Evidence of Time-dependent Diffusive Shock Acceleration in the 2022 September 5 Solar Energetic Particle Event

On 2022 September 5, a large solar energetic particle (SEP) event was detected by Parker Solar Probe (PSP) and Solar Orbiter (SolO) at heliocentric distances of 0.07 and 0.71 au, respectively. PSP observed an unusual velocity dispersion signature: particles below ∼1 MeV exhibited a normal velocity dispersion, while higher-energy particles displayed an inverse velocity arrival (IVA) feature, with the most energetic particles arriving later than those at lower energies. The maximum energy increased from about 20–30 MeV upstream to over 60 MeV downstream of the shock. The arrival of SEPs at PSP was significantly delayed relative to the expected onset of the eruption. In contrast, SolO detected a typical large SEP event characterized by a regular velocity dispersion at all energies up to 100 MeV. To understand these features, we simulate particle acceleration and transport from the shock to the observers with our newly developed SEP model—Particle ARizona and MIchigan Solver on Advected Nodes. Our results reveal that the IVA and delayed particle onset detected by PSP originate from the time-dependent diffusive shock acceleration processes. After shock passage, PSP’s magnetic connectivity gradually shifted due to its high velocity near perihelion, detecting high-energy SEPs streaming sunward. Conversely, SolO maintained a stable magnetic connection to the strong shock region where efficient acceleration was achieved. These results underscore the importance of spatial and temporal dependence in SEP acceleration at interplanetary shocks and provide new insights to understand SEP variations in the inner heliosphere.

This work was supported in part by the NASA LWS Strategic Capabilities project at the University of Michigan under NASA grant 80NSSC22K0892 (SCEPTER) and NASA SWxC grant 80NSSC23M0191 (CLEAR). L.Z. acknowledges NASA LWS grant 80NSSC21K0417, NASA R2O2R grant 80NSSC22K0269, NASA HSR grant 80NSSC23K0091, and NSF ANSWERS grant GEO-2149771. N.S. acknowledges NASA LWS grant 80NSSC24K1104, NSF Solar Terrestrial grant 2323303, and NASA R2O2R grant 80NSSC23K0450. A.K. acknowledges financial support from NASA’s NNN06AA01C (Parker Solar Probe EPI-Lo) contract and NASA LWS grant 80NSSC25K0130. Parker Solar Probe was designed and built and is now operated by the Johns Hopkins Applied Physics Laboratory as part of NASA’s Living with a Star (LWS) program (contract NNN06AA01C). Support from the LWS management and technical team has played a critical role in the success of the Parker Solar Probe mission. We acknowledge the PSP/IS⊙IS team (PI: David McComas, Princeton University) and the PSP/FIELDS team (PI: Stuart D. Bale, UC Berkeley) for use of data. We acknowledge the EPD and magnetic field data from Solar Orbiter, generated and maintained by the EPD team and magnetometer team on the Solar Orbiter Archive (SOAR). This work utilizes data produced collaboratively between AFRL/ADAPT and NSO/NISP. We thank the referee for helpful comments. Resources supporting this work were provided in part by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. The authors acknowledge the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing HPC resources that have contributed to the research results reported in this paper.