A1 Refereed original research article in a scientific journal
Shock Properties for Solar Energetic Particle Events with Signatures of Inverse Velocity Arrival; 
Authors: Kouloumvakos, A.; Lario, D.; Mason, G. M.; Vourlidas, A.; Allen, R. C.; Wijsen, N.; Chen, X.; Ding, Z.; Jebaraj, I. C.; Riley, P.; McComas, D. J.; Cohen, C. M. S.; Paouris, E.; Raptis, S.; Rodriguez-Garcia, L.; Xu, Z. G.; Berland, G. D.; Ho, G. C.; Mitchell, D. G.; Roelof, E. C.; Rodriguez-Pacheco, J.; Hill, M. E.; Wimmer-Schweingruber, R. F.
Publisher: Institute of Physics Publishing
Publication year: 2026
Journal: Astrophysical Journal
Article number: 188
Volume: 1002
Issue: 2
ISSN: 0004-637X
eISSN: 1538-4357
DOI: https://doi.org/10.3847/1538-4357/ae5e65
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Open Access publication channel
Web address : https://iopscience.iop.org/article/10.3847/1538-4357/ae5e65
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/526556500
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
We present a detailed investigation of the shock properties associated with solar energetic particle (SEP) events that exhibit a concave (“nose-like”) shape in their energy spectrogram, characterized by inverse velocity arrival (IVA) of the particles, where high-energy particles arrive later than mid-energy ones. Using measurements from Solar Orbiter and Parker Solar Probe between 2018 and 2025, we identify 26 such SEP events and reconstruct the observed shock fronts in three dimensions. We derive shock parameters along the magnetic field lines connected to each spacecraft using kinematic modeling and coronal magnetohydrodynamic simulations. Our analysis indicates that IVA-SEP events arise due to the spatial and temporal evolution of the shock properties and magnetic connectivity. In most of the cases analyzed here, the magnetic connectivity starts on the flanks of coronal mass ejection-driven shocks, where shocks tend to be weak, and shifts toward the shock apex, sampling stronger portions of the shock front. This evolution of the shock properties at the connected field lines likely leads to the delayed arrival of high-energy particles and the progressive hardening of the SEP energy spectrum, observed in some of the events. We find a correlation between the transition energy at which the IVA begins and the shock speed along the connected field lines, consistent with expectations from time-dependent diffusive shock acceleration. Our results underscore the importance of the evolving shock properties, magnetic connectivity, and instrumental sensitivity in shaping SEP intensity profiles and the formation of IVA signatures.
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Funding information in the publication:
A.K. acknowledges financial support from the NASA contract NNN06AA01C (Solar Orbiter SIS, Parker Solar Probe EPI-Lo). S.R. acknowledges funding from Johns Hopkins University Applied Physics Laboratory independent R&D fund. A.K., E.P., and A.V. acknowledge financial support from NASA’s LWS grant 80NSSC25K0130. A.V. is supported by NASA’s grant Nos. 80NSSC24K0555 and 80NSSC22K1028. P.R. was supported by NASA (80NSSC22K0893, 80NSSC20C0187, and 80NSSC20K1285), NSF’s PREEVENTS program (ICER-1854790), and NRL (N00173-24-C-0004). I.C.J. acknowledges support from the Research Council of Finland (X-Scale, grant No. 371569). L.R.-G. acknowledges support through the European Space Agency (ESA) research fellowship program. Solar Orbiter is a mission of international cooperation between ESA and NASA, operated by ESA. The Suprathermal Ion Spectrograph (SIS) is a European facility instrument funded by ESA under contract number SOL.ASTR.CON.00004. Solar Orbiter post-launch work at JHU/APL is supported by NASA contract NNN06AA01C, at the Southwest Research Institute by NASA 80GFSC25CA035.
