Pith. sign in

REVIEW 2 major objections 5 minor 50 references

Modelling Mg II During Solar Flares. I. Partial Frequency Redistribution, Opacity, and Coronal Irradiation

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read Even in the strongest solar flare models, the Mg II h & k lines must be computed with partial frequency redistribution (PRD), not complete redistribution (CRD), because CRD overestimates wing intensities by up to ~1000% and introduces…

desk verdict Systematic RH sensitivity study that settles PRD requirements for flare Mg II, with an acknowledged SE caveat that makes the irradiation numbers provisional. read the letter →

arxiv 1908.05329 v2 pith:NBQ5OPO3 submitted 2019-08-14 astro-ph.SR

G. S. Kerr , Joel C. Allred , Mats Carlsson This is my paper · ORCID
classification astro-ph.SR
keywords solarflaresMgIIh&klinespartialfrequencyredistributioncompleteradiativetransferchromosphereIRISnumericalmethods
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 establishes a baseline recipe for forward-modelling the Mg II h & k and subordinate lines in solar flares, then tests what happens when pieces of physics are added or removed. Its central result is that partial frequency redistribution (PRD) remains essential even in the strongest flare simulation, where densities are high enough that one might expect complete redistribution (CRD) to suffice. The CRD solution overestimates wing intensities by roughly 200% in the strongest case and up to 1000% in the weakest, and it produces spurious wing features that could be mistaken for plasma motions. The same experiments show that a fast hybrid angle-dependent PRD approximation changes intensities by only 15–20% relative to the full treatment, and that lower-transition-region irradiation can alter line intensities by up to ~30% early in a strong flare. A sympathetic reader should care because much published flare Mg II modelling uses CRD or small atoms; these results say those short-cuts change the answer in ways that affect interpretation of IRIS observations.

What carries the argument

The load-bearing mechanism is partial frequency redistribution (PRD): when a line forms in a low-density, strongly scattering medium, an absorbed wing photon is re-emitted coherently at nearly the same frequency rather than being redistributed across the whole line profile, so the source function depends on frequency and wing photons escape more easily. The paper contrasts PRD with complete frequency redistribution (CRD), where wing photons are re-emitted anywhere in the line, trapping them in the optically thick core. The quantitative comparisons are made through emergent intensities and contribution functions computed with the RH radiation-transfer code, using the hybrid angle-dependent PRD approximation (H-PRD) as the baseline and full angle-dependent PRD (AD-PRD) as the reference in high-velocity snapshots. The 10-level-plus-continuum Mg II model atom and the fixed non-equilibrium hydrogen populations supplied from the flare simulations support the comparison.

What would settle it

Recompute the F9, F10, and F11 snapshots with time-dependent (non-equilibrium) Mg II populations instead of statistical equilibrium and compare the CRD and PRD emergent profiles; if the wing-intensity difference drops below a few percent, or the PRD-only blue-wing feature disappears, the claim that PRD is required during flares fails. As an observational check, search a sample of IRIS flare-ribbon spectra for the predicted PRD-only blue-wing bump at the corresponding phase; if the feature is absent while red-wing condensation bumps are common, the redistribution mechanism would need revision.

Watch

Extended reading notes

Core claim

The paper claims that, for the Mg II resonance lines observed by IRIS during flares, the line source function is frequency-dependent and coherent scattering in the line wings persists even at electron densities near $10^{13}$ cm$^{-3}$ reached in the strongest (F11) simulation. In the CRD approximation, every absorbed photon is re-emitted at a frequency drawn from the absorption profile, so wing photons are redistributed into the opaque core; in PRD, a wing photon is re-emitted near its original frequency and can escape. The consequence is that CRD overestimates the inner-wing intensity by up to about 200% in the F11 case and up to 1000% in the F9 case, and it fails to reproduce a blue-wing emission feature that is purely a redistribution effect, not a Doppler shift from an upflow. The same conclusion holds for the subordinate 2791 Å line, where CRD differs by tens of percent. The paper also claims that the fast 'hybrid' angle-dependent PRD scheme reproduces the full angle-dependent solution to within 15–20% in localized wavelength regions while being roughly 400 times faster, and that a 10-level-plus-continuum Mg II model atom is required because a 3-level-plus-continuum atom cannot support the recombination-cascade path that populates the h & k upper levels.

Load-bearing premise

The load-bearing premise is that Mg II level populations are in statistical equilibrium in every RH solution, even though non-equilibrium effects are known to be significant during the first seconds of flare heating and cooling, so the quantitative comparisons between CRD and PRD, and the size of the irradiation effect, could change once time-dependent populations are used.

Editorial extensions

If this is right

  • Flare studies that model Mg II with CRD will overestimate inner-wing intensities by factors of 2–10 and may report Doppler features that are actually redistribution artifacts; such results should be re-examined or caveated.
  • The hybrid angle-dependent PRD (H-PRD) approximation is a safe default for flare studies even with large velocity fields, reducing computation time by roughly a factor of 400 relative to full AD-PRD, provided users accept localized 15–20% intensity errors.
  • A model atom with only the ground state, h & k upper levels, and continuum is inadequate; any Mg II flare modelling must include higher excited levels that funnel recombinations down to the h & k upper levels.
  • For the Mg II line cores and near wings, only Mg II and hydrogen need be treated in NLTE; additional species matter only for the far wings and the NUV quasi-continuum.
  • Lower-mid transition region irradiation should be included when modelling the strongest flares, because it can depress Mg II line intensities by 10–30% during the first few seconds, an effect that depends on the Si and C transitions included in the irradiating spectrum.

Reading between the lines

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

  • If PRD-only wing features like the blue-wing bump are real, then some reported upflow/downflow asymmetries in observed flare Mg II profiles may be misattributed to mass motions; a direct comparison of the synthetic PRD profiles with IRIS observations at the same flare phase would settle how often this happens.
  • The same CRD-vs-PRD failure mode likely affects other optically thick chromospheric lines formed by scattering, such as Ca II K, where the paper notes a similar blue-wing bump appears; the density thresholds found here may transfer to those lines.
  • Because the paper assumes statistical equilibrium for Mg II, and the authors themselves found NEQ effects matter in the heating/cooling phase, the irradiation effect (largest at t < 5 s) and the exact percentage CRD/PRD differences could shift once Paper II introduces NEQ Mg II populations; the early-time numbers are the least secure.
  • A testable extension: run the same RH experiments with microturbulence treated as a free parameter across a grid (e.g., 0–20 km/s) to map when the CRD and PRD wing intensities converge; the paper's single 10 km/s test suggests the conclusion is robust, but a systematic grid would give observers a way to invert for turbulence.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This paper systematically tests how the choice of radiation-transfer physics affects forward models of the flaring Mg II spectrum. The authors post-process snapshots from three RADYN electron-beam flare simulations (F9, F10, F11) with the RH code and compare a standard baseline setup against variants: complete versus partial frequency redistribution (CRD versus PRD), hybrid versus angle-dependent PRD, smaller versus larger Mg II model atoms, omission versus inclusion of Mg I, statistical-equilibrium versus non-equilibrium hydrogen populations, inclusion of additional NLTE species, and the addition of downward transition-region/coronal irradiation. The main claims are that PRD remains necessary even for the strongest flare, that the fast hybrid PRD is acceptable for most purposes, that only hydrogen and Mg II need to be solved in NLTE for the line cores, that Mg I matters mainly for the NUV quasi-continuum, that the non-equilibrium hydrogen populations from RADYN are preferable to SE populations, that a minimal three-level-plus-continuum Mg II atom is insufficient, and that lower-mid transition-region irradiation can affect Mg II formation. The paper also describes two RH code modifications: fixing user-provided active-species populations and injecting a CHIANTI-based irradiating spectrum.

Significance. If the results hold, this paper provides a valuable benchmark for the IRIS-era Mg II flare modeling community. Its strengths are the quantitative, internally consistent comparisons; the use of contribution functions to diagnose line formation; the explicit testing of alternatives such as microturbulence and irradiation thresholds; and the detailed description of code modifications that others can adopt. The PRD-required conclusion is robust and well supported by the comparison of CRD and PRD profiles, including the wing-feature analysis in Section 3.2. The main limitation acknowledged by the authors is that all Mg II populations are computed in statistical equilibrium, which is a significant caveat for the quantitative claims, particularly the irradiation result.

major comments (2)
  1. [Section 9, final paragraph; Section 8, t < 5 s] Every RH solution in this paper computes Mg II populations in statistical equilibrium (Section 2.3), and the paper states in Section 9 that non-equilibrium effects 'do have an impact during the initial heating and cooling phase of the flares.' The irradiation effect is confined to exactly that phase: Section 8 states the effect 'was only present at t < 5 s, when the coronal irradiation was maximum.' Because the quantitative comparisons throughout the paper, and especially the 10-30% irradiation-induced intensity changes reported in Section 9(vii), rest on SE Mg II populations at early times, the SE assumption is load-bearing for the quantitative content of the conclusions. The PRD-required conclusion in Section 3.1 is robust to this caveat, but the abstract and conclusions should either explicitly state that all quantitative percentages are conditional on the adequacy of SE for Mg II, or the authors should add a test comparing SE and NEQ Mg II populations for at least one snapshot at t < 5 s. Deferring this test to Paper II is acceptable only if the present paper's claims are worded as provisional.
  2. [Section 8, Figures 14 and 15] The irradiation module assumes optically thin emission from cells above T > 50 kK and integrates the CHIANTI emissivity to form a downward-directed injected spectrum. The paper itself notes that certain species, such as Si IV and C III, can become optically thick in flares, and the sensitivity experiments in Figure 14(g,h) and Figure 15 remove Si I-IV and C I-III transitions. Since removing these transitions substantially reduces the reported intensity changes, the magnitude of the irradiation effect in the 'standard' case is strongly dependent on the optically thin assumption for lines that the authors suspect are not optically thin. The paper should state explicitly that the 20-40% values are upper bounds under the optically thin assumption, or provide an estimate of the effect of finite line opacity on the injected spectrum. As written, Section 9(vii) presents the irradiation result more decisively than the modeling assumptions support.
minor comments (5)
  1. [Section 3.2] The text says the line core is located in the redshifted component at '~lambda_rest,k + 25 Å'; this should presumably be approximately +0.25 Å (or the equivalent Doppler shift in km/s), since 25 Å is far outside the plotted wavelength range.
  2. [Section 9(iv)] The sentence 'The dominant sources of opacity at the MgII resonance line cores and near wings are are Mg II and hydrogen' contains a duplicated 'are'; please correct this typo.
  3. [Section 8] In the description of converting emissivities to an injected intensity, the text 'This is is then integrated through height' contains a duplicated 'is'; please correct the typo.
  4. [Section 4] The timing comparison between H-PRD and AD-PRD (3-4 days versus a few minutes, and the factor of 400) would be more reproducible if the machine, number of cores, and convergence criteria were specified in a footnote or in the code description.
  5. [References] Kerr et al. (2019a), the companion paper containing the non-equilibrium Mg II results, is listed as 'In Prep.'; since the SE caveat is central to the present paper's conclusions, a published or at least public reference would strengthen the discussion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: all central results are internal model experiments with no Mg II fitting; the SE assumption is an acknowledged limitation, not a constructed equivalence.

full rationale

The paper's claims are comparative radiative-transfer experiments performed on the same RADYN flare snapshots, and no Mg II spectrum or line quantity is fitted and then re-presented as a prediction. The CRD-vs-PRD conclusion follows from directly solving the same atmosphere under two redistribution prescriptions and comparing emergent intensities; the H-PRD approximation is tested within the paper against AD-PRD rather than assumed on the authority of Leenaarts et al. (2012). The NEQ hydrogen populations are supplied by RADYN, an independent radiation-hydrodynamics code, and their effect is shown by contrasting RH solutions with SE hydrogen. The coronal-irradiation module uses a CHIANTI emissivity grid and its effect is demonstrated by turning the injected radiation on and off, including a threshold sensitivity test. The only significant caveat is statistical equilibrium for Mg II, explicitly flagged in Sections 2.3 and 9 and deferred to Kerr et al. (2019a, Paper II). That is a correctness and robustness limitation on early-time quantitative percentages, not a circular step: SE is imposed uniformly on all configurations and is not derived from, nor fitted to, the Mg II spectra being modelled. No load-bearing self-citation supplies the main result, so there is no circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the fidelity of the RH and RADYN models and on two explicit modeling choices the paper itself flags: statistical equilibrium for Mg II and optically thin irradiation from cells with T > 50 kK. The electron beam parameters and microturbulence are experimental inputs, not fitted to the Mg II spectra; the irradiation threshold is a hand-chosen cutoff on which the irradiation conclusion depends. No new physical entities are postulated.

free parameters (4)
  • Microturbulence = 2 km/s nominal; 10 km/s test
    Sets the Doppler core width and affects PRD/CRD differences. The paper uses RADYN's nominal 2 km/s and confirms the PRD conclusion at 10 km/s (Section 3.2).
  • Irradiation temperature threshold = 50 kK (100 kK test)
    The conclusion that TR irradiation affects Mg II vanishes when the threshold rises to 100 kK (Section 8), so the irradiation claim depends on this chosen cutoff.
  • Electron beam parameters (F, delta, E_c) = F = 1e9, 1e10, 1e11 erg cm^-2 s^-1; delta = 5; E_c = 20 keV
    Define the three flare simulations; all results are specific to these beam parameters and the loop geometry (Section 2.2).
  • Irradiating spectrum content = CHIANTI transitions except He and RH-solved lines; variants removing Si i-IV and C i-III
    The irradiation-induced Mg II intensity drop decreases when Si/C transitions are removed, so claim (7) depends on which transitions are included (Section 8, Figure 15).
assumptions (5)
  • domain assumption RH's coupled NLTE statistical equilibrium and radiation transfer solver (MALI) with the specified atomic models produces correct synthetic Mg II spectra for a given atmosphere and populations.
    The paper inherits the RH code (Uitenbroek 2001) and atomic data without independent validation of the Mg II model in flares.
  • domain assumption The RADYN 1D plane-parallel electron-beam flare atmospheres are representative of the flaring chromosphere where IRIS Mg II forms.
    All conclusions are drawn from three RADYN runs with specific beam parameters and loop geometry (Section 2.2).
  • domain assumption Non-equilibrium hydrogen populations from RADYN, computed under CRD with non-thermal rates, are adequate fixed inputs for RH background opacity.
    Partially tested in Section 2.4 and Appendix A (Ly alpha PRD versus CRD for F10/F11), but not for all times or species.
  • ad hoc to paper TR and coronal irradiation can be treated as optically thin emission from cells above T > 50 kK, with CHIANTI emissivities, injected downward from the loop apex.
    The paper states: 'This assumes optically thin emission, though it is likely that opacity effects will be present for certain species' (Section 8).
  • ad hoc to paper Statistical equilibrium for Mg II level populations is sufficient for the comparative conclusions of this study.
    Section 1 states all Mg II modelling uses SE; Section 9 says Paper II found NEQ effects do have an impact during the initial heating and cooling phase, so this assumption is known to be violated at early times.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Modelling Mg II During Solar Flares. I. Partial Frequency Redistribution, Opacity, and Coronal Irradiation." pith.science (2026). https://pith.science/paper/NBQ5OPO3

@misc{pith2026190805329,
  author       = {Pith},
  title        = {Pith review of: Modelling Mg II During Solar Flares. I. Partial Frequency Redistribution, Opacity, and Coronal Irradiation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NBQ5OPO3}},
  note         = {Machine review of arXiv:1908.05329}
}
read the original abstract

The Interface Region Imaging Spectrograph (IRIS) has routinely observed the flaring Mg II NUV spectrum, offering excellent diagnostic potential and a window into the location of energy deposition. A number of studies have forward modelled both the general properties of these lines and specific flare observations. Generally these have forward modelled radiation via post-processing of snapshots from hydrodynamic flare simulations through radiation transfer codes. There has, however, not been a study of how the physics included in these radiation transport codes affects the solution. A baseline setup for forward modelling MgII in flares is presented and contrasted with approaches that add or remove complexity. It is shown for Mg II: (1) PRD is still required during flare simulations despite the increased densities, (2) using full angle-dependent PRD affects the solution but takes significantly longer to process a snapshot, (3) including Mg I in NLTE results in negligible differences to the Mg II lines but does affect the NUV quasi-continuum, (4) only hydrogen and Mg II need to be included in NLTE, (5) ideally the non-equilibrium hydrogen populations, with non-thermal collisional rates, should be used rather than the statistical equilibrium populations, (6) an atom consisting of only the ground state, h & k upper levels, and continuum level is insufficient to model the resonance lines, and (7) irradiation from a hot, dense flaring transition region can affect the formation of Mg II. We discuss modifications to the RH code allowing straightforward inclusion of transition region and coronal irradiation in flares.

Figures

Figures reproduced from arXiv: 1908.05329 by the authors.

Figure 1
Figure 1. The stratification of temperature (a,b,c), electron density (d,e,f), and macroscopic velocity (g,h,i; uplows are negative) in the three flare simulations. The first column shows the F9 simulation, second column shows the F10 simulation, and third column shows the F11 simulation. Colour represents time. Recall that heating ceased at t = 10 s heating applied to maintain the corona and photosphere (col￾umn masses cmass… view at source ↗
Figure 3
Figure 3. Same as [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Same as [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (11 more)
Figure 6
Figure 6. Figure 6: Illustrating Mg ii k line formation in the PRD (a,b) and CRD (c,d) scenarios. The background images in panels (a) & (c) are the source function S λ(z) as a function of height, and wavelength (shown as a Doppler shift scale, centred on δv = 0 km s−1 , corresponding to λ…
Figure 7
Figure 7. Figure 7: Detailed line formation at selected wavelengths. Panel (a) shows the Mg ii k line profile computed in PRD (black) & CRD (dashed red), at t = 7 s in the F11 simulation. The dashed vertical lines are the wavelengths for which the contribution functions, opacities, and so…
Figure 8
Figure 8. Figure 8: Illustrating Mg ii 2791 Å line formation in the PRD (a,b) and CRD (c,d) scenarios. Images and lines are as described in [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Comparing full angle-dependent PRD (AD-PRD) to the Hybrid PRD (H-PRD) scheme of Leenaarts et al. (2012), for various snapshots in the F11 simulation. The black lines are the H-PRD solution, the red lines are the AD-PRD solution, and the grey lines show the percentage c…
Figure 10
Figure 10. Figure 10: Illustrating the impact of the number of levels in model Mg ii atom. In all panels the black lines are the 10-level-plus-continuum model atom, and the red are the 3-level-plus-continuum model atom. Panel (a) shows the Mg ii k line profile at t = 5 s in the F11 simulat…
Figure 11
Figure 11. Figure 11: Source functions (a) and contribution functions (b) for the Mg ii k line at t = 7 s in the F11 simulation using the 3-level￾plus-continuum model atom. Images and lines are as described in [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: Illustrating the impact of including Mg i in the model atom. In all panels black shows the ‘standard’ case, and red shows the solution when Mg i is included, at t = 5 s in the F11 simulation. Panel (a) shows the ionisation fraction stratification for Mg i (dashed line…
Figure 13
Figure 13. Figure 13: Illustrating the impact of the treatment of hydrogen. (a) the Mg ii k line profile at t = 4 s in the F11 simulation, computed with NEQ & non-thermal hydrogen populations (black line), and SE hydrogen populations (red line). The grey line shows the percentage differenc…
Figure 14
Figure 14. Figure 14: A portion of the irradiating spectrum in the F11 simulation at different times. Panels (a,c,e) show the spectrum where emissivities originating from cells with T > 50 kK were summed to obtain the intensity. Panels (b,d,f) show the spectrum where a higher threshold of …
Figure 15
Figure 15. Figure 15: The Mg ii k line (a,c,e) and 2791 Å subordinate line (b,d,f) in the standard setup (black line) and when TR/coronal irradiation (from T > 50 kK) is included (red dashed lines) at = 2.5 s in the F11 simulation. The grey lines show the percentage change. The irradiance …
Figure 16
Figure 16. Figure 16: Comparing the Ly α line in CRD and PRD. Black solid lines show the SE PRD solution, the blue dashed lines show the SE CRD solution, and the green dashed lines show the NEQ CRD solution (populations directly from RADYN. The upper left block show the F9 flare, the upper…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

50 extracted references · 38 canonical work pages

  1. [1]

    P., & Hawley, S

    Abbett, W. P., & Hawley, S. L. 1999, ApJ, 521, 906

    work page 1999

  2. [2]

    C., Hawley, S

    Allred, J. C., Hawley, S. L., Abbett, W. P., & Carlsson, M. 2005, ApJ, 630, 573

    2005

  3. [3]

    C., Kowalski, A

    Allred, J. C., Kowalski, A. F., & Carlsson, M. 2015, ApJ, 809, 104

    2015

  4. [4]

    C., Kowalski, A

    Allred, J. C., Kowalski, A. F., Kerr, G. S., & Alaoui, M. 2019, In Prep

    work page 2019

  5. [5]

    Brown, J. C. 1971, SoPh, 18, 489

    work page 1971

  6. [6]

    A., Fletcher, L., Kerr, G

    Brown, S. A., Fletcher, L., Kerr, G. S., et al. 2018, ApJ, 862, 59 Caffau, E., Ludwig, H.-G., Steffen, M., Freytag, B., & Bonifacio, P. 2011, SoPh, 268, 255

    work page 2018

  7. [7]

    1998, in Lecture Notes in Physics, Berlin Springer

    Carlsson, M. 1998, in Lecture Notes in Physics, Berlin Springer

    work page 1998

  8. [8]

    Carlsson, M., & Judge, P. G. 1993, ApJ, 402, 344

    work page 1993

Show all 50 references
  1. [9]

    2015, ApJL, 809, L30

    Carlsson, M., Leenaarts, J., & De Pontieu, B. 2015, ApJL, 809, L30

    2015

  2. [10]

    Carlsson, M., & Stein, R. F. 1992, ApJL, 397, L59 —. 1997, ApJL, 481, 500 —. 2002, ApJ, 572, 626 De Pontieu, B., Title, A. M., Lemen, J. R., et al. 2014, SoPh, 289, 2733

    1992

  3. [11]

    Young, P. R. 1997, A&AS, 125, doi:10.1051/aas:1997368

    1997 doi

  4. [12]

    C., & Gan, W

    Fang, C., Henoux, J. C., & Gan, W. Q. 1993, A&A, 274, 917

    1993

  5. [13]

    Feldman, U., & Doschek, G. A. 1977, ApJL, 212, L147

    1977

  6. [14]

    Fletcher, L., & Hudson, H. S. 2008, ApJ, 675, 1645

    2008

  7. [15]

    R., Hudson, H

    Fletcher, L., Dennis, B. R., Hudson, H. S., et al. 2011, SSRv, 159, 19

    2011

  8. [16]

    P., Carlsson, M., & Leenaarts, J

    Golding, T. P., Carlsson, M., & Leenaarts, J. 2014, ApJ, 784, 30

    2014

  9. [17]

    R., & Cauzzi, G

    Graham, D. R., & Cauzzi, G. 2015, ApJL, 807, L22

    2015

  10. [18]

    D., Aschwanden, M

    Holman, G. D., Aschwanden, M. J., Aurass, H., et al. 2011, SSRv, 159, 107 Huben´y, I. 1982, JQSRT, 27, 593

    2011

  11. [19]

    Hubeny, I., & Lites, B. W. 1995, ApJ, 455, 376

    1995

  12. [20]

    A., Judge, P

    Jaeggli, S. A., Judge, P. G., & Daw, A. N. 2018, ApJ, 855, 134

    2018

  13. [21]

    S., Fletcher, L., Russell, A

    Kerr, G. S., Fletcher, L., Russell, A. J. B., & Allred, J. C. 2016, ApJ, 827, 101

    2016

  14. [22]

    S., Sim˜oes, P

    Kerr, G. S., Sim˜oes, P. J. A., Qiu, J., & Fletcher, L. 2015, A&A, 582, A50

    2015

  15. [23]

    L., & Parkinson, W

    Kohl, J. L., & Parkinson, W. H. 1976, ApJ, 205, 599

    1976

  16. [24]

    F., Allred, J

    Kowalski, A. F., Allred, J. C., Daw, A., Cauzzi, G., & Carlsson, M. 2017, ApJ, 836, 12

    2017

  17. [25]

    Kuridze, D., Mathioudakis, M., Sim˜oes, P. J. A., et al. 2015, ApJ, 813, 125

    2015

  18. [26]

    R., Dere, K

    Landi, E., Young, P. R., Dere, K. P., Del Zanna, G., & Mason, H. E. 2013, ApJ, 763, 86

    2013

  19. [27]

    2012, A&A, 543, A109

    Leenaarts, J., Pereira, T., & Uitenbroek, H. 2012, A&A, 543, A109

    2012

  20. [28]

    1984, SoPh, 90, 63

    Lemaire, P., Choucq-Bruston, M., & Vial, J.-C. 1984, SoPh, 90, 63

    1984

  21. [29]

    1973, A&A, 22, 61

    Lemaire, P., & Skumanich, A. 1973, A&A, 22, 61

    1973

  22. [30]

    2019, A&A, 621, A35

    Libbrecht, T., de la Cruz Rodr´ıguez, J., Danilovic, S., Leenaarts, J., & Pazira, H. 2019, A&A, 621, A35

    2019

  23. [31]

    2015, ApJ, 813, 34

    Lin, H.-H., & Carlsson, M. 2015, ApJ, 813, 34

    2015

  24. [32]

    P., Dennis, B

    Lin, R. P., Dennis, B. R., Hurford, G. J., et al. 2002, SoPh, 210, 3

    2002

  25. [33]

    2015, SoPh, 290, 3525

    Liu, W., Heinzel, P., Kleint, L., & Kaˇsparov´a, J. 2015, SoPh, 290, 3525

    2015

  26. [34]

    2009, Landolt B¨ornstein, 712

    Lodders, K., Palme, H., & Gail, H.-P. 2009, Landolt B¨ornstein, 712

    2009

  27. [35]

    1986, A&A, 163, 135

    Magain, P. 1986, A&A, 163, 135

    1986

  28. [36]

    W., & Mihalas, D

    Milkey, R. W., & Mihalas, D. 1974, ApJ, 192, 769

    1974

  29. [37]

    O., Kerr, G

    Milligan, R. O., Kerr, G. S., Dennis, B. R., et al. 2014, ApJ, 793, 70

    2014

  30. [38]

    2018, ApJ, 861, 62

    Panos, B., Kleint, L., Huwyler, C., et al. 2018, ApJ, 861, 62

    2018

  31. [39]

    Pereira, T. M. D., Carlsson, M., De Pontieu, B., & Hansteen, V . 2015, ApJ, 806, 14

    2015

  32. [40]

    W., Bradshaw, S

    Reep, J. W., Bradshaw, S. J., Crump, N. A., & Warren, H. P. 2019, ApJ, 871, 18

    2019

  33. [41]

    W., Russell, A

    Reep, J. W., Russell, A. J. B., Tarr, L. A., & Leake, J. E. 2018, ApJ, 853, 101 20 K err, Allred, Carlsson Rubio da Costa, F., & Kleint, L. 2017, ApJ, 842, 82

    2018

  34. [42]

    B., & Hummer, D

    Rybicki, G. B., & Hummer, D. G. 1991, A&A, 245, 171 —. 1992, A&A, 262, 209

    1991

  35. [43]

    T., Reames, D

    Schmelz, J. T., Reames, D. V ., von Steiger, R., & Basu, S. 2012, ApJ, 755, 33

    2012

  36. [44]

    F., & Auer, L

    Smith, D. F., & Auer, L. H. 1980, ApJ, 238, 1126

    1980

  37. [45]

    1995, A&A, 295, 517

    Staath, E., & Lemaire, P. 1995, A&A, 295, 517

    1995

  38. [46]

    J., et al

    Tei, A., Sakaue, T., Okamoto, T. J., et al. 2018, PASJ, 70, 100

    2018

  39. [47]

    2018, ApJ, 856, 34

    Tian, H., & Chen, N.-H. 2018, ApJ, 856, 34

    2018

  40. [48]

    2001, ApJ, 557, 389 —

    Uitenbroek, H. 2001, ApJ, 557, 389 —. 2002, ApJ, 565, 1312

    2001

  41. [49]

    2016, ApJ, 819, 89

    Xu, Y ., Cao, W., Ding, M., et al. 2016, ApJ, 819, 89

    2016

  42. [50]

    F., Tian, H., et al

    Zhu, Y ., Kowalski, A. F., Tian, H., et al. 2019, arXiv e-prints, arXiv:1904.12285 Mg ii PRD, Opacity, Irradiation 21 APPENDIX A. LYα PRD Here we show Lyα line profiles and hydrogen populations, for RADYN flare snapshots forward modelled using RH, comparing the PRD and CRD solut...

    2019 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.