Parker Solar Probe observations of solar energetic particle events with inverse-velocity-arrival features

In solar energetic particle (SEP) events, velocity dispersion (VD) is characterized by the earlier arrival of faster, higher energy particles relative to slower ones, assuming negligible acceleration time and scattering effects. This characteristic enables estimation of the time of particle release near the Sun. The "Labor Day event" at the Parker Solar Probe (PSP) on 2022 September 5 provided a unique arrival profile, in which the medium energy (∼ a few megaelectronvolts) particles arrive earlier than both lower and higher energy particles. This created a so-called "nose" structure in the intensity spectrogram formed by measurements from the two energetic particle instruments, EPI-Lo and EPI-Hi, of the Integrated Science Investigation of the Sun ( suite. Unlike typical VD, the delayed arrival of higher energy particles compared to medium energy particles---i.e., ”inverse velocity arrival” (IVA)---could be caused by various acceleration, transport, and instrumental effects, including shock acceleration. The shock requires time to accelerate particles to higher energies; the connectivity between the spacecraft and the particle source modify arrival time profiles, and even the instrument sensitivity modifies the time profile since higher energy particles are generally less abundant than lower energy particles. By applying a new method based on the contour line of the intensity, we found 14 IVA events in the observations up to the end of 2024. Several parameters that may modify velocity dispersion characteristics are further explored including the spacecraft radial distance, the speed of corresponding CMEs and shocks, the angle between the shock normal and the upstream magnetic field, and the spacecraft's magnetic footpoint longitudinal separation from the flare location. The energy of the early arriving particles, i.e., the nose energy, can be grouped into low (L, $<$ 0.5 MeV), medium (M, 0.5 - 5 MeV), and high (H, $>$ 5 MeV) categories. Most (11/14) of the IVA events have medium nose energies. We emphasize the importance of instrumental effects on the shape of the IVA pattern. The IVA SEP list provides ingredients for examination of shock acceleration in the inner heliosphere, and the existence of IVA events sheds new light on the acceleration and propagation of SEPs.