Pith. sign in

REVIEW 4 major objections 6 minor 65 references

Ion Charge States from a Global Time-Dependent Wave-Turbulence-Driven Model of the Solar Wind: Comparison with in-situ Measurements

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A global 3D model of the corona, coupled to a non-equilibrium ionization code, reproduces the ion charge states measured in the solar wind at Earth and removes a discrepancy seen in one-dimensional calculations.

desk verdict Solid, honest 3D charge-state modeling with a useful two-rotation ACE comparison, but the abstract's claim that it 'rectifies' the 1D under-ionization problem is not demonstrated by the evidence shown. read the letter →

arxiv 2501.04868 v1 pith:RZ7MC4E2 submitted 2025-01-08 physics.space-ph

Pete Riley , Roberto Lionello , Yeimy J. Rivera This is my paper · ORCID
classification physics.space-ph
keywords solarwindMHDsimulationsionchargestatesinsitumeasurementswave-turbulence-drivenheatingnon-equilibriumionizationfreeze-in
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 claims that a global three-dimensional magnetohydrodynamic (MHD) model of the solar corona and inner heliosphere, driven by wave-turbulence heating and coupled to a non-equilibrium ionization code, reproduces the essential features of the solar wind's ion charge states measured at 1 AU, for two Carrington rotations at different phases of the solar cycle. The match matters because charge-state ratios such as $\mathrm{O}^{7+}/\mathrm{O}^{6+}$ are the best available remote probe of the temperatures and densities in coronal source regions, and the model was not fitted to charge-state data. In earlier one-dimensional versions, the computed charge-state ratios came out systematically too low and had to be repaired by artificially slowing the low-coronal flow; the three-dimensional solutions remove that deficit. If the claim holds, in-situ composition measurements can be traced unambiguously back along the model's field lines to their freeze-in location in the low corona, turning charge-state maps into a probe of coronal heating and magnetic topology.

What carries the argument

The load-bearing mechanism is freeze-in. As the plasma expands, the electron density falls until, below roughly $n \approx 600\ \mathrm{cm}^{-3}$, the ionization and recombination timescales exceed the wind's expansion timescale; each charge-state ratio is then locked at the value set by the local temperature and density and is simply advected outward to 1 AU. The evolution is computed with the rate equations of Shen et al. (2015) and CHIANTI v10 atomic data, run through the steady-state velocity, density, and temperature fields of the 3D thermodynamic MHD model, whose wave-turbulence-driven heating is prescribed by an Elsässer amplitude $z_0 = 9.63\ \mathrm{km/s}$, a correlation scale $\lambda_0 = 0.02\,R_\odot$, a field scaling $B_0 = 8.53\ \mathrm{G}$, and two exponential heating terms. The squashing factor $Q$ of the modeled magnetic field provides the topological map: the charge-state beams trace the streamer cusps, pseudo-streamers, and current-sheet crossings rather than the plasma density or speed profiles.

What would settle it

Run the same coupled model for a dozen Carrington rotations spanning cycles 23 and 24, bin the modeled $\mathrm{O}^{7+}/\mathrm{O}^{6+}$ and $\langle Q_{\mathrm{Fe}}\rangle$ by solar wind speed, and compare with ACE/SWICS: a systematic deficit in the fast-wind bins, the signature of the old 1-D failure, or an equally systematic surplus at solar maximum, would show that the 3D geometry redistributes but does not remove the charge-state bias.

Watch

Extended reading notes

Core claim

The central claim is that a time-dependent non-equilibrium ionization module, run on the steady-state fields of a global wave-turbulence-driven MHD solution, produces ion charge states that match the essential features of the ACE/SWICS observations for both a late-declining-phase rotation (CR2063, November 2007) and a post-maximum rotation (CR2002, mid-2003). The dominant charge states of carbon, oxygen, and iron, the ratios $\mathrm{O}^{7+}/\mathrm{O}^{6+}$ and $\mathrm{C}^{6+}/\mathrm{C}^{5+}$, and the mean iron charge state $\langle Q_{\mathrm{Fe}}\rangle$ agree with the measurements in absolute value and, at least for CR2063, in temporal structure; at CR2002 the model over-varies the composition while the plasma parameters vary too little in the simulation. The authors argue that the earlier 1-D deficit — charge-state ratios that were too low unless the low-coronal flow speed was heuristically reduced — is essentially gone in the 3D calculation, because the three-dimensional magnetic field sets a more realistic heating, density, and flow geometry. They further show that charge-state enhancements align with crossings of the heliospheric current sheet identified by the squashing factor, and the model predicts that the enhancement of freeze-in ratios around the plasma sheet is substantially larger near solar maximum than near minimum.

Load-bearing premise

The comparison stands on a premise the authors themselves flag: the heating parameters of the wave-turbulence-driven model, tuned long ago on data from the end of solar cycle 22 and the start of cycle 23, still describe the corona during 2003 and 2007, and a single time-averaged magnetic map per rotation — with no transient events included — captures the steady conditions that fix the measured charge states.

Editorial extensions

If this is right

  • Charge-state ratios measured at 1 AU can be traced backward along the model's field lines to a well-defined freeze-in surface in the low corona, giving a direct linkage between in-situ composition and coronal source structure.
  • The systematic low bias of the 1-D wave-turbulence-driven model is resolved in three dimensions without any heuristic slowing of the low-coronal flow, indicating that the 3D heating and flow geometry, not an extra parameter, supplies the missing ionization.
  • The model predicts that $\mathrm{O}^{7+}/\mathrm{O}^{6+}$ and $\mathrm{C}^{6+}/\mathrm{C}^{5+}$ peak where the modeled squashing factor changes sign, i.e., at heliospheric current-sheet crossings, with a markedly larger contrast between plasma sheet and surrounding wind near solar maximum than near minimum.
  • Because the mean iron charge state freezes in higher in the corona than the oxygen and carbon ratios, $\langle Q_{\mathrm{Fe}}\rangle$ tracks plasma speed and density more closely while the O and C ratios trace low-coronal topology; the two kinds of composition data carry complementary information about heating at different heights.

Reading between the lines

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

  • The tight correspondence the paper finds between charge-state peaks and squashing-factor boundaries could be turned into a synoptic diagnostic: global freeze-in ratio maps might locate the heliospheric current sheet and the S-web of open-field corridors even where direct magnetic field measurements are sparse.
  • Since the paper attributes part of the residual mismatch to the Sun's secular decline in activity since the heating parameters were tuned, a decisive follow-up is to re-derive the wave-turbulence parameters from modern observations and re-run CR2002 and CR2063; this would separate genuine parameter drift from model physics.
  • Because oxygen and carbon ratios freeze in lower than iron, jointly inverting all three species against the modeled freeze-in altitudes could constrain the radial profile of the coronal heating rate, which the wave-turbulence model currently prescribes rather than derives.
  • The 'beam' of elevated $\mathrm{O}^{7+}/\mathrm{O}^{6+}$ that keeps a roughly constant width while density and speed pinch down means composition can identify plasma parcel trajectories that skirt the streamer cusp even when speed and density alone would misclassify them — a use of freeze-in maps the paper illustrates but does not exploit.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. Riley, Lionello, and Rivera couple a non-equilibrium ionization module (Shen et al., 2015; CHIANTI v10 rates) to the MAS global MHD model with wave-turbulence-driven heating. They present steady-state coronal and heliospheric solutions for two Carrington rotations (CR2002, near solar maximum, and CR2063, late declining phase), drive them with synoptic magnetograms, and compare modeled O7+/O6+, C6+/C5+, and mean Fe charge states, as well as plasma and magnetic-field parameters, with ACE/SWICS, SWEPAM, and MAG measurements at 1 AU. They also analyze meridional slices, squashing factors, and scatterplot distributions. The paper's principal claim is that the model reproduces the essential observed features and resolves an earlier inconsistency found in 1-D calculations (Lionello et al., 2019), allowing unambiguous tracing of charge-state evolution from the base of the corona to 1 AU.

Significance. If the claims are substantiated, the paper demonstrates a valuable capability: a global 3-D MHD model that, without tuning to charge-state data, produces realistic O, C, and Fe freeze-in states, with the potential to connect remote-sensing and in-situ diagnostics. Strengths of the work include the use of standard, publicly available rate coefficients and data, the presentation of EUV validation, and the explicit comparison of charge-state maps with magnetic topology (squashing factor). The main weaknesses are that the validation is purely qualitative and that the headline 'rectifying 1-D inconsistency' is not tested against the same observational target, which limits the current significance.

major comments (4)
  1. [Section 4, 'Our work can be compared...' paragraph] The claim that 'That disagreement has largely disappeared in the current 3-D results' is not established because the 1-D discrepancy (Lionello et al. 2019) was diagnosed against Ulysses high-latitude fast wind, while the present 3-D comparison uses ACE in the ecliptic. No 1-D baseline for CR2002/CR2063 with the same WTD parameters is presented, and no Ulysses fast-wind comparison is made. If the improvement arises simply because ecliptic wind is slower and denser, the rectification is a selection effect rather than a resolution of the original physics problem. The authors should either run the 1-D counterpart for these rotations, compare the same model's output to Ulysses fast-wind intervals, or restrict the claim to 'the deficit is not seen in the ecliptic samples considered here.'
  2. [Section 4, same paragraph] The paper lists three mechanisms (stronger photospheric magnetic field, higher density, and lower flow speed) that could raise frozen-in charge states, but it does not diagnose which of these is active in the 3-D solutions. Without such a diagnostic (e.g., comparing freeze-in heights, electron density/temperature profiles along open field lines, or flow speed between 1-D and 3-D solutions), the causal claim that global 3-D structure resolves the 1-D deficit is unsupported.
  3. [Section 3.3 and Figures 9-16] All comparisons are qualitative; no quantitative metrics (e.g., correlation coefficients, root-mean-square differences, Kolmogorov-Smirnov statistics) are provided, and no observational uncertainties are shown. Because the abstract's central claim is that the model 'reproduces the essential features,' the absence of any quantitative assessment makes the claim difficult to evaluate and does not permit a distinction between the model and a null hypothesis.
  4. [Sections 2.2.1 and 4] The WTD heating parameters were tuned on cycle 22/23 data and adopted unchanged for CR2002 and CR2063. The paper acknowledges this in Section 4 as a possible source of mismatch, but the assumption is load-bearing for the claim of agreement: if those parameters are not transferable across the secular activity change, the modeled densities, temperatures, and hence charge states may be biased in ways a qualitative comparison cannot expose. A sensitivity analysis (even for one of the main parameters, such as z0 or lambda0) or validation against a third interval would materially strengthen the central claim.
minor comments (6)
  1. [Section 4] The phrase 'solar minimum (CR6063)' is a typo for CR2063.
  2. [Section 3.3] The sentence 'there is are weaker negative correlations' contains a grammatical error; it should read 'there are weaker negative correlations.'
  3. [Figures 13 and 14] The x-axis ranges are adjusted separately for observed and model panels, which can mislead the distribution comparison; the same axes should be used or the ranges listed in the caption.
  4. [Sections 2.2.2 and Figure 2] The text cites the CHIANTI atomic database via Dere et al. (1997) and Landi et al. (2013), while the figure caption and Section 2.2.2 state CHIANTI v10 (Del Zanna et al., 2021); the CITATION should be consistent.
  5. [References] The reference list contains several duplicated entries (e.g., Linker et al. (2011), Szente et al. (2022), and Oran et al. (2015) appear twice); these should be merged.
  6. [Title] The title calls the model 'Time-Dependent,' but the MHD solution presented is a steady-state equilibrium; the charge-state module is time-dependent in the advective sense, but the title may mislead readers. Consider clarifying the title or the text.

Circularity Check

0 steps flagged · score 1.0 of 10

No material circularity: the charge-state results are genuine forward-model outputs, with only self-citation and parameter-transferability caveats.

full rationale

The paper's derivation chain is not circular. The target quantities—O7+/O6+, C6+/C5+, and mean Fe charge states at 1 AU—are produced by integrating a non-equilibrium ionization equation (Eq. 2, with CHIANTI rate coefficients) over the steady-state MHD plasma fields from the MAS/WTD model; none of the ACE/SWICS charge-state data for CR2002 or CR2063 are used to set the model parameters. The WTD parameters (z0=9.63 km/s, lambda0=0.02 R_sun, B0=8.53 G, and the two exponential heating terms) are taken from Lionello et al. (2023) and Mikić et al. (2018), where they were tuned on plasma data from earlier solar cycles; the paper explicitly concedes this in Section 4, and the transferability caveat is a correctness/robustness concern, not a circular reduction. The comparison against STEREO/EIT EUV emission and ACE in-situ plasma/magnetic-field data provides independent, external checks, even though these checks are qualitative. The abstract's claim that the 3-D model 'rectifies' the earlier 1-D low charge-state bias is under-supported—no 1-D baseline is recomputed for these CRs and ACE samples mostly ecliptic wind (the authors themselves note the test 'may not be as sensitive to this')—but an unsupported or weakly supported claim is not a circular one. No fitted parameter is renamed as a prediction, and no load-bearing result is imported solely from the authors' own prior work.

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

The central simulation rests on MHD parameters inherited from prior tuning, standard atomic rate data, and a set of modeling assumptions that the authors themselves flag. The charge-state data are not used to fit any parameter, so the comparison is a genuine prediction, but the prediction inherits all biases of the WTD model and the steady-state approximation.

free parameters (6)
  • z0 (Elsässer variable amplitude) = 9.63 km/s
    Prescribes Poynting flux of Alfvén waves at the coronal base; affects heating and solar wind speed, hence freeze-in charge states. Taken from Lionello et al. (2023).
  • λ0 (transverse correlation scale) = 0.02 R⊙
    Determines perpendicular correlation length for wave turbulence; set with B0 = 8.53 G.
  • B0 (magnetic scaling factor) = 8.53 G
    Used in λ⊥ = λ0 sqrt(B/B0); from prior WTD model tuning.
  • H0, λ0 exponential heating terms = 2.7e-5 erg/cm3/s with λ0=0.03 R⊙; 1.6e-8 erg/cm3/s with λ0=R⊙
    Extra heating terms to match observed low-corona temperatures; parameters from prior work.
  • chromospheric base density and temperature = n0=4e12 cm^-3, T0=17,500 K
    Fixed boundary values at r=R⊙ to form a chromospheric temperature plateau; affect the low corona solution.
  • Numerical resistivity and viscosity ratios = τR/τA = 1e5 (corona), 1e6 (heliosphere); τA/τν = 0.015, 0.001
    Chosen to dissipate unresolved scales; standard numerical parameters, but they can influence the solution.
assumptions (5)
  • domain assumption CHIANTI v10 rate coefficients accurately represent ionization and recombination for C, O, and Fe.
    Used to compute C_i and α_i in Eq. (2); inaccuracies propagate directly to freeze-in charge states.
  • standard math The non-equilibrium ionization equation (Eq. 2) from Shen et al. (2015) is the correct evolution law for fractional charge states.
    Assumes the transport equation with ionization and recombination source terms; standard in the field.
  • domain assumption Electrons are Maxwellian at the same temperature as the MHD plasma, with no suprathermal tails or ion differential flow.
    The model uses CHIANTI rate coefficients computed for Maxwellian distributions; the discussion notes that suprathermal tails were proposed to explain similar discrepancies in other models.
  • domain assumption A steady-state MHD solution driven by a single CR-averaged magnetogram is representative of the corona for CR2002 and CR2063.
    Excludes transient phenomena such as interchange reconnection; discussed as a limitation in Section 4.
  • ad hoc to paper The WTD heating parameters tuned on earlier solar cycle data are transferable to CR2002 and CR2063.
    The paper states the heliospheric model relies on parameters 'tuned' on data from end of cycle 22 and start of cycle 23, and that the Sun has undergone secular changes.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Ion Charge States from a Global Time-Dependent Wave-Turbulence-Driven Model of the Solar Wind: Comparison with in-situ Measurements." pith.science (2026). https://pith.science/paper/RZ7MC4E2

@misc{pith2026250104868,
  author       = {Pith},
  title        = {Pith review of: Ion Charge States from a Global Time-Dependent Wave-Turbulence-Driven Model of the Solar Wind: Comparison with in-situ Measurements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RZ7MC4E2}},
  note         = {Machine review of arXiv:2501.04868}
}
read the original abstract

Solar wind charge-state measurements contain a wealth of knowledge related to the properties of the solar corona from where they originated. However, their interpretation has remained challenging because it convolves coronal temperature, density, and velocity along the particles' trajectory through the corona before they ``freeze in'' and are convected outward through the solar wind. In this study, we calculate ion charge states by coupling a non-equilibrium ionization model with a global magnetohydrodynamic model of the corona and inner heliosphere. We present results for two periods characteristic of solar minimum and maximum and compare them with observations from the ACE spacecraft. We find that the model reproduces the essential features of the observations, rectifying an earlier inconsistency that was apparent in 1-D calculations, and allows us to unambiguously trace the evolution of charge states from the base of the corona into the solar wind.

Figures

Figures reproduced from arXiv: 2501.04868 by the authors.

Figure 1
Figure 1. Timeline showing the availability of heavy ion in-situ measurements. The transition from ACE/SWICS v1.1 to V2.0 is indicated by the transition from purple to pink. The monthly averaged, smoothed sunspot number is overlaid with the solid black line. Carrington rotations 2002 and 2063 are marked by the vertical blue and red lines, respectively. heating the corona and accelerating the solar wind. The model has been des… view at source ↗
Figure 2
Figure 2. Ionization and recombination rates for (a) carbon, (b) oxygen, and (c) Iron where the dotted lines represent the ionization and solid lines represent the recombination rate coefficients for the individual ions. where Ni is the number density of ions in charge state i, Ni+1 is the number density of ions in charge state i + 1, ne is the electron density, Ci(T) is the ionization rate coefficient for ions in charge stat… view at source ↗
Figure 3
Figure 3. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Comparison between observed (a, c, and e) and modeled (b, d, and f) logarithmic emission for SOHO’s (a) EIT 171 ˚A, (b) EIT 195 ˚A, and (c) EIT 284 ˚A for CR2002. The Carrington longitude of the observer was set to 180◦ , corresponding to 08:36 UT on 2003/04/29. observ…
Figure 5
Figure 5. Figure 5: Meridional slices of (a) radial velocity, (b) plasma density, (c) temperature, (d) O 7+/O6+, (e) C 6+/C5+, and (f) the average charge state of Fe, at Carrington longitude 180◦ , for CR 2063. A selection of magnetic field lines have been traced both from the inner and o…
Figure 6
Figure 6. Figure 6: As [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Comparison of slogQ with (a) O 7+/O6+ and (b) < QF e > for CR2063. slogQ is shown in red, and the charge information is shown in black. In (c), the full map of slogQ is shown, together with the trajectory of the ACE spacecraft (purple). Note that the trajectory starts …
Figure 8
Figure 8. Figure 8: As [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: Comparison between observed (a) and modeled (b) in-situ measurements at ACE for CR2063, corresponding to November 04 to December 01, 2007 (doy: 308 to 335). The top three panels show heat maps of the charge state distributions of C, O, and Fe, respectively, with the av…
Figure 10
Figure 10. Figure 10: As [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: Direct comparison between modeled (black) and observed (blue) in-situ measurements at ACE for CR 2063, corresponding to November 04 to December 02, 2007 (doy: 308 to 336). We now consider the same comparison for CR2002. Here we note several differences, both between t…
Figure 12
Figure 12. Figure 12: As [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]
Figure 13
Figure 13. Figure 13: Scatterplot matrices for two-hour averaged (a) observations and (b) model results of density, speed, the average charge state of iron, O 7+/O6+, C 6+/C5+, and the magnitude of the magnetic field for CR2063. The diagonal panel summarises the distribution of that variab…
Figure 14
Figure 14. Figure 14: As [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]
Figure 15
Figure 15. Figure 15: Average charge state of iron (< QF e >) versus the ion ratios for O 7+/O6+ (blue), C 6+/C5+ (red), and C 6+/C4+ (yellow) from the observations (a) and simulation (b) for CR2063. In [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]
Figure 16
Figure 16. Figure 16: As [PITH_FULL_IMAGE:figures/full_fig_p018_16.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

65 extracted references · 28 canonical work pages

  1. [1]

    2024, ACE SWICS Level 2 Version 2 Release Notes

    ACE Science Center. 2024, ACE SWICS Level 2 Version 2 Release Notes. https://izw1.caltech.edu/ACE/ASC/ DATA/level2/ss2/swics lv2 V2 release notes.txt

    work page 2024

  2. [2]

    Linker, J. A. 2011, Astrophys. J., 731, 112, doi: 10.1088/0004-637X/731/2/112

    doi:10.1088/0004-637x/731/2/112 2011

  3. [3]

    D., Badman, S

    Bale, S. D., Badman, S. T., Bonnell, J. W., et al. 2019, Nature, 576, 237, doi: 10.1038/s41586-019-1818-7

    doi:10.1038/s41586-019-1818-7 2019

  4. [4]

    H., Ugarte-Urra, I., & Warren, H

    Brooks, D. H., Ugarte-Urra, I., & Warren, H. P. 2015, Nature Communications, 6, 5947, doi: 10.1038/ncomms6947

    doi:10.1038/ncomms6947 2015

  5. [5]

    R., Gibson, S

    Cranmer, S. R., Gibson, S. E., & Riley, P. 2017, Space Science Reviews, 212, 1345, doi: 10.1007/s11214-017-0416-y Del Zanna, G., Dere, K. P., Young, P. R., & Landi, E. 2021, ApJ, 909, 38, doi: 10.3847/1538-4357/abd8ce

    doi:10.1007/s11214-017-0416-y 2017

  6. [6]

    P., Landi, E., Mason, H

    Dere, K. P., Landi, E., Mason, H. E., Monsignori Fossi, B. C., & Young, P. R. 1997, A&AS, 125, 149, doi: 10.1051/aas:1997368

    doi:10.1051/aas:1997368 1997

  7. [7]

    A., Miki´ c, Z., et al

    Downs, C., Linker, J. A., Miki´ c, Z., et al. 2013, Science, 340, 1196, doi: 10.1126/science.1236550

    doi:10.1126/science.1236550 2013

  8. [8]

    A., & Velli, M

    Downs, C., Lionello, R., Miki´ c, Z., Linker, J. A., & Velli, M. 2016, ApJ, 832, 180, doi: 10.3847/0004-637X/832/2/180

    doi:10.3847/0004-637x/832/2/180 2016

Show all 65 references
  1. [9]

    A., Caplan, R

    Downs, C., Linker, J. A., Caplan, R. M., et al. 2024, Science

    2024

  2. [10]

    D., Badman, S

    Ervin, T., Bale, S. D., Badman, S. T., et al. 2024, ApJ, 969, 83, doi: 10.3847/1538-4357/ad4604

    2024 doi

  3. [11]

    2002, Advances in Space Research, 30, 481

    Esser, R., & Edgar, R. 2002, Advances in Space Research, 30, 481

    2002

  4. [12]

    Esser, R., & Edgar, R. J. 2000, The Astrophysical Journal, 532, L71 —. 2001, The Astrophysical Journal, 563, 1055

    2000

  5. [13]

    R., & Cranmer, S

    Gilly, C. R., & Cranmer, S. R. 2020, ApJ, 901, 150, doi: 10.3847/1538-4357/abb1ad

    2020 doi

  6. [14]

    1992, A&AS, 92, 267

    Gloeckler, G., Geiss, J., Balsiger, H., et al. 1992, A&AS, 92, 267

    1992

  7. [15]

    Gosling, J. T. 1995, Rev. Geophys., 33, 597, doi: 10.1029/95RG00125

    1995 doi

  8. [16]

    R., Lepri, S

    Gruesbeck, J. R., Lepri, S. T., & Zurbuchen, T. H. 2012, The Astrophysical Journal, 760, 141

    2012

  9. [17]

    S., Bale, S

    Halekas, J. S., Bale, S. D., Berthomier, M., et al. 2023, ApJ, 952, 26, doi: 10.3847/1538-4357/acd769

    2023 doi

  10. [18]

    J., & Gentry, R

    Hundhausen, A. J., & Gentry, R. A. 1968, Astron. J., 73, 63 Ionizationcalc. 2024, Time Dependent Fortran, https: //github.com/ionizationcalc/time dependent fortran

    1968

  11. [19]

    M., Provornikova, E., & Ko, Y.-K

    Laming, J. M., Provornikova, E., & Ko, Y.-K. 2023, The Astrophysical Journal, 954, 145

    2023

  12. [20]

    2012, The Astrophysical Journal, 761, 48

    Fisk, L. 2012, The Astrophysical Journal, 761, 48

    2012

  13. [21]

    2014, The Astrophysical Journal, 790, 111

    Landi, E., Oran, R., Lepri, S., et al. 2014, The Astrophysical Journal, 790, 111

    2014

  14. [22]

    2014, ApJ, 787, 33, doi: 10.1088/0004-637X/787/1/33

    Landi, E., & Testa, P. 2014, ApJ, 787, 33, doi: 10.1088/0004-637X/787/1/33

    2014 doi

  15. [23]

    Mason, H. E. 2013, ApJ, 763, 86, doi: 10.1088/0004-637X/763/2/86

    2013 doi

  16. [24]

    A., Belic, D

    Lecointre, J., Kouzakov, K. A., Belic, D. S., et al. 2013, Journal of Physics B Atomic Molecular Physics, 46, 205201, doi: 10.1088/0953-4075/46/20/205201

    2013 doi

  17. [25]

    2017, The Astrophysical Journal, 848, 70

    Linker, J., Caplan, R., Downs, C., et al. 2017, The Astrophysical Journal, 848, 70

    2017

  18. [26]

    Antiochos, S. K. 2011, ApJ, 731, 110, doi: 10.1088/0004-637X/731/2/110

    2011 doi

  19. [27]

    Antiochos, S. K. 2011, The Astrophysical Journal, 731, 110

    2011

  20. [28]

    A., Miki´ c, Z., Lionello, R., et al

    Linker, J. A., Miki´ c, Z., Lionello, R., et al. 2003, Physics of Plasmas, 10, 1971, doi: 10.1063/1.1563668

    2003 doi

  21. [29]

    A., Miki´ c, Z., Biesecker, D

    Linker, J. A., Miki´ c, Z., Biesecker, D. A., et al. 1999, J. Geophys. Res., 104, 9809, doi: 10.1029/1998JA900159

    1999 doi

  22. [30]

    A., et al

    Lionello, R., Downs, C., Linker, J. A., et al. 2019, SoPh, 294, 13, doi: 10.1007/s11207-019-1401-2

    2019 doi

  23. [31]

    A., et al

    Lionello, R., Downs, C., Linker, J. A., et al. 2019, Solar Physics, 294, 1

    2019

  24. [32]

    A., et al

    Lionello, R., Downs, C., Linker, J. A., et al. 2013, ApJ, 777, 76, doi: 10.1088/0004-637X/777/1/76

    2013 doi

  25. [33]

    I., et al

    Lionello, R., Downs, C., Mason, E. I., et al. 2023, ApJ, 959, 77, doi: 10.3847/1538-4357/ad00be 21

    2023 doi

  26. [34]

    A., & Miki´ c, Z

    Lionello, R., Linker, J. A., & Miki´ c, Z. 2009, ApJ, 690, 902, doi: 10.1088/0004-637X/690/1/902

    2009 doi

  27. [35]

    A., Miki´ c, Z., & Riley, P

    Lionello, R., Linker, J. A., Miki´ c, Z., & Riley, P. 2006, ApJL, 642, L69, doi: 10.1086/504289

    2006 doi

  28. [36]

    A., & Miki´ c, Z

    Lionello, R., Riley, P., Linker, J. A., & Miki´ c, Z. 2005, ApJ, 625, 463, doi: 10.1086/429268

    2005 doi

  29. [37]

    T., Raines, J

    Livi, S., Lepri, S. T., Raines, J. M., et al. 2023, A&A, 676, A36, doi: 10.1051/0004-6361/202346304

    2023 doi

  30. [38]

    I., Lionello, R., Downs, C., et al

    Mason, E. I., Lionello, R., Downs, C., et al. 2023, ApJL, 959, L4, doi: 10.3847/2041-8213/ad00bd

    2023 doi

  31. [39]

    J., Bame, S

    McComas, D. J., Bame, S. J., Barker, P., et al. 1998, SSRv, 86, 563, doi: 10.1023/A:1005040232597 Miki´ c, Z., Linker, J. A., Schnack, D. D., Lionello, R., &

    1998 doi

  32. [40]

    1999, Physics of Plasmas, 6, 2217, doi: 10.1063/1.873474 Miki´ c, Z., Downs, C., Linker, J

    Tarditi, A. 1999, Physics of Plasmas, 6, 2217, doi: 10.1063/1.873474 Miki´ c, Z., Downs, C., Linker, J. A., et al. 2018, Nature Astronomy, 2, 913, doi: 10.1038/s41550-018-0562-5

    1999 doi

  33. [41]

    2015, ApJ, 806, 55, doi: 10.1088/0004-637X/806/1/55

    Oran, R., Landi, E., van der Holst, B., et al. 2015, ApJ, 806, 55, doi: 10.1088/0004-637X/806/1/55

    2015 doi

  34. [42]

    2015, The Astrophysical Journal, 806, 55

    Oran, R., Landi, E., van der Holst, B., et al. 2015, The Astrophysical Journal, 806, 55

    2015

  35. [43]

    J., & Forsyth, R

    Owens, M. J., & Forsyth, R. J. 2013, Living Reviews in Solar Physics, 10, 5, doi: 10.12942/lrsp-2013-5

    2013 doi

  36. [44]

    2021, SSRv, 217, 78, doi: 10.1007/s11214-021-00856-1

    Parenti, S., Chifu, I., Del Zanna, G., et al. 2021, SSRv, 217, 78, doi: 10.1007/s11214-021-00856-1

    2021 doi

  37. [45]

    E., Laming, J

    Rakowski, C. E., Laming, J. M., & Lepri, S. T. 2007, The Astrophysical Journal, 667, 602

    2007

  38. [46]

    T., Weiss, L

    Riley, P., Gosling, J. T., Weiss, L. A., & Pizzo, V. J. 1996, J. Geophys. Res., 101, 24349, doi: 10.1029/96JA02447

    1996 doi

  39. [47]

    A., & Miki´ c, Z

    Riley, P., Linker, J. A., & Miki´ c, Z. 2001, J. Geophys. Res., 106, 15889, doi: 10.1029/2000JA000121

    2001 doi

  40. [48]

    A., Mikic, Z., et al

    Riley, P., Linker, J. A., Mikic, Z., et al. 2019, ApJ, 884, 18, doi: 10.3847/1538-4357/ab3a98

    2019 doi

  41. [49]

    M., et al

    Riley, P., Lionello, R., Caplan, R. M., et al. 2021, A&A, 650, A19, doi: 10.1051/0004-6361/202039815

    2021 doi

  42. [50]

    A., et al

    Riley, P., Lionello, R., Linker, J. A., et al. 2011, Solar Phys., 145, doi: 10.1007/s11207-010-9698-x

    2011 doi

  43. [51]

    J., Landi, E., Lepri, S

    Rivera, Y. J., Landi, E., Lepri, S. T., & Gilbert, J. A. 2019, The Astrophysical Journal, 874, 164

    2019

  44. [52]

    J., Landi, E., Lepri, S

    Rivera, Y. J., Landi, E., Lepri, S. T., & Gilbert, J. A. 2020, ApJ, 899, 11, doi: 10.3847/1538-4357/aba4a9

    2020 doi

  45. [53]

    J., Raymond, J

    Rivera, Y. J., Raymond, J. C., Reeves, K. K., et al. 2023, ApJ, 955, 65, doi: 10.3847/1538-4357/aceef8

    2023 doi

  46. [54]

    J., Higginson, A., Lepri, S

    Rivera, Y. J., Higginson, A., Lepri, S. T., et al. 2022, Frontiers in Astronomy and Space Sciences, 9, 417, doi: 10.3389/fspas.2022.1056347

    2022

  47. [55]

    J., Badman, S

    Rivera, Y. J., Badman, S. T., Stevens, M. L., et al. 2024a, ApJ, 974, 198, doi: 10.3847/1538-4357/ad7815 —. 2024b, Science, 385, 962, doi: 10.1126/science.adk6953

    doi

  48. [56]

    2006, Living Reviews in Solar Physics, 3, 2, doi: 10.12942/lrsp-2006-2

    Schwenn, R. 2006, Living Reviews in Solar Physics, 3, 2, doi: 10.12942/lrsp-2006-2

    2006 doi

  49. [57]

    C., Murphy, N

    Shen, C., Raymond, J. C., Murphy, N. A., & Lin, J. 2015, Astronomy and Computing, 12, 1, doi: 10.1016/j.ascom.2015.04.003

    2015 doi

  50. [58]

    W., L’Heureux, J., Ness, N

    Smith, C. W., L’Heureux, J., Ness, N. F., et al. 1998, SSRv, 86, 613, doi: 10.1023/A:1005092216668

    1998 doi

  51. [59]

    C., Frandsen, A

    Stone, E. C., Frandsen, A. M., Mewaldt, R. A., et al. 1998, SSRv, 86, 1, doi: 10.1023/A:1005082526237

    1998 doi

  52. [60]

    2022, ApJ, 926, 35, doi: 10.3847/1538-4357/ac391810.1002/essoar.10508664.1

    Szente, J., Landi, E., & van der Holst, B. 2022, ApJ, 926, 35, doi: 10.3847/1538-4357/ac391810.1002/essoar.10508664.1

    2022

  53. [61]

    2022, The Astrophysical Journal, 926, 35

    Szente, J., Landi, E., & van der Holst, B. 2022, The Astrophysical Journal, 926, 35

    2022

  54. [62]

    2011, The Astrophysical Journal, 731, 111

    Titov, V., Miki´ c, Z., Linker, J., Lionello, R., & Antiochos, S. 2011, The Astrophysical Journal, 731, 111

    2011

  55. [63]

    Titov, V. S. 2007, Astrophys. J., 660, 863

    2007

  56. [64]

    S., & Hornig, G

    Titov, V. S., & Hornig, G. 2002, Adv. Space Res., 29, 1087 T¨ or¨ ok, T., Downs, C., Linker, J. A., et al. 2018, ApJ, 856, 75, doi: 10.3847/1538-4357/aab36d Van Rossum, G., & Drake, F. L. 2009, Python 3 Reference Manual (Scotts Valley, CA: CreateSpace)

    2002 doi

  57. [65]

    2024, Gnuplot 6.0: an interactive plotting program, http://www.gnuplot.info/

    Williams, T., Kelley, C., & many others. 2024, Gnuplot 6.0: an interactive plotting program, http://www.gnuplot.info/

    2024

Pith tools

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