Simulation of Thermal Nonequilibrium Cycles in the Solar Wind

Jeffrey W. Reep; Mark G. Linton; Roger B. Scott; Stephen J. Bradshaw

REVIEW 2 major objections 6 minor 46 references

Simulation of Thermal Nonequilibrium Cycles in the Solar Wind

T0 review · 2 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Strong foot-point heating can push a transonic solar wind out of steady state, triggering cycles of condensation and evaporation.

desk verdict First clear demonstration of TNE limit cycles in a self-consistent transonic solar wind, but the quantitative threshold and period curve are tied to the assumed foot-point heating scale height. read the letter →

arxiv 2411.10215 v1 pith:4SV55J4O submitted 2024-11-15 astro-ph.SR physics.space-ph

Roger B. Scott , Jeffrey W. Reep , Mark G. Linton , Stephen J. Bradshaw This is my paper · ORCID

classification astro-ph.SRphysics.space-ph

keywords thermalnonequilibriumsolarwindcoronalrainheatingfoot-pointtransitionregioninstabilityopenmagneticfieldlines

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 whether thermal nonequilibrium (TNE), the runaway cooling that makes hot coronal plasma condense and rain back to the Sun, can occur not just in closed magnetic loops but in the open magnetic field lines that feed the solar wind. It reports that it can: in a one-dimensional model of an open flux tube with a transonic outflow, steady solutions exist only up to a foot-point heating ratio of about 3.45, and slightly stronger heating triggers repeated cycles of condensation, precipitation, ablation, and re-evaporation. The cycle period is about 24 hours near the threshold and falls to roughly 3 hours for heating ratios around 10. If correct, steady-state solar wind models would have to respect a quantitative heating limit, and periodic density and ionization fluctuations in the heliosphere could be traced to this lower-corona instability.

What carries the argument

The load-bearing setup is a prescribed two-scale heating profile, $H(s)=A(s)^{-1}[H_b e^{-(s-s_0)/\ell_b}+H_g e^{-(s-s_0)/\ell_g}]$, with $\ell_b = 0.01\,R_\odot$ and $\ell_g = R_\odot$, and the control parameter $\alpha = H_b\ell_b/(H_g\ell_g)$ that measures the ratio of foot-point to global energy deposition. The argument is carried by the 'thermal sink': a region near $s_0+h_n$ ($h_n$ about 25 Mm, the base-corona density scale height) where enhanced foot-point heating produces a local temperature minimum, an upward conductive heat flux, and radiative cooling that grows with density. The tipping point is the emissivity break at $T' = 10^{5.67}$ K, below which the radiative loss function $\Lambda(T)$ becomes $\propto T^{-1}$, so that cooling accelerates as the plasma cools; the paper uses the Field condensation-mode growth rate to estimate the runaway timescale and defines a 'cooling factor' $\Gamma = \langle \tau_d^{-1}\rangle/\langle \tau_u^{-1}\rangle$ that must stay below 1 for a steady state to exist.

What would settle it

Repeat the same HYDRAD simulation at $\alpha = 3.5$ with the same two-scale heating but with the foot-point scale height doubled to $\ell_b = 0.02\,R_\odot$; if a steady transonic solution is recovered, the quantitative threshold is a consequence of the chosen 7 Mm stratification rather than a general property of open-field heating. Alternatively, if a steady-state simulation at $\alpha=3.5$ with the original profile exists using a different but still plausible emissivity that has no $T^{-1}$ branch below 0.47 MK, the instability trigger is an artifact of the radiative loss function.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that thermal nonequilibrium is not restricted to closed coronal loops: it can develop in a steadily outflowing, transonic solar wind when the heating is split into a small-scale component concentrated near the footpoints (scale height $0.01\,R_\odot$, about 7 Mm) and a global component (scale height $R_\odot$) that accelerates the wind. Holding the global heating at $H_g = 2\times10^{-6}\,\mathrm{erg\,cm^{-3}\,s^{-1}}$, the simulations find steady states for heating ratio $\alpha = H_b \ell_b/(H_g \ell_g)$ up to 3.45, corresponding to $H_b = 6.9\times10^{-4}\,\mathrm{erg\,cm^{-3}\,s^{-1}}$. A 1.5% increase to $\alpha = 3.5$ ($H_b = 7.0\times10^{-4}$) removes the steady state: the extra heating raises the density in the lower corona, which slows the wind and weakens the enthalpy flux, so that a radiation-dominated 'thermal sink' near the density scale height (about 25 Mm) can no longer be balanced by conduction. The plasma there cools below the emissivity break temperature $T' = 10^{5.67}\,\mathrm{K}$, where radiative loss increases as temperature falls, and a thermal instability produces a falling condensate; the subsequent evaporation, relaxation, and re-condensation repeat as a limit cycle. The period falls from about 24 h near threshold to about 3 h at $\alpha = 10$, and the paper argues that the condensates' formation height directly reflects the scale height of the foot-point heating.

Load-bearing premise

Everything rests on the assumption that coronal heating near the footpoints is stratified on a small scale of about 7 Mm on top of a global scale of a solar radius; the paper itself notes that in a physics-based heating model this scale should emerge rather than be prescribed, and if the Sun's heating is stratified differently the quantitative threshold and the very occurrence of TNE in open-field wind could change.

Editorial extensions

If this is right

Steady-state solar wind models must respect an upper bound on foot-point heating: for the global heating used here, heating ratios above about 3.45 cannot be made steady on open field lines.
TNE cycle periods carry a signature of the heating rate: about 24 h at the threshold, dropping to roughly 5 h at $\alpha=4$ and asymptoting near 3 h for $\alpha\ge10$.
The height at which condensates form along open field lines is set by the scale height of the foot-point heating, so coronal-rain observations could be inverted to infer how heating is stratified in the lower corona.
Each cycle launches outward-propagating density and acoustic disturbances that reach white-light coronagraph fields of view with periods of about 3-4 hours, a potential source of periodic structures in streamers and pseudostreamers.
Time-dependent nonequilibrium ionization calculations show oxygen charge states return near baseline while iron remains suppressed with cyclic fluctuations, so combined oxygen/iron charge states can diagnose both the heating and the non-steadiness of the lower corona.

Reading between the lines

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

Editorial extension: the threshold $\alpha\approx3.45$ is likely to move if the small-scale heating layer is thickened; repeating the simulation with $\ell_b$ varied by a factor of two and checking whether steady transonic solutions reappear at $\alpha=3.5$ would map the sensitivity of this limit to heating stratification.
Editorial extension: because the falling condensate is denser and slower than the ambient wind, it should act as a transient reflector of Alfvén waves, briefly turning the sub-condensate volume into a resonant cavity; this could imprint a period of order the cycle time on wave-driven heating and on first-ionization-potential fractionation, an idea the authors suggest but do not model.
Editorial extension: if open-field TNE actually powers slow-solar-wind variability, then density and charge-state periodicity at 3-24 h periods should appear in in-situ solar wind time series, a prediction that can be tested against existing spacecraft data.
Editorial extension: the cycle-period versus heating-ratio relation offers a remote diagnostic, because measuring a quasi-periodic coronal-rain or white-light fluctuation period would then constrain the foot-point heating rate without needing to resolve the heating scale directly.

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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

The thing to know: this paper actually does show TNE limit cycles surviving in a transonic solar wind with the sonic point in the domain, on explicitly open field lines. That removes the ambiguity in Schlenker et al. (2021) and is the first result of its kind. The cycle is directly visible in the time-distance plots, the four-phase taxonomy (precipitation, ablation, relaxation, condensation) is physically plausible and matches the simulated evolution, and the period scaling from ~24 h near threshold to ~3 h at high alpha is a concrete, falsifiable signature. The ionization-state calculation (O versus Fe behaving differently) is a nice bonus that could matter for heliospheric diagnostics. Credit where due: the central existence claim is well-supported within the model, and the paper is honest about its own limitations.

The soft spots are real but mostly known to the authors. The threshold alpha ~ 3.5 and the period curve are set by the prescribed foot-point heating scale length lb = 0.01 Rsun through the location of the thermal sink. The stress-test note is right that this is not yet a robust solar constraint; the paper says so itself in Section 8. That weakness is structural, not a fixable error, and it mainly limits the quantitative generalization rather than the qualitative existence claim.

Two smaller issues. The robustness checks (more elaborate emissivity, two-fluid treatment) are asserted but not shown; I'd want those in an appendix or at least a quantitative summary. And the Section 5.4 Field (1965) instability analysis is acknowledged by the authors to rest on an equilibrium assumption that TNE by definition lacks; they use it as a diagnostic, which is fine, but they should present it that way up front rather than as a derivation of the condensation timescale. Also, no code or data is provided, which for a purely numerical paper makes independent verification impossible. That is a concrete reproducibility problem, not just a style complaint.

Verdict: the paper deserves a serious referee. It is a solid, clearly-written modeling study with a genuinely new result and useful observable predictions. I would send it to review, with the expectation that the authors be asked to (a) release the HYDRAD setup or at least the input files and complete run parameters, (b) show the robustness checks rather than asserting them, and (c) reframe the Field analysis strictly as a diagnostic. The quantitative solar limit should be presented as conditional on the heating parameterization, which they already concede. I would cite this if I worked on coronal rain or solar wind sources.

Referee Report

2 major / 6 minor

Summary. This paper presents 1D field-aligned hydrodynamic simulations of a transonic solar wind along an open flux tube, using the HYDRAD code extended to 30 R_sun. The heating is prescribed as the sum of a small-scale exponential foot-point component (scale height ℓ_b=0.01R_sun) and a global exponential component (scale height R_sun), with the ratio α=H_bℓ_b/(H_gℓ_g) scanned from 0 to 10. For fixed H_g=2×10^-6 erg cm^-3 s^-1, the authors find steady-state wind solutions up to α=3.45 and, for α≥3.5, self-sustained TNE cycles in which coronal plasma condenses near a thermal sink at s≈25-50 Mm, precipitates to the chromosphere, ablates back into the corona, and relaxes before the next cycle. The simulations are supplemented by a Lagrangian 'cooling factor' Γ criterion (Eq. 14), a Field (1965) thermal-instability growth rate (Eq. 23), and an analysis of heliospheric signatures in white-light density fluctuations and O/Fe charge states. The paper concludes that open-field solar wind regions can host TNE when foot-point heating is strongly stratified, with implications for coronal-hole plumes and slow wind.

Significance. The central existence result is new and, if correct, extends TNE studies from closed loops to open, transonic geometries. The cycles are directly visible in the time-distance diagnostics of Figures 3-8, and the emergent nature of the loss of equilibrium (α is scanned, not imposed) is a strength. The analytic Γ and Field-growth-rate diagnostics are derived from the model equations and checked against the simulations, making the paper internally consistent. The claimed threshold α_c=3.45 and the period curve in Fig. 9 are potentially important quantitative predictions. However, their solar applicability is currently limited by the prescribed heating stratification scale ℓ_b, which the authors themselves identify in Section 8 as a model parameter rather than an emergent quantity. The paper also reports, but does not display, robustness checks against a more sophisticated emissivity and a two-fluid treatment. With these caveats, the paper makes a credible case for the existence of TNE in the solar wind, while the specific numerical limits should be treated as conditional on the adopted heating model.

major comments (2)

[Section 6 / Figure 9; Section 8] The quantitative claims that steady-state solutions exist only for α≤3.45 and that TNE periods vary from ~24 h at threshold to ~3 h at α=10 are established only for ℓ_b=0.01R_sun. Because the thermal sink is located at s_n-s_0≈25 Mm, the local heating balance there contains H_b exp(-(s_n-s_0)/ℓ_b); changing ℓ_b by a factor of two changes the exponent by a factor of two and therefore shifts the critical H_b by a large factor. Section 8 correctly concedes that ℓ_b is a parameter and should emerge from a physics-based heating model. As a result, the abstract's phrase 'limits on the amount of foot-point heating that can be withstood under steady-state conditions' overstates the robustness of the result. I recommend adding a parameter study varying ℓ_b (e.g., 0.005 and 0.02 R_sun) and reporting the resulting α_c and period curves; if this is beyond the scope of the paper, the quantitative claims should be explicitly framed as conditional on the adopted stratification.
[Section 8] The robustness checks reported in Section 8 are asserted but not shown. The statements that more sophisticated emissivity profiles produce 'little qualitative difference' and that a two-fluid treatment leaves the necessary conditions and timescales unchanged are load-bearing for the generality of the threshold and period results, yet no figures, tables, or numerical values are provided. Moreover, the same paragraph notes that the two-fluid treatment introduces coherent oscillations that 'precede and eventually trigger the thermal runaway,' which suggests a qualitative change that needs to be reconciled with the claim of unchanged conditions. Please present these tests quantitatively (e.g., a table of α_c and periods for each case) or clearly label them as preliminary tests that do not yet support the reported numbers.

minor comments (6)

[Section 5.4] At the thermal sink location s_n≈s_0+25 Mm, the foot-point heating term H_b exp(-(s_n-s_0)/ℓ_b) is approximately 2×10^-5 erg cm^-3 s^-1 for α=3.5, about an order of magnitude larger than H_g, so the statement H(s∼s_n)≈H_g is inaccurate; using the correct value changes the derived growth rate and condensation time by roughly 10-15%.
[Section 3 and Section 5.2] The text gives inconsistent values for the density jump across the transition region: Section 3 says the density decreases by roughly an order of magnitude, while Section 5.2 uses n_c/n_b≈1/100.
[Section 6] The sentence 'the cycle period of the marginal case (α=3.45) is about 24 h' should read α=3.5, since α=3.45 is the last steady-state solution and has no cycle.
[Figure 3 caption] The caption refers to a 72 h period, but the time axis in the figure spans -20 to 40 h; please reconcile.
[General] The manuscript contains several typographical errors and an inconsistent date ('Accepted August 23, 2021'); examples include 'Obseratory', 'separatix', 'mas', 'snaphsot', and 'wherin'. A careful proofread is needed.
[Eq. (17)] The notation |[Pu]|_TR used in Eq. (17) is not defined; please define the jump operator.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: TNE threshold and cycle periods emerge from scanned heating rates, with analytic diagnostics used only as consistency checks.

full rationale

The central claim is that for the prescribed heating profile of Eq. (6) the simulated plasma loses thermal equilibrium between alpha = 3.45 and alpha = 3.5 and then exhibits sustained TNE limit cycles. This is an emergent time-dependent result obtained by scanning the free parameter alpha, not an imposed or fitted outcome: the paper varies the heating ratio and reports whether a steady state exists (Figures 2 and 3) and then measures the resulting cycle periods (Figure 9). The analytic diagnostics are consistency checks rather than circular predictions. The Gamma < 1 criterion in Eq. (14) is derived from the model energy equation and then used to interpret why the flow can no longer carry plasma through the thermal sink; the Field-type growth rate in Eqs. (19)-(25) is evaluated with parameters taken from the simulation and compared with the observed condensation interval; the phase timescales (tau_g, tau_a, tau_rho, tau_c) are order-of-magnitude estimates anchored in the simulated flow and density structures. None of these quantities is recycled as an input that forces the headline result. The dependence of the quantitative threshold and period curve on the assumed foot-point heating scale length lb is a model-generality caveat that the paper itself acknowledges in Section 8 ('In our simulations the length scale of the foot-point heating is a parameter of the model; however, in a physics-based heating model the spatial scale should emerge naturally'). That is a limitation on robustness, not a circular reduction. Self-citations to Bradshaw & Cargill (2013) for the HYDRAD code, Scott et al. (2022) for the model setup and initialization, and Scott et al. (2019) for prior work are ordinary code and literature references; no load-bearing uniqueness theorem or prior result is imported from them to force the present conclusion. The paper is therefore self-contained in its derivation chain, and no step reduces by construction to its own inputs.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The central result rests on a handful of hand-chosen parameters, dominated by the heating ratio alpha and the foot-point heating scale lb, plus domain assumptions about geometry, emissivity, and single-fluid coupling. No new physical entities are introduced. The authors transparently flag the heating stratification as a model parameter and the Field (1965) application as technically inconsistent with TNE.

free parameters (6)

Heating ratio alpha = Hb*lb/(Hg*lg) = Threshold at alpha about 3.5; scanned 0 to 10
The central quantitative result, the steady-state limit on foot-point heating, is a threshold in this parameter; its value depends on all other model choices.
Foot-point heating scale height lb = 0.01 R_sun = 7 Mm
Chosen by hand in Equation 6; the paper states condensate formation height on open field lines directly reflects this scale.
Global heating amplitude Hg = 2 x 10^-6 erg cm^-3 s^-1
Chosen value sets the wind energy flux and asymptotic wind temperature; the TNE threshold scales with it via alpha.
Transition-region reference height s0 = 10 Mm
Chosen base of the transition region; enters the heating prescription and all height diagnostics.
Condensate density growth factor and mode length = factor 25; kc = pi/(2 hn)
Section 5.4: the quarter-wavelength mode assumption and growth factor 25 are selected to reproduce the simulated density contrast (1.7e10 vs 7e8 cm^-3); used to estimate condensation time.
Chromospheric lift delta_ch and density jump nc/nb = 500 km; 1/100
Section 5.2: values 'determined by inspection' of the simulation, used in the ablation timescale estimate tau_a about 1.1 h.

assumptions (7)

domain assumption 1D field-aligned Navier-Stokes equations along a radially expanding flux tube with A(s) = A0 r^2/R_sun^2
Section 2. Ignores super-radial expansion, field-line curvature, and cross-field transport; realistic null-point and pseudostreamer geometries are deferred to future work (Section 8).
ad hoc to paper External heating is the sum of two exponentials with fixed scale heights lb and lg
Equation 6. The heating stratification is prescribed rather than derived from a physics-based model; Section 8 concedes the length scale is a model parameter.
domain assumption Klimchuk et al. (2008) piecewise power-law emissivity with T' = 10^5.67 K and Lambda ~ T^-1 below T'
Section 2. The threshold for thermal runaway is set by T'; authors state more sophisticated emissivities shift thresholds only slightly.
domain assumption Single-fluid condition Ti = Te imposed by increased collisional coupling
Section 2, justified by Scott et al. (2022); authors report two-fluid runs leave TNE conditions and timescales unchanged (Section 8).
ad hoc to paper Field (1965) linear thermal instability analysis applies to the near-steady state at threshold
Section 5.4. The paper itself flags: 'This assumption is inconsistent with the presumed lack of an underlying equilibrium condition in TNE,' then applies it on near-steady grounds.
domain assumption Optically thin radiation cutoff at T0 = 2 x 10^4 K emulating an optically thick chromosphere
Section 2. Standard treatment for loop and wind models.
domain assumption Adaptive grid resolves transition region and condensates across all 12 runs
Section 2 describes refinement to about 0.1 km minimum spacing, but no convergence study is shown, so the threshold and cycle periods carry unquantified grid dependence.

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Cite this review

Pith. "Pith review of Simulation of Thermal Nonequilibrium Cycles in the Solar Wind." pith.science (2026). https://pith.science/paper/4SV55J4O

@misc{pith2026241110215,
  author       = {Pith},
  title        = {Pith review of: Simulation of Thermal Nonequilibrium Cycles in the Solar Wind},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4SV55J4O}},
  note         = {Machine review of arXiv:2411.10215}
}

read the original abstract

Thermal nonequilibrium (TNE) is a condition of the plasma in the solar corona in which the local rate of energy loss due to radiation increases to the point that it cannot be sustained by the various heating terms acting on the plasma, precluding the existence of a steady state. The limit cycles of precipitation and evaporation that result from TNE have been simulated in 1D models of coronal loops, as well as 2D and 3D models of the solar chromosphere and lower corona. However, a careful study of TNE in the solar wind has not been performed until now. Here we demonstrate that for suitable combinations of local and global heating rates it is possible for the plasma to exhibit a TNE condition, even in the context of a transonic solar wind with appreciable mass and energy fluxes. This implies limits on the amount of foot-point heating that can be withstood under steady-state conditions in the solar wind, and may help to explain the variability of solar wind streams that emanate from regions of highly concentrated magnetic flux on the solar surface. The implications of this finding pertain to various sources of high-density solar wind, including plumes that form above regions of mixed magnetic polarity in polar coronal holes and the slow solar wind (SSW) that emanates from coronal hole boundaries.

Figures

Figures reproduced from arXiv: 2411.10215 by the authors.

**Figure 1.** Profiles of plasma number density and temperature (top most panel), pressure and wind speed (second panel), and rates of heating per particle (lower two panels) are depicted for two steady state solutions with different footpoint heating rates. The values of α ∈ {0.0, 1.0} correspond to heating rates of Hb ∈ {0.0, 2.0} × 10−4 erg cm−3 s −1 . The global heating in each case is Hg = 2.0 × 10−6 erg cm−3 s −1 . While … view at source ↗

**Figure 2.** for the cases of α = {2.0, 3.0, 3.45}. Looking at the heating and cooling rates in the bottom two panels there is little qualitative change in the profiles of H/2n at heights s ≳ ℓb as Hb is increased, although there is a visible enhancement in the radiative cooling term R/2n near sn. This coincides with an increase in the density, which falls off more slowly with height between the TR and sn as Hb is increased. Th… view at source ↗

**Figure 3.** Time-distance plots of temperature (top), number density (middle), and linear mass flux (bottom) over a 72 h period during which the heating ratio α increases from 3.45 to 3.5, corresponding to foot-point heating rates of Hb ∈ {6.9, 7.0} × 10−4 erg cm−3 s −1 . During the first 24 h (α = 3.45) the plasma is in a steady state. Following the increase in foot-point heating (α = 3.5) at t = 0 the plasma undergoes two TN… view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: The dynamic cooling time, transit time, integrated cooling factor Γ, and minimum value of the temperature within the thermal sink are shown over a period of approximately 36 h that spans from just before the increase in heating from α = 3.45 to α = 3.5 at time t = 0 …

**Figure 5.** Figure 5: The time evolution of n, T, and nuA are depicted during the precipitation phase, which lasts approximately 1 h for the case of marginal nonequilibrium, beginning with the formation of a cold condensation in the corona near sn, and ending with the up-welling of material…

**Figure 6.** Figure 6: The time evolution of n, T, and nuA are depicted during the ablation phase, which lasts approximately 2.2 h for the case of marginal nonequilibrium, beginning with the upwelling of material at the base of the TR and ending when all of the precipitated condensate materi…

**Figure 7.** Figure 7: The time evolution of n, T, and nuA are depicted during the relaxation phase, which lasts approximately 17 h for the case of marginal nonequilibrium, beginning with the deceleration of the outward mass flux near sp and ending when the mass flux develops a local converg…

**Figure 8.** Figure 8: The time evolution of n, T, and nuA are depicted during the condensation phase, which lasts approximately 1.5 h for the case of marginal nonequilibrium, beginning with the development of a convergent flow near sn and ending when the temperature near sn drops to chromos…

**Figure 9.** Figure 9: Dependence of TNE-induced cycle duration (and frequency) on the heating ratio α. These values represent the average cycle duration over a 56 h simulation interval for each value of α, measured from the moment of condensation. To explore this dependence, we performed ad…

**Figure 10.** Figure 10: A time-distance plot of temperature (left), linear particle density (center), and log10 of the normalized particle density (right) for an interval of 105 s (∼ 27 hr) following an increase in the heating ratio to α = Hbℓb/Hgℓg = 6. Outward propagating density fluctuati…

**Figure 11.** Figure 11: The charge-state distributions (left) at r = 21 R⊙ (s ∼ 1.5 × 104 Mm) and average charge-state (right) of Oxygen (Z = 8) and Iron (Z = 26) as functions of height for three characteristic values of the heating, indicated in blue, red, and black. On the right, the dashe…

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Works this paper leans on

46 extracted references · 40 canonical work pages

[1]

K., & Klimchuk, J

Antiochos, S. K., & Klimchuk, J. A. 1991, ApJ, 378, 372

work page 1991
[2]

Klimchuk, J. A. 1999, ApJ, 512, 985

1999
[3]

Linker, J. A. 2011, ApJ, 731, 112

work page 2011
[4]

2022, ApJL, 926, L29

Antolin, P., Mart´ ınez-Sykora, J., & S ¸ahin, S. 2022, ApJL, 926, L29

work page 2022
[5]

2008, ApJ, 688, 669

Antolin, P., Shibata, K., Kudoh, T., Shiota, D., & Brooks, D. 2008, ApJ, 688, 669

work page 2008
[6]

2010, ApJ, 716, 154

Antolin, P., Shibata, K., & Vissers, G. 2010, ApJ, 716, 154

work page 2010
[7]

I., Wyper, P

Aslanyan, V., Pontin, D. I., Wyper, P. F., et al. 2021, ApJ, 909, 10

work page 2021
[8]

J., & Cargill, P

Bradshaw, S. J., & Cargill, P. J. 2013, ApJ, 770, 12

work page 2013

Show all 46 references

[9]

L., & McKee, C

Cowie, L. L., & McKee, C. F. 1977, ApJ, 211, 135 De Groof, A., Bastiaensen, C., M¨ uller, D. A. N.,

1977
[10]

2005, A&A, 443, 319 De Groof, A., Berghmans, D., van Driel-Gesztelyi, L., &

Berghmans, D., & Poedts, S. 2005, A&A, 443, 319 De Groof, A., Berghmans, D., van Driel-Gesztelyi, L., &

2005
[11]

2004, A&A, 415, 1141 Delaboudini` ere, J

Poedts, S. 2004, A&A, 415, 1141 Delaboudini` ere, J. P., Artzner, G. E., Brunaud, J., et al. 1995, Solar Physics, 162, 291

2004
[12]

A., & Velli, M

Downs, C., Lionello, R., Miki´ c, Z., Linker, J. A., & Velli, M. 2016, ApJ, 832, 180

2016
[13]

Evans, J. W. 1949, J. Opt. Soc. Am., 39, 229 —. 1958, J. Opt. Soc. Am., 48, 142

1949
[14]

2015, ApJ, 807, 142

Fang, X., Xia, C., Keppens, R., & Van Doorsselaere, T. 2015, ApJ, 807, 142

2015
[15]

Field, G. B. 1965, ApJ, 142, 531

1965
[16]

H., Longcope, D

Fisher, G. H., Longcope, D. W., Metcalf, T. R., & Pevtsov, A. A. 1998, ApJ, 508, 885

1998
[17]

2018, ApJ, 855, 52

Froment, C., Auch` ere, F., Miki´ c, Z., et al. 2018, ApJ, 855, 52

2018
[18]

M., & Pantellini, F

Grappin, R., Wang, Y. M., & Pantellini, F. 2011, ApJ, 727, 30

2011
[19]

N., Acton, L

Handy, B. N., Acton, L. W., Kankelborg, C. C., et al. 1999, SoPh, 187, 229

1999
[20]

K., Antiochos, S

Higginson, A. K., Antiochos, S. K., DeVore, C. R., Wyper, P. F., & Zurbuchen, T. H. 2017, ApJ, 837, 113

2017
[21]

D., Cargill, P

Johnston, C. D., Cargill, P. J., Antolin, P., et al. 2019, A&A, 625, A149

2019
[22]

1970, PASJ, 22, 405

Kawaguchi, I. 1970, PASJ, 22, 405

1970
[23]

G., Priest, E

Kliem, B., Lin, J., Forbes, T. G., Priest, E. R., & T¨ or¨ ok, T. 2014, ApJ, 789, 46

2014
[24]

Klimchuk, J. A. 2019, SoPh, 294, 173

2019
[25]

A., & Luna, M

Klimchuk, J. A., & Luna, M. 2019, ApJ, 884, 68

2019
[26]

A., Patsourakos, S., & Cargill, P

Klimchuk, J. A., Patsourakos, S., & Cargill, P. J. 2008, ApJ, 682, 1351

2008
[27]

Hansteen, V. H. 2020, A&A, 639, A20 21

2020
[28]

M., Vourlidas, A., Korendyke, C., et al

Laming, J. M., Vourlidas, A., Korendyke, C., et al. 2019, ApJ, 879, 124

2019
[29]

R., Title, A

Lemen, J. R., Title, A. M., Akin, D. J., et al. 2012, SoPh, 275, 17

2012
[30]

1972, SoPh, 25, 413

Leroy, J.-L. 1972, SoPh, 25, 413

1972
[31]

P., & Song, H

Li, L., Peter, H., Chitta, L. P., & Song, H. 2020, ApJ, 905, 26

2020
[32]

2022, ApJ, 926, 216

Li, X., Keppens, R., & Zhou, Y. 2022, ApJ, 926, 216

2022
[33]

I., Antiochos, S

Mason, E. I., Antiochos, S. K., & Viall, N. M. 2019, ApJL, 874, L33

2019
[34]

I., & Kniezewski, K

Mason, E. I., & Kniezewski, K. L. 2022, ApJ, 939, 21

2022
[35]

1957, Annales d’Astrophysique, 20, 127

Newkirk, Gordon, J. 1957, Annales d’Astrophysique, 20, 127

1957
[36]

2015, Living Reviews in Solar Physics, 12, 7

Poletto, G. 2015, Living Reviews in Solar Physics, 12, 7

2015
[37]

Mason, E. I. 2021, ApJ, 916, 115

2021
[38]

Schrijver, C. J. 2001, SoPh, 198, 325

2001
[39]

B., Bradshaw, S

Scott, R. B., Bradshaw, S. J., & Linton, M. G. 2022, ApJ, 933, 72

2022
[40]

B., Pontin, D

Scott, R. B., Pontin, D. I., & Wyper, P. F. 2019, The Astrophysical Journal, 882, 125

2019
[41]

S., Golub, L., & Rosner, R

Serio, S., Peres, G., Vaiana, G. S., Golub, L., & Rosner, R. 1981, ApJ, 243, 288

1981
[42]

1953, Phys

Spitzer, L., & H¨ arm, R. 1953, Phys. Rev., 89, 977

1953
[43]

2022, ApJ, 926, 35

Szente, J., Landi, E., & van der Holst, B. 2022, ApJ, 926, 35

2022
[44]

O., Pontin, D

Thurgood, J. O., Pontin, D. I., & McLaughlin, J. A. 2019, A&A, 621, A106

2019
[45]

M., & Vourlidas, A

Viall, N. M., & Vourlidas, A. 2015, ApJ, 807, 176 von Steiger, R., & Zurbuchen, T. H. 2011, Journal of Geophysical Research (Space Physics), 116, A01105

2015
[46]

2011, A&A Rv, 19, 35

Wilhelm, K., Abbo, L., Auch` ere, F., et al. 2011, A&A Rv, 19, 35

2011

Pith tools

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

[1] [1]

K., & Klimchuk, J

Antiochos, S. K., & Klimchuk, J. A. 1991, ApJ, 378, 372

work page 1991

[2] [2]

Klimchuk, J. A. 1999, ApJ, 512, 985

1999

[3] [3]

Linker, J. A. 2011, ApJ, 731, 112

work page 2011

[4] [4]

2022, ApJL, 926, L29

Antolin, P., Mart´ ınez-Sykora, J., & S ¸ahin, S. 2022, ApJL, 926, L29

work page 2022

[5] [5]

2008, ApJ, 688, 669

Antolin, P., Shibata, K., Kudoh, T., Shiota, D., & Brooks, D. 2008, ApJ, 688, 669

work page 2008

[6] [6]

2010, ApJ, 716, 154

Antolin, P., Shibata, K., & Vissers, G. 2010, ApJ, 716, 154

work page 2010

[7] [7]

I., Wyper, P

Aslanyan, V., Pontin, D. I., Wyper, P. F., et al. 2021, ApJ, 909, 10

work page 2021

[8] [8]

J., & Cargill, P

Bradshaw, S. J., & Cargill, P. J. 2013, ApJ, 770, 12

work page 2013