Shock Properties for Solar Energetic Particle Events with Signatures of Inverse Velocity Arrival

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.