model, the LIS is a steady-state boundary condition, which is a function of energy (or momentum).…”

“…Additionally, to avoid the situation of the pseudoparticle's direct crossing of the HCS, a forth-order Runge-Kutta method is implemented to treat the HCS drift in our SDE numerical model. See Luo et al (2017Luo et al ( , 2018 for additional detail on our HCS drift model.…”

“…This particular approach has already been used to reproduce PAMELA proton spectra (Potgieter et al 2014) and electron spectra (Potgieter et al 2015;Di Felice et al 2017) from 2006 to 2009. Luo et al (2018) also adapted this functional form to simulate electron Fds for the first time; see also Munini et al (2018). In this context, we prefer to simplify rather than complicate our modeling approach using SDEs, which is inherently complicated and rather tedious, especially when comparisons are made to observations.…”

“…They are adjusted until the simulated monthly spectra reproduce the corresponding AMS-02 proton spectra. To simulate a GMIR, a three-dimensional (3D) propagating diffusion barrier is incorporated in the model, defined by the following analytical function (Luo et al 2011(Luo et al , 2017(Luo et al , 2018:…”

“…Following Luo et al (2017Luo et al ( , 2018, simulating a much smaller Fd event, the barrier's width is reduced to L=0.5 au, with a limited longitudinal and latitudinal extent, i.e., f br =2π/3, θ br =π/4.…”