Multi-spacecraft constraints on relativistic solar energetic particle transport in the widespread 28 October 2021 event

Abstract

Aims. We investigated the transport of solar energetic particles (SEPs) during the relativistic widespread event of 28 October 2021, quantifying the role of parallel and perpendicular diffusion and constraining the spatial extent of the injection region. Methods. We employed inverse modeling of particle focused transport and 2D numerical simulations including cross-field diffusion. Multi-spacecraft observations from STEREO-A, Solar Orbiter, and near-Earth spacecraft are used to reproduce particle intensity profiles and anisotropies across a wide range of electron and proton energies. Simulated flux profiles are compared across different heliolongitudes to derive consistent transport parameters. Results. The analysis yields parallel mean free paths within or slightly above the Palmer consensus range, and perpendicular mean free paths that correspond to $\sim 1$--$3\%$ of parallel for electrons and $\sim 5$--$10\%$ for protons. The injection region is found to be relatively narrow ($\leq 20^\circ$), and decreasing with particle rigidity. Multipoint simulations indicate that the observed flux and anisotropy profiles can only be reproduced by a narrow injection region and significant cross-field diffusion. Electron and proton release times align well with the parent X1.0 flare and associated coronal mass injection (CME) onset, indicating that a compact acceleration region coupled with efficient interplanetary diffusion governed the event's broad spatial extent.

Figures (13)

• Figure 1: View of the ecliptic plane (top right) from solar north showing the positions of various spacecraft, and their respective Parker spirals, on 28 October 2021 at 15:15 UT. The black arrow and dashed black curve show the flare reference location and corresponding Parker spiral. The insets show the electron flux intensity time series for each corresponding spacecraft. The top right figure is derived from the Solar MAgnetic Connection Haus tool Gieseler_2023.
• Figure 2: Inverse solution for STA/SEPT electrons at 314 keV using the 1D SEP propagator model, for the particle flux (middle panel) and anisotropy (bottom panel) time profiles. The corresponding Reid-Axford injection profile is displayed in the top panel. The simulated and observed profiles are shown as red and blue lines, respectively. In the flux plot, the thick gray line corresponds to the average background and the dashed line to the average background $+3\sigma$, the latter defining the cutoff for onset detection. The solution parameters ($\lambda_{\parallel}$, $t_a$, $t_e$, and $R^2$ score) are also noted in the flux plot (middle panel).
• Figure 3: Rigidity dependence of the parallel and perpendicular mean free path, as inferred by the inverse solutions listed in Tables \ref{['tab:tab2']} and \ref{['tab:tab3']}. The green triangles and magenta squares correspond to electrons and protons, respectively. The area denoted by the dashed gray line corresponds to the Palmer consensus. The other dashed curves depict the empirical relation suggested by Droge_2000 (purple), the analytical approximations of Teufel_2002Teufel_2003 for electrons under damping turbulence (DT) and random sweeping (RS) (green and cyan, respectively); the corresponding relation for protons under both DT and RS is also depicted (violet).
• Figure 4: Evolution of PAD for 115 and 314 keV electrons, from $\sim$0.5 h (dark blue) to 5 h (brown) after the injection. Actual measurements from the four STA/SEPT sectors are depicted as circles and the corresponding simulated PADs as solid lines with the same color. The color-coding of the successive timestamps is explained in the legend.
• Figure 5: Inverse solution to particle flux (top) and anisotropy (bottom) of three observers (left: STA/SEPT, middle: Solar Orbiter/EPT, right: Wind/3DP) for $\sim$314 keV electrons. The observed particle fluxes and anisotropies are depicted in blue and the simulated ones in red. The solid gray line in the flux profiles indicates the background level and the dashed line the background level plus 3$\sigma$. Simulated anisotropies have been reversed for Solar Orbiter and Wind, which were in an opposite polarity HMF to STEREO (see Fig. \ref{['fig:pads_314keV']} in the Appendix).