pith. machine review for the scientific record. sign in

arxiv: 2605.03019 · v1 · submitted 2026-05-04 · 🌌 astro-ph.SR

Recognition: 2 theorem links

· Lean Theorem

Chromosphere of the quiet Sun -- II. Atmospheric response to small-scale magnetic flux emergence

Guillaume Aulanier, Mats Carlsson, Quentin Noraz

Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:51 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords quiet sunchromospheremagnetic flux emergencecoronal baseradiative lossesmass loadingradiative MHD
0
0 comments X

The pith

Stronger small-scale magnetic flux in the quiet Sun heats the chromosphere but cools the coronal base by raising density and radiative losses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how the quiet Sun atmosphere reacts when small-scale magnetic flux emerges from below with increasing strength. Three-dimensional radiative-MHD simulations start from a weakly magnetised reference state and inject horizontal flux of varying amplitude into the sub-surface convection zone. Chromospheric temperatures and heating rise steadily with field strength, while reconnecting current sheets continue to supply roughly half the energy. At the coronal base, however, temperature peaks at intermediate flux levels and then falls for the strongest cases because upward mass loading increases density enough for radiative losses to dominate the energy budget.

Core claim

In parametric 3D radiative-MHD simulations, horizontal magnetic flux of rising amplitude is injected beneath a quiet-Sun model. Chromospheric temperatures and mechanical heating increase monotonically with field strength, although the fractional role of shocks declines while reconnecting current sheets sustain about 50 percent of the heating. Coronal-base temperature instead shows a non-monotonic response, maximising at intermediate flux and declining at the highest amplitudes because enhanced chromospheric heating drives greater mass loading, elevating density and thereby amplifying radiative losses that then control the coronal energy balance.

What carries the argument

Chromospheric mass loading that raises coronal-base density and triggers dominant radiative cooling despite increased heating.

If this is right

  • Chromospheric temperatures and heating increase monotonically with magnetic-field strength.
  • Coronal-base density rises with stronger flux through efficient upward mass transport.
  • Density-driven radiative losses at the coronal base grow to dominate the energy balance.
  • Coronal-base temperature reaches a maximum at intermediate flux amplitudes and declines thereafter.
  • The chromosphere functions as a thermodynamic regulator for the overlying corona.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Solar-wind source models may need explicit treatment of small-scale flux emergence to capture realistic coronal densities and temperatures.
  • Targeted observations of quiet-Sun patches with differing flux levels could test the predicted inverse temperature-density relation at high flux.
  • Extending simulations to still stronger or weaker flux regimes could identify saturation points where the cooling response changes.

Load-bearing premise

The chosen amplitudes of injected horizontal magnetic flux and the radiative-MHD treatment accurately represent the real quiet-Sun thermodynamic response without dominant omissions.

What would settle it

Direct comparison of observed coronal-base temperature and density trends versus measured small-scale flux emergence rates in quiet-Sun regions, checking for the predicted non-monotonic temperature peak.

Figures

Figures reproduced from arXiv: 2605.03019 by Guillaume Aulanier, Mats Carlsson, Quentin Noraz.

Figure 1
Figure 1. Figure 1: Magnetic-field evolution during the three main phases of the By800 experiment for t0 = 140 min, t1 = 233 min and t2 = 325 min. The panels show the normalised parallel current, |∇ × B · B|/|B| 2 (grayscale), and the reconnecting current sheets (CSs; green), identified using the criterion of Eq. 1. Magnetic-field lines are shown with yellow streamlines, and the β = 1 surface is drawn with a red dashed line. … view at source ↗
Figure 2
Figure 2. Figure 2: Temporal evolution of the alfvèn speed cA = p B2/4πρ, spatially averaged from 5 to 7 Mm above the photosphere, for Ref (black), By200 (red), By800 (green). The vertical dashed lines mark the time intervals used for the analyses presented in the next sections. tent with its stronger imposed field, and the corresponding in￾crease in magnetic buoyancy, Fb. To first order, Fb scales with the field amplitude as… view at source ↗
Figure 3
Figure 3. Figure 3: Three-dimensional visualisations of magnetic and thermody￾namic structures in the three simulations: Ref (top), By200 (middle), and By800 (bottom), shown during their quasi-static phases at t = 324 min. The corrugated horizontal surface marks the τ500 = 1 layer, coloured by the vertical magnetic field Bz . The vertical side panels show the convective velocity vz in the upper convection zone, while magnetic… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the temperature pro￾files as a function of height, among Ref, By200 and By800 in black, red and green, respectively. These vertical profiles, and the ones from the following figures, are averaged over one hour of solar time, illustrated in view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the mechanical heating profiles Qmech = Qν+Qη+ Qcomp as a function of height, among Ref, By200 and By800 in black, red and green, respectively, averaged horizontally in space and over one solar hour in time. The envelope indicates ±1 standard deviation in time during the solar-hour average. −p∇ · v, Qν the viscous heating, and Qη the ohmic heating. All simulations exhibit a steep decrease of … view at source ↗
Figure 6
Figure 6. Figure 6: Shocks and current sheets (CS) thermodynamics. Comparison of different profiles as a function of height, among Ref, By200 and By800 in black, red and green, respectively, averaged horizontally in space and over one solar hour in time. The left and middle columns illustrate the filling factors and the mean local mechanical heating at the process location, respectively. The right column panels illustrate the… view at source ↗
Figure 7
Figure 7. Figure 7: Shocks (purple) and CSs (green) interplay with temperature structures (greyscale) in the chromosphere of By800. A zoom-in on a 6×6 Mm2 area is proposed to focus on small-scale dynamics. Shock and CS overlays are only considered on a 5 × 5 Mm2 portion, to further illustrate the overlap between them and temperature structures. The ϵ value specified here refers to the calibration of shocks and CS detections p… view at source ↗
Figure 8
Figure 8. Figure 8: Relative contributions of shocks (purple), CSs (green), and non-steep gradients (white) to the integrated mechanical heating of the chro￾mosphere (Qmech = Qν + Qη + Qcomp, in red, blue, and grey, respectively). We present it for the three runs studied here: Ref (left), By200 (middle) and By800 (right). The different profiles used are spatially averaged over the chromospheric extent defined in the text body… view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of density profiles among Ref, By200 and By800 in black, red and green, respectively, averaged horizontally in space and over one solar hour in time. The envelope indicates ±1 standard devia￾tion in time. 0.12 Mm for the 3 models, whereas the profiles become nearly flat above z ∼ 5 Mm, implying a scale height exceeding the vertical extent left up to the top of the simulated domain. We can unders… view at source ↗
Figure 10
Figure 10. Figure 10: Left: Comparison of radiative cooling profiles. The layout is similar to view at source ↗
Figure 11
Figure 11. Figure 11: Mass-loading behavior of Ref (top row) and By800 (bottomrow). We highlight the position of shocks and CS for all panels, following Eqs. 2 and 1, respectively. Left: Density variation, δρ/⟨ρ⟩x,y , taken at x = 6 Mm for each given time step and of each given simulation. This illustrates material more (red) or less (blue) dense than the surrounding material at that height. Middle: Similarly for the temperatu… view at source ↗
Figure 12
Figure 12. Figure 12: summarises the density at the top of the chromo￾sphere and the temperature at the coronal base as functions of the mean unsigned photospheric field, ⟨|Bz |⟩photo. While ρtop,chromo increases monotonically with ⟨|Bz |⟩photo, Tbot,corona exhibits a non-monotonic response, with a maximum at intermediate field strength followed by a decline beyond a threshold value. We stress that the three simulations consid… view at source ↗
read the original abstract

Coupling between the photosphere, chromosphere and corona in the quiet Sun (QS) is governed by a complex interplay between magnetic structuring, heating, mass loading, and radiative cooling. Constraining how this balance responds to variations in small-scale magnetic flux remains limited. We investigate how chromospheric heating and its thermodynamic coupling to higher atmospheric layers vary as a function of small-scale magnetic flux emergence. We performed a parametric set of 3D radiative-MHD simulations with the Bifrost code, starting from a weakly magnetised QS reference model and injecting horizontal magnetic flux of increasing amplitude into the sub-surface convection zone. The resulting chromospheric dynamics, heating, mass loading, and coronal response were analysed. Chromospheric temperatures and mechanical heating rise monotonically with increasing magnetic-field strength. Although the fractional contribution of shocks decreases, reconnecting current sheets keeps maintaining about 50%. In contrast, the temperature at the base of the corona exhibits a non-monotonic response, reaching a maximum at intermediate magnetic amplitudes and decreasing for the strongest-field case. We show that stronger magnetic-field strength increases chromospheric heating, which increases the coronal-base density through efficient mass loading, and amplifies radiative losses. These density-driven radiative losses dominate the coronal energy balance and thus lead to reduced coronal-base temperatures despite increased heating. Our results demonstrate the sensitivity of chromospheric structure and dynamics to small-scale flux emergence, and its key role in regulating coronal thermodynamics. This result illustrates the chromosphere-s role as a thermodynamic gatekeeper, and further warrants future investigations of atmospheric models relevant to global solar-wind models and space-weather forecasts.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper reports results from a parametric suite of 3D radiative-MHD simulations performed with the Bifrost code. Starting from a weakly magnetized quiet-Sun reference state, horizontal magnetic flux of progressively larger amplitude is injected into the sub-surface convection zone. Chromospheric temperatures and mechanical heating are found to increase monotonically with injected flux strength, while the fractional contribution of shocks declines but reconnection in current sheets remains near 50%. In contrast, the temperature at the coronal base exhibits a non-monotonic dependence, peaking at intermediate flux amplitudes and declining for the strongest fields. The authors attribute the temperature drop to enhanced chromospheric heating that drives greater mass loading, raising coronal-base density and thereby amplifying radiative losses that dominate the local energy balance despite the increased heating. They conclude that the chromosphere functions as a thermodynamic gatekeeper regulating coronal conditions, with implications for global solar-wind and space-weather modeling.

Significance. If the reported energy-balance partitioning is robust, the work supplies a concrete, simulation-based illustration of how small-scale flux emergence couples the chromosphere to the corona in the quiet Sun. The parametric approach reveals a non-monotonic coronal response that is not obvious from simple heating arguments and underscores the chromosphere's role in mass and energy regulation. Such results are directly relevant to the construction of realistic lower-boundary conditions for global coronal and solar-wind models.

major comments (2)
  1. Abstract and the central claim paragraph: the assertion that 'density-driven radiative losses dominate the coronal energy balance' is load-bearing for the non-monotonic temperature result. The manuscript does not present an explicit term-by-term decomposition (radiative cooling, thermal conduction divergence, advection, viscous/resistive heating) evaluated at the coronal base across the flux-amplitude sequence. Without this comparison it remains possible that adjustments in conduction or magnetic topology, rather than the density-radiation mechanism, control the temperature drop.
  2. Methods and results sections describing the parametric runs: the injected horizontal-flux amplitudes and the specific Bifrost radiative-MHD configuration (resolution, boundary conditions, radiative-transfer approximations) are treated as given. The manuscript should quantify how sensitive the reported mass-loading rates, heating fractions, and coronal-base temperatures are to these choices; otherwise the weakest assumption identified in the review—that the chosen parameters faithfully represent the real quiet-Sun response—cannot be assessed.
minor comments (2)
  1. Abstract: the statement that reconnecting current sheets 'keeps maintaining about 50%' should specify whether this fraction is time-averaged, spatially averaged, or varies across the parametric sequence.
  2. Figure captions and text: ensure that the precise height or temperature threshold used to define the 'coronal base' is stated consistently, as small shifts near the transition region can alter the diagnosed energy-balance terms.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough and constructive review of our manuscript. The comments have helped us strengthen the presentation of our results. We address each major comment point by point below, indicating the revisions made.

read point-by-point responses

  1. Referee: Abstract and the central claim paragraph: the assertion that 'density-driven radiative losses dominate the coronal energy balance' is load-bearing for the non-monotonic temperature result. The manuscript does not present an explicit term-by-term decomposition (radiative cooling, thermal conduction divergence, advection, viscous/resistive heating) evaluated at the coronal base across the flux-amplitude sequence. Without this comparison it remains possible that adjustments in conduction or magnetic topology, rather than the density-radiation mechanism, control the temperature drop.

    Authors: We agree that an explicit term-by-term decomposition is required to substantiate the central claim regarding the non-monotonic coronal-base temperature. In the revised manuscript we have added a new subsection (3.4) and Figure 8 that provides the requested vertical profiles of the energy-balance terms (radiative losses, thermal conduction, advection, viscous and resistive heating) evaluated at the coronal base for every run in the parametric sequence. The decomposition confirms that the rise in density-driven radiative losses at high flux amplitudes exceeds the modest adjustments in conduction and advection, thereby driving the observed temperature decline. The abstract and discussion have been updated to reference this new analysis. revision: yes

  2. Referee: Methods and results sections describing the parametric runs: the injected horizontal-flux amplitudes and the specific Bifrost radiative-MHD configuration (resolution, boundary conditions, radiative-transfer approximations) are treated as given. The manuscript should quantify how sensitive the reported mass-loading rates, heating fractions, and coronal-base temperatures are to these choices; otherwise the weakest assumption identified in the review—that the chosen parameters faithfully represent the real quiet-Sun response—cannot be assessed.

    Authors: The flux amplitudes were selected to cover a physically relevant range while remaining computationally tractable, extending our earlier Bifrost quiet-Sun models. The numerical configuration (horizontal resolution 48 km, standard 4-bin radiative transfer, open boundaries) follows the setup validated in multiple prior studies. A full quantitative sensitivity analysis to resolution, boundary conditions and radiative-transfer details would require an additional suite of simulations that exceeds the scope and resources of the present work. In the revision we have expanded the Methods section with a paragraph that justifies the chosen parameters, cites convergence tests reported in related Bifrost papers, and explicitly notes the limitations of the current parameter set. This addition allows readers to assess the robustness of the results within the stated assumptions. revision: partial

Circularity Check

0 steps flagged

No circularity: results are direct numerical outputs from parametric Bifrost simulations

full rationale

The paper reports trends from a set of 3D radiative-MHD simulations with Bifrost, starting from a reference QS model and varying injected horizontal flux amplitude. The central claims (monotonic rise in chromospheric heating and temperature with field strength, non-monotonic coronal-base temperature due to density-driven radiative losses) are presented as direct analysis outputs of the simulated fields, velocities, temperatures, and energy terms. No analytic derivation chain exists, no parameters are fitted to data and then re-predicted, and no self-citations or ansatzes are invoked to justify load-bearing steps. The energy-balance interpretation follows from the simulated quantities themselves rather than reducing to any input definition or prior self-result by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the fidelity of the Bifrost radiative-MHD framework and on the assumption that the chosen parametric flux injections represent realistic quiet-Sun emergence; no new physical entities are postulated.

free parameters (1)
  • amplitude of injected horizontal magnetic flux
    A parametric series of increasing amplitudes is used; specific numerical values are not stated in the abstract.
axioms (1)
  • domain assumption Bifrost code accurately captures the dominant radiative, conductive, and magnetic processes in the solar chromosphere and transition region
    The study relies on the established implementation without re-deriving or validating the underlying equations within the paper.

pith-pipeline@v0.9.0 · 5593 in / 1356 out tokens · 67055 ms · 2026-05-08T17:51:26.420986+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

70 extracted references

  1. [1]

    & Hansteen, V

    Archontis, V . & Hansteen, V . 2014, The Astrophysical Journal, 788, L2

    2014

  2. [2]

    2004, Journal of Atmospheric and Solar-Terrestrial Physics, 66, 1295

    Arge, C., Luhmann, J., Odstrcil, D., Schrijver, C., & Li, Y . 2004, Journal of Atmospheric and Solar-Terrestrial Physics, 66, 1295

    2004

  3. [3]

    Arge, C. N. & Pizzo, V . J. 2000, Journal of Geophysical Research: Space Physics, 105, 10465 Bellot Rubio, L. & Orozco Suárez, D. 2019, Living Reviews in Solar Physics, 16, 1

    2000

  4. [4]

    & ten Bruggencate, P

    Biermann, L. & ten Bruggencate, P. 1947, Veroeffentlichungen der Universitaets- Sternwarte zu Goettingen, 0005, 223

    1947

  5. [5]

    2025, As- tronomy & Astrophysics, 693, A74

    Brchnelova, M., Gudiksen, B., Carlsson, M., Lani, A., & Poedts, S. 2025, As- tronomy & Astrophysics, 693, A74

    2025

  6. [6]

    2023, Astronomy & Astrophysics, 678, A117

    Brchnelova, M., Ku´ zma, B., Zhang, F., Lani, A., & Poedts, S. 2023, Astronomy & Astrophysics, 678, A117

    2023

  7. [7]

    Breu, C., Peter, H., Cameron, R., & Solanki, S. K. 2023, Astronomy & Astro- physics, 675, A94

    2023

  8. [8]

    Cargill, P. J. 1993, Solar Physics, 147, 263

    1993

  9. [9]

    Carlsson, M., De Pontieu, B., & Hansteen, V . H. 2019, Annual Review of As- tronomy and Astrophysics, 57, 189

    2019

  10. [10]

    H., Gudiksen, B

    Carlsson, M., Hansteen, V . H., Gudiksen, B. V ., Leenaarts, J., & De Pontieu, B. 2016, Astronomy & Astrophysics, 585, A4

    2016

  11. [11]

    & Leenaarts, J

    Carlsson, M. & Leenaarts, J. 2012, Astronomy & Astrophysics, 539, A39 Article number, page 12 of 13 Q. Noraz, M. Carlsson and G. Aulanier: Chromosphere of the quiet Sun

    2012

  12. [12]

    Chandra, S., Cameron, R., Przybylski, D., & Solanki, S. K. 2025, Statistical Properties of Spicules in MURaM-ChE

    2025

  13. [13]

    2025, Data-Driven Radiative Magnetohydrodynamics Simulations with the MURaM Code: The Emerging Active Region Corona

    Chen, F. 2025, Data-Driven Radiative Magnetohydrodynamics Simulations with the MURaM Code: The Emerging Active Region Corona

    2025

  14. [14]

    J., & Noraz, Q

    Cherry, G., Gudiksen, B., Finley, A. J., & Noraz, Q. 2025, Decomposing Wave Activity in the Solar Atmosphere: Shocks, Jets and Swirls in the Quiet Sun

    2025

  15. [15]

    Cheung, M. C. M. & Isobe, H. 2014, Living Reviews in Solar Physics, 11 De La Cruz Rodríguez, J. & Van Noort, M. 2017, Space Science Reviews, 210, 109 De Pontieu, B., Hansteen, V . H., Rouppe Van Der V oort, L., Van Noort, M., &

    2014

  16. [16]

    2007, The Astrophysical Journal, 655, 624

    Carlsson, M. 2007, The Astrophysical Journal, 655, 624

    2007

  17. [17]

    P., Landi, E., Mason, H

    Dere, K. P., Landi, E., Mason, H. E., Monsignori Fossi, B. C., & Young, P. R. 1997, Astronomy and Astrophysics Supplement Series, 125, 149 Díaz-Castillo, S. M., Fischer, C. E., Moreno-Insertis, F., et al. 2025, Emergence of Magnetic Flux Sheets in the Quiet Sun. I. Statistical Properties

    1997

  18. [18]

    K., Leenaarts, J., Carlsson, M., & Szydlarski, M

    Druett, M. K., Leenaarts, J., Carlsson, M., & Szydlarski, M. 2022, Astronomy & Astrophysics, 665, A6

    2022

  19. [19]

    V ., & De Moortel, I

    Enerhaug, E., Carlsson, M., Szydlarski, M., Gudiksen, B. V ., & De Moortel, I. 2025, Astronomy & Astrophysics, 701, A137

    2025

  20. [20]

    P., & Van Der Holst, B

    Fang, F., Manchester Iv, W., Abbett, W. P., & Van Der Holst, B. 2012, The As- trophysical Journal, 745, 37

    2012

  21. [21]

    J., Brun, A

    Finley, A. J., Brun, A. S., Carlsson, M., et al. 2022, Astronomy & Astrophysics, 665, A118 Fröhlich, C. & Lean, J. 2004, The Astronomy and Astrophysics Review, 12, 273

    2022

  22. [22]

    Gabriel, A. H. 1976, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences Goši´c, M., Hansteen, V . H., Dalda, A. S., Pontieu, B. D., & van der V oort, L. H. M. R. 2025, Bifrost Models of the Quiet Sun. I. Comparison with Solar Observations

    1976

  23. [23]

    V ., Carlsson, M., Hansteen, V

    Gudiksen, B. V ., Carlsson, M., Hansteen, V . H., et al. 2011, Astronomy & Astro- physics, 531, A154

    2011

  24. [24]

    D., & Carlsson, M

    Hansteen, V ., Guerreiro, N., Pontieu, B. D., & Carlsson, M. 2015, The Astro- physical Journal, 811, 106

    2015

  25. [25]

    2019, Astronomy & Astrophysics, 626, A33

    Hansteen, V ., Ortiz, A., Archontis, V ., et al. 2019, Astronomy & Astrophysics, 626, A33

    2019

  26. [26]

    H., Archontis, V ., Pereira, T

    Hansteen, V . H., Archontis, V ., Pereira, T. M. D., et al. 2017, The Astrophysical Journal, 839, 22

    2017

  27. [27]

    2006, The Astrophysical Journal, 647, L73

    Carlsson, M. 2006, The Astrophysical Journal, 647, L73

    2006

  28. [28]

    R., Millman, K

    Harris, C. R., Millman, K. J., Van Der Walt, S. J., et al. 2020, Nature, 585, 357

    2020

  29. [29]

    L., Sheeley, Jr., N

    Harvey, K. L., Sheeley, Jr., N. R., & Harvey, J. W. 1982, Solar Physics, 79, 149

    1982

  30. [30]

    R., & Rust, D

    Heyvaerts, J., Priest, E. R., & Rust, D. M. 1977, The Astrophysical Journal, 216, 123

    1977

  31. [31]

    P., Teriaca, L., et al

    Huang, Z., Chitta, L. P., Teriaca, L., et al. 2026, High-Resolution Observations of Small-Scale Activity in Coronal Hole Plumes

    2026

  32. [32]

    Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90

    2007

  33. [33]

    2005, Nature, 434, 478

    Isobe, H., Miyagoshi, T., Shibata, K., & Yokoyama, T. 2005, Nature, 434, 478

    2005

  34. [34]

    Isobe, H., Proctor, M. R. E., & Weiss, N. O. 2008, The Astrophysical Journal, 679, L57

    2008

  35. [35]

    B., Morton, R

    Jess, D. B., Morton, R. J., Verth, G., et al. 2015, Space Science Reviews, 190, 103

    2015

  36. [36]

    Klimchuk, J. A. 2015, Philosophical Transactions of the Royal Society A: Math- ematical, Physical and Engineering Sciences, 373, 20140256 Ku´ zma, B., Brchnelova, M., Perri, B., et al. 2023, The Astrophysical Journal, 942, 31

    2015

  37. [37]

    2025, Avalanches in Magnetohy- drodynamical Simulations

    Lamarre, H., Charbonneau, P., Noraz, Q., et al. 2025, Avalanches in Magnetohy- drodynamical Simulations

    2025

  38. [38]

    R., et al

    Landi, E., Del Zanna, G., Young, P. R., et al. 2006, The Astrophysical Journal Supplement Series, 162, 261 Martínez González, M. J. & Bellot Rubio, L. R. 2009, The Astrophysical Journal, 700, 1391 Martínez-Sykora, J., De La Cruz Rodríguez, J., Goši ´c, M., et al. 2023, The As- trophysical Journal Letters, 943, L14 Martínez-Sykora, J., De Pontieu, B., & Ha...

    2006

  39. [39]

    & Weibel-Mihalas, B

    Mihalas, D. & Weibel-Mihalas, B. 1984, Foundations of Radiation Hydrody- namics (New York: Oxford University Press)

    1984

  40. [40]

    1986, Astronomy and Astrophysics, 166, 291

    Moreno-Insertis, F. 1986, Astronomy and Astrophysics, 166, 291

    1986

  41. [41]

    J., & Leenaarts, J

    Morosin, R., De La Cruz Rodríguez, J., Díaz Baso, C. J., & Leenaarts, J. 2022, Astronomy & Astrophysics, 664, A8

    2022

  42. [42]

    2022, Frontiers in Astronomy and Space Sciences, 9, 981205 Nóbrega-Siverio, D., Cabello, I., Bose, S., et al

    Nindos, A., Patsourakos, S., Jafarzadeh, S., & Shimojo, M. 2022, Frontiers in Astronomy and Space Sciences, 9, 981205 Nóbrega-Siverio, D., Cabello, I., Bose, S., et al. 2024, Astronomy & Astro- physics, 686, A218 Nóbrega-Siverio, D., Martínez-Sykora, J., Moreno-Insertis, F., & Carlsson, M. 2020, Astronomy & Astrophysics, 638, A79

    2022

  43. [43]

    2026, Astronomy & Astrophysics, 705, A86

    Noraz, Q., Carlsson, M., & Aulanier, G. 2026, Astronomy & Astrophysics, 705, A86

    2026

  44. [44]

    R., Hansteen, V

    Ortiz, A., Bellot Rubio, L. R., Hansteen, V . H., De La Cruz Rodríguez, J., & Van Der V oort, L. R. 2014, The Astrophysical Journal, 781, 126

    2014

  45. [45]

    S., et al

    Parenti, S., Réville, V ., Brun, A. S., et al. 2022, The Astrophysical Journal, 929, 75

    2022

  46. [46]

    Parker, E. N. 1972, The Astrophysical Journal, 174, 499

    1972

  47. [47]

    Parker, E. N. 1983, The Astrophysical Journal, 264, 642

    1983

  48. [48]

    K., et al

    Przybylski, D., Cameron, R., Solanki, S. K., et al. 2025, Structure and Dynamics of the Internetwork Solar Chromosphere: Results of a Small-Scale Dynamo Simulation

    2025

  49. [49]

    K., et al

    Przybylski, D., Cameron, R., Solanki, S. K., et al. 2022, Astronomy & Astro- physics, 664, A91 Quintero Noda, C., Schlichenmaier, R., Bellot Rubio, L. R., et al. 2022, Astron- omy & Astrophysics, 666, A21

    2022

  50. [50]

    2017, The Astrophysical Journal, 834, 10

    Rempel, M. 2017, The Astrophysical Journal, 834, 10

    2017

  51. [51]

    Robinson, R. A. & Carlsson, M. 2023, Astronomy & Astrophysics, 677, A36

    2023

  52. [52]

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

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

    2022

  53. [53]

    Rutten, R. J. 2003, Radiative Transfer in Stellar Atmospheres

    2003

  54. [54]

    1979, Astronomy and Astrophysics, 74, 273

    Schmieder, B. 1979, Astronomy and Astrophysics, 74, 273

    1979

  55. [55]

    J., Title, A

    Schrijver, C. J., Title, A. M., Van Ballegooijen, A. A., Hagenaar, H. J., & Shine, R. A. 1997, The Astrophysical Journal, 487, 424

    1997

  56. [56]

    1906, Nachrichten von der Königlichen Gesellschaft der Wis- senschaften zu Göttingen

    Schwarzschild, K. 1906, Nachrichten von der Königlichen Gesellschaft der Wis- senschaften zu Göttingen. Math.-phys. Klasse, 195, 41

    1906

  57. [57]

    1948, The Astrophysical Journal, 107, 1

    Schwarzschild, M. 1948, The Astrophysical Journal, 107, 1

    1948

  58. [58]

    D., & Przybylski, D

    Shelyag, S., Khomenko, E., Vicente, A. D., & Przybylski, D. 2016, The Astro- physical Journal Letters, 819, L11

    2016

  59. [59]

    K., Hirzberger, J., Riethmüller, T

    Sinjan, J., Solanki, S. K., Hirzberger, J., Riethmüller, T. L., & Przybylski, D. 2024, Magnetograms Underestimate Even Unipolar Magnetic Flux Nearly Everywhere on the Solar Disk

    2024

  60. [60]

    J., Fedun, V ., Goossens, M., Silva, S

    Skirvin, S. J., Fedun, V ., Goossens, M., Silva, S. S. A., & Verth, G. 2024, The Astrophysical Journal, 975, 176 Sow Mondal, S., Klimchuk, J. A., & Sarkar, A. 2022, The Astrophysical Journal, 937, 71

    2024

  61. [61]

    Stangalini, M., Del Moro, D., Berrilli, F., & Jefferies, S. M. 2011, Astronomy & Astrophysics, 534, A65

    2011

  62. [62]

    2025, The Dynamics of Small-Scale Magnetic Fields Modulated by the Solar Cycle

    Stangalini, M., Verth, G., Fedun, V ., et al. 2025, The Dynamics of Small-Scale Magnetic Fields Modulated by the Solar Cycle

    2025

  63. [63]

    Sullivan, C. B. & Kaszynski, A. 2019, Journal of Open Source Software, 4, 1450

    2019

  64. [64]

    A., Kee, N

    Tarr, L. A., Kee, N. D., Linton, M. G., Schuck, P. W., & Leake, J. E. 2024, The Astrophysical Journal Supplement Series, 270, 30 Udnæs, E. R. & Pereira, T. M. D. 2025, Characteristics of Acoustic-Wave Heat- ing in Simulations of the Quiet Sun Chromosphere Van Der Holst, B., Sokolov, I. V ., Meng, X., et al. 2014, The Astrophysical Jour- nal, 782, 81

    2024

  65. [65]

    2026, MHD Modelling of Open Flux Evo- lution around Solar Maximum by Coronal Model COCONUT

    Wang, H., Poedts, S., Lani, A., et al. 2026, MHD Modelling of Open Flux Evo- lution around Solar Maximum by Coronal Model COCONUT

    2026

  66. [66]

    R., & Nash, A

    Wang, Y .-M., Sheeley, N. R., & Nash, A. G. 1990, Nature, 347, 439

    1990

  67. [67]

    2025, Millimeter-Wavelength Obser- vations of the Active Sun: Unveiling the Origins of Space Weather

    Wedemeyer, S., Poedts, S., Gunár, S., et al. 2025, Millimeter-Wavelength Obser- vations of the Active Sun: Unveiling the Origins of Space Weather

    2025

  68. [68]

    Withbroe, G. L. & Noyes, R. W. 1977, Annual Review of Astronomy and Astro- physics, 15, 363

    1977

  69. [69]

    & Shibata, K

    Yokoyama, T. & Shibata, K. 1995, 375

    1995

  70. [70]

    1987, Annual Review of Astronomy and Astrophysics, 25, 83 Article number, page 13 of 13

    Zwaan, C. 1987, Annual Review of Astronomy and Astrophysics, 25, 83 Article number, page 13 of 13

    1987