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Shock and SEP Modeling Study for the 5 September 2022 SEP Event

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The inverse velocity dispersion seen by Parker Solar Probe on 5 September 2022 is attributed to slow acceleration at the expanding shock's weak flank, not to cross-field diffusion.

desk verdict A credible, well-documented case study whose central IVD reproduction is largely baked into a tuned roll-over momentum prescription, so the flank-acceleration mechanism is plausible but not independently confirmed. read the letter →

arxiv 2501.03066 v1 pith:6T53KUTD submitted 2025-01-06 astro-ph.SR physics.space-ph

A. Kouloumvakos , N. Wijsen , I. C. Jebaraj , A. Afanasiev , D. Lario , C. M. S. Cohen , P. Riley , D. G. Mitchell
show 5 more authors
Z. Ding A. Vourlidas J. Giacalone X. Chen M. E. Hill
This is my paper · ORCID
classification astro-ph.SRphysics.space-ph
keywords solarenergeticparticlescoronalmassejectionshocksinversevelocitydispersiondiffusiveshockaccelerationParkerProbeSEPonsettimingcross-fielddiffusionparticletransportmodeling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

On 5 September 2022, Parker Solar Probe was only 15.4 solar radii from the Sun when a fast coronal mass ejection shock swept past it, and its particle instruments recorded an odd arrival pattern: above about 1 MeV, the higher-energy protons arrived later than the lower-energy ones, the opposite of normal velocity dispersion. The paper sets out to show that this inverse velocity dispersion, together with a roughly 35-minute delay in SEP release relative to Solar Orbiter, came from the shock itself. PSP was magnetically connected to the weak east flank of the expanding shock, where particle acceleration was slow and the maximum accelerated energy rose only gradually as the shock strengthened and moved onto stronger regions. A 3D shock reconstruction combined with a data-driven focused-transport simulation reproduces the observed SEP onset, the evolving energy spectrum, and the inverse velocity dispersion when cross-field diffusion is omitted; adding cross-field diffusion makes the match worse. The authors conclude that the local strength evolution of the connected shock flank governed the delayed release, so release-time interpretations and forecasting need to treat shock acceleration as spatially and temporally inhomogeneous.

What carries the argument

The machinery that carries the argument is the prescription of the proton spectrum injected at each point of the reconstructed shock front: a power law in momentum with an exponential cutoff at a roll-over momentum $p_c$. The cutoff is set by $p_c = \eta\, p_{\mathrm{inj}}\left(\frac{\pi \epsilon \sigma}{4\, r_s/d_i}\right)^{1/(\sigma-3)}$, in which $p_{\mathrm{inj}}$ is the injection momentum, $\sigma$ the diffusive-shock-acceleration spectral index, $r_s$ the radial distance of the shock point, and $d_i$ the proton inertial length. Because a shock flank that formed only recently has had little time to trap and accelerate particles, its $p_c$ is low; as the shock expands and strengthens, $p_c$ at the PSP-connected point rises from below 1 MeV to about 10 MeV. The constant reduction factor $\eta = 0.35$ is calibrated against the PSP observations. The time- and space-dependent cutoff, carried to the observer by a focused-transport solver, is what produces the inverse velocity dispersion in the simulated spectrograms. The 3D ellipsoidal shock reconstruction and the coronal and heliospheric MHD background make the prescription specific to this event.

What would settle it

Measure the proton energy spectrum in the foreshock region upstream of the shock during the roughly 40 minutes before the shock reaches PSP at 17:27 UT on 5 September 2022. The model predicts that the energy at which the spectrum rolls over climbs from well below 1 MeV near onset (16:48 UT) to about 10 MeV at crossing, with higher-energy protons arriving later as the cutoff rises. If the cutoff energy stays roughly constant during that interval, or if a rising cutoff is not accompanied by later arrival of the highest-energy protons, the flank-acceleration explanation is falsified.

Watch

Extended reading notes

Core claim

The central claim is that the SEPs observed at PSP were not released promptly at the Sun and then transported, but were accelerated gradually at the flank of the CME-driven shock to which PSP was magnetically connected. The paper derives release times from velocity dispersion analysis: SEPs reached Solar Orbiter promptly along a Parker-spiral path (release 16:09 ± 4 min), while at PSP the inferred release time is 16:45 ± 1 min with a much shorter path length (about 6.3 $R_\odot$), indicating release higher in the corona rather than near the solar surface. The shock reconstruction shows PSP's connection point started on a subcritical, oblique flank ($M_{fm} \approx 1.2$, $\Theta_{BN} \approx 32^\circ$) and only later became supercritical, so the roll-over energy of the accelerated spectrum at that connection point climbed from well below 1 MeV to about 10 MeV by the time the shock crossed the spacecraft. In the simulation this gradual rise of the cutoff energy is what makes protons above ~1 MeV arrive after lower-energy protons. The paper also shows that including cross-field diffusion degrades the timing agreement, and concludes that perpendicular transport had only a minor effect for this near-Sun event.

Load-bearing premise

The conclusion rests on the assumption that a single calibration factor, set to 0.35 and chosen to make the simulated spectra match Parker Solar Probe, correctly describes how the maximum accelerated energy grows at every point of the shock flank that was connected to the spacecraft; if that factor actually varies across the shock surface, or if the steady-state acceleration theory is invalid for this weak oblique flank, the reproduced delay and inverse velocity dispersion could be an artifact of the tuning.

Editorial extensions

If this is right

  • Release-time estimates from near-Sun spacecraft will be biased late whenever the connected shock flank starts subcritical; the path length derived from velocity dispersion analysis then reflects the height at which the shock first becomes an efficient accelerator rather than a particle path along the Parker spiral.
  • SEP timing predictions should be made energy-dependent: a weak flank can supply low-energy protons promptly while high-energy protons are delayed by tens of minutes, so forecasts based on a single shock speed or a single release site will miss the observed dispersion pattern.
  • If cross-field diffusion really was minor for this event, fitting SEP profiles to infer transport coefficients without modeling the spatially varying shock acceleration will overestimate perpendicular diffusion.
  • The failure of the same injection prescription at Solar Orbiter's strong quasi-parallel connection means the calibration is flank-specific; simulations of other events should adopt position-dependent injection efficiency rather than one global factor.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A survey of Parker Solar Probe energetic-particle events should find inverse velocity dispersion preferentially when the spacecraft is connected to a young, weak shock flank; if IVD events occur under other connectivity geometries, the causal link to local flank acceleration would need revision.
  • The short VDA path length at PSP could be repurposed as a diagnostic of where supercritical conditions first appear along the connected field line, turning a transport-derived quantity into a probe of shock acceleration onset.
  • The conclusion that cross-field diffusion was minor should not be generalized to all near-Sun events: PSP was inside the steep radial-intensity gradient near the shock, where the direct shock source dominates; farther from the flank, perpendicular transport may matter more.
  • A position-dependent reduction factor $\eta$ that decreases at strong shock regions would likely correct the Solar Orbiter overestimate while preserving the PSP match; this is a concrete, testable modification of the model.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper analyzes the 5 September 2022 SEP event observed by Parker Solar Probe (PSP) and Solar Orbiter. It combines multi-spacecraft EUV/coronagraph observations, a 3D ellipsoidal shock reconstruction, MAS-derived coronal MHD parameters, and PARADISE focused-transport simulations with a prescribed diffusive-shock-acceleration source spectrum. The simulation reproduces the PSP onset times (Table 1) and the observed inverse velocity dispersion (IVD) above about 1 MeV when a reduction factor eta = 0.35 is applied to the roll-over momentum in Eq. (3). A run with perpendicular diffusion yields worse onset-time agreement, leading the authors to conclude that cross-field diffusion was minor. The same model overestimates Solar Orbiter intensities by roughly an order of magnitude, and the authors attribute this to uncertainties in the roll-over momentum at the shock apex.

Significance. If the central interpretation is correct, the paper would provide a compelling multi-spacecraft case that the delayed SEP release and inverse velocity dispersion at PSP are governed by the time-evolving strength of the connected shock flank rather than by cross-field transport. The study is valuable as a detailed event analysis that integrates 3D shock reconstruction, MHD background modeling, and focused transport, and it is commendably transparent about its calibrated parameter and its disagreement at Solar Orbiter. However, because the delayed high-energy onset is effectively prescribed by Eq. (3) and eta is tuned to the PSP observations, the reported match does not independently confirm the proposed physical mechanism; the central claim therefore requires a careful reframing or additional sensitivity analysis.

major comments (3)
  1. [§3.3, Eq. (3), Fig. 8, Table 1] The inverse velocity dispersion is not an emergent result of the simulation. In Eq. (3), the roll-over momentum pc is prescribed as a monotonically increasing function of the shock radius rs through rs/di, and the reduction factor eta = 0.35 is explicitly calibrated to match the PSP observations in the simulations presented below. Because pc sets the energy above which the source spectrum is suppressed, the delayed arrival of >1 MeV protons at PSP is built into the time-dependent source. The agreement in Table 1 therefore demonstrates that a suitable choice of cutoff evolution can reproduce the observations, but it does not independently establish that the IVD is caused by slow ongoing acceleration at the shock flank, as stated in the abstract.
  2. [§4 and Fig. 11] The use of a single calibrated eta is undermined by the Solar Orbiter comparison. With eta = 0.35, the model overproduces Solar Orbiter intensities by roughly an order of magnitude and gives a harder spectrum, and the authors state in §3.3 that 'it is expected that eta varies across the shock surface.' The same paper therefore demonstrates that a constant eta is not accurate and that the PSP match may be specific to the calibrated value. The claim that the model is data-driven is weakened because the key free parameter is tuned to the target dataset, and the authors' own acknowledgment of the Solar Orbiter discrepancy should be given more weight in the interpretation.
  3. [§3.3, Table 1, Fig. 10] The conclusion that cross-field diffusion had a minor effect on this event is not strongly supported. The comparison between the D⊥ = 0 and D⊥ ≠ 0 runs uses the same source calibration, which was optimized for the D⊥ = 0 case; the worsening of the D⊥ ≠ 0 onset-time agreement is therefore not an independent test of transport. Moreover, the authors note that the shift of the IVD transition energy from about 1 MeV to 3 MeV may not be significant given the shock modeling uncertainties. A sensitivity study over the diffusion parameters, rather than a single diffusion on/off comparison, would be needed to justify the 'minor effect' conclusion.
minor comments (5)
  1. [§2.2] The VDA-derived path length L ~ 6.3 R_sun is used to infer a release altitude of about 9 R_sun, but the VDA assumptions of scatter-free propagation and simultaneous release are not consistent with the extended, time-dependent source model used later in the paper; this interpretation should be framed more cautiously or cross-checked with the simulation.
  2. [§3.3] The cross-reference to 'Figure 10' when discussing the east flank's roll-over energy below the depicted energy channels appears to be a typo; it should likely refer to Figure 9.
  3. [§3.3, Eq. (2)] The normalization of the source spectrum would benefit from an explicit statement of the units and reference radius for np, so that the source amplitude in Eq. (2) is reproducible from the text.
  4. [Acknowledgments] The Acknowledgments contain a sentence thanking 'the anonymous reviewer' for helping improve the paper; this sentence is inappropriate in a submitted manuscript and should be removed or rewritten.
  5. [General] The paper lacks an explicit data and code availability statement; given that the study relies on open-source tools such as PyThea, PARADISE, and MAS/EUHFORIA, a clear statement of the versions used and the availability of input data would improve reproducibility.

Circularity Check

1 steps flagged · score 6.0 of 10

PSP match is partly a calibration check: η = 0.35 is tuned to PSP and directly sets the roll-over momentum, so the reproduced onset, spectrum, and IVD are not fully independent predictions.

  1. fitted input called prediction [Section 3.3, Eq. (3); match claimed in Abstract and Section 4]
    "To account for this, we have introduced the reduction factor η in Eq. (3), which we set equal to 0.35. The latter value gives a good match with PSP observations in the simulations presented below."

    η multiplies pc in Eq. (3), and pc sets the exponential roll-over energy of the injected shock spectrum; the roll-over energy controls both the energy above which the inverse velocity dispersion appears and the delayed onset of high-energy protons at PSP. Choosing η = 0.35 to agree with the PSP observations means that the subsequent claim that the data-driven simulation reproduces the PSP event onset, evolving energy spectrum, and IVD is a calibration check for this parameter rather than an independent prediction. The shock geometry, MHD background, and transport are independent inputs, but the central timing and spectral match at PSP is partly forced by the fitted value of pc.

full rationale

Most of the modeling chain is self-contained: the 3D shock reconstruction, MAS/EUFHORIA background, and PARADISE transport are externally developed tools, and Eq. (3) is taken from the independent Vainio et al. (2014) theory rather than from a self-citation. The main circularity is the one-parameter calibration: η = 0.35 is explicitly set to give a good match to PSP observations, and because η directly controls the roll-over momentum that determines where and when the IVD forms, the reported reproduction of the PSP onset, spectrum, and IVD is partly a restatement of the fit. The qualitative IVD itself follows from the prescribed radial growth of pc in Eq. (3); that radial dependence has independent theoretical grounding, but the absolute energy scale and timing are tuned. The Solar Orbiter comparison is a genuine external test, and its failure (order-of-magnitude overproduction and a harder spectrum) further indicates that the PSP match owes much to the calibrated η rather than to a universally accurate prescription. This warrants a partial-circularity score of 6, not a higher score, because the shock geometry and transport results retain independent content.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the prescribed shock acceleration spectrum with a roll-over parameter calibrated to the target observation, plus the assumed validity of the transport and MHD models. The shock geometry itself is fitted to coronagraph images. No new physical entities are introduced.

free parameters (3)
  • Roll-over reduction factor η = 0.35
    Introduced in Eq. (3) and set to 0.35 because 'The latter value gives a good match with PSP observations in the simulations presented below' (§3.3). Controls the roll-over energy scale and thus the energy at which inverse velocity dispersion appears.
  • Shock ellipsoid shape and position = center at 170° longitude, -41° latitude; κ=0.65, α=1.03, ε=-0.27 (mean values)
    Free parameters of the ellipsoid shock model iteratively adjusted to give a good visual fit to STEREO-A and LASCO coronagraph images (§3.1). Uncertainties are assessed only indirectly.
  • Injection fraction ε = 5e-5
    Fraction of protons injected into DSA (Eq. 2), taken from Afanasiev et al. 2024 rather than fitted here; sets absolute intensities.
assumptions (5)
  • domain assumption The focused transport equation (A1) with QLT pitch-angle diffusion and NLGC perpendicular diffusion describes SEP transport in the corona and inner heliosphere.
    Standard SEP transport modeling framework, cited to Skilling 1971 and van den Berg et al. 2020; assumed valid in the near-Sun environment.
  • domain assumption The accelerated particle distribution at the shock is given by steady-state DSA with a prescribed spectrum fs(p) (Eq. 2) and roll-over momentum pc (Eq. 3) from Vainio et al. 2014.
    The authors do not simulate shock acceleration self-consistently; they prescribe the injection spectrum. This is the main modeling assumption on which the predicted spectra and IVD depend (§3.3).
  • domain assumption The ellipsoid fitted to coronagraph images represents the true 3D CME-driven shock front throughout the corona.
    Used to compute shock speed, Mach numbers, and connectivity (§3.1, §3.2); validated against in-situ arrival times at PSP and Solar Orbiter with mixed success.
  • ad hoc to paper Particles are injected only where the modeled fast-magnetosonic Mach number exceeds 1.
    Filters the shock surface to regions where a shock actually forms; directly determines the source extent and the initial absence of high-energy particles near PSP (§3.3).
  • ad hoc to paper The reduction factor η is constant across the shock surface.
    The authors set η=0.35 globally, then note 'it is expected that η varies across the shock surface' (§3.3); if η varies, the Solar Orbiter overestimation and PSP match could change.

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Cite this review

Pith. "Pith review of Shock and SEP Modeling Study for the 5 September 2022 SEP Event." pith.science (2026). https://pith.science/paper/6T53KUTD

@misc{pith2026250103066,
  author       = {Pith},
  title        = {Pith review of: Shock and SEP Modeling Study for the 5 September 2022 SEP Event},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6T53KUTD}},
  note         = {Machine review of arXiv:2501.03066}
}
abstract

On September 5, 2022, during Parker Solar Probe's (PSP) 13th encounter, a fast shock wave and a related solar energetic particle (SEP) event were observed as the spacecraft approached the perihelion of its orbit. Observations from the Integrated Science Investigation of the Sun (ISOIS) instrument suite show that SEPs arrived at the spacecraft with a significant delay from the onset of the parent solar eruption and that the first arriving SEPs exhibited an Inverse Velocity Dispersion (IVD) for energetic protons above $\sim$1~MeV. Utilizing data from multiple spacecraft we investigate the eruption dynamics and shock wave propagation. Our analysis includes 3D shock modeling and SEP transport simulations to examine the origins of this SEP event and explore the causes of the delayed SEP onset and the observed IVD. The data-driven SEP simulation reproduces the SEP event onset observed at PSP, its evolving energy spectrum and the IVD. This IVD is attributed to a relatively slow, ongoing particle acceleration process occurring at the flank of the expanding shock wave intercepted by PSP. This has significant implications for the role of shocks in the release of SEPs at widespread events and for methods used to infer the SEP release times. Furthermore, the match between the simulation and observations worsens when cross-field diffusion is considered, indicating that SEP diffusion had a minor effect on this event. These findings underscore the complexity of SEP events and emphasize the need for advanced modelling approaches to better understand the role of shock waves and other physical processes in SEP acceleration and release.

Figures

Figures reproduced from arXiv: 2501.03066 by the authors.

Figure 1
Figure 1. A view of the ecliptic that shows the positions of the planets and spacecraft in the inner heliosphere on September 5, 2022, at 16:00 UT. The orbits of the space￾craft(planets) are shown with the colored(grey) dashed lines. The Parker spiral connecting the different observers to the solar surface are shown with the solid colored lines. The arrow marks the direction of propagation of the CME. The orange circle at the… view at source ↗
Figure 2
Figure 2. Remote sensing observations during the eruption. Panel (a) shows a plain image from EUI/FSI at 304 ˚A. Panel (b) and (c) show running-difference white-light coronagraphic images of the CME and the shock from LASCO/C2 and STEREO￾A/COR2, respectively. We label on panel (a) the location of AR 13088 and a coronal hole located at the south-eastern hemisphere, and on panels (b) and (c) the CME and the white-light shock. H… view at source ↗
Figure 3
Figure 3. Observations of solar energetic protons from So￾lar Orbiter (top panel) and PSP (bottom panel). Top panel: shows the energy spectrogram of proton fluxes from HET￾Sun telescope on Solar Orbiter at an energy range from ∼10 MeV to ∼90 MeV. Bottom panel: shows the energy spectrogram of proton fluxes from the Epi-Lo instrument on PSP. This spectrogram incorporates proton data from all viewing directions of Epi-Lo. At eac… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: STEREO-A COR2 running-differences images. The reconstructed shock surface is shown at each frame with the red wiremesh. The shock apex and center are marked with the black circle and cross, respectively. ages from COR2. The geometric model aligns well with COR2 observa…
Figure 5
Figure 5. Figure 5: Kinematic time profiles of the reconstructed shock wave. The two red curves show the shock kinematics at the apex, the blue and green curves show the kinematics of the flanks. The solid lines show the height(length) and the dashed lines the speed of the apex(flanks). T…
Figure 6
Figure 6. Figure 6: The modeled shock wave parameters are plotted in 3D along the reconstructed wavefront surface. The panels from left to right show three selected frames at different times, noted at the bottom. The top row panels (a1 to a3) show the distributions of the modeled fast-mag…
Figure 7
Figure 7. Figure 7: Temporal evolution of the shock Mfm (top panel) and ΘBN angle (bottom panel). The black dashed lines show the shock parameters at the magnetic field lines connecting the two spacecraft to the Sun, and the colored solid lines show the mean values of the shock parameter …
Figure 8
Figure 8. Figure 8: The roll-over energy of the particle spectrum at the shock points that connect to the Solar Orbiter and PSP. the jump in the solar wind speed across the shock wave. This assumption is based on the scenario in which up￾stream solar wind protons experience head-on collis…
Figure 9
Figure 9. Figure 9: A snapshot from the northern ecliptic pole from the PARADISE Model on 2022 Sep 5, 16:59UT. Left panels show omnidirectional proton intensities for energies 675 keV to 1 MeV), while right panels show the same for energies 50 – 80 MeV. Top row: the model results with no …
Figure 10
Figure 10. Figure 10: Modeled omnidirectional particle intensities at PSP. The left and right figures are for simulations without and with cross-field diffusion, respectively. The top panels show particle spectrograms, while the lower panels show time-intensity profiles for a selection of …
Figure 11
Figure 11. Figure 11: Modeled omnidirectional particle intensities at Solar Orbiter. The top panel shows the particle spectro￾gram, while the lower panel shows time-intensity profiles for a selection of energy channels. In these profiles, the shaded area indicates the variation of intensit…

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Inverse Velocity Dispersion of Solar Energetic Protons Observed by Solar Orbiter and Its Shock Acceleration Explanation

    astro-ph.SR 2025-07 conditional novelty 6.0 of 10

    Solar Orbiter observed 10 solar energetic proton events with inverse velocity dispersion, which the authors explain as delayed release from diffusive shock acceleration and use to infer shock acceleration parameters.

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