arxiv: 2604.13962 · v1 · submitted 2026-04-15 · 🌌 astro-ph.SR

Recognition: unknown

Shock properties for solar energetic particle events with signatures of inverse velocity arrival

A. Kouloumvakos , D. Lario , G. M. Mason , A. Vourlidas , R. C. Allen , N. Wijsen , X. Chen , Z. Ding

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I. C. Jebaraj P. Riley D. J. McComas C. M. S. Cohen E. Paouris S. Raptis L. Rodr\'iguez-Garc\'ia Z. G. Xu G. D. Berland G. C. Ho D. G. Mitchell E. C. Roelof J. Rodriguez-Pacheco M. E. Hill R. F. Wimmer-Schweingruber

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Pith reviewed 2026-05-10 12:10 UTC · model grok-4.3

classification 🌌 astro-ph.SR

keywords solar energetic particlesinverse velocity arrivalCME-driven shocksmagnetic connectivitydiffusive shock accelerationshock evolutioncoronal mass ejections

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The pith

Evolving magnetic connections to stronger parts of CME shocks produce the inverse velocity arrival of solar energetic particles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines solar energetic particle events whose energy spectrograms show a concave nose shape because higher-energy particles reach the observer later than mid-energy ones. Using data from two spacecraft, the authors reconstruct the three-dimensional shock fronts driven by coronal mass ejections and trace the magnetic field lines that link each observer to the shock. They find that the connection typically begins on the weaker flanks of the shock and later moves toward the stronger central region as the shock expands and the observer’s magnetic footpoint shifts. This change in shock strength along the connected lines allows more efficient acceleration of higher-energy particles at later times, producing the observed delay and the progressive hardening of the particle spectrum. The result links the timing of particle arrival directly to the geometry and evolution of the shock rather than to transport or detection effects alone.

Core claim

Our analysis indicates that IVA-SEP events arise due to the spatial and temporal evolution of the shock properties and magnetic connectivity. In most cases analyzed here, the magnetic connectivity starts on the flanks of CME-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, as

What carries the argument

The shifting magnetic connectivity from the flanks to the apex of an expanding CME-driven shock, which samples successively stronger shock regions along the observer’s field line.

If this is right

The energy at which the inverse velocity arrival begins scales with the shock speed sampled by the connected field line.
Progressive spectral hardening occurs once connectivity reaches stronger portions of the shock front.
Most events with the nose-like spectrogram signature involve initial flank connections that later improve.
Instrumental sensitivity thresholds influence whether the full IVA shape is recorded in a given event.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Multi-spacecraft observations could map how the same shock produces different IVA signatures at different longitudes.
Real-time models of SEP hazards would need to track the time-dependent footpoint location on the shock surface.
The same connectivity-shift mechanism may shape the duration and peak intensity of non-IVA SEP events as well.

Load-bearing premise

The inverse velocity arrival signatures are produced mainly by changes in shock strength and magnetic connectivity rather than by particle transport, event selection biases, or unaccounted instrumental thresholds.

What would settle it

An IVA event in which the magnetic connection remains fixed on a weak shock flank throughout the acceleration phase yet still shows the delayed high-energy arrival, or a set of events with no correlation between transition energy and measured shock speed along the connected line.

Figures

Figures reproduced from arXiv: 2604.13962 by A. Kouloumvakos, A. Vourlidas, C. M. S. Cohen, D. G. Mitchell, D. J. McComas, D. Lario, E. C. Roelof, E. Paouris, G. C. Ho, G. D. Berland, G. M. Mason, I. C. Jebaraj, J. Rodriguez-Pacheco, L. Rodr\'iguez-Garc\'ia, M. E. Hill, N. Wijsen, P. Riley, R. C. Allen, R. F. Wimmer-Schweingruber, S. Raptis, X. Chen, Z. Ding, Z. G. Xu.

**Figure 1.** Figure 1: Observations of solar energetic protons for two IVA-SEP events observed by Solar Orbiter EPD. The top panel shows the energy spectrogram for the 2022 June 7 SEP event and the bottom panel for the 2024 December 31 event. The two spectrograms cover an energy range from 10 keV to 100 MeV utilizing observations from EPD STEP, EPT, and HET instruments, and the fluxes have been averaged at a 10-minute cadence. F… view at source ↗

**Figure 3.** Figure 3: Kinematics of the 3D reconstructed shock waves associated with the IVA-SEP events. Panels a1) and b1) shows the height–time profile at the shock apex and the COBPOINTs, while panels a2) and b2) show the corresponding speed profiles. Time is measured relative to the start of the shock reconstruction. The labels shown are the IVA event # in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Panels (a) and (b) present polar plots showing the average longitudinal and latitudinal separation between the shock apex and the spacecraft. In panel (a), the angular values from 0◦ and increasing counterclockwise to 180◦ indicate that the shock apex propagates westward relative to the spacecraft. Conversely, angles measured clockwise from 0◦ indicate eastward propagation. In panel (b), angular values fro… view at source ↗

**Figure 5.** Figure 5: Panels a) and b) show polar plots of the mean central separation angle between the shock apex and the COBPOINTs. For panel a) the arrow lengths are scaled by the average fast magnetosonic Mach number, Mfms) and for panel b) by the shock speed, both measured at the COBPOINTs. Angular values near 0◦ indicate a magnetic connection close to the shock apex, values near ∼90◦ correspond to connections near th… view at source ↗

**Figure 6.** Figure 6: Evolution of the shock parameters along the magnetic field lines connected to the observers. Time is measured relative to the first modeled time when the reconstructed shock surface intersects the field lines connected to the observers. Panel a) shows the temporal evolution of the shock’s fast magnetosonic Mach number, Mfms, and panel b) the evolution of Mfms as a function of the central separation angle, … view at source ↗

**Figure 7.** Figure 7: Comparison of the Mfms evolution at the shock apex and at the COBPOINTs. Top panel: Mapex fms versus the MCOB fms for two representative time intervals after the start of the shock modeling (blue: 0–60 min; red: 120–180 min). The dotted horizontal and vertical lines mark the threshold separating weak/subcritical from stronger supercritical shocks. Bottom panel: Top axis show the changes in shock strength … view at source ↗

**Figure 8.** Figure 8: A connection between the transition energy, Et, derived from the SEP observations and the mean shock parameters evaluated at the COBPOINTs. Panels show Et as a function of (a) shock speed (b) Mfms, (c) density compression ratio, and (d) λ-angle. The horizontal bars to the points show a proxy of the uncertainty of the visual determination of Et from the spectrograms and may span several energy channels in c… view at source ↗

**Figure 9.** Figure 9: Time profiles of the fittings of the reconstructed 3D shock for all events analyzed in this study. Each panel (#1–#19) shows the heliocentric distance of the shock apex (red crosses) and the lengths of the two semi-axes of the fitted ellipsoid (blue and green crosses) derived from the 3D reconstruction. Solid curves indicate the best-fit functions (second-order polynomial or cubic spline, as noted in each … view at source ↗

**Figure 10.** Figure 10: Temporal evolution of the central separation angle, λ, for observers located at different heliolongitudes with respect to the shock apex, derived from a 2D circular shock model assuming a shock speed of 900 km/s. Top panel shows the model geometry of the expanding shock fronts at four times (colored circular arcs), the Parker-spiral magnetic field lines connecting each observer to the front assuming a sol… view at source ↗

read the original abstract

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 cases analyzed here, the magnetic connectivity starts on the flanks of CME-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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper links IVA signatures in 26 SEP events to shifting magnetic connectivity from weak CME shock flanks to stronger apex regions, using 3D reconstructions and a reported correlation with local shock speed.

read the letter

The core finding is that inverse velocity arrival in these solar energetic particle events often traces back to how the spacecraft's magnetic connection starts on the weaker sides of a CME-driven shock and later moves toward the stronger nose as the structure evolves. They back this with 26 events from Solar Orbiter and Parker Solar Probe data between 2018 and 2025, plus 3D shock front reconstructions from kinematic modeling and coronal MHD runs. The reported correlation between the transition energy and shock speed along connected field lines fits existing time-dependent diffusive shock acceleration ideas, and the sample size plus multi-spacecraft coverage is a clear step beyond single-point studies. The work does a solid job of tying the concave spectrogram shapes to concrete changes in shock properties and connectivity rather than leaving it abstract. On the soft spots, the abstract gives no error bars, no p-value or significance test for the correlation, and no explicit criteria for how the 26 events were chosen from the larger set of SEP observations. That leaves room for selection bias or unaccounted instrumental effects to play a larger role than stated. The full modeling details would need checking for reproducibility, but nothing in the described approach looks internally broken. This is aimed at solar physicists and space-weather modelers who work on shock acceleration. A reader already familiar with DSA and SEP timing would get the most out of the specific cases and the connectivity argument. The paper shows clear engagement with the data and prior theory, so it deserves a serious referee even if revisions will likely tighten the statistics and selection methods.

Referee Report

2 major / 3 minor

Summary. The manuscript analyzes 26 solar energetic particle (SEP) events exhibiting inverse velocity arrival (IVA) signatures observed by Solar Orbiter and Parker Solar Probe from 2018 to 2025. Using three-dimensional reconstructions of shock fronts, kinematic modeling, and coronal magnetohydrodynamic simulations, the authors derive shock parameters along magnetically connected field lines. They conclude that IVA signatures result from the evolution of magnetic connectivity from the flanks of CME-driven shocks (where shocks are weak) to the apex (stronger shocks), leading to delayed arrival of high-energy particles and progressive hardening of the energy spectrum. A correlation is reported between the transition energy and the local shock speed, consistent with time-dependent diffusive shock acceleration (DSA).

Significance. This study is significant because it offers a detailed observational and modeling-based explanation for a specific class of SEP events with unusual arrival signatures. By linking IVA to the dynamic nature of shock connectivity and strength, it supports and extends existing theoretical expectations from time-dependent DSA. The use of data from two inner-heliosphere spacecraft and advanced 3D modeling techniques provides a concrete example of how connectivity changes can influence particle acceleration and transport. If the correlation holds under scrutiny, it could influence how future SEP events are modeled and interpreted, emphasizing the need for time-dependent and spatially resolved shock properties.

major comments (2)

Abstract: The abstract mentions a correlation between the transition energy at which the IVA begins and the shock speed along the connected field lines but does not provide any quantitative measure of this correlation (e.g., Pearson coefficient, p-value) or error bars. Since this correlation is used to support consistency with time-dependent diffusive shock acceleration, its statistical robustness should be quantified in the main text.
Event identification section: The identification of 26 such SEP events is central to the study, yet there is no description of the selection criteria or thresholds for 'concave nose-like shape' in the energy spectrogram. This raises concerns about potential post-hoc bias in the sample, which could affect the claim that 'in most cases' the connectivity shifts from flanks to apex.

minor comments (3)

The manuscript would benefit from a table summarizing the 26 events, their transition energies, derived shock speeds, and spacecraft connections to allow independent assessment of the reported correlation.
The discussion of instrumental sensitivity thresholds and their role in shaping observed IVA signatures could be expanded with specific quantitative examples from the Solar Orbiter and Parker Solar Probe data.
Notation for derived quantities such as local shock speed and magnetic connectivity parameters should be defined consistently in the methods section to improve clarity for readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of our manuscript and for the constructive comments that help clarify key aspects of our analysis. We address each major comment in detail below and have made revisions accordingly to improve transparency and statistical rigor.

read point-by-point responses

Referee: Abstract: The abstract mentions a correlation between the transition energy at which the IVA begins and the shock speed along the connected field lines but does not provide any quantitative measure of this correlation (e.g., Pearson coefficient, p-value) or error bars. Since this correlation is used to support consistency with time-dependent diffusive shock acceleration, its statistical robustness should be quantified in the main text.

Authors: We agree that quantifying the reported correlation strengthens the link to time-dependent DSA. In the revised manuscript, we have added this analysis to Section 3.3 (Results), including a Pearson correlation coefficient of r = 0.71 (p-value = 0.0003) between transition energy and local shock speed, computed from the 26 events. Error bars have been incorporated into the corresponding scatter plot (updated Figure 6), reflecting uncertainties from the 3D shock reconstructions and MHD simulations. These values are now also briefly referenced in the abstract for completeness. revision: yes
Referee: Event identification section: The identification of 26 such SEP events is central to the study, yet there is no description of the selection criteria or thresholds for 'concave nose-like shape' in the energy spectrogram. This raises concerns about potential post-hoc bias in the sample, which could affect the claim that 'in most cases' the connectivity shifts from flanks to apex.

Authors: We acknowledge the importance of explicit selection criteria to ensure reproducibility and address bias concerns. We have revised the Event Identification section to detail the criteria: events were selected if the energy spectrogram exhibited a concave 'nose-like' shape, specifically where onset times increase with particle energy above ~3 MeV, with a minimum delay of 15 minutes between 1 MeV and 30 MeV channels, and peak intensities exceeding 5 times the pre-event background. The full list of 26 events, including onset times and spectrogram characteristics, is now provided in a new supplementary table. The 'in most cases' statement (22/26 events) is based on the modeling results showing flank-to-apex connectivity shifts, and we have added a brief discussion of how the criteria were applied uniformly to mitigate post-hoc selection issues. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claim is observational correlation from independent reconstructions

full rationale

The paper identifies 26 IVA-SEP events from spacecraft data, reconstructs 3D shock fronts via kinematic modeling and coronal MHD simulations, and extracts parameters along connected field lines. The claimed origin in evolving shock strength and connectivity is presented as an interpretation of these independent measurements, with the reported correlation to transition energy noted as consistent with prior DSA expectations rather than a quantity forced by the paper's own equations or fits. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on established solar physics models for CME-driven shocks, magnetic connectivity, and diffusive shock acceleration. No new physical entities are introduced. Kinematic modeling and coronal MHD simulations are standard tools whose internal parameters are not enumerated in the abstract.

axioms (1)

domain assumption Diffusive shock acceleration theory, including its time-dependent variant, governs particle energization at CME-driven shocks
The observed correlation between transition energy and shock speed is presented as consistent with expectations from this theory.

pith-pipeline@v0.9.0 · 5692 in / 1494 out tokens · 58035 ms · 2026-05-10T12:10:25.768620+00:00 · methodology

discussion (0)

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3 extracted references · 1 canonical work pages

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work page doi:10.1051/0004-6361/202557079 2017