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REVIEW 4 major objections 5 minor 65 references

Bidirectional anisotropic solar energetic particle events observed by Solar Orbiter

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Bidirectional particle bursts trace a flux rope's long field lines.

desk verdict A genuinely new two-event SEP observation with a plausible flux-rope interpretation; event 2's long path length is the weak link but not fatal. read the letter →

arxiv 2507.16990 v2 pith:P27SMMRD submitted 2025-07-22 astro-ph.SR

Zheyi Ding , Robert F. Wimmer-Schweingruber , Yu Chen , Lingling Zhao , Alexander Kollhoff , Patrick Kühl , Liu Yang , Lars Berger
show 7 more authors
Verena Heidrich-Meisner Javier Rodriguez-Pacheco George C. Ho Glenn M. Mason Gang Li Tomáš Formánek Christopher J. Owen
This is my paper · ORCID
classification astro-ph.SR
keywords solarenergeticparticlesbidirectionalanisotropyvelocitydispersionanalysissmall-scalemagneticfluxropeshelicityOrbiterCME-drivenshockaccelerationflares
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

Solar energetic particle events usually stream outward along open magnetic field lines, but this paper reports two rare events, observed by Solar Orbiter, in which protons streamed simultaneously toward and away from the Sun. In both events the two streams arrived with separate velocity-dispersion signatures, so their release times and path lengths could be derived independently. The paper argues that the promptly released anti-sunward stream came from flare acceleration, while the delayed, harder-spectrum, more intense sunward stream came from CME-driven shock acceleration, and that a small-scale magnetic flux rope encountered in situ guided the two populations along different, unusually long field lines. If this is right, bidirectional events become a direct way to measure the topology and central axis length of small flux ropes in the inner heliosphere.

What carries the argument

The argument runs on two diagnostics in parallel. Velocity dispersion analysis fits onset time as a function of inverse particle speed, giving release time and path length separately for the sunward and anti-sunward populations, while the first-order anisotropy tells which population dominates at each energy and time. On the magnetic side, an automated Grad-Shafranov-based flux-rope identification routine and a wavelet-derived normalized reduced magnetic helicity locate the small-scale flux rope, with cross-helicity and residual-energy checks distinguishing a twisted rope from Alfvenic fluctuations. The link between the two is the path-length excess: the fitted lengths exceed the nominal Parker spiral length, and that excess is assigned to helical winding around the flux rope's axis, allowing an estimate of the rope's central axis length.

What would settle it

Re-measure event 2's anti-sunward onset from background-subtracted spectra with an automated change-point detector; if a shift of roughly ten minutes or more removes the sunward/anti-sunward path-length asymmetry or brings the lengths back to the nominal Parker value, the flux-rope-guided long-path interpretation for that event fails. A future bidirectional event inside a flux rope with near-equal release times, intensities, and spectral indices for both streams would instead support the mirror-reflection alternative.

Watch

Extended reading notes

Core claim

The paper reports two solar energetic particle events in which protons arriving at Solar Orbiter showed two distinct velocity-dispersion tracks with opposite first-order anisotropies at the same time. In each event, the promptly arriving anti-sunward stream matched the timing of a type III radio burst, so it is assigned to flare acceleration; the delayed, more intense, spectrally harder sunward stream is assigned to a CME-driven shock that takes roughly half an hour to become an efficient accelerator. Small-scale magnetic flux ropes were identified in situ during both events, and the velocity dispersion analysis implies path lengths of 1.75 au and 3.04 au in event 1 and 1.51 au and 4.62 au in event 2, all substantially longer than the nominal Parker spiral length. The paper concludes that the flux rope's closed, twisted field lines guide the two populations along different, longer paths, and that simultaneous velocity dispersion from two distinct sources can directly constrain the flux rope's topology and central axis length.

Load-bearing premise

The load-bearing premise is that the anti-sunward onset time in the second event, which had to be estimated by eye against a bright, scattered background, is accurate enough for velocity dispersion analysis to yield the 4.62 au path length that underlies the flux-rope argument.

Editorial extensions

If this is right

  • If the interpretation holds, a single spacecraft can estimate the central axis length of a small flux rope by combining velocity-dispersion path lengths with the observed helical twist, as done in Appendix B for event 1.
  • The near-zero prompt release of the anti-sunward stream and the roughly 30-minute delayed release of the sunward stream become a usable discriminator between flare and CME-shock acceleration inside a closed magnetic structure.
  • Small-scale flux ropes, not only large magnetic clouds, must be included in solar energetic particle transport models to account for sunward streams and path lengths longer than nominal Parker spirals.
  • The rarity of clean bidirectional events is partly a detection effect: the first injection must be much weaker than the second, or its anisotropy signature masks the second source.

Reading between the lines

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

  • Beyond the paper, if small flux ropes are as frequent in the slow solar wind as the cited surveys indicate, some solar energetic particle events with anomalously long path lengths or unusual anisotropies may be connectivity effects of these ropes rather than scattering effects.
  • A testable extension is to search archival events for two velocity-dispersion tracks and check whether the path-length ratio of sunward to anti-sunward streams correlates with flux-rope twist, as the helical winding picture would predict.
  • The spectral asymmetry proposed here implies a statistical prediction: sunward shock-accelerated streams should cluster near the strong-compression spectral index near minus one, while flare-related anti-sunward streams should be softer, which could be checked across a larger sample.
  • A rival explanation, mirror reflection, would predict similar release times, intensities, and spectral indices for the two streams; future multipoint observations inside a well-resolved flux rope could test this cleanly by comparing fluxes at the two feet.
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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

4 major / 5 minor

Summary. The manuscript reports two solar energetic particle (SEP) events observed by Solar Orbiter on July 13, 2023, and July 23, 2024, in which the proton anisotropy reveals two oppositely directed streaming populations during the onset phase. For each event the authors identify two separate velocity-dispersion tracks, perform velocity dispersion analysis (VDA) to derive release times and path lengths, and combine the path lengths with in situ magnetic-field diagnostics (automated flux-rope identification via PyGS and wavelet magnetic helicity) to argue that a small-scale flux rope channels flare-accelerated anti-sunward particles along a shorter leg and CME-shock-accelerated sunward particles along a longer leg. The paper concludes that the sunward population is delayed, has a harder spectrum, and is more intense, and that the inferred path-length asymmetry constrains the flux-rope topology.

Significance. Event 1 is a convincing and rare observation: two clean velocity-dispersion tracks with opposite anisotropies, a type III radio burst coincident with the prompt release, a PyGS-identified flux rope, and bidirectional suprathermal electrons. If the interpretation is correct, the work provides a direct observational link between small-scale flux ropes and bidirectional SEP transport, and it proposes a new way to use simultaneous injections to constrain flux-rope topology. The paper is generally careful in stating its assumptions and in acknowledging the weaker constraints for event 2; the use of the public PyGS package and the explicit caveat about the event-2 path length are positive features. However, the strength of the event-2 evidence is currently overstated in the abstract, and the quantitative path-length asymmetry in event 2 rests on a visually estimated onset under strong scattering, so the central claim is only partly supported by the second event.

major comments (4)
  1. [§3, Event 2 (Fig. 3 right panels) and Appendix B, Eq. (B.1)] The 4.62 au S2 path length is the main quantitative support for the path-length asymmetry in event 2 and enters the flux-rope topology argument, yet it is derived from a visually estimated anti-sunward onset in a period of strong scattering and high background. The manuscript itself states that "the path length for this event might be less robust, especially for the S2." Because the S2 onset is measured on top of a decaying, velocity-dispersed S1 population, an energy-dependent late bias in the low-energy onset times would steepen the VDA slope and inflate the inferred path length; the present analysis offers no test of this bias. Please provide a quantitative robustness check, for example a background-subtracted onset fit, a fit restricted to the least contaminated high-energy channels, or a Monte Carlo over plausible onset choices; if such a check is not possible, state explicitly in the abstract and conclusions that the event-2 path-length asymmetry is only qualitative and does not by itself constrain flux-rope topology.
  2. [Abstract and §3 (Event 2)] The abstract says that "in both cases, small-scale flux ropes were identified in situ," but for event 2 the PyGS algorithm did not reliably detect a flux rope and the identification rests on wavelet helicity with thresholds |σm|≥0.6 and σr≤−0.5, described in the text as a "potentially Alfvénic SFR." This overstates the certainty for event 2. The abstract and the conclusions should carry the same qualification as the body of the paper, namely that the event-2 flux rope is inferred rather than identified.
  3. [§3 (Event 2) and Fig. 4] The spectral arguments are made without uncertainties: the text contrasts a −2.45 spectral index for S1 with −1.24 for S2 and states that the latter is "close to the limit of theoretical spectral index −1," but no fit uncertainties, energy ranges, or goodness-of-fit values are quoted. Since the spectral hardness is one of the three main discriminants between shock and flare origin, please report the fit errors and the fitting range for each spectrum, or downgrade the spectral claim to a qualitative statement.
  4. [§3 (release-time interpretation)] The 30-minute release delay is interpreted as shock-acceleration time using assumed values of 1.43 R⊙ for the shock formation height, 3 R⊙ for the release height, and 750 km/s for the average shock speed. These parameters are not measured for these events, and the resulting 24-minute estimate is therefore only a plausibility argument; the delay could also reflect energy-dependent release or transport effects. Please frame this paragraph explicitly as a consistency check and state how the conclusion would change if the assumed heights and speeds were varied over the ranges quoted in the cited statistical studies.
minor comments (5)
  1. [§3 and Fig. 3] The text refers to "solid lines" and "purple lines" in Fig. 3, while the figure caption describes "dashed black and magenta lines"; please make the line-style and color terminology consistent between text and figure.
  2. [Appendix B] The notation L0,sun and L0,asun is confusing: L0,sun is derived from the 1.75 au path of the anti-sunward streaming population, whereas the phrase "sunward streaming" elsewhere refers to the 3.04 au population. Please rename these quantities so that the mapping between telescopes, streaming directions, and path lengths is explicit.
  3. [§3 and Fig. 1] The comparison of derived path lengths with the nominal Parker spiral should quote the actual solar wind speed used, and its uncertainty, for each event; Fig. 1 assumes 400 km/s while Appendix B quotes 300 km/s, and the conclusion that the paths are "substantially greater" depends on this choice.
  4. [§3 and Fig. 3 caption] Please clarify the radio-burst timing convention: the caption says the vertical line is shifted 7.9 and 7.2 minutes earlier, while the text says the burst began at approximately 06:41 UT from the Sun; state explicitly whether the quoted onset is the time at the Sun or the observed time at the spacecraft.
  5. [§3] There are two occurrences of "consisting with" where "consistent with" is meant; please correct these in the paragraph discussing the acceleration-time estimate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: VDA path lengths, SFR identification, and flux-rope topology inference rest on independent measurements and are not recycled as inputs.

full rationale

The derivation chain is self-contained. VDA release times and path lengths are fitted from the observed energy-dependent onset times in the sunward and anti-sunward telescope channels; these quantities are subsequently compared with, not fitted to, the independent type III radio burst timing and the nominal Parker spiral length. The flux-rope identification uses separate magnetic-field and plasma diagnostics (PyGS GS reconstruction and wavelet helicity/cross-helicity/residual-energy criteria), and Appendix B combines the independently inferred particle path length with the separately measured mean Bt/Bz ratio to estimate the flux-rope axis length. No equation reduces to its own input, and no fitted parameter is renamed as a prediction. The acknowledged weakness in event 2's anti-sunward onset time, visually estimated under strong scattering and conceded by the authors as potentially less robust, is a measurement-uncertainty concern rather than a circularity; it does not make the VDA output equivalent to the flux-rope hypothesis by construction. Self-citations to PyGS and the helicity methodology are supporting references to externally developed or independently published tools, not load-bearing uniqueness claims.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central interpretation rests on standard VDA, on the assumption that the in situ structure is a closed flux rope, and on representative shock parameters borrowed from statistical studies. No new physical entities are introduced. The most fragile inputs are the assumed shock formation and release heights, the assumed shock speed, and the chosen helicity thresholds for identifying the event 2 flux rope.

free parameters (6)
  • Shock formation height = 1.43 solar radii
    Adopted from Gopalswamy et al. (2013) statistics rather than measured for these events; used with the release height and shock speed to estimate the available acceleration time of about 24 minutes.
  • Proton release height = 3 solar radii
    Adopted from Kouloumvakos et al. (2015) and Ameri et al. (2024) statistics; used to compute the time available for shock acceleration before release.
  • Average shock speed = 750 km/s for both events
    Representative value, not measured; the far-side CME speeds from DONKI have significant uncertainty, so the 24-minute acceleration-time estimate is only approximate.
  • Radio burst onset shift = 7.9 min (event 1), 7.2 min (event 2)
    Applied in Fig. 3 to align the radio burst line with the particle release comparison; the physical basis for the shift is not fully explained.
  • Parker spiral solar wind speed for path-length comparison = 400 km/s (Fig. 1), 300 km/s (Appendix B)
    The nominal Parker spiral length depends on the assumed solar wind speed; different values change how anomalous the derived path lengths are relative to the reference.
  • SFR identification thresholds = |sigma_m| >= 0.6, sigma_r <= -0.5
    Chosen criteria for identifying small-scale flux ropes from wavelet helicity; because event 2's flux rope is only identified through these thresholds, the detection depends on their choice.
assumptions (5)
  • domain assumption All energies of a given particle population are released simultaneously at the source (VDA assumption).
    Invoked in Section 3 for converting arrival-time delays into release times and path lengths; the paper notes about 5 minutes uncertainty for electrons but acknowledges shock-accelerated ions may violate it by the acceleration timescale.
  • domain assumption The in situ structure carrying bidirectional particles is a closed flux rope with both legs anchored to the Sun.
    The central topology picture in Fig. 5 requires both legs connected to the Sun; the mirror-effect alternative is argued against only indirectly via intensity and spectral differences.
  • domain assumption The wavelet helicity criteria identify flux ropes rather than Alfvenic turbulence.
    Appendix A.2 uses |sigma_m| >= 0.6 and sigma_r <= -0.5 together with high |sigma_c| to select Alfvenic small-scale flux ropes; the paper acknowledges such signatures can be ambiguous in turbulent solar wind, especially for event 2.
  • domain assumption EPT ion fluxes are proton-dominated.
    Section 2 states EPT does not distinguish species and fluxes are commonly interpreted as protons; if heavy ions contribute significantly, the inferred release times and spectra would be biased.
  • domain assumption Shock acceleration delay is governed by t_acc ~ kappa/u^2 equated to the shock dynamic timescale.
    Used in Section 3 to estimate a 24-minute acceleration time for 70 MeV protons; the diffusion coefficient and upstream speed are not measured for these events, so the estimate is schematic.

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Cite this review

Pith. "Pith review of Bidirectional anisotropic solar energetic particle events observed by Solar Orbiter." pith.science (2026). https://pith.science/paper/P27SMMRD

@misc{pith2026250716990,
  author       = {Pith},
  title        = {Pith review of: Bidirectional anisotropic solar energetic particle events observed by Solar Orbiter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P27SMMRD}},
  note         = {Machine review of arXiv:2507.16990}
}
read the original abstract

Solar Energetic Particle (SEP) events are critical for understanding particle acceleration and transport in the heliosphere. While most SEP events involve outward streaming particles along open magnetic field lines, bidirectional events characterized by simultaneous sunward and anti-sunward particle flows offer unique insights into magnetic field topology and the interplay of multiple acceleration sources. We aim to investigate the origin and transport of energetic particles in two rare bidirectional anisotropic SEP events observed by Solar Orbiter. Both events showed two clear velocity dispersion signatures with opposite particle anisotropies during their onset phase. The sunward streaming protons, characterized by delayed release time, harder spectral index, and higher intensities, may be attributed to coronal mass ejection-driven shock acceleration, while the promptly released anti-sunward streaming protons are likely linked to flare acceleration. Notably, in both cases, small-scale flux ropes were identified in situ during the time intervals corresponding to the bidirectional particle streaming. Path lengths derived for sunward and anti-sunward injections were substantially greater than nominal values of the Parker field lines, further supporting the role of the flux rope in shaping particle trajectories. These observations demonstrate that magnetic flux rope could significantly affect magnetic connectivity to the source region and SEP propagation in the inner heliosphere, while simultaneous velocity dispersion from two distinct particle sources allows for direct constraints on the topology of the flux rope. Our results highlight the value of combining particle anisotropy, release time, source spectra, and magnetic structure diagnostics to unravel SEP transport in complex transient magnetic structures, and also present new challenges for the current SEP transport model.

Figures

Figures reproduced from arXiv: 2507.16990 by the authors.

Figure 1
Figure 1. Upper panels: Positions of the spacecraft during events 1 and 2 from Solar-MACH (Gieseler et al. 2023). The location of Solar Orbiter is indicated by a blue dot. The arrow shows the direction of the associated solar flare. The Parker spiral magnetic field line corresponds to an assumed solar wind speed of 400 km/s. Lower panels: Corresponding halo CMEs observed by the LASCO-C2 coronagraph on board SOHO for both even… view at source ↗
Figure 2
Figure 2. Overview of SEP events 1 (left) and 2 (right). The top horizontal bars show the in situ magnetic field polarity, with red (blue) indicating a magnetic field direction outwards from (inwards towards) the Sun. Panels (a): Omnidirectional proton dynamic spectra measured by EPT and HET. The colour-coded bins represent scaled intensity I · E 2 in units of cm−2 s −1 sr−1 MeV. Panels (b): First-order anisotropy of protons.… view at source ↗
Figure 3
Figure 3. Top panel: Radio dynamic spectrum observed by SolO/RPW. Lower four panels: Proton intensity as a function of inverse beta (c/v, where c is the speed of light and v is the particle velocity) and time for the sunward, anti-sunward, north, and south telescopes of both EPT and HET. The vertical line marks the onset time of the radio burst, which has been shifted 7.9 and 7.2 minutes earlier to facilitate comparison with … view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Time-averaged proton spectra from the HET sunward and anti-sunward telescopes. The black and magenta points correspond to the boxes of source 1 (S1) and source 2 (S2) in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: presents a two-dimensional schematic illustration of the possible origin of bidirectional SEPs within a magnetic flux rope, as discussed in this study. In this scenario, the observer is situated inside a flux rope rooted at the Sun, with both legs an￾chored in the lowe…

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.