Conditions for Solar Prominence Formation Triggered by Single Localized Heating

Takaaki Yokoyama; Takafumi Kaneko; Takero Yoshihisa

REVIEW 3 major objections 6 minor 75 references

Conditions for Solar Prominence Formation Triggered by Single Localized Heating

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A single footpoint heating pulse triggers prominence condensation when its Field number exceeds unity.

desk verdict A credible numerical demonstration that a single localized heating event can trigger prominence condensation, with a sharp but under-sampled threshold and a Field-number criterion that is more diagnostic than causal. read the letter →

arxiv 2411.18193 v1 pith:XI2NLSUT submitted 2024-11-27 astro-ph.SR

Takero Yoshihisa , Takaaki Yokoyama , Takafumi Kaneko This is my paper · ORCID

classification astro-ph.SR

keywords Sun:prominencescoronacoronalrainthermalnon-equilibriumFieldlengthchromosphericevaporationmagnetohydrodynamics(MHD)localizedheating

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 prominences and coronal rain are usually explained by steady or quasi-steady footpoint heating, but the paper asks whether a single, short heating event along a single magnetic field line can act as the elemental trigger. Using 1.5D magnetohydrodynamic simulations of a dipped 100 Mm coronal loop with wave-driven background heating, it finds that one localized heating pulse at a footpoint does cause condensation when its peak rate is roughly $10^4$ times the steady background rate. The runaway cooling begins once the Field number $F_i$ exceeds unity — equivalently, when the Field length $\lambda_F$ drops below half the loop length $L/2$ — because thermal conduction can no longer balance radiative losses. The paper also shows that what controls the outcome is the total amount of deposited heating, not the heating profile, which extends the standard thermal-non-equilibrium condition to non-steady and asymmetric heating. If correct, a single nanoflare-like event is a viable building block for prominence and coronal rain formation.

What carries the argument

The carrying object is the Field number $F_i$, defined as $F_i = (L/2)/\lambda_F$, where $\lambda_F = 2\pi\sqrt{\kappa_0 T^{7/2}/(n^2\Lambda(T) - Q_{\rm heat})}$ is the Field length, the scale over which thermal conduction can smooth a temperature perturbation against radiative cooling. When $F_i > 1$, conduction acts too slowly to stabilize the plasma and cooling runs away into condensation; in the simulations the threshold is $F_i \gtrsim 1$ once radiative cooling exceeds wave heating. The second mechanism is the total heating amount, $\int dt\,ds\,Q$, which the paper shows is the conserved control parameter across heating profiles (single both-sided, steady Gaussian, and steady exponential in the survey), allowing the analytical thermal-non-equilibrium condition to be rewritten as an integrated ratio.

What would settle it

Run the same single Gaussian footpoint heating pulse in a 3D simulation of the same loop; condensation should appear whenever the 1.5D criterion $F_i > 1$ is satisfied during the cooling phase, and should not appear below the threshold. If a 3D run with matching local parameters fails to condense, or an observed single nanoflare-like event with energy near $10^{25}$ erg is followed by no prominence while a much weaker event is, the threshold as stated is wrong.

Watch

Extended reading notes

Core claim

The paper claims that a single, short, one-sided footpoint heating pulse — lasting a few hundred seconds, far shorter than the radiative cooling time — can trigger prominence condensation in a dipped coronal loop. In the authors' parameter survey, condensation appears when the peak localized heating rate reaches $Q_{\rm local} \gtrsim 17\ \mathrm{erg\,cm^{-3}\,s^{-1}}$, about $2\times10^4$ times the background wave-heating rate, and the criterion is captured by the Field number: condensation occurs for $F_i \gtrsim 1$, i.e. $\lambda_F \lesssim L/2$ under conditions where cooling exceeds heating. The paper further recasts the analytical thermal-non-equilibrium condition as a ratio of time- and space-integrated heating amounts, so that it applies regardless of whether the heating is steady, a single pulse, or asymmetric. A corollary of the simulations is that the deposited heating amount needed for condensation is nearly the same for single, steady, and exponentially decaying both-sided heating, with the one-sided single event needing more than double that amount.

Load-bearing premise

The threshold is computed in a 1.5D single flux tube with a fixed loop length of 100 Mm, fixed expansion profile and dip depth, and a fixed background wave-heating model; if 3D effects or variations in these geometric parameters change how the Field number evolves, the $10^4$ ratio and the $F_i > 1$ threshold would not carry over.

Editorial extensions

If this is right

A single heating event with peak rate about $10^4$ times the steady background rate (total energy near $10^{25}$ erg) is sufficient to drive chromospheric evaporation and later condensation in a 100 Mm loop.
The onset of condensation can be predicted from the loop-averaged Field number $F_i$: once $F_i$ exceeds unity while cooling exceeds heating, runaway cooling is inevitable.
The thermal-non-equilibrium condition can be reformulated as a ratio of integrated heating amounts, so it no longer assumes exponential steady footpoint heating and applies to arbitrary time-dependent localized events.
Across the heating types tested, the total heating amount needed for condensation is the same to within a factor of a few, while one-sided single heating requires more than twice the amount of both-sided heating.
Prominence mass decreases after formation because propagating shocks dissipate energy at the prominence–corona boundary, a behavior that contrasts with earlier steady-heating simulations where prominence mass kept growing.

Reading between the lines

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

If the threshold is robust to geometry, the required energy per strand becomes the real control parameter: any heating mechanism — waves, nanoflares, or reconnection — that deposits the same total energy at a footpoint should trigger condensation, regardless of its temporal profile.
The timing of shock passages offers a testable refinement: a loop that has been pre-cooled until $F_i$ is near unity may need far less than the single-pulse threshold energy, so a sequence of sub-threshold events could collectively trigger condensation.
In a 3D braided loop, the Field length will vary along and across field lines; the same $F_i > 1$ criterion would then predict where condensation nucleates, potentially explaining the observed discrete thread widths and the irregular spacing of coronal rain blobs.
The negative prominence mass trend suggests a wave-driven drainage cycle that previous steady-heating models missed; if it persists in 3D, it would help close the mass budget of quiescent prominences by accounting for both inflow and outflow.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this paper does something genuinely new and mostly does it carefully. It runs 1.5D MHD with wave-driven background heating and shows a single, short, one-sided heating pulse at 17 erg cm^-3 s^-1 produces condensation, while 16 does not. The 10^4 ratio to steady heating and the total-heating-amount formulation are new in this form, and the comparison runs (B, C, D) that tie the steady-heating cases to the Klimchuk-Luna condition are a good check. I'd trust the central result: single heating events can be elemental units for prominence and coronal rain formation, provided the loop is populated by evaporation before conduction stabilizes it.

Where I'm warier. The 16 vs 17 boundary is a single pair of runs. No random seeds, no grid test, no variation of the background wave realization, no comment on how the fixed expansion profile and dip depth shift the threshold. The paper itself admits that moving speak upward suppresses condensation, so the 10^4 number is clearly setup-specific. That is fine, but it should be labeled as such in the abstract rather than presented as a general requirement.

The Field-number story is the weakest link. Fi as defined in Eq. (44) excludes background heating and is evaluated with corona-averaged quantities, and the criterion Fi > 1 is read off the same runs that set the threshold. It is an a posteriori diagnostic, not an independent predictor. The “extension” to heating amount, Eq. (50), is a space-time integral of Eq. (47), so calling it an extension overstates the analytical content. That said, the paper does not lean on the criterion to explain the mechanism elsewhere; the shock-wave seeding of condensation is a separate, plausible claim, but it is not isolated by a control run without shock perturbations.

The authors are honest about limitations: they flag the speak dependence, the geometry, the 1D reduction, and the mass-loss discrepancy with Xia et al. That counts for a lot. The citation pattern looks normal; the relevant prior work is engaged, and the claim of novelty relative to Huang, Kohutova, and Reep is fair. No code or data are provided, which is a minor inconvenience for a paper whose threshold rests on one simulation per case.

Bottom line: this deserves a serious referee. I'd want the authors to add sensitivity runs or at least explicitly frame the threshold as a point estimate, and to soften the Field-number language from condition to marker. But the core result is worth publishing. I'd cite it once it's out, and it would make a good reading-group paper because it is short, clearly written, and would spark a useful argument about what counts as a TNE criterion.

Referee Report

3 major / 6 minor

Summary. The paper investigates whether a single, short, localized heating event at one footpoint of a coronal loop can trigger prominence condensation. Using 1.5D MHD simulations with a loop dip, a phenomenological wave-heating background, and a stochastic photospheric driver, the authors compare one-sided transient heating (Type A) with two-sided single, steady Gaussian, and steady exponential heating (Types B, C, D). They report a threshold in Qlocal between 16 and 17 erg cm^-3 s^-1 for one-sided heating, claim that condensation is consistently accompanied by a Field number Fi greater than about 1 (Eq. 46), and propose an extension of the Klimchuk & Luna (2019) thermal non-equilibrium condition to a heating-amount form (Eq. 50). They also report a new negative prominence-mass trend and attribute it to shock-wave dissipation at the PCTR.

Significance. If the central claims hold, the demonstration that a single nanoflare-like event can act as an elemental unit for prominence and coronal-rain formation would be a valuable step beyond the quasi-steady heating paradigm, and the Field-number condition would provide a compact diagnostic. The model is more self-consistent than many earlier 1D loop studies because the background corona is produced by wave heating and turbulent dissipation rather than by an ad hoc steady heating term. However, the quantitative threshold and the Field-number criterion are not yet robustly established, and the heating-amount extension adds limited independent content because it is essentially a direct integration of a prior steady-state inequality. The paper is publishable in principle, but the headline claims need to be either supported by additional sensitivity tests or substantially tempered.

major comments (3)

[Section 3.3, Table 1] The condensation threshold is determined by single runs at Qlocal = 16 and 17 erg cm^-3 s^-1, a 6% difference, with no reported variation of the random-noise seeds, grid resolution, or background wave realizations. Because the background heating is driven by stochastic photospheric motions (Eqs. 37-38), the threshold and the derived ~10^4 ratio (Eq. 48) may be sensitive to run-to-run variability; the authors should provide a sensitivity analysis or explicitly frame the threshold as realization-dependent.
[Section 4.1, Eqs. (44)-(46)] The Field-number criterion Fi ≳ 1 is asserted as the condition for condensation, but it is computed a posteriori from the same simulations that set the Qlocal threshold. Since Fi depends on the density and temperature that are themselves altered by the localized heating, the criterion may describe the post-heating state rather than provide a predictive condition. The omission of Qheat from Eq. (44) is justified only by the heuristic statement that Qturb < QR/5 during condensation, and the paper does not test whether variations in loop geometry or heating profile that change Fi actually change the condensation outcome independently of Qlocal. Eq. (46) should be presented as a diagnostic correlate, not as a derived necessary and sufficient condition.
[Section 4.2, Eq. (50)] The "extension" to a heating-amount formulation is obtained by directly integrating the Klimchuk & Luna (2019) inequality (47) over space and time. This is not an independent derivation; it inherits the assumptions of (47), namely steady exponential heating, symmetric footpoints, and specific definitions of Qmin, QλH, c1, and ΓλH. The agreement with Table 2 is a consistency check, not a validation, and the conclusion that the extended condition applies when the heating is not steady and not exponentially decaying is not supported by any simulation with such profiles. The authors should either test the integrated condition against a non-steady, non-exponential heating case or temper the claim.

minor comments (6)

[Title, Abstract] The title contains "F ormation" and the abstract contains "T riggered"; these formatting errors should be corrected.
[Table 1 and Section 2.5] The table caption appears as "T able 1" and the text in Section 4.2 refers to "Case C1-5" and "Case D1-5", whereas Table 1 lists only four cases for Type C and Type D; the numbering should be made consistent.
[Eq. (48)] The notation "Qlocal/e" in Eq. (48) is ambiguous: it is not clear whether "e" is Euler's number, a subscript, or a misprint; the quantity should be defined explicitly.
[Section 4.1] The sentence about an additional calculation with a simplified radiative-loss function mentions a result but does not report it or show it in a figure; either provide the outcome or remove the sentence.
[Eq. (49)] The definition of \bar{Q}bg is written as a spatial average but is then used as if it were a function of s ("We substitute \bar{Q}bg(s) = ..."); the notation should be cleaned up.
[Conclusion] The phrase "the Field number Fi approximately exceeded unity" is vague; the paper uses Eq. (46) with Fi ≳ 1, so the conclusion should state the criterion quantitatively and should also state the limitation that the threshold is specific to the chosen loop geometry and heating location.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the condensation threshold is determined by independent 1.5D MHD simulations, and the Field-number criterion is presented as a diagnostic interpretation rather than as a fitted input.

full rationale

The paper's central result, that single localized heating with Qlocal ≈ 17–30 erg cm^-3 s^-1 can trigger condensation, comes from a parameter survey of numerical MHD runs. The critical heating rate is not obtained from the Field-number formula or from Eq. (50); it is read directly from the simulation outcomes (Case A3 vs. A2). The Field number Fi in Eq. (44) is computed from the simulated density and temperature, and the statement 'condensation in our simulations is consistently accompanied by the Field number exceeding unity' (Eq. 46) is an a posteriori physical interpretation, not a quantity fitted to the condensation label. The ratio QλH/Qmin ∼ 2×10^4 in Eq. (48) is likewise a ratio of two measured simulation quantities, and the paper explicitly notes that the value is 'specific to our numerical setting.' The extension of the Klimchuk & Luna (2019) condition to heating-amount form in Eq. (50) is an asserted generalization supported by the separate Type B, C, and D simulations and their agreement with the analytic condition; it is not derived from itself. No load-bearing self-citation or uniqueness argument appears: citations to the authors' prior work concern the numerical code and wave-heating model, not the condensation criterion. The lack of extensive sensitivity studies on speak, loop geometry, and background wave realization is a robustness/correctness concern, not circularity. Therefore the derivation chain is self-contained and no circular step is exhibited.

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

The central numerical experiment depends on a substantial set of modeling assumptions: a wave-heating parameterization, radiative loss tables, a 1.5D geometry with fixed expansion, and synthetic boundary drivers. The only numbers fitted to the simulation output are the critical heating rates and integrated heating amounts from the parameter survey. The analytical condition (50) is an integral of the KL19 inequality and adds no new free parameters.

free parameters (5)

Qlocal critical threshold (Case A3) = 17.0 erg cm^-3 s^-1
Determined by the parameter survey as the smallest single-heating rate that produces condensation; used in Eq. (48) to derive the ~10^4 ratio to background heating.
Heating peak location speak = 8.5 Mm
Chosen as about 1 Mm above the transition region; the paper states that if speak increases, condensation will not occur even with the same heating amount, so the threshold depends on this ad hoc choice.
Heating temporal profile tau1, tau2 = 100 s, 300 s
Gaussian rise and decay times chosen by hand following Huang et al. (2021) for the single event; total deposited heating amount and threshold are sensitive to these values.
Heating width ell = 0.15 Mm
Spatial width of the Gaussian localized heating; affects the peak volumetric heating rate and evaporation mass supply.
Total heating amount thresholds (Table 2) = B4 3.5e10, C4 1.8e10, D4 1.2-3.1e10 erg cm^-2
Simulation-derived minimum integrated heating amounts used to support the claim that total amount, not rate, controls condensation across heating types.

assumptions (6)

standard math Field (1965) thermal instability criterion with Spitzer conduction applies locally in a coronal loop with negligible net heating.
Used in Eqs. (44)-(46) to define the Field number Fi and to interpret Fi>1 as the condensation condition.
domain assumption The optically thin radiative loss function Lambda(T) from CHIANTI v7 and the Goodman-Judge chromospheric cooling represent the true cooling of the loop plasma.
QR in Eq. (20) is taken from external databases; the authors only test one simplified loss function in Section 4.1.
domain assumption Phenomenological Alfven wave turbulent dissipation (Shoda et al. 2018b) with cd=0.25 and the given lambda_cor profile reproduces the background coronal heating.
Equations (29)-(32) and (40) parameterize unresolved turbulence; no independent verification within the paper beyond matching quiet-Sun heat flux.
domain assumption A 1.5D single-field-line model with fixed expansion factor and line-tied boundaries captures the essential condensation physics.
The loop is reduced to one spatial dimension with imposed fex(s) in Eqs. (11)-(14); the paper acknowledges 3D effects and geometry variations are unexplored.
domain assumption Fully ionized hydrogen plasma with mean molecular weight mu=0.5.
Used in Eq. (8) and throughout; ignores helium and partial ionization effects in the chromosphere and transition region.
domain assumption Boundary velocity perturbations with pink noise represent photospheric motion and generate the waves that heat the corona.
Equation (37)-(38) injects synthetic motions with chosen amplitudes; no observed time series is used.

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Cite this review

Pith. "Pith review of Conditions for Solar Prominence Formation Triggered by Single Localized Heating." pith.science (2026). https://pith.science/paper/XI2NLSUT

@misc{pith2026241118193,
  author       = {Pith},
  title        = {Pith review of: Conditions for Solar Prominence Formation Triggered by Single Localized Heating},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XI2NLSUT}},
  note         = {Machine review of arXiv:2411.18193}
}

abstract

We performed numerical simulations to study mechanisms of solar prominence formation triggered by a single heating event. In the widely accepted ``chromospheric-evaporation condensation" model, localized heating at footpoints of a coronal loop drives plasma evaporation and eventually triggers condensation. The occurrence of condensation is strongly influenced by the characteristics of the heating.Various theoretical studies have been conducted along one-dimensional field lines with quasi-steady localized heating. The quasi-steady heating is regarded as the collection of multiple heating events among multiple strands constituting a coronal loop. However, it is reasonable to consider a single heating event along a single field line as an elemental unit.We investigated the condensation phenomenon triggered by a single heating event using 1.5-dimensional magnetohydrodynamic simulations. By varying the magnitude of the localized heating rate, we explored the conditions necessary for condensation. We found that when a heating rate approximately $\sim 10^{4}$ times greater than that of steady heating was applied, condensation occurred. Condensation was observed when the thermal conduction efficiency in the loop became lower than the cooling efficiency, with the cooling rate significantly exceeding the heating rate. Using the loop length $L$ and the Field length $\lambda_{\mathrm{F}}$, the condition for condensation is expressed as $\lambda_{\mathrm{F}} \lesssim L/2$ under conditions where cooling exceeds heating. We extended the analytically derived condition for thermal non-equilibrium to a formulation based on heating amount.

Figures

Figures reproduced from arXiv: 2411.18193 by the authors.

**Figure 1.** Schematic picture of the model. determined by following: e = p γ − 1 , (7) p = ρkBT µmH , (8) where mH is the hydrogen mass, kB is the Boltzmann constant, and γ = 5/3 is the adiabatic index. µ represents the mean molecular weight. For simplicity, we assume a fully ionized state consisting only of hydrogen and fix the value of µ = 0.5. The gravitational acceleration along the loop g(s) in the left half of the loop (… view at source ↗

**Figure 2.** The optically thin radiative loss function Λ(T). The dashed line represents a simplified used in Section 4.1. where TTR = 15000 K is temperature at the transition region and δT = 5000 K. Because of the fully ionized atmosphere, the number density of hydrogen nH and electron ne can be described as nH = ne = ρ mH . (22) Λ(T) is the radiative loss function with photospheric abundances from Chianti Atomic Database ver. … view at source ↗

**Figure 3.** The temperature and density profiles at the quasisteady state (t = 35, 000 s) are plotted by solid and dashed lines, respectively. B, a temporally single, spatially Gaussian heating is applied at the left side and both sides of the loop. In Type A, we consider five cases with Qlocal = 5.0, 16.0, 17.0, 30.0, 100.0 erg cm−3 s −1 (Case A1-5), and in Type B, we consider four cases with Qlocal = 2.0, 3.7, 3.8, 8.0 erg c… view at source ↗

Figures from the paper (5 more)

**Figure 5.** Figure 5: (a-g) Space-time diagrams for density, pressure, temperature, velocity along the loop vs, thermal conduction QC, turbulent heating Qturb and cooling rate QR in Case A4 are shown from tp = 0 to 1.8 × 104 s. The horizontal and vertical axes represent the distance from th…

**Figure 6.** Figure 6: Space-time diagrams of density and temperature from tp = 2, 500 to 5, 000 s are shown. The horizontal axis represents the distance from the left footpoint of the loop. To enhance the visibility of the condensation process, the color bar ranges have been adjusted compar…

**Figure 7.** Figure 7: Space-time diagrams of density in Case (a) A1, (b) A2, (c) A3, and (d) A5. The initial condition at tp = 0 s is same with the condition in [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: The time evolution of coronal averaged density (top) and temperature (bottom) for each case in the parameter survey is shown. Red and blue solid lines represent Case A5 and A3, which exhibit condensations, while purple and green dashed lines represent Case A2 and A1, …

**Figure 10.** Figure 10: The schematic picture of two cases: (upper) condensation occurring due to a single heating event (refer to tp = 2, 000 to 3, 000 s in Case A4) and (lower) no condensation occurring. Solid lines represent half of the loop, while dashed lines denote the Field length. Th…

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Works this paper leans on

75 extracted references · 73 canonical work pages

[1]

1991, The Astrophysical Journal, 378, 372

Antiochos, S., & Klimchuk, J. 1991, The Astrophysical Journal, 378, 372

work page 1991
[2]

2000, The Astrophysical Journal, 536, 494

Antiochos, S., MacNeice, P., & Spicer, D. 2000, The Astrophysical Journal, 536, 494

work page 2000
[3]

Klimchuk, J. A. 1999, The Astrophysical Journal, 512, 985

work page 1999
[4]

2019, Plasma Physics and Controlled Fusion, 62, 014016

Antolin, P. 2019, Plasma Physics and Controlled Fusion, 62, 014016

work page 2019
[5]

2022, Frontiers in Astronomy and Space Sciences, 22

Antolin, P., & Froment, C. 2022, Frontiers in Astronomy and Space Sciences, 22

work page 2022
[6]

2010, The Astrophysical Journal, 716, 154

Antolin, P., Shibata, K., & Vissers, G. 2010, The Astrophysical Journal, 716, 154

work page 2010
[7]

2015, The Astrophysical Journal, 806, 81

Scullion, E. 2015, The Astrophysical Journal, 806, 81

work page 2015
[8]

J., Nightingale, R

Aschwanden, M. J., Nightingale, R. W., & Alexander, D. 2000, The Astrophysical Journal, 541, 1059

work page 2000

Show all 75 references

[9]

J., Schrijver, C

Aschwanden, M. J., Schrijver, C. J., & Alexander, D. 2001, The Astrophysical Journal, 550, 1036 Auch` ere, F., Bocchialini, K., Solomon, J., & Tison, E. 2014, Astronomy & Astrophysics, 563, A8

2001
[10]

E., Liu, W., & Low, B

Berger, T. E., Liu, W., & Low, B. 2012, The Astrophysical Journal Letters, 758, L37

2012
[11]

2003, Astronomy & Astrophysics, 401, 699

Bradshaw, S., & Mason, H. 2003, Astronomy & Astrophysics, 401, 699

2003
[12]

1992, Solar physics, 138, 291

Choe, G.-S., & Lee, L. 1992, Solar physics, 138, 291

1992
[13]

R., Van Ballegooijen, A

Cranmer, S. R., Van Ballegooijen, A. A., & Edgar, R. J. 2007, The Astrophysical Journal Supplement Series, 171, 520

2007
[14]

M., & Young, P

Dere, K., Landi, E., Mason, H., Fossi, B. M., & Young, P. 1997, Astronomy and Astrophysics Supplement Series, 125, 149 Donn´ e, D., & Keppens, R. 2024, arXiv preprint arXiv:2405.20048

1997 arXiv
[15]

Elsasser, W. M. 1950, Physical Review, 79, 183

1950
[16]

1976, Solar Physics, 49, 283

Engvold, O. 1976, Solar Physics, 49, 283

1976
[17]

Field, G. B. 1965, The Astrophysical Journal, 142, 531

1965
[18]

2015, The Astrophysical Journal, 807, 158

Froment, C., Auch` ere, F., Bocchialini, K., et al. 2015, The Astrophysical Journal, 807, 158

2015
[19]

2018, The Astrophysical Journal, 855, 52 15

Froment, C., Auch` ere, F., Miki´ c, Z., et al. 2018, The Astrophysical Journal, 855, 52 15

2018
[20]

L., & Judge, P

Goodman, M. L., & Judge, P. G. 2012, The Astrophysical Journal, 751, 75

2012
[21]

V., & Nordlund, ˚A

Gudiksen, B. V., & Nordlund, ˚A. 2005, The Astrophysical Journal, 618, 1031

2005
[22]

2021, The Astrophysical Journal, 920, 131

Guo, J., Zhou, Y., Guo, Y., et al. 2021, The Astrophysical Journal, 920, 131

2021
[23]

1999, The Astrophysical Journal, 513, 969

Hara, H., & Ichimoto, K. 1999, The Astrophysical Journal, 513, 969

1999
[24]

2012, The Astrophysical Journal, 746, 120

Hillier, A., Berger, T., Isobe, H., & Shibata, K. 2012, The Astrophysical Journal, 746, 120

2012
[25]

Hollweg, J. V. 1982, Astrophysical Journal, Part 1, vol. 257, June 1, 1982, p. 345-353., 257, 345

1982
[26]

V., Bird, M., Volland, H., et al

Hollweg, J. V., Bird, M., Volland, H., et al. 1982, Journal of Geophysical Research: Space Physics, 87, 1

1982
[27]

2021, The Astrophysical Journal Letters, 913, L8

Huang, C., Guo, J., Ni, Y., Xu, A., & Chen, P. 2021, The Astrophysical Journal Letters, 913, L8

2021
[28]

M., & Keppens, R

Jenkins, J. M., & Keppens, R. 2022, Nature Astronomy, 6, 942 Jerˇ ci´ c, V., & Keppens, R. 2023, Astronomy & Astrophysics, 670, A64 Jerˇ ci´ c, V., Keppens, R., & Zhou, Y. 2022, Astronomy & Astrophysics, 658, A58

2022
[29]

J., & Wang, H

Jing, J., Lee, J., Spirock, T. J., & Wang, H. 2006, Solar Physics, 236, 97

2006
[30]

J., et al

Jing, J., Lee, J., Spirock, T. J., et al. 2003, The Astrophysical Journal, 584, L103

2003
[31]

2019, Astronomy & Astrophysics, 625, A149

Johnston, C., Cargill, P., Antolin, P., et al. 2019, Astronomy & Astrophysics, 625, A149

2019
[32]

2015, The Astrophysical Journal, 806, 115 —

Kaneko, T., & Yokoyama, T. 2015, The Astrophysical Journal, 806, 115 —. 2017, The Astrophysical Journal, 845, 12 —. 2018, The Astrophysical Journal, 869, 136

2015
[33]

2008, The Astrophysical Journal, 676, 658

Karpen, J., & Antiochos, S. 2008, The Astrophysical Journal, 676, 658

2008
[34]

2001, The Astrophysical Journal, 553, L85

MacNeice, P. 2001, The Astrophysical Journal, 553, L85

2001
[35]

2003, The Astrophysical Journal, 593, 1187

Karpen, J., Antiochos, S., Klimchuk, J., & MacNeice, P. 2003, The Astrophysical Journal, 593, 1187

2003
[36]

2005, The Astrophysical Journal, 635, 1319

Karpen, J., Tanner, S., Antiochos, S., & DeVore, C. 2005, The Astrophysical Journal, 635, 1319

2005
[37]

2015, The Astrophysical Journal Letters, 806, L13

Keppens, R., Xia, C., & Porth, O. 2015, The Astrophysical Journal Letters, 806, L13

2015
[38]

Klimchuk, J. A. 2019, Solar Physics, 294, 173

2019
[39]

A., & Luna, M

Klimchuk, J. A., & Luna, M. 2019, The Astrophysical Journal, 884, 68

2019
[40]

2020, Astronomy & Astrophysics, 639, A20

Hansteen, V. 2020, Astronomy & Astrophysics, 639, A20

2020
[41]

2019, Astronomy & Astrophysics, 630, A123

Kohutova, P., Verwichte, E., & Froment, C. 2019, Astronomy & Astrophysics, 630, A123

2019
[42]

A., Klimchuk, J

Kucera, T. A., Klimchuk, J. A., & Luna, M. 2024, The Astrophysical Journal, 965, 53

2024
[43]

2012, The Astrophysical Journal, 744, 99

Landi, E., Del Zanna, G., Young, P., Dere, K., & Mason, H. 2012, The Astrophysical Journal, 744, 99

2012
[44]

1984, Astronomy and Astrophysics, 131, 33

Leroy, J., Bommier, V., & Sahal-Brechot, S. 1984, Astronomy and Astrophysics, 131, 33

1984
[45]

Berger, T. E. 2005, Solar Physics, 226, 239

2005
[46]

A., Lionello, R., Miki´ c, Z., & Amari, T

Linker, J. A., Lionello, R., Miki´ c, Z., & Amari, T. 2001, Journal of Geophysical Research: Space Physics, 106, 25165

2001
[47]

E., & Low, B

Liu, W., Berger, T. E., & Low, B. 2012, The Astrophysical Journal Letters, 745, L21

2012
[48]

2024, The Astrophysical Journal Letters, 973, L1

Lu, Z., Chen, F., Guo, J., et al. 2024, The Astrophysical Journal Letters, 973, L1

2024
[49]

2012, The Astrophysical Journal, 746, 30

Luna, M., Karpen, J., & DeVore, C. 2012, The Astrophysical Journal, 746, 30

2012
[50]

2010, The Astrophysical Journal Letters, 716, L19

Matsumoto, T., & Kitai, R. 2010, The Astrophysical Journal Letters, 716, L19

2010
[51]

A., Sigalotti, L

Mendoza-Briceno, C. A., Sigalotti, L. D. G., & Erd´ elyi, R. 2005, The Astrophysical Journal, 624, 1080

2005
[52]

D., Balsara, D

Meyer, C. D., Balsara, D. S., & Aslam, T. D. 2012, Monthly Notices of the Royal Astronomical Society, 422, 2102 —. 2014, Journal of Computational Physics, 257, 594 Miki´ c, Z., Lionello, R., Mok, Y., Linker, J. A., &

2012
[53]

Winebarger, A. R. 2013, The Astrophysical Journal, 773, 94

2013
[54]

1990, The Astrophysical Journal, 359, 228

Mok, Y., Drake, J., Schnack, D., & Van Hoven, G. 1990, The Astrophysical Journal, 359, 228

1990
[55]

2004, The Astrophysical Journal, 601, L107 M¨ uller, D., Hansteen, V., & Peter, H

Moriyasu, S., Kudoh, T., Yokoyama, T., & Shibata, K. 2004, The Astrophysical Journal, 601, L107 M¨ uller, D., Hansteen, V., & Peter, H. 2003, Astronomy & Astrophysics, 411, 605 M¨ uller, D., Peter, H., & Hansteen, V. 2004, Astronomy & Astrophysics, 424, 289

2004
[56]

Parker, E. N. 1953, The Astrophysical Journal, 117, 431

1953
[57]

2022, Astronomy & Astrophysics, 658, A71

Pelouze, G., Auch` ere, F., Bocchialini, K., et al. 2022, Astronomy & Astrophysics, 658, A71

2022
[58]

W., Antolin, P., & Bradshaw, S

Reep, J. W., Antolin, P., & Bradshaw, S. J. 2020, The Astrophysical Journal, 890, 100

2020
[59]

2009, The Astrophysical Journal, 691, 640

Rempel, M., Sch¨ ussler, M., & Kn¨ olker, M. 2009, The Astrophysical Journal, 691, 640

2009
[60]

A., Carlsson, M., & Aulanier, G

Robinson, R. A., Carlsson, M., & Aulanier, G. 2022, Astronomy & Astrophysics, 668, A177

2022
[61]

Shimizu, K., Shoda, M., & Suzuki, T. K. 2022, The Astrophysical Journal, 931, 37

2022
[62]

2021, Astronomy & Astrophysics, 656, A111

Shoda, M., & Takasao, S. 2021, Astronomy & Astrophysics, 656, A111

2021
[63]

1953, Physical Review, 89, 977

Spitzer, L., & H¨ arm, R. 1953, Physical Review, 89, 977

1953
[64]

C., & Hollweg, J

Sterling, A. C., & Hollweg, J. V. 1988, Astrophysical

1988
[65]

327, April 15, 1988, p

Journal, Part 1 (ISSN 0004-637X), vol. 327, April 15, 1988, p. 950-963., 327, 950

1988
[66]

2010, The Astrophysical Journal, 709, 499

Susino, R., Lanzafame, A., Lanza, A., & Spadaro, D. 2010, The Astrophysical Journal, 709, 499

2010
[67]

2007, The Astrophysical Journal, 662, 669 V¨ ogler, A., Shelyag, S., Sch¨ ussler, M., et al

Verdini, A., & Velli, M. 2007, The Astrophysical Journal, 662, 669 V¨ ogler, A., Shelyag, S., Sch¨ ussler, M., et al. 2005, Astronomy & Astrophysics, 429, 335

2007
[68]

Washinoue, H., Shoda, M., & Suzuki, T. K. 2022, The Astrophysical Journal, 938, 126

2022
[69]

L., & Noyes, R

Withbroe, G. L., & Noyes, R. W. 1977, Annual review of astronomy and astrophysics, 15, 363

1977
[70]

Xia, C., Chen, P., Keppens, R., & van Marle, A. J. 2011, The Astrophysical Journal, 737, 27

2011
[71]

2016, The Astrophysical Journal, 823, 22

Xia, C., & Keppens, R. 2016, The Astrophysical Journal, 823, 22

2016
[72]

W., Hashimoto, Y., et al

Yamasaki, D., Huang, Y. W., Hashimoto, Y., et al. 2023, Publications of the Astronomical Society of Japan, psad027

2023
[73]

2012, Astronomy & Astrophysics, 542, A52

Zhang, Q., Chen, P., Xia, C., & Keppens, R. 2012, Astronomy & Astrophysics, 542, A52

2012
[74]

2020, Nature Astronomy, 4, 994

Zhou, Y., Chen, P., Hong, J., & Fang, C. 2020, Nature Astronomy, 4, 994

2020
[75]

1998, Nature, 396, 440

Zirker, J., Engvold, O., & Martin, S. 1998, Nature, 396, 440

1998

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

1991, The Astrophysical Journal, 378, 372

Antiochos, S., & Klimchuk, J. 1991, The Astrophysical Journal, 378, 372

work page 1991

[2] [2]

2000, The Astrophysical Journal, 536, 494

Antiochos, S., MacNeice, P., & Spicer, D. 2000, The Astrophysical Journal, 536, 494

work page 2000

[3] [3]

Klimchuk, J. A. 1999, The Astrophysical Journal, 512, 985

work page 1999

[4] [4]

2019, Plasma Physics and Controlled Fusion, 62, 014016

Antolin, P. 2019, Plasma Physics and Controlled Fusion, 62, 014016

work page 2019

[5] [5]

2022, Frontiers in Astronomy and Space Sciences, 22

Antolin, P., & Froment, C. 2022, Frontiers in Astronomy and Space Sciences, 22

work page 2022

[6] [6]

2010, The Astrophysical Journal, 716, 154

Antolin, P., Shibata, K., & Vissers, G. 2010, The Astrophysical Journal, 716, 154

work page 2010

[7] [7]

2015, The Astrophysical Journal, 806, 81

Scullion, E. 2015, The Astrophysical Journal, 806, 81

work page 2015

[8] [8]

J., Nightingale, R

Aschwanden, M. J., Nightingale, R. W., & Alexander, D. 2000, The Astrophysical Journal, 541, 1059

work page 2000