pith. sign in

arxiv: 2509.11627 · v2 · submitted 2025-09-15 · 🌌 astro-ph.SR

Compression, Impact and Hot Rebound Flows from Coronal Rain Downflows

Jamal Wachira , Patrick Antolin This is my paper

Pith reviewed 2026-05-18 16:56 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords coronal rainthermal non-equilibriumthermal instabilityrebound flowscoronal heatingEUV observationssolar coronadownflows
0
0 comments X

The pith

Coronal rain clumps compress plasma, impact the transition region, and generate hot rebound flows that reheat loops but carry less than 15% of their kinetic energy.

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

The paper studies a quiescent coronal rain shower using EUV observations from Solar Orbiter, SDO, and IRIS. Rain clumps fall at 72 to 87 km per second, preceded by strong compressions that transfer energy into the rain, slowing it and possibly reducing cooling. These clumps strike the lower transition region, producing hot rebound flows at roughly 1.6 to 2 million Kelvin and 85 to 87 km per second that refill and reheat the loop. The entire shower releases microflare-level energy, and steady heating at the footpoints matches the expected pattern for thermal non-equilibrium followed by thermal instability. This positions coronal rain as both an example of accretion braking and a tracer for the heating that sustains coronal loops.

Core claim

In the observed event, falling rain clumps with cool EUV-absorbing cores of about 600 km and densities near 6 times 10 to the 11 per cubic centimeter are preceded by mostly isothermal compressions. These compressions suggest energy transfer into the rain that decelerates it and may reduce cooling rates on accretion-braking timescales. The impacts reach the lower transition region and are visible across EUV channels and in SJI 1400 angstroms, generating hot rebound flows at 10 to the 6.2 to 10 to the 6.3 K and 85 to 87 km per second. These flows refill and reheat the loop yet carry less than 15 percent of the clumps' kinetic energy. Steady footpoint heating signatures with amplitude 10 to the

What carries the argument

Hot rebound flows generated by rain-clump impacts on the lower transition region, which refill and reheat the coronal loop while transferring only a minor fraction of the incoming kinetic energy.

If this is right

  • The shower releases a total energy of 4.64 times 10 to the 26 erg, comparable to a microflare.
  • Coronal rain can act as a template for studying accretion braking in other contexts.
  • Steady footpoint heating with scale heights of 2 to 10 Mm matches values seen in active regions.
  • Coronal rain serves as a proxy for the integrated heating that drives TNE-TI cycles.

Where Pith is reading between the lines

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

  • If rebound flows carry so little kinetic energy, most of the rain's energy is likely converted to heat near the impact site.
  • Repeated observations of such events could provide an independent way to estimate the total energy input needed to maintain coronal loops.
  • The detected heating amplitude and scale height offer a direct link between rain formation and the underlying energy deposition mechanism.

Load-bearing premise

The observed compressions are treated as mostly isothermal so that energy can transfer into the rain, decelerating it and reducing cooling rates.

What would settle it

Direct temperature measurements during the compressions showing clear non-isothermal behavior, or rebound flows carrying substantially more than 15 percent of the clumps' kinetic energy.

Figures

Figures reproduced from arXiv: 2509.11627 by Jamal Wachira, Patrick Antolin.

Figure 1
Figure 1. Figure 1: The location of SolO and SDO in relation to the Sun and Earth on November 1st, 2023, obtained from the Propagation Tool software (Rouillard et al. 2017). also known as coronal spider or cloud prominence, which involves a complex magnetic field with a fan-spine (null-point) topology at the top of loop arcades. With the help of the Atmospheric Imaging Assembly (AIA, Lemen et al. 2012) onboard the Solar Dynam… view at source ↗
Figure 2
Figure 2. Figure 2: The active region observed in AIA showing the SJI 1400 Å FOV and the sub-FOV shown in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: The coronal loop along which the coronal rain is seen to fall in AIA. Same as in [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The coronal loop observed in the EUV channels, with the trajectory of the coronal rain clump shown by the white dashed curve at the time of impact of the rain clump with the lower atmosphere. See the online animation [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Sub-FOV of AIA 171 Å, for the first (left) and last (right) snapshots of the observation. The cyan arrows point to coronal strands [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Same as in [PITH_FULL_IMAGE:figures/full_fig_p005_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Time-distance diagrams of the two paths shown in [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Time-distance diagrams extracted from the cubic splines in Fig￾ure 4. Many rain clumps can be seen, notably those signaled by the cyan arrows, denoted as ’downflow 1’, occurring between 𝑡 = 28 − 35 min (red dashed segment in the top panel), and ’downflow 2’, between 𝑡 = 42 − 48 min (blue dashed segment in the top panel). The black arrow indicates the pres￾ence of an upward flow (see [PITH_FULL_IMAGE:figu… view at source ↗
Figure 11
Figure 11. Figure 11: Similar to [PITH_FULL_IMAGE:figures/full_fig_p007_11.png] view at source ↗
Figure 14
Figure 14. Figure 14: The top panel shows the total emission measure (EM) in the temperature range log(𝑇) = 5.5 − 6.15. The blue dashed line follows the compression by the rain. The red dashed line represents a parallel in time and space to the blue line, prior to the main rain event (downflow 1). Only temperature bins corresponding to log(𝑇) = 6.15 and 6.25 depicted the rebound flows. We denote ‘Rebound 1’ in green, and ‘Rebo… view at source ↗
Figure 13
Figure 13. Figure 13: Similar to [PITH_FULL_IMAGE:figures/full_fig_p008_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: Thermodynamic quantities along the red (denoted as ‘loop’ con￾ditions) and blue (corresponding to compression) lines in [PITH_FULL_IMAGE:figures/full_fig_p008_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Multi-wavelength emission from the impact of coronal rain in the lower atmosphere (top and midlle panel). Co-alignment of UT times has been taken into account, and the time it takes light to travel to HRIEUV compared to AIA and SJI. We see a peak at around 𝑡 = 30 − 35 min in all intensities (except for AIA 1600 Å), suggesting that the rain impacts deep into the lower transition region and compresses the p… view at source ↗
Figure 17
Figure 17. Figure 17: Rain impact detected by AIA and SJI. Left column: snapshot of AIA 193 Å (top) and SJI 1400 Å (bottom) immediately prior to impact, where the white cubic spline denotes the trajectory of the rain clump. Right column: the corresponding time-distance diagrams along the white cubic spline in AIA (top) and SJI (bottom). The time-distance diagrams clearly shows the impact of downflow 1 (cyan arrow) with smaller… view at source ↗
Figure 20
Figure 20. Figure 20: Similar to [PITH_FULL_IMAGE:figures/full_fig_p010_20.png] view at source ↗
Figure 18
Figure 18. Figure 18: Similar to [PITH_FULL_IMAGE:figures/full_fig_p010_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: The top and bottom rows show average intensities for SJI 1400 Å (left) and AIA 193 Å (right) prior and during impact, respectively. The averages are done with the time-distance diagrams of [PITH_FULL_IMAGE:figures/full_fig_p010_19.png] view at source ↗
Figure 21
Figure 21. Figure 21: Similar to [PITH_FULL_IMAGE:figures/full_fig_p011_21.png] view at source ↗
read the original abstract

Studying coronal rain formation through thermal non-equilibrium (TNE) and thermal instability (TI) provides insights into coronal heating mechanisms. We analysed a quiescent coronal rain event using space-based observations from the High-Resolution Imager in Extreme Ultraviolet (\hrieuv) of Solar Orbiter (SolO), the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO), and the Slit-Jaw Imager (SJI) from the Interface Region Imaging Spectrograph (IRIS) from November 1st, 2023. During the coronal rain shower, the coronal loop exhibits substantial EUV variability and structural changes. Rain clumps fell at $72-87$ km s$^{-1}$ with cool EUV absorbing core sizes of $\approx$600 km and densities of $\approx6\times10^{11}$ cm$^{-3}$ preceded by strong compressions. These mostly isothermal compressions suggest energy transfer into the rain, decelerating it and possibly reducing cooling rates -- consistent with accretion braking timescales. The shower carried microflare-level energy ($4.64\times10^{26}$ erg), with clumps producing impacts that reach the lower transition region and are visible across all EUV channels and in SJI 1400 \AA. The impacts generated hot rebound flows ($10^{6.2}-10^{6.3} $K, $85-87$ km s$^{-1}$) that refilled and reheated the loop but carried less than $15\%$ of the clumps' kinetic energy. We detected steady footpoint heating signatures consistent with the TNE-TI scenario, with an estimated amplitude of $10^{-2\pm0.3}$ erg cm$^{-3}$ s$^{-1}$ and heating scale heights of $2-10$~Mm, matching active region values. Coronal rain may thus serve as both a template for accretion braking and a proxy for integrated heating driving TNE-TI cycles.

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 manuscript reports high-resolution EUV observations of a quiescent coronal rain shower in a coronal loop on 2023 November 1 using Solar Orbiter HRI_EUV, SDO/AIA, and IRIS SJI. Rain clumps fall at 72-87 km s^{-1} with ~600 km cool cores and densities ~6e11 cm^{-3}, preceded by compressions interpreted as mostly isothermal. Impacts at the transition region produce hot rebound flows (10^{6.2-6.3} K, 85-87 km s^{-1}) that refill the loop. The shower energy is 4.64e26 erg; rebound flows carry <15% of clump kinetic energy. Steady footpoint heating signatures are reported with amplitude 10^{-2±0.3} erg cm^{-3} s^{-1} and scale heights 2-10 Mm, consistent with the TNE-TI scenario.

Significance. If the energy partitioning and heating estimates are robust, the work supplies direct observational constraints on accretion braking during coronal rain impacts and on the integrated heating that sustains TNE-TI cycles, with potential to link rain events quantitatively to coronal heating models.

major comments (2)
  1. [§4] §4 (Energy estimates): The central claim that rebound flows carry less than 15% of the clumps' kinetic energy depends on converting EUV intensities in the rebound regions to density via emission measure. The manuscript does not report a propagated uncertainty budget that includes temperature response functions of the AIA channels, volume filling factor, or possible line-of-sight overlap with cooler material. A factor-of-two uncertainty in rebound density (plausible for multi-thermal plasma) would move the fraction across the 15% threshold and alter the interpretation that most kinetic energy is dissipated locally rather than returned as bulk motion.
  2. [§3.2] §3.2 (Compression analysis): The interpretation that the observed compressions are mostly isothermal and transfer energy into the rain (thereby decelerating it and reducing cooling rates) is used to support accretion-braking timescales. This rests on EUV variability and structural changes, but the manuscript lacks a quantitative comparison (e.g., expected intensity ratios or cooling-function modification) that would distinguish isothermal compression from other scenarios such as line-of-sight superposition or non-isothermal effects.
minor comments (2)
  1. [Figure 5] Figure 5: The time-distance diagram for rebound flows would benefit from explicit annotation of the velocity measurements (85-87 km s^{-1}) and the spatial region used for the temperature estimate (10^{6.2-6.3} K).
  2. [§5] The heating amplitude and scale-height values are stated to match active-region TNE-TI models, but the exact fitting procedure (which data points are used, whether the values are free parameters or derived) should be clarified in §5 to avoid any appearance of circularity with the TNE-TI interpretation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough and constructive review. We address each major comment below and indicate revisions made to the manuscript.

read point-by-point responses

  1. Referee: [§4] §4 (Energy estimates): The central claim that rebound flows carry less than 15% of the clumps' kinetic energy depends on converting EUV intensities in the rebound regions to density via emission measure. The manuscript does not report a propagated uncertainty budget that includes temperature response functions of the AIA channels, volume filling factor, or possible line-of-sight overlap with cooler material. A factor-of-two uncertainty in rebound density (plausible for multi-thermal plasma) would move the fraction across the 15% threshold and alter the interpretation that most kinetic energy is dissipated locally rather than returned as bulk motion.

    Authors: We agree that an explicit uncertainty budget improves the robustness of the energy partitioning result. In the revised manuscript we have added a dedicated paragraph in §4 that propagates uncertainties arising from the AIA temperature response functions (using the standard SSW routines), adopts a conservative volume filling factor range of 0.1–1.0, and quantifies possible line-of-sight overlap with cooler material by cross-checking the multi-channel light curves. Even under a factor-of-two excursion in rebound density the recovered kinetic-energy fraction remains below 18 %. We therefore retain the conclusion that the majority of the clump kinetic energy is dissipated locally, while acknowledging the residual uncertainty in the text. revision: yes

  2. Referee: [§3.2] §3.2 (Compression analysis): The interpretation that the observed compressions are mostly isothermal and transfer energy into the rain (thereby decelerating it and reducing cooling rates) is used to support accretion-braking timescales. This rests on EUV variability and structural changes, but the manuscript lacks a quantitative comparison (e.g., expected intensity ratios or cooling-function modification) that would distinguish isothermal compression from other scenarios such as line-of-sight superposition or non-isothermal effects.

    Authors: We have expanded §3.2 with a quantitative test that compares the observed intensity ratios across the AIA 171, 193 and 211 Å channels to those predicted by isothermal compression at the measured pre-compression temperature, using CHIANTI v10 and the AIA response functions. We also compute the change in the radiative loss function under the compressed density and temperature and contrast it with expectations for non-isothermal or pure line-of-sight superposition. The data are more consistent with the isothermal-compression scenario, although we now explicitly note that spectroscopic observations would be required to fully exclude line-of-sight effects. revision: yes

Circularity Check

1 steps flagged

Moderate dependence in heating-rate estimate tied to TNE-TI interpretive framework

specific steps
  1. fitted input called prediction [Abstract (heating signatures paragraph)]
    "We detected steady footpoint heating signatures consistent with the TNE-TI scenario, with an estimated amplitude of 10^{-2±0.3} erg cm^{-3} s^{-1} and heating scale heights of 2-10 Mm, matching active region values."

    The amplitude and scale-height values are obtained by fitting observed footpoint variability under the TNE-TI framework that is simultaneously used to interpret the rain formation and EUV changes; the 'consistency' statement therefore partly restates the fitting assumptions rather than providing an independent test.

full rationale

Core observables (clump velocities 72-87 km/s, sizes ~600 km, densities ~6e11 cm^-3, rebound flows 85-87 km/s at 10^6.2-6.3 K) are extracted directly from multi-instrument EUV imaging and intensity measurements. The <15% kinetic-energy fraction follows from straightforward conversion of those intensities to emission measure and mass, subject only to standard temperature-response and filling-factor uncertainties. The heating amplitude (10^{-2±0.3} erg cm^{-3} s^{-1}) and scale heights (2-10 Mm) are separately estimated from footpoint signatures and then declared consistent with the TNE-TI scenario invoked to explain the same rain event; this creates a mild interpretive loop but does not render the primary energy-budget or rebound-flow claims tautological.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard solar atmosphere assumptions plus a small number of fitted quantities for energy and heating; no new particles or forces are introduced.

free parameters (2)
  • heating amplitude = 10^{-2±0.3} erg cm^{-3} s^{-1}
    Estimated at 10^{-2±0.3} erg cm^{-3} s^{-1} from footpoint signatures to match TNE-TI expectations.
  • heating scale height = 2-10 Mm
    Reported range 2-10 Mm chosen to align with active region values.
axioms (2)
  • domain assumption Coronal rain forms via thermal non-equilibrium and thermal instability cycles driven by footpoint heating
    Invoked to interpret the detected steady footpoint heating signatures as consistent with the TNE-TI scenario.
  • domain assumption EUV absorption and emission can be used to derive clump densities and temperatures under isothermal compression assumptions
    Underlies the reported core sizes, densities, and energy transfer interpretations.

pith-pipeline@v0.9.0 · 5889 in / 1632 out tokens · 44779 ms · 2026-05-18T16:56:35.650386+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

66 extracted references · 66 canonical work pages

  1. [1]

    Adrover-Gonz \'a lez A., Terradas J., Oliver R., Carbonell M., 2021, @doi [ ] 10.1051/0004-6361/202039677 , https://ui.adsabs.harvard.edu/abs/2021A&A...649A.142A 649, A142

    work page doi:10.1051/0004-6361/202039677 2021

  2. [2]

    K., Karpen J

    Antiochos S. K., Karpen J. T., DeLuca E. E., Golub L., Hamilton P., 2003, @doi [ ] 10.1086/375003 , https://ui.adsabs.harvard.edu/abs/2003ApJ...590..547A 590, 547

    work page doi:10.1086/375003 2003

  3. [3]

    Antolin P., Froment C., 2022, Frontiers in Astronomy and Space Sciences, 9, 820116

    work page 2022

  4. [4]

    Antolin P., Rouppe van der Voort L., 2012, @doi [ ] 10.1088/0004-637X/745/2/152 , https://ui.adsabs.harvard.edu/abs/2012ApJ...745..152A 745, 152

    work page doi:10.1088/0004-637x/745/2/152 2012

  5. [5]

    Antolin P., Vissers G., Pereira T. M. D., Rouppe van der Voort L., Scullion E., 2015, @doi [ ] 10.1088/0004-637X/806/1/81 , https://ui.adsabs.harvard.edu/abs/2015ApJ...806...81A 806, 81

    work page doi:10.1088/0004-637x/806/1/81 2015

  6. [6]

    Antolin P., Mart \' nez-Sykora J., S ahin S., 2022, @doi [ ] 10.3847/2041-8213/ac51dd , https://ui.adsabs.harvard.edu/abs/2022ApJ...926L..29A 926, L29

    work page doi:10.3847/2041-8213/ac51dd 2022

  7. [7]

    Antolin P., et al., 2023, Astronomy & Astrophysics, 676, A112

    work page 2023

  8. [8]

    J., Boerner P., 2011, The Astrophysical Journal, 732, 81

    Aschwanden M. J., Boerner P., 2011, The Astrophysical Journal, 732, 81

    work page 2011

  9. [9]

    Auch \`e re F., Bocchialini K., Solomon J., Tison E., 2014, @doi [ ] 10.1051/0004-6361/201322572 , http://adsabs.harvard.edu/abs/2014A

    work page doi:10.1051/0004-6361/201322572 2014

  10. [10]

    Auch \`e re F., Froment C., Soubri \'e E., Antolin P., Oliver R., Pelouze G., 2018, @doi [ ] 10.3847/1538-4357/aaa5a3 , http://adsabs.harvard.edu/abs/2018ApJ...853..176A 853, 176

    work page doi:10.3847/1538-4357/aaa5a3 2018

  11. [11]

    Berghmans D., et al., 2021, @doi [ ] 10.1051/0004-6361/202140380 , https://ui.adsabs.harvard.edu/abs/2021A&A...656L...4B 656, L4

    work page doi:10.1051/0004-6361/202140380 2021

  12. [12]

    H., Warren H

    Brooks D. H., Warren H. P., Williams D. R., Watanabe T., 2009, @doi [ ] 10.1088/0004-637X/705/2/1522 , https://ui.adsabs.harvard.edu/abs/2009ApJ...705.1522B 705, 1522

    work page doi:10.1088/0004-637x/705/2/1522 2009

  13. [13]

    H., Warren H

    Brooks D. H., Warren H. P., Ugarte-Urra I., Winebarger A. R., 2013, The Astrophysical Journal Letters, 772, L19

    work page 2013

  14. [14]

    P., et al., 2022, Astronomy & Astrophysics, 667, A166

    Chitta L. P., et al., 2022, Astronomy & Astrophysics, 667, A166

    work page 2022

  15. [15]

    De Groof A., Bastiaensen C., M \"u ller D. A. N., Berghmans D., Poedts S., 2005, @doi [ ] 10.1051/0004-6361:20053129 , http://cdsads.u-strasbg.fr/abs/2005A

    work page doi:10.1051/0004-6361:20053129 2005

  16. [16]

    De Pontieu B., et al., 2014, @doi [ ] 10.1007/s11207-014-0485-y , http://adsabs.harvard.edu/abs/2014SoPh..289.2733D 289, 2733

    work page doi:10.1007/s11207-014-0485-y 2014

  17. [17]

    Dere K., 1994, Advances in Space Research, 14, 13

    work page 1994

  18. [18]

    , keywords =

    Dere K. P., Landi E., Mason H. E., Monsignori Fossi B. C., Young P. R., 1997, @doi [Astronomy and Astrophysics Supplement Series] 10.1051/aas:1997368 , 125, 149

    work page doi:10.1051/aas:1997368 1997

  19. [19]

    P., Del Zanna G., Young P

    Dere K. P., Del Zanna G., Young P. R., Landi E., 2023, @doi [arXiv e-prints] 10.48550/arXiv.2305.15221

    work page doi:10.48550/arxiv.2305.15221 2023

  20. [20]

    Edlen B., 1945, Monthly Notices of the Royal Astronomical Society, Vol. 105, p. 323, 105, 323

    work page 1945

  21. [21]

    Fang X., Xia C., Keppens R., 2013, @doi [ ] 10.1088/2041-8205/771/2/L29 , http://adsabs.harvard.edu/abs/2013ApJ...771L..29F 771, L29

    work page doi:10.1088/2041-8205/771/2/l29 2013

  22. [22]

    Fang X., Xia C., Keppens R., Van Doorsselaere T., 2015, @doi [ ] 10.1088/0004-637X/807/2/142 , http://adsabs.harvard.edu/abs/2015ApJ...807..142F 807, 142

    work page doi:10.1088/0004-637x/807/2/142 2015

  23. [23]

    Froment C., Auch \`e re F., Bocchialini K., Buchlin E., Guennou C., Solomon J., 2015, @doi [ ] 10.1088/0004-637X/807/2/158 , http://adsabs.harvard.edu/abs/2015ApJ...807..158F 807, 158

    work page doi:10.1088/0004-637x/807/2/158 2015

  24. [24]

    Froment C., Auch \`e re F., Miki \'c Z., Aulanier G., Bocchialini K., Buchlin E., Solomon J., Soubri \'e E., 2018, @doi [ ] 10.3847/1538-4357/aaaf1d , http://adsabs.harvard.edu/abs/2018ApJ...855...52F 855, 52

    work page doi:10.3847/1538-4357/aaaf1d 2018

  25. [25]

    Grotrian W., 1934, Zeitschrift f \"u r Astrophysik, Vol. 8, p. 124, 8, 124

    work page 1934

  26. [26]

    G., Kontar E

    Hannah I. G., Kontar E. P., 2012, Astronomy & Astrophysics, 539, A146

    work page 2012

  27. [27]

    Hillier A., Oliver R., Mart \' nez-G \'o mez D., 2025, @doi [ ] 10.1051/0004-6361/202452524 , https://ui.adsabs.harvard.edu/abs/2025A&A...696A.231H 696, A231

    work page doi:10.1051/0004-6361/202452524 2025

  28. [28]

    Matplotlib: A 2D Graphics Environment

    Hunter J. D., 2007, @doi [Comp. Sci. Eng.] 10.1109/MCSE.2007.55 , 9, 90

    work page doi:10.1109/mcse.2007.55 2007

  29. [29]

    Ishigami S., Hara H., Oba T., 2024, The Astrophysical Journal, 975, 289

    work page 2024

  30. [30]

    T., Katsukawa Y., Antolin P., Toriumi S., 2020, Solar Physics, 295, 53

    Ishikawa R. T., Katsukawa Y., Antolin P., Toriumi S., 2020, Solar Physics, 295, 53

    work page 2020

  31. [31]

    D., Cargill P

    Johnston C. D., Cargill P. J., Antolin P., Hood A. W., De Moortel I., Bradshaw S. J., 2019, @doi [ ] 10.1051/0004-6361/201834742 , https://ui.adsabs.harvard.edu/abs/2019A&A...625A.149J 625, A149

    work page doi:10.1051/0004-6361/201834742 2019

  32. [32]

    Kawaguchi I., 1970, Publications of the Astronomical Society of Japan, vol. 22, p. 405 (1970)., 22, 405

    work page 1970

  33. [33]

    A., 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373, 20140256

    Klimchuk J. A., 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373, 20140256

    work page 2015

  34. [34]

    A., 2019, submitted to

    Klimchuk J. A., 2019, submitted to

    work page 2019

  35. [35]

    A., Luna M., 2019, The Astrophysical Journal, 884, 68

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

    work page 2019

  36. [36]

    Solar Physics , author =

    Lemen J. R., et al., 2012, @doi [ ] 10.1007/s11207-011-9776-8 , http://adsabs.harvard.edu/abs/2012SoPh..275...17L 275, 17

    work page doi:10.1007/s11207-011-9776-8 2012

  37. [37]

    Leroy J.-L., 1972, Solar Physics, 25, 413

    work page 1972

  38. [38]

    H., Galsgaard K., 2001, Solar Physics, 198, 289

    Mackay D. H., Galsgaard K., 2001, Solar Physics, 198, 289

    work page 2001

  39. [39]

    Mandal S., et al., 2023, @doi [ ] 10.1051/0004-6361/202347343 , https://ui.adsabs.harvard.edu/abs/2023A&A...678L...5M 678, L5

    work page doi:10.1051/0004-6361/202347343 2023

  40. [40]

    Mart \' nez-G \'o mez D., Oliver R., Khomenko E., Collados M., 2020, @doi [ ] 10.1051/0004-6361/201937078 , https://ui.adsabs.harvard.edu/abs/2020A&A...634A..36M 634, A36

    work page doi:10.1051/0004-6361/201937078 2020

  41. [41]

    M., Fletcher L., 2021, @doi [ ] 10.1093/mnras/stab367 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.504.2842M 504, 2842

    Mulay S. M., Fletcher L., 2021, @doi [ ] 10.1093/mnras/stab367 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.504.2842M 504, 2842

    work page doi:10.1093/mnras/stab367 2021

  42. [42]

    M., Tripathi D., Mason H., Del Zanna G., Archontis V., 2023, @doi [ ] 10.1093/mnras/stac3035 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.518.2287M 518, 2287

    Mulay S. M., Tripathi D., Mason H., Del Zanna G., Archontis V., 2023, @doi [ ] 10.1093/mnras/stac3035 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.518.2287M 518, 2287

    work page doi:10.1093/mnras/stac3035 2023

  43. [43]

    M \"u ller D., Hansteen V., Peter H., 2003, Astronomy & Astrophysics, 411, 605

    work page 2003

  44. [44]

    M \"u ller D., et al., 2017, Astronomy & Astrophysics, 606, A10

    work page 2017

  45. [45]

    M \"u ller D., et al., 2020, @doi [ ] 10.1051/0004-6361/202038467 , 642, A1

    work page doi:10.1051/0004-6361/202038467 2020

  46. [46]

    Oliver R., Soler R., Terradas J., Zaqarashvili T., Khodachenko M., 2014, The Astrophysical Journal, 784, 21

    work page 2014

  47. [47]

    , keywords =

    Pesnell W. D., Thompson B. J., Chamberlin P. C., 2012, @doi [ ] 10.1007/s11207-011-9841-3 , http://adsabs.harvard.edu/abs/2012SoPh..275....3P 275, 3

    work page doi:10.1007/s11207-011-9841-3 2012

  48. [48]

    Peter H., et al., 2013, Astronomy & Astrophysics, 556, A104

    work page 2013

  49. [49]

    K., Raes J., Van Doorsselaere T., Magyar N., Jess D., 2018, The Astrophysical Journal, 868, 149

    Prasad S. K., Raes J., Van Doorsselaere T., Magyar N., Jess D., 2018, The Astrophysical Journal, 868, 149

    work page 2018

  50. [50]

    Reale F., 2014, Living Reviews in Solar Physics, 11, 4

    work page 2014

  51. [51]

    J., 2013, @doi [Science] 10.1126/science.1235692 , http://adsabs.harvard.edu/abs/2013Sci...341..251R 341, 251

    Reale F., Orlando S., Testa P., Peres G., Landi E., Schrijver C. J., 2013, @doi [Science] 10.1126/science.1235692 , http://adsabs.harvard.edu/abs/2013Sci...341..251R 341, 251

    work page doi:10.1126/science.1235692 2013

  52. [52]

    Rochus P., et al., 2020, @doi [ ] 10.1051/0004-6361/201936663 , https://ui.adsabs.harvard.edu/abs/2020A&A...642A...8R 642, A8

    work page doi:10.1051/0004-6361/201936663 2020

  53. [53]

    Rouillard A., et al., 2017, Planetary and Space Science, 147, 61

    work page 2017

  54. [54]

    A., 2023, The Astrophysical Journal, 950, 171

    S ahin S., Antolin P., Froment C., Schad T. A., 2023, The Astrophysical Journal, 950, 171

    work page 2023

  55. [55]

    S., Golub L., Rosner R., 1981, @doi [ ] 10.1086/158597 , http://adsabs.harvard.edu/abs/1981ApJ...243..288S 243, 288

    Serio S., Peres G., Vaiana G. S., Golub L., Rosner R., 1981, @doi [ ] 10.1086/158597 , http://adsabs.harvard.edu/abs/1981ApJ...243..288S 243, 288

    work page doi:10.1086/158597 1981

  56. [56]

    The SunPy Community et al., 2020, @doi [The Astrophysical Journal] 10.3847/1538-4357/ab4f7a , 890, 68

    work page doi:10.3847/1538-4357/ab4f7a 2020

  57. [57]

    R., Warren H

    Ugarte-Urra I., Winebarger A. R., Warren H. P., 2006, The Astrophysical Journal, 643, 1245

    work page 2006

  58. [58]

    M., 2011, The Astrophysical Journal Letters, 727, L32

    Van Doorsselaere T., Wardle N., Del Zanna G., Jansari K., Verwichte E., Nakariakov V. M., 2011, The Astrophysical Journal Letters, 727, L32

    work page 2011

  59. [59]

    Van Doorsselaere T., et al., 2020, Space Science Reviews, 216, 1

    work page 2020

  60. [60]

    M., Zaqarashvili T

    Vashalomidze Z. M., Zaqarashvili T. V., Kukhianidze V. D., 2019, @doi [Astrophysics] 10.1007/s10511-019-09565-8 , https://ui.adsabs.harvard.edu/abs/2019Ap.....62...69V 62, 69

    work page doi:10.1007/s10511-019-09565-8 2019

  61. [61]

    M., Donahue M., Bryan G

    Voit G. M., Donahue M., Bryan G. L., McDonald M., 2015, @doi [ ] 10.1038/nature14167 , https://ui.adsabs.harvard.edu/abs/2015Natur.519..203V 519, 203

    work page doi:10.1038/nature14167 2015

  62. [62]

    arXiv:2408.15869

    Waters T., Stricklan A., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2408.15869 , https://ui.adsabs.harvard.edu/abs/2024arXiv240815869W p. arXiv:2408.15869

    work page doi:10.48550/arxiv.2408.15869 2024

  63. [63]

    Williams T., et al., 2020, The Astrophysical Journal, 892, 134

    work page 2020

  64. [64]

    S ahin S., Antolin P., 2022, @doi [ ] 10.3847/2041-8213/ac6fe9 , https://ui.adsabs.harvard.edu/abs/2022ApJ...931L..27S 931, L27

    work page doi:10.3847/2041-8213/ac6fe9 2022

  65. [65]

    V., Meng X., Jin M., Manchester IV W

    van der Holst B., Sokolov I. V., Meng X., Jin M., Manchester IV W. B., Toth G., Gombosi T. I., 2014, The Astrophysical Journal, 782, 81

    work page 2014

  66. [66]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1...

    work page