Investigation of the inverse velocity dispersion in a solar energetic particle event observed by Solar Orbiter

¹ Institute of Experimental and Applied Physics, Kiel University, Leibnizstrasse 11, D-24118 Kiel, Germany
² Johns Hopkins Applied Physics Lab, Laurel, MD 20723, USA
³ Centre for mathematical Plasma Astrophysics, KU Leuven Campus Kulak, 8500 Kortrijk, Belgium
⁴ National Key Laboratory of Deep Space Exploration/School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China
⁵ Institute of Physics, University of Graz, Graz, Austria
⁶ Universidad de Alcalá, Alcalá de Henares 28805, Spain
⁷ Southwest Research Institute, San Antonio, TX 78228, USA
⁸ California Institute of Technology, MC 290-17, Pasadena, CA 91125, USA

^⋆ Corresponding author: ding@physik.uni-kiel.de

Received: 18 January 2025
Accepted: 15 March 2025

Abstract

Context. Solar energetic particle (SEP) events provide crucial insights into particle acceleration and transport mechanisms in the heliosphere. Inverse velocity dispersion (IVD) events, characterized by higher-energy particles that arrive later than lower-energy particles, challenge the classical understanding of SEP events and are increasingly observed by spacecraft, such as Parker Solar Probe and Solar Orbiter. However, the mechanisms underlying IVD events remain poorly understood.

Aims. We investigate the physical processes that cause long-duration IVD events by analyzing the SEP event observed by Solar Orbiter on 2022 June 7. We explore the role of evolving shock connectivity, particle acceleration at interplanetary (IP) shocks, and cross-field transport in shaping the observed particle profiles.

Methods. We used data from the Energetic Particle Detector (EPD) suite on board Solar Orbiter to analyze the characteristics of the IVD, and we modeled the event using the heliospheric energetic particle acceleration and transport (HEPAT) model. The simulations tracked evolutions of shock properties, particle acceleration and transport to assess the influence of shock expansion, shock connectivity, and transport processes on the formation of IVD events.

Results. The IVD event exhibited a distinct and long-duration IVD signature across proton energies from 1 to 20 MeV, and it lasted for approximately 10 hours. Heavy ions exhibited varying nose energies, defined as the energy corresponding to the first-arriving particles. Simulations suggest that evolving shock connectivity and the evolution of the shock play a primary role in the IVD signature. The magnetic connection shifts from the shock flank to the nose over time, which results in a gradual increase in the maximum particle energy along the field line. Furthermore, the model results show that limited cross-field diffusion can influence both the nose energy and the duration of the IVD event.

Conclusions. This study demonstrates that long-duration IVD events are primarily driven by evolving magnetic connectivity along a nonuniform shock that evolves over time, where the connection moves to more efficient acceleration sites as the shock propagates farther from the Sun. Other mechanisms, such as the acceleration time at the shock, may also contribute to the observed IVD features. The interplay of these factors remains an open question that warrants further investigation in other events.