Three-dimensional properties of a coronal shock and the longitudinal distribution of its related solar energetic particles

¹ Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences Nanjing 210023, China
² School of Astronomy and Space Science, University of Science and Technology of China Hefei 230026, China
³ National Key Laboratory of Deep Space Exploration/School of Earth and Space Sciences, University of Science and Technology of China Hefei 230026, China
⁴ CAS Center for Excellence in Comparative Planetology, University of Science and Technology of China Hefei 230026, China
⁵ School of Physics and Optoelectronic Engineering, Institute of Space Weather, Nanjing University of Information Science and Technology Nanjing 210044, China
⁶ State Key Laboratory of Solar Activity and Space Weather, National Space Science Center, Chinese Academy of Sciences Beijing 100190, PR China
⁷ University of Chinese Academy of Sciences Nanjing 211135, China

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 11 November 2025
Accepted: 16 January 2026

Abstract

Context. The widespread longitudinal distribution of solar energetic particles (SEPs) is influenced by magnetic connectivity from the observers to coronal mass ejection (CME)-driven shocks. This connectivity determines shock properties encountered by magnetic-field lines, which in turn regulate the initial particle injection and acceleration efficiency.

Aims. We aim to investigate the relationship between the spatial–temporal evolution of shock properties and the longitudinal dependence of SEP intensities and spectra.

Methods. The shock parameters, including the normal speed, oblique angles, compression ratio, and Alfvén Mach number, were derived by combining a steady-state solar-wind simulation with the three-dimensional (3D) reconstruction of the shock surface based on multi-view observations. We compared the local shock parameters at the magnetic connecting points with in situ proton intensities and peak spectra to establish the link between shock evolution and SEP characteristics.

Results. The shock nose consistently exhibited higher particle-acceleration efficiency with the largest normal speed, compression ratio, and supercritical Alfvén Mach number, while the flanks showed delayed transition to supercritical Alfvén Mach number with weaker efficiency. The earliest and most rapid proton enhancement of STEREO-B correlated with efficient shock acceleration and prompt magnetic connectivity to the shock. Spectral analysis revealed that proton energy spectra were consistent with the relativistic diffusive shock acceleration (DSA) estimations.

Conclusions. The initial shock acceleration began at about 1.4 ∼ 5 R_⊙ and caused the widespread longitudinal SEP distribution. The longitudinal dependence of SEP intensity and spectral variations arise from the combined influence of 3D shock properties, magnetic connectivity, and particle transport processes. The agreement between in situ proton indices and relativistic DSA estimations supports DSA in this SEP event and provides insights into the early-stage acceleration at the source region.