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Comparing Methods for Calculating Solar Energetic Particle Intensities: Re-binning versus Spectral Binning

T0 review · 2 major / 7 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The two standard procedures for merging energy bins measure different things: one follows a spectral-index-dependent effective energy, the other a fixed log-centered energy, and they can differ by a factor of five.

desk verdict Solid methods paper: correct analytic distinction between count-space and spectral averaging, but the empirical factor-of-five is muddied by an unquantified zero-count replacement. read the letter →

arxiv 2501.14923 v1 pith:O7HJDFKP submitted 2025-01-24 astro-ph.SR astro-ph.IMphysics.space-ph

M. E. Cuesta , L. Y. Khoo , G. Livadiotis , M. M. Shen , J. R. Szalay , D. J. McComas , J. S. Rankin , R. Bandyopadhyay
show 8 more authors
H. A. Farooki J. T. Niehof C. M. S. Cohen R. A. Leske Z. Xu E. R. Christian M. I. Desai M. A. Dayeh
This is my paper · ORCID
classification astro-ph.SRastro-ph.IMphysics.space-ph
keywords solarenergeticparticlesparticleintensityre-binnedspectralbinnedeffectiveenergylog-centeredpower-lawspectraParkerProbe
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

This paper asks a deceptively simple question: when narrow detector energy bins are merged into one wider bin, what is the correct single intensity to report? The authors show that the two standard answers are not interchangeable. The re-binned intensity, a linear average of intensity in energy, is actually the intensity at an effective energy that moves with the time-varying spectral index; the spectral-binned intensity, an average of log intensity in log energy, is the intensity at the fixed log-centered energy of the merged bin. For power-law SEP spectra the two values can differ by up to a factor of five, matching what the authors find in Parker Solar Probe IS☉IS proton data from two solar energetic particle events. The practical criterion that follows is simple: use the re-binned intensity when the question is about counts in a wide energy range, and the spectral-binned intensity when the question is about the intensity at a well-defined, time-invariant energy.

What carries the argument

The machinery is the generalized averaging identity of Eq. (1), which separates the transformation of the energy axis ($\hat{X}$) from the transformation of the intensity ($\hat{Y}$) before averaging; setting both to identity gives $\overline{j}_{\rm linlin}$, and setting both to logarithms gives $\overline{j}_{\rm loglog}$. Under the two assumptions named above, the paper derives closed forms for both averages, for the effective energy $E_{\rm eff}$ (Eq. 10), for the log-centered energy $E_g$ (Eq. 14), and for the ratio $\overline{j}_{\rm loglog}/\overline{j}_{\rm linlin}$ (Eq. 15). The ratio formula is what carries the argument: it turns the difference between the two measures into a function of three controllable parameters, and it is the expression used to interpret the observed factor-of-five gap in PSP/IS☉IS data.

What would settle it

Take a high-count simulated SEP spectrum with a known power-law index $\gamma$ and known bin geometry, generate Poisson count samples, compute both intensities, and compare each to the true spectrum at the predicted $E_{\rm eff}$ and $E_g$; if the sample values do not reproduce $j(E_{\rm eff})$ and $j(E_g)$ within counting error, the point-value and single-power-law assumptions fail. On real PSP/IS☉IS data, one could check whether the observed ratio of the two intensities tracks Eq. (15) when $\gamma$ is independently fitted at each time step.

Watch

Extended reading notes

Core claim

The paper's central claim is that $\overline{j}_{\rm linlin}$ and $\overline{j}_{\rm loglog}$ are different physical measures, not two estimators of the same averaged intensity. Treating each original bin's intensity as a point value at its log-centered energy and assuming a single power law $j(E)=A E^{-\gamma}$ across the merged range, the re-binned intensity equals $j(E_{\rm eff})$ with $E_{\rm eff}$ given in Eq. (10), while the spectral-binned intensity equals $j(E_g)$ with $E_g=\sqrt{E_0E_N}$, a purely geometric quantity. Their ratio, Eq. (15), depends only on the spectral index $\gamma$, the range ratio $E_N/E_0$, and the original logarithmic bin width $\Delta\log E$; it equals one only for $\gamma=0$ and $\gamma=2$. In PSP/IS☉IS proton measurements of two August 2022 SEP events, the re-binned intensity is consistently larger than the spectral-binned intensity, up to a factor of about five, even though the two time series are strongly correlated. The paper also shows that the zero-count treatment for $\overline{j}_{\rm loglog}$ introduces a bias that grows as counting statistics drop.

Load-bearing premise

The entire analytic structure treats each original narrow bin as if its measured intensity sits exactly at the bin's central energy on a log scale, and it assumes the spectrum across the merged bin is a single power law; if real SEP spectra are strongly curved or the bins are wide, the ratio in Eq. (15) is only approximate.

Editorial extensions

If this is right

  • Any study that labels a merged-bin intensity by the bin's log-centered energy will overstate the intensity at that energy by up to a factor of several for typical SEP spectral indices, unless it uses the spectral-binned intensity.
  • Because the two time series are strongly correlated, studies of relative intensity evolution are robust to either choice, while studies comparing magnitudes across energy ranges or across times are not.
  • The spectral-binned intensity keeps a time-invariant energy label, making it the appropriate measure for spectral evolution and for comparisons of spectra at a fixed energy; the re-binned intensity's energy label shifts as the spectral index changes, shortening the time scale over which it can be compared meaningfully.
  • Equation (15) gives a ready conversion factor: with a fitted spectral index and known bin geometry, one can translate between the two measures or decide when the difference is negligible.
  • Using one measure instead of the other can change the inferred time at which a spectrum transitions from falling to rising, which matters for identifying spectral roll-ups and velocity dispersion effects in SEP events.

Reading between the lines

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

  • A natural step the paper leaves implicit is to derive the analogous ratio for differential energy flux $E\,j$, since the paper only notes that the loglin average is the count-space operation for that quantity; the same power-law machinery would give a corresponding correction factor.
  • The zero-count replacement by the Gehrels upper limit is one reasonable convention; a Bayesian estimator that treats zero counts as censored Poisson samples could reduce the low-count bias of $\overline{j}_{\rm loglog}$ and would be a testable improvement.
  • The same derivation could be repeated for non-uniform or overlapping energy bins, which the paper explicitly excludes; the factor-of-five bound may differ, and quantifying it would extend the method to instruments with irregular bin spacing.
  • The paper's energy ranges from different IS☉IS instruments (EPI-Lo, LET, HET) are separate; placing them on a common $\overline{j}_{\rm loglog}$ grid would make cross-instrument spectra directly comparable at fixed energies, an application the paper does not pursue.
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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

2 major / 7 minor

Summary. The manuscript contrasts two ways of combining a measured energy-differential intensity across several logarithmically spaced energy bins: the re-binned intensity jlinlin (Eq. 2), a linear average that returns to count space and corresponds to the value of the spectrum at an effective energy Eeff that depends on the spectral index gamma, and the spectral binned intensity jloglog (Eq. 3), a logarithmic average that corresponds to the value at the fixed log-centered energy Eg. For a single power law, the authors derive closed-form expressions for jlinlin, jloglog, Eeff, Eg, and the ratio jloglog/jlinlin (Eq. 15), which depends only on the spectral index, the merged energy range EN/E0, and the original bin width in log energy; no parameters are fitted. Modeled spectra illustrate the ratio (Fig. 3). The same definitions are then applied to PSP/ISIS proton data from the 26-30 August 2022 period (EPI-Lo, LET, HET), yielding time series in which jlinlin exceeds jloglog, in places by nearly a factor of five, with strongly correlated time evolution (Fig. 6). The paper concludes with practical guidance on when each measure is appropriate, and it explicitly acknowledges the zero-count complication in computing jloglog.

Significance. The distinction drawn here is practically important: re-binning to improve counting statistics is ubiquitous in SEP work, and plotting jlinlin at the log-centered energy silently conflates two different energies whenever gamma is not 0 or 2. The analytic development is a genuine strength: Eqs. (4)-(15) are derived in closed form with no free parameters, the ratio formula is falsifiable and could be used to correct published re-binned intensities, and the effective energy and log-centered energy are clearly distinguished. The manuscript is also candid about the zero-count issue and about the interpolation procedure for EPI-Lo thick-foil apertures. The observational section is illustrative rather than definitive: the factor-of-five comparison is computed on spectra in which zero-count bins have been replaced by upper-limit intensities, and the paper does not quantify the resulting bias (see major comments). If the empirical comparison withstands a count-space cross-check, this will be a useful methods reference for the SEP community; the parameter-free analytic ratio and the decision criteria do not depend on the contested zero-count handling.

major comments (2)
  1. [Section 2.2 (zero-count paragraph); Section 4.2, Fig. 6] The observational comparison in Fig. 6 does not implement the count-space re-binning defined in Eq. (2). Section 2.2 states that measured zeros are replaced by their Gehrels 84.13% upper-limit intensities before applying Eq. (3), and that "for now, we compute jlinlin and jloglog on the same modified spectra." A zero-count bin contributes nothing to Eq. (2) before replacement; after replacement it contributes a positive intensity, inflating jlinlin precisely in the low-count epochs where the same paragraph admits the result is "strongly dependent" on the replacement fraction. The abstract's "up to a factor of 5" therefore characterizes the modified-spectra quantities, not the pure jlinlin-versus-jloglog difference, and the magnitude of the inflation is unquantified. To make this headline empirical claim robust, please report the fraction of 1-minute samples in the 26-30 August 2022 interval that contain zero-count bins within each merged energy range, recompute jlinlin directly from summed counts with zeros retained as a cross-check, and state how much of the ratio in the right column of Fig. 6 survives that recomputation.
  2. [Section 4.2, Fig. 6 (right column)] The observed ratio is matched to the analytic prediction only qualitatively ("as expected from the dependence of the effective energy on the spectral index"). Because Eq. (15) is a parameter-free prediction once the time-varying spectral index is known, the right column of Fig. 6 can be directly overlaid with Eq. (15) evaluated at the fitted gamma per sample. Such an overlay would separate the intrinsic binning effect from the zero-count contamination identified above and would convert the factor-of-five statement from an illustration into a quantitative validation; it would also reveal whether the epochs of largest deviation from Eq. (15) coincide with the zero-count epochs, which is the decisive test of the paper's core empirical claim.
minor comments (7)
  1. [Abstract; Section 4.2] The abstract reports results "for two SEP events observed by PSP," but Section 4.2 describes "a period consisting of a series of SEP events" on 26-30 August 2022 and never isolates or names exactly two events; please reconcile the event count and the event identification between the abstract and the body.
  2. [Eq. (7)] The factor A * E_{g,i}^{-gamma} in Eq. (7) carries the summation index i outside the sum; to be consistent with Eqs. (8)-(10), it should read A * E_{g,0}^{-gamma}.
  3. [Eqs. (9)-(10) and (15); Fig. 3] Eqs. (9)-(10) and (15) have removable singularities at gamma = 1, and Eq. (10) is also singular at gamma = 0, yet the model grid in Fig. 3 includes gamma = 1; the limiting forms should be stated explicitly, since the expressions as printed evaluate to 0/0 at that spectral index.
  4. [Abstract] The sentence about "the intensity at the log-centered energy that is independent of the spectral index and remains constant over time" can be misread as claiming that the binned intensity value is time-invariant; the intended statement is that the energy Eg is independent of gamma and constant in time, and the wording should be adjusted accordingly.
  5. [Section 4.2 (Fig. 5 discussion)] The statement that jloglog represents "the intensity of a single power law fit at the log-centered energy" even "in the presence of nonlinear behavior of the spectrum" is only exactly true when the fitted line is evaluated at the arithmetic mean of log E in an unweighted fit; for a curved spectrum jloglog is simply the geometric mean of the binned intensities, and the sentence should be rephrased to avoid implying equality with the fitted value.
  6. [Section 4.2 (error propagation)] The description "Upper and lower uncertainties are propagated individually using the inverse variance method" is not sufficiently detailed to reproduce the shaded regions in Fig. 6; one sentence on how the asymmetric Gehrels limits enter the inverse-variance weighting, and how the 11-minute smoothing interacts with the propagation, should be added.
  7. [Sections 2.1, 2.2, and Appendix A] Minor language issues include "as been demonstrated" (should be "has been demonstrated"), "using jlinlin at his energy" (should be "at this energy"), and "does not need to be applied" (should agree in number with "steps"); the citation for the dust-affected aperture exclusion is given as Shen et al. 2024 "in prep." and should be updated or replaced with an in-line description.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the analytic formulas follow from the definitions by exact algebra, and the PSP observations are independent illustrations.

full rationale

The paper's central results—Eqs. (7)-(10) for jlinlin and Eeff, Eqs. (11)-(14) for jloglog and Eg, and Eq. (15) for their ratio—are obtained by direct substitution of j(E)=A E^{-gamma} into the definitions in Eqs. (2)-(3) and exact algebraic manipulation. No parameter is fitted to the data to produce these formulas, and no external result is invoked to force the conclusion; the only invoked theorem (Aczel 1948, with supplementary citations to Livadiotis 2007 and Livadiotis & McComas 2012) supports the generalized-averaging formalism and is not load-bearing for the ratio. The PSP observations in Section 4 are independent data used to illustrate the derived difference, not to tune it. The zero-count replacement and the point-value assumption are stated approximations that affect numerical magnitudes, but they are acknowledged limitations rather than circular steps. The property that jloglog equals the intensity at the log-centered energy for a power law is an algebraic consequence of the definition in Eq. (3), not a circularly assumed prediction. No step reduces a prediction to a fitted value or to a self-citation chain.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central derivation has no fitted parameters. The listed processing choices affect the observational values of jloglog and jlinlin. The axioms are standard math, reasonable domain assumptions for logarithmically spaced particle detectors, and one explicit ad hoc treatment of zero counts.

free parameters (4)
  • Zero-count replacement for jloglog = Gehrels (1986) 84.13% upper-limit uncertainty
    Applied before taking the logarithm so that zero-count bins contribute a finite value; the paper notes the low-count bias depends on this choice and calls future improvement an active area.
  • Intensity offset for EPI-Lo interpolation = +1 intensity unit (then subtracted)
    Used when interpolating thick-foil apertures onto thin-foil energy grids in log space; the choice avoids log(0) and the paper reports insignificant impact from varying it.
  • Time smoothing window = 11 minutes
    Applied to the intensity and ratio time series in Figure 6 to remove short-timescale variations; this affects displayed correlations and ratios.
  • Merged energy ranges = 100-400 and 400-800 keV (EPI-Lo), 2-10 MeV (LET), 10-40 MeV (HET)
    The chosen ranges set the energy-span factor EN/E0 in the ratio, which strongly controls the difference between jlinlin and jloglog.
assumptions (5)
  • standard math Aczel's representation of quasi-arithmetic means for continuous strictly increasing transforms
    Used in Eq. (1) to define averaging in transformed spaces.
  • domain assumption Measured intensities in original bins can be represented as point values at the log-centered energy
    Used in Eqs. (2)-(3); supported by Kronberg & Daly 2013 for narrow bins.
  • domain assumption Energy bins are equally spaced in logarithmic energy and are non-overlapping
    Used to derive Eqs. (5)-(6); approximately true for IS☉IS and typical particle instruments.
  • domain assumption The observed spectrum is a single power law over the merged bin for the analytic ratio
    Used to derive Eqs. (4)-(15); the paper notes real SEP spectra can be nonlinear and applies the formulas as approximations.
  • ad hoc to paper Zero counts are real Poisson outcomes and are replaced by upper-limit uncertainties
    Needed to avoid log(0) in jloglog; the paper states the bias increases with decreasing count statistics.

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Cite this review

Pith. "Pith review of Comparing Methods for Calculating Solar Energetic Particle Intensities: Re-binning versus Spectral Binning." pith.science (2026). https://pith.science/paper/O7HJDFKP

@misc{pith2026250114923,
  author       = {Pith},
  title        = {Pith review of: Comparing Methods for Calculating Solar Energetic Particle Intensities: Re-binning versus Spectral Binning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O7HJDFKP}},
  note         = {Machine review of arXiv:2501.14923}
}
abstract

Solar energetic particle (SEP) events have been observed for decades in the interplanetary medium by spacecraft measuring the intensity of energetic ions and electrons. These intensities provide valuable information about particle acceleration, the effects of bulk plasma dynamics on particle transport, and the anisotropy of particle distributions. Since measured intensities are typically reported in narrow energy bins, it is common to re-bin intensities over a wider energy range to improve counting statistics. We investigate two methods for calculating intensities across multiple energy bins: a) \textit{re-binned intensity} (\(\overline{j}_{\rm linlin}\)), which is calculated by integrating the intensity over energy space and corresponds to the intensity at an effective energy that depends on the time-varying spectral index, and b) \textit{spectral binned intensity} (\(\overline{j}_{\rm loglog}\)), calculated by integrating the log-intensity in log-energy space, yielding the intensity at the log-centered energy that is independent of the spectral index and remains constant over time. We compare these methods using Parker Solar Probe (PSP) IS\(\odot\)IS measurements of energetic protons, and we prescribe criteria for selecting the appropriate method for different scenarios. Our results show that the re-binned intensity is consistently larger (up to a factor of 5) than the spectral binned intensity for two SEP events observed by PSP, although the time series of the two methods are strongly correlated. Overall, both measures are important for SEP spectral analysis, and the selection of the appropriate measure depends on whether a physical (spectral binned intensity) or a statistical (re-binned intensity) representation is needed for a given analysis.

Figures

Figures reproduced from arXiv: 2501.14923 by the authors.

Figure 1
Figure 1. An illustration explaining the grouping of discrete, non-overlapping energy bins in logarithmic space for a number of N energy bins. The average intensity over a specific energy range is given by, jxy = Yˆ −1 h ⟨Yˆ (j)⟩Xˆ (E) i = Yˆ −1 R Yˆ (j)d(Xˆ (E)) R d(Xˆ (E))  , (1) where Y is the function that transforms the space for averaging ˆ j separately from the function X that describes the space of energy, ˆ Yˆ −1 i… view at source ↗
Figure 2
Figure 2. A simulated intensity-energy spectrum E −γ with spectral index γ = 4. The red-× and blue-⋆ mark the values of j linlin and j loglog, respectively, calculated over 100 – 1,000 keV. Error bars for j linlin and j loglog mark the new energy bin from the combination of the original energy bins (black circles with their energy bin widths equal in logarithmic space). The vertical red/blue dashed lines mark the effective/lo… view at source ↗
Figure 3
Figure 3. ). With ∆logE = 0.08 fixed (small original energy bins) while varying EN/E0 ∈ {2,4,6,8,10} (increasing new energy range), the value of j linlin can quickly become greater than 2 times the value of j loglog, as in the case EN/E0 = 4 and γ = 5. The right panel of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The spectrogram of particle intensity for HET-A, HET-B, LET-A, LET-B, LET-C, and EPI-Lo in descending order at a 1-minute resolution [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Proton spectra observed by LET-A from 2 – 10 MeV for three different 1-minute samples during the 28 August 2022 SEP event. The red-× and blue-⋆ mark the values of j linlin and j loglog, respectively. The dashed lines represent linear fits of the spectra in logarithmic …
Figure 6
Figure 6. Figure 6: The values of j linlin (red) and j loglog (blue) on the left column for HET-A, HET-B, LET-A, LET-B, LET-C, and EPI-Lo in descending order, smoothed to 11 minutes to remove sharp variations over shorter time scales. On the right column is the ratio j loglog/ j linlin fo…
Figure 7
Figure 7. Figure 7: The time series of proton intensities for individual energy bins measured by EPI-Lo, LET-A, and HET-A (top panel), in addition to their corresponding spectral binned intensities j loglog (middle panel) and re-binned intensities j linlin (bottom panel). Although this pr…
Figure 8
Figure 8. Figure 8: A flowchart on which average measure to use depending on the physical or statistical description desired. In this paper, we demonstrated the importance of using j loglog for comparing intensities at the same log-centered energy in favor of j linlin. However, j linlin i…

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Works this paper leans on

41 extracted references · 25 canonical work pages

  1. [1]

    1948, Bulletin of the American Mathematical Society, 54, 392, doi: 10.1090/S0002-9904-1948-09016-4

    Acz´el, J. 1948, Bulletin of the American Mathematical Society, 54, 392, doi: 10.1090/S0002-9904-1948-09016-4

    work page doi:10.1090/s0002-9904-1948-09016-4 1948

  2. [2]

    I., Leer, E., & Skadron, G

    Axford, W. I., Leer, E., & Skadron, G. 1977, in International Cosmic Ray Conference, V ol. 11, International Cosmic Ray Conference, 132

    work page 1977

  3. [3]

    Bell, A. R. 1978, MNRAS, 182, 147, doi: 10.1093/mnras/182.2.147

    doi:10.1093/mnras/182.2.147 1978

  4. [4]

    D., & Ostriker, J

    Blandford, R. D., & Ostriker, J. P. 1978, ApJL, 221, L29, doi: 10.1086/182658 Buˇc´ık, R., Mason, G. M., G´omez-Herrero, R., et al. 2023, A&A, 669, A13, doi: 10.1051/0004-6361/202245037

    doi:10.1086/182658 1978

  5. [5]

    2024, ApJL, 967, L33, doi: 10.3847/2041-8213/ad4a79

    Chen, X., & Li, C. 2024, ApJL, 967, L33, doi: 10.3847/2041-8213/ad4a79

    work page doi:10.3847/2041-8213/ad4a79 2024

  6. [6]

    G., Blake, J

    Claudepierre, S. G., Blake, J. B., Boyd, A. J., et al. 2021, SSRv, 217, 80, doi: 10.1007/s11214-021-00855-2

    work page doi:10.1007/s11214-021-00855-2 2021

  7. [7]

    Cohen, C. M. S., Christian, E. R., Cummings, A. C., et al. 2021, A&A, 656, A29, doi: 10.1051/0004-6361/202140967

    doi:10.1051/0004-6361/202140967 2021

  8. [8]

    E., McComas, D

    Cuesta, M. E., McComas, D. J., Khoo, L. Y ., et al. 2024, ApJ, 964, 114, doi: 10.3847/1538-4357/ad245d

    work page doi:10.3847/1538-4357/ad245d 2024

Show all 41 references
  1. [9]

    E., Cummings, A

    Cuesta, M. E., Cummings, A. T., Livadiotis, G., et al. 2024, The Astrophysical Journal, 973, 76, doi: 10.3847/1538-4357/ad68fd

    2024 doi

  2. [10]

    A., Desai, M

    Dayeh, M. A., Desai, M. I., Dwyer, J. R., et al. 2009, ApJ, 693, 1588, doi: 10.1088/0004-637X/693/2/1588

    2009 doi

  3. [11]

    C., et al

    Dresing, N., Rodr´ıguez-Garc´ıa, L., Jebaraj, I. C., et al. 2023, A&A, 674, A105, doi: 10.1051/0004-6361/202345938

    2023 doi

  4. [12]

    Fisk, L. A. 1971, J. Geophys. Res., 76, 1662, doi: 10.1029/JA076i007p01662

    1971 doi

  5. [13]

    A., & Gloeckler, G

    Fisk, L. A., & Gloeckler, G. 2006, ApJL, 640, L79, doi: 10.1086/503293

    2006 doi

  6. [14]

    J., Velli, M

    Fox, N. J., Velli, M. C., Bale, S. D., et al. 2016, SSRv, 204, 7, doi: 10.1007/s11214-015-0211-6

    2016 doi

  7. [15]

    1986, ApJ, 303, 336, doi: 10.1086/164079

    Gehrels, N. 1986, ApJ, 303, 336, doi: 10.1086/164079

    1986 doi

  8. [16]

    2022, SSRv, 218, 22, doi: 10.1007/s11214-022-00890-7

    Giacalone, J., Fahr, H., Fichtner, H., et al. 2022, SSRv, 218, 22, doi: 10.1007/s11214-022-00890-7

    2022 doi

  9. [17]

    Giacalone, J., Cohen, C. M. S., McComas, D. J., et al. 2023, ApJ, 958, 144, doi: 10.3847/1538-4357/acfb86

    2023 doi

  10. [18]

    2023, Frontiers in Astronomy and Space Sciences, 9, 384, doi: 10.3389/fspas.2022.1058810

    Gieseler, J., Dresing, N., Palmroos, C., et al. 2023, Frontiers in Astronomy and Space Sciences, 9, 384, doi: 10.3389/fspas.2022.1058810

    2023

  11. [19]

    T., Asbridge, J

    Gosling, J. T., Asbridge, J. R., Bame, S. J., & Feldman, W. C. 1979, in American Institute of Physics Conference Series, V ol. 56, Particle Acceleration Mechanisms in Astrophysics, ed. J. Arons, C. McKee, & C. Max, 81–99, doi: 10.1063/1.32069

    1979 doi

  12. [20]

    E., Mitchell, D

    Hill, M. E., Mitchell, D. G., Andrews, G. B., et al. 2017, Journal of Geophysical Research (Space Physics), 122, 1513, doi: 10.1002/2016JA022614

    2017 doi

  13. [21]

    M., Ho, G

    Kouloumvakos, A., Mason, G. M., Ho, G. C., et al. 2023, ApJ, 956, 123, doi: 10.3847/1538-4357/acf44e

    2023 doi

  14. [22]

    Kouloumvakos, A., Papaioannou, A., Waterfall, C. O. G., et al. 2024, A&A, 682, A106, doi: 10.1051/0004-6361/202346045

    2024 doi

  15. [23]

    A., & Daly, P

    Kronberg, E. A., & Daly, P. W. 2013, Geoscientific

    2013

  16. [24]

    Instrumentation, Methods and Data Systems, 2, 257, doi: 10.5194/gi-2-257-201310.5194/gid-3-533-2013

    2013 arXiv

  17. [25]

    Lee, M. A. 1983, J. Geophys. Res., 88, 6109, doi: 10.1029/JA088iA08p06109 —. 1997, Geophysical Monograph Series, 99, 227, doi: 10.1029/GM099p0227

    1983 doi

  18. [26]

    A., Christian, E

    Leske, R. A., Christian, E. R., Cohen, C. M. S., et al. 2020, ApJS, 246, 35, doi: 10.3847/1538-4365/ab5712

    2020 doi

  19. [27]

    2007, Physica A Statistical Mechanics and its Applications, 375, 518, doi: 10.1016/j.physa.2006.09.027

    Livadiotis, G. 2007, Physica A Statistical Mechanics and its Applications, 375, 518, doi: 10.1016/j.physa.2006.09.027

    2007 doi

  20. [28]

    Livadiotis, G., & McComas, D. J. 2012, ApJ, 749, 11, doi: 10.1088/0004-637X/749/1/11

    2012 doi

  21. [29]

    T., Cuesta, M

    Livadiotis, G., Cummings, A. T., Cuesta, M. E., et al. 2024, ApJ, 973, 6, doi: 10.3847/1538-4357/ad5e72

    2024 doi

  22. [30]

    M., & Gloeckler, G

    Mason, G. M., & Gloeckler, G. 2012, SSRv, 172, 241, doi: 10.1007/s11214-010-9741-0

    2012 doi

  23. [31]

    J., Alexander, N., Angold, N., et al

    McComas, D. J., Alexander, N., Angold, N., et al. 2016, SSRv, 204, 187, doi: 10.1007/s11214-014-0059-1

    2016 doi

  24. [32]

    G., Cohen, C

    Mitchell, J. G., Cohen, C. M. S., Eddy, T. J., et al. 2023, ApJS, 264, 31, doi: 10.3847/1538-4365/aca4c8

    2023 doi

  25. [33]

    1974, Journal of the Royal Statistical Society: Series C (Applied Statistics), 23, 323

    Nelder, J. 1974, Journal of the Royal Statistical Society: Series C (Applied Statistics), 23, 323

    1974

  26. [34]

    S., McComas, D

    Rankin, J. S., McComas, D. J., Leske, R. A., et al. 2021, ApJ, 912, 139, doi: 10.3847/1538-4357/abec7e

    2021 doi

  27. [35]

    A., Bale, S., Bonnell, J., et al

    Schwadron, N. A., Bale, S., Bonnell, J., et al. 2020, ApJS, 246, 33, doi: 10.3847/1538-4365/ab5527

    2020 doi

  28. [36]

    A., Bale, S

    Schwadron, N. A., Bale, S. D., Bonnell, J., et al. 2024, ApJ, 970, 98, doi: 10.3847/1538-4357/ad527f

    2024 doi

  29. [37]

    S., & Blake, J

    Selesnick, R. S., & Blake, J. B. 2000, J. Geophys. Res., 105, 2607, doi: 10.1029/1999JA900445

    2000 doi

  30. [38]

    M., Szalay, J

    Shen, M. M., Szalay, J. R., Pokorny, P., et al. 2024, in prep

    2024

  31. [39]

    R., Pokorn´y, P., Bale, S

    Szalay, J. R., Pokorn´y, P., Bale, S. D., et al. 2020, ApJS, 246, 27, doi: 10.3847/1538-4365/ab50c1

    2020 doi

  32. [40]

    E., Burnham, J

    Wiedenbeck, M. E., Burnham, J. A., Cohen, C. M. S., et al. 2021, A&A, 650, A27, doi: 10.1051/0004-6361/202039754

    2021 doi

  33. [41]

    2024, ApJ, 963, 119, doi: 10.3847/1538-4357/ad1e57

    Zhuang, B., Lugaz, N., Lario, D., et al. 2024, ApJ, 963, 119, doi: 10.3847/1538-4357/ad1e57

    2024 doi

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Reviewed August 10, 2026 · model on record in the stance chip above.