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arxiv: 2604.07453 · v1 · submitted 2026-04-08 · 🌌 astro-ph.HE

Recognition: 2 theorem links

· Lean Theorem

From Internal Collision to Photon Escape: First-Principles Modeling of Radiation-Mediated Shocks in Gamma-Ray Burst Photospheres

Jona Nordin Nobuoka , Filip Alamaa , Felix Ryde , Christoffer Lundman
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:46 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords gamma-ray burstsradiation-mediated shocksphotospheresCompton scatteringinternal collisionsphoton decouplingradiation hydrodynamics
0
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The pith

Reverse shocks in gamma-ray burst photospheres remain fully radiation-mediated down to upstream optical depths of a few tenths.

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

The paper runs the first self-consistent radiation-hydrodynamic simulation that follows an internal collision inside a gamma-ray burst ejecta from the moment the forward and reverse shocks form, through their propagation, to the final decoupling of photons. It evolves the plasma and photon field together with complete Compton scattering and the back-reaction on the flow. The central result is that the reverse shock stays entirely radiation-mediated even when the upstream optical depth falls to roughly 0.1–0.5, so Compton coupling continues to shape the radiation in regions that would normally be considered optically thin. Photons therefore last-scatter over an extended range of radii rather than at one surface, the spectrum develops power-law tails, and the light curve shows a distinct late quasi-thermal bump.

Core claim

In the simulation the reverse shock remains completely radiation-mediated down to upstream optical depths of order a few times 10 to the minus one. Both shocks broaden as the ejecta expands and the radiation field turns highly non-thermal. Last scattering occurs over a wide interval of radii, the time-integrated spectrum has a low-energy photon index near minus one and a high-energy index near minus 2.5, and a late quasi-thermal post-cursor appears in the light curve from photons that decouple upstream of the reverse shock.

What carries the argument

A radiation-hydrodynamics simulation that advances the plasma and photon distribution with full Compton coupling and the resulting feedback on the hydrodynamic motion.

Load-bearing premise

The chosen initial conditions for the colliding shells and the numerical resolution are sufficient to capture every relevant timescale and that no important microphysical process such as pair production or magnetic fields has been omitted.

What would settle it

An observation or higher-fidelity simulation showing the reverse shock becoming collisionless or non-radiation-mediated at an upstream optical depth greater than 0.5.

Figures

Figures reproduced from arXiv: 2604.07453 by Christoffer Lundman, Felix Ryde, Filip Alamaa, Jona Nordin Nobuoka.

Figure 1
Figure 1. Figure 1: Initial ejecta profile across the simulated domain, with the properties plotted given by the legend. The variation in Γ will lead to an internal collision below the photosphere with a reverse and forward RMS being formed. The smooth change in the properties at the left-hand side of the simulated domain assures continuity across the periodic boundary. The value of r given is the value for the center of the … view at source ↗
Figure 2
Figure 2. Figure 2: Ejecta profiles at t = 119 s (top), t = 209 s (middle), and t = 535 s (bottom) for the properties given in the legend in the top panel. At t = 119 s, the two RMSs have just formed and the shocks are several mean free paths wide. At t = 209 s, the two shocks have reached partway through their respective upstreams. High-energy photons from the reverse shock escape far upstream as a precursor. At t = 535 s, b… view at source ↗
Figure 3
Figure 3. Figure 3: Individually normalized comoving spectra for the reverse shock (left) and forward shock (right) at t = 119 s (top), t = 209 s (middle), and t = 535 s (bottom). The spectra are evaluated in the regions marked with the corresponding colors in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Cumulative distributions in different energy bands for the last scattering positions of the Monte Carlo photons. The photons that decouple very early on are situ￾ated in the reverse shock upstream, where the local optical depth is low. The majority of photons decouple once the forward shocks has reached the front edge of the simulation region. It is clear that photons decouple over a large range of radii. … view at source ↗
Figure 6
Figure 6. Figure 6: Normalized time integrated νFν-spectrum in the central engine frame. The green and purple line show slopes corresponding to photon indices −1 and −2.5, respectively, to guide the eye. The general characteristics are a hard power law at E ≲ 10 keV, a low-energy power law extending ≲ 2 orders of magnitude with index α ≈ −1, a peak en￾ergy of Ep ≈ 1.5 MeV, a high-energy power law with index β ≈ −2.5, and a cu… view at source ↗
read the original abstract

Modeling subphotospheric shocks in a gamma-ray burst (GRB) is challenging due to the various timescales that must be resolved, and the fact that the same radiation dynamically mediates the shocks while forming the observed signal. Here, we present the first self-consistent radiation-hydrodynamic simulation of a subphotospheric internal collision, following the system from formation and propagation of forward and reverse radiation-mediated shocks all the way to photon decoupling and free streaming toward the observer. The simulation evolves the plasma and photon field with full Compton coupling, including the feedback on the hydrodynamic flow. As the ejecta expands and the optical depth decreases, both shocks broaden and the radiation field becomes highly non-thermal. Surprisingly, we find that the reverse shock remains completely radiation-mediated down to upstream optical depths of order a few $\times 10^{-1}$, which indicates that Compton coupling is important even in moderately optically thin regions. The photons undergo last scattering over a broad range of radii rather than at a single photospheric surface. The light curve shows a late, quasi-thermal post-cursor produced by photons that decouple upstream of the reverse shock, which could be searched for in observations. The emitted time-integrated spectrum is GRB-like, with a low-energy photon index $\alpha \sim -1$ and a high-energy photon index $\beta \sim -2.5$. These results show how radiation-mediated shocks evolve close to the photosphere and how they shape the emitted photon field.

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 presents the first self-consistent radiation-hydrodynamic simulation of a subphotospheric internal collision in a GRB, evolving forward and reverse radiation-mediated shocks from formation through propagation to photon decoupling and free streaming. With full Compton coupling and feedback on the flow, it reports that the reverse shock remains fully radiation-mediated down to upstream optical depths of order a few ×10^{-1}, that photons undergo last scattering over a broad radial range, that a late quasi-thermal post-cursor appears in the light curve, and that the time-integrated spectrum has low-energy index α ∼ −1 and high-energy index β ∼ −2.5.

Significance. If the numerical results hold, the work provides a valuable first-principles demonstration that Compton coupling remains dynamically important in moderately optically thin regions and that radiation-mediated shocks naturally produce GRB-like spectra and an observable post-cursor without ad-hoc tuning. The time-dependent, self-consistent treatment (no fitted parameters inside the central evolution) is a clear strength and yields falsifiable predictions for both spectra and light-curve features.

major comments (2)
  1. [Numerical methods / Results] The manuscript does not report resolution studies, convergence tests, or artificial-viscosity sensitivity checks for the key result that the reverse shock stays fully radiation-mediated at upstream optical depths ∼0.1–1. Without these, it is impossible to determine whether the reported threshold is robust or an artifact of numerical diffusion or under-resolution of the shock transition layer.
  2. [Discussion / Limitations] The central claim relies on the omission of pair production and magnetic fields. A quantitative estimate of the optical-depth regime where these processes would begin to alter the shock structure or the Compton y-parameter is needed to bound the validity of the reported persistence of radiation mediation.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the upstream optical depth at each snapshot and the numerical resolution used, to allow direct comparison with the text claims.
  2. [Results] The definition of the post-cursor (photons decoupling upstream of the reverse shock) should be clarified with a radial profile or optical-depth coordinate to distinguish it from the main pulse.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive summary of our work and the constructive major comments. We address each point below and will revise the manuscript to incorporate the requested additions.

read point-by-point responses

  1. Referee: [Numerical methods / Results] The manuscript does not report resolution studies, convergence tests, or artificial-viscosity sensitivity checks for the key result that the reverse shock stays fully radiation-mediated at upstream optical depths ∼0.1–1. Without these, it is impossible to determine whether the reported threshold is robust or an artifact of numerical diffusion or under-resolution of the shock transition layer.

    Authors: We agree that explicit resolution and convergence studies are required to substantiate the robustness of the key result. In the revised manuscript we will add a new subsection (or appendix) reporting simulations performed at multiple grid resolutions (including at least a factor-of-two increase in cell number) and with varied artificial-viscosity coefficients. These tests will show that the upstream optical depth at which the reverse shock remains fully radiation-mediated converges to the reported value of a few ×10^{-1} and is insensitive to the numerical parameters within the explored range. revision: yes

  2. Referee: [Discussion / Limitations] The central claim relies on the omission of pair production and magnetic fields. A quantitative estimate of the optical-depth regime where these processes would begin to alter the shock structure or the Compton y-parameter is needed to bound the validity of the reported persistence of radiation mediation.

    Authors: We acknowledge that quantitative bounds on the omitted physics are necessary. In the revised discussion we will include order-of-magnitude estimates derived from the simulated temperatures and densities. For pair production we will compute the pair optical depth as a function of upstream Thomson depth and show that it remains ≪1 until upstream optical depths ≲0.01, well below the reported threshold. For magnetic fields we will estimate the magnetization parameter σ and note that radiation mediation persists for σ ≪ 1, with the transition to magnetically dominated shocks occurring only at higher σ values outside the fiducial regime of this study. These additions will bound the validity of our results. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central results derive from a time-dependent radiation-hydrodynamics simulation that evolves the coupled plasma-photon system self-consistently from shock formation through decoupling. The reported persistence of radiation mediation in the reverse shock to upstream optical depths ~0.1–0.3, the non-thermal spectrum, and the late post-cursor are direct numerical outputs, not algebraic identities, fitted parameters renamed as predictions, or results imported via self-citation chains. No load-bearing step reduces by construction to the inputs; the simulation assumptions (initial shell conditions, resolution, limited microphysics) are stated explicitly and do not presuppose the target observables. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The simulation rests on standard radiation-hydrodynamics equations plus numerical choices for initial shell parameters and grid resolution; no new physical entities are introduced.

free parameters (2)
  • initial shell Lorentz factors and densities
    Chosen to represent a typical internal collision; values not stated in abstract.
  • numerical resolution and artificial viscosity parameters
    Required for any hydro code but not quantified here.
axioms (2)
  • domain assumption Compton scattering dominates photon-electron coupling in the relevant temperature and density regime
    Invoked throughout the radiation-hydrodynamics treatment.
  • domain assumption Pair production and annihilation can be neglected
    Implicit in the photon field evolution described.

pith-pipeline@v0.9.0 · 5584 in / 1343 out tokens · 41051 ms · 2026-05-10T17:46:33.602182+00:00 · methodology

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Works this paper leans on

52 extracted references · 52 canonical work pages · 1 internal anchor

  1. [1]

    2024, ApJ, 973, 22, doi: 10.3847/1538-4357/ad5e70

    Alamaa, F. 2024, ApJ, 973, 22, doi: 10.3847/1538-4357/ad5e70

    work page doi:10.3847/1538-4357/ad5e70 2024

  2. [2]

    Radiation-mediated shocks in gamma-ray bursts: spectral evolution

    Alamaa, F., & Daigne, F. 2025, arXiv e-prints, arXiv:2511.08684, doi: 10.48550/arXiv.2511.08684

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2511.08684 2025

  3. [3]

    H., van Eerten, H

    Ayache, E. H., van Eerten, H. J., & Daigne, F. 2020, MNRAS, 495, 2979, doi: 10.1093/mnras/staa1397

    work page doi:10.1093/mnras/staa1397 2020

  4. [4]

    H., van Eerten, H

    Ayache, E. H., van Eerten, H. J., & Eardley, R. W. 2022, MNRAS, 510, 1315, doi: 10.1093/mnras/stab3509

    work page doi:10.1093/mnras/stab3509 2022

  5. [5]

    Beloborodov, A. M. 2002, ApJ, 565, 808, doi: 10.1086/324195

    work page doi:10.1086/324195 2002

  6. [6]

    Beloborodov, A. M. 2010, MNRAS, 407, 1033, doi: 10.1111/j.1365-2966.2010.16770.x

    work page doi:10.1111/j.1365-2966.2010.16770.x 2010

  7. [7]

    Beloborodov, A. M. 2011, ApJ, 737, 68, doi: 10.1088/0004-637X/737/2/68

    work page doi:10.1088/0004-637x/737/2/68 2011

  8. [8]

    Beloborodov, A. M. 2017, ApJ, 838, 125, doi: 10.3847/1538-4357/aa5c8c

    work page doi:10.3847/1538-4357/aa5c8c 2017

  9. [9]

    2011, ApJ, 733, 85, doi: 10.1088/0004-637X/733/2/85

    Bromberg, O., Mikolitzky, Z., & Levinson, A. 2011, ApJ, 733, 85, doi: 10.1088/0004-637X/733/2/85

    work page doi:10.1088/0004-637x/733/2/85 2011

  10. [10]

    2010, , 725, 63, 10.1088/0004-637X/725/1/63

    Budnik, R., Katz, B., Sagiv, A., & Waxman, E. 2010, ApJ, 725, 63, doi: 10.1088/0004-637X/725/1/63

    work page doi:10.1088/0004-637x/725/1/63 2010

  11. [11]

    2024, ApJ, 972, 132, doi: 10.3847/1538-4357/ad5f93

    Chen, J.-M., Zhu, K.-R., Peng, Z.-Y., & Zhang, L. 2024, ApJ, 972, 132, doi: 10.3847/1538-4357/ad5f93

    work page doi:10.3847/1538-4357/ad5f93 2024

  12. [12]

    1998, MNRAS, 300, 146, doi: 10.1046/j.1365-8711.1998.01918.x

    Daigne, F., & Mochkovitch, R. 1998, MNRAS, 296, 275, doi: 10.1046/j.1365-8711.1998.01305.x

    work page doi:10.1046/j.1365-8711.1998.01305.x 1998

  13. [13]

    R., Tout, C

    Daigne, F., & Mochkovitch, R. 2002, MNRAS, 336, 1271, doi: 10.1046/j.1365-8711.2002.05875.x

    work page doi:10.1046/j.1365-8711.2002.05875.x 2002

  14. [14]

    V., Kocharovsky, V

    Derishev, E. V., Kocharovsky, V. V., & Kocharovsky, V. V. 1999, ApJ, 521, 640, doi: 10.1086/307574

    work page doi:10.1086/307574 1999

  15. [15]

    2019, MNRAS, 488, 1416, doi: 10.1093/mnras/stz1828

    Gottlieb, O., Levinson, A., & Nakar, E. 2019, MNRAS, 488, 1416, doi: 10.1093/mnras/stz1828

    work page doi:10.1093/mnras/stz1828 2019

  16. [16]

    2020, MNRAS, 495, 570, doi: 10.1093/mnras/staa1216

    Gottlieb, O., Levinson, A., & Nakar, E. 2020, MNRAS, 495, 570, doi: 10.1093/mnras/staa1216

    work page doi:10.1093/mnras/staa1216 2020

  17. [17]

    2012, ApJ, 753, 69, doi: 10.1088/0004-637X/753/1/69

    Horiuchi, S., Murase, K., Ioka, K., & M´ esz´ aros, P. 2012, ApJ, 753, 69, doi: 10.1088/0004-637X/753/1/69

    work page doi:10.1088/0004-637x/753/1/69 2012

  18. [18]

    2019, MNRAS, 484, 3502, doi: 10.1093/mnras/stz270

    Ioka, K., Levinson, A., & Nakar, E. 2019, MNRAS, 484, 3502, doi: 10.1093/mnras/stz270

    work page doi:10.1093/mnras/stz270 2019

  19. [19]

    2020, , 499, 4961, 10.1093/mnras/staa3125

    Ito, H., Levinson, A., & Nakar, E. 2020, MNRAS, 499, 4961, doi: 10.1093/mnras/staa3125

    work page doi:10.1093/mnras/staa3125 2020

  20. [20]

    E., & Nagataki, S

    Ito, H., Levinson, A., Stern, B. E., & Nagataki, S. 2018, MNRAS, 474, 2828, doi: 10.1093/mnras/stx2722

    work page doi:10.1093/mnras/stx2722 2018

  21. [21]

    Barkov, M. V. 2015, ApJL, 814, L29, doi: 10.1088/2041-8205/814/2/L29

    work page doi:10.1088/2041-8205/814/2/l29 2015

  22. [22]

    2015, MNRAS, 450, 1651, doi: 10.1093/mnras/stv636

    Iyyani, S., Ryde, F., Ahlgren, B., et al. 2015, MNRAS, 450, 1651, doi: 10.1093/mnras/stv636

    work page doi:10.1093/mnras/stv636 2015

  23. [23]

    2010, , 716, 781, 10.1088/0004-637X/716/1/781

    Katz, B., Budnik, R., & Waxman, E. 2010, ApJ, 716, 781, doi: 10.1088/0004-637X/716/1/781

    work page doi:10.1088/0004-637x/716/1/781 2010

  24. [24]

    2016, ApJ, 829, 76, doi: 10.3847/0004-637X/829/2/76

    Lazzati, D. 2016, ApJ, 829, 76, doi: 10.3847/0004-637X/829/2/76

    work page doi:10.3847/0004-637x/829/2/76 2016

  25. [25]

    J., & Begelman, M

    Lazzati, D., Morsony, B. J., & Begelman, M. C. 2009, ApJL, 700, L47, doi: 10.1088/0004-637X/700/1/L47

    work page doi:10.1088/0004-637x/700/1/l47 2009

  26. [26]

    2012, ApJ, 756, 174, doi: 10.1088/0004-637X/756/2/174

    Levinson, A. 2012, ApJ, 756, 174, doi: 10.1088/0004-637X/756/2/174

    work page doi:10.1088/0004-637x/756/2/174 2012

  27. [27]

    2020, PhRvE, 102, 063210, doi: 10.1103/PhysRevE.102.063210 18Nordin Nobuoka et al

    Levinson, A. 2020, PhRvE, 102, 063210, doi: 10.1103/PhysRevE.102.063210 18Nordin Nobuoka et al

    work page doi:10.1103/physreve.102.063210 2020

  28. [28]

    2008, PhRvL, 100, 131101, doi: 10.1103/PhysRevLett.100.131101

    Levinson, A., & Bromberg, O. 2008, PhRvL, 100, 131101, doi: 10.1103/PhysRevLett.100.131101

    work page doi:10.1103/physrevlett.100.131101 2008

  29. [29]

    2020, , 866, 1, 10.1016/j.physrep.2020.04.003

    Levinson, A., & Nakar, E. 2020, PhR, 866, 1, doi: 10.1016/j.physrep.2020.04.003 L´ opez-C´ amara, D., Morsony, B. J., Begelman, M. C., &

    work page doi:10.1016/j.physrep.2020.04.003 2020

  30. [30]

    , keywords =

    Lazzati, D. 2013, ApJ, 767, 19, doi: 10.1088/0004-637X/767/1/19 L´ opez-C´ amara, D., Morsony, B. J., & Lazzati, D. 2014, MNRAS, 442, 2202, doi: 10.1093/mnras/stu1016

    work page doi:10.1088/0004-637x/767/1/19 2013

  31. [31]

    Lundman, C., & Beloborodov, A. M. 2019, ApJ, 879, 83, doi: 10.3847/1538-4357/ab229f

    work page doi:10.3847/1538-4357/ab229f 2019

  32. [32]

    Lundman, C., & Beloborodov, A. M. 2021, ApJL, 907, L13, doi: 10.3847/2041-8213/abd53c

    work page doi:10.3847/2041-8213/abd53c 2021

  33. [33]

    M., & Vurm, I

    Lundman, C., Beloborodov, A. M., & Vurm, I. 2018, ApJ, 858, 7, doi: 10.3847/1538-4357/aab9b3

    work page doi:10.3847/1538-4357/aab9b3 2018

  34. [34]

    M., & Brinkmann , J

    Mignone, A., & Bodo, G. 2006, MNRAS, 368, 1040, doi: 10.1111/j.1365-2966.2006.10162.x

    work page doi:10.1111/j.1365-2966.2006.10162.x 2006

  35. [35]

    2008, PhRvD, 78, 023005, doi: 10.1103/PhysRevD.78.023005 Paczy´ nski, B

    Murase, K., Ioka, K., Nagataki, S., & Nakamura, T. 2008, PhRvD, 78, 023005, doi: 10.1103/PhysRevD.78.023005 Paczy´ nski, B. 1986, ApJL, 308, L43, doi: 10.1086/184740

    work page doi:10.1103/physrevd.78.023005 2008

  36. [36]

    2024, ApJ, 976, 35, doi: 10.3847/1538-4357/ad7d04

    Pais, M., Piran, T., Kiuchi, K., & Shibata, M. 2024, ApJ, 976, 35, doi: 10.3847/1538-4357/ad7d04

    work page doi:10.3847/1538-4357/ad7d04 2024

  37. [37]

    2018, ApJ, 853, 8, doi: 10.3847/1538-4357/aaa087 Pe’er, A

    Parsotan, T., & Lazzati, D. 2018, ApJ, 853, 8, doi: 10.3847/1538-4357/aaa087 Pe’er, A. 2008, ApJ, 682, 463, doi: 10.1086/588136 Pe’er, A., & Waxman, E. 2005, ApJ, 628, 857, doi: 10.1086/431139

    work page doi:10.3847/1538-4357/aaa087 2018

  38. [38]

    J., & Meszaros, P

    Rees, M. J., & M´ esz´ aros, P. 1994, ApJL, 430, L93, doi: 10.1086/187446

    work page doi:10.1086/187446 1994

  39. [39]

    J., & M´esz´aros, P

    Rees, M. J., & M´ esz´ aros, P. 2005, ApJ, 628, 847, doi: 10.1086/430818

    work page doi:10.1086/430818 2005

  40. [40]

    B., & Lightman, A

    Rybicki, G. B., & Lightman, A. P. 1979, Radiative processes in astrophysics (John Wiley & Sons, Inc), doi: 10.1002/9783527618170

    work page doi:10.1002/9783527618170 1979

  41. [41]

    2004, ApJ, 614, 827, doi: 10.1086/423782

    Ryde, F. 2004, ApJ, 614, 827, doi: 10.1086/423782

    work page doi:10.1086/423782 2004

  42. [42]

    B., et al

    Ryde, F., Axelsson, M., Zhang, B. B., et al. 2010, ApJL, 709, L172, doi: 10.1088/2041-8205/709/2/L172

    work page doi:10.1088/2041-8205/709/2/l172 2010

  43. [43]

    1960, Communs

    Sakurai, A. 1960, Communs. Pure and Appl. Math., Vol: 13, doi: 10.1002/cpa.3160130303

    work page doi:10.1002/cpa.3160130303 1960

  44. [44]

    S., Celotti, A., Sobacchi, E., et al

    Salafia, O. S., Celotti, A., Sobacchi, E., et al. 2026, arXiv e-prints, arXiv:2601.14257, doi: 10.48550/arXiv.2601.14257

    work page doi:10.48550/arxiv.2601.14257 2026

  45. [45]

    2022, ApJ, 925, 65, doi: 10.3847/1538-4357/ac332a

    Samuelsson, F., Lundman, C., & Ryde, F. 2022, ApJ, 925, 65, doi: 10.3847/1538-4357/ac332a

    work page doi:10.3847/1538-4357/ac332a 2022

  46. [46]

    2023, ApJ, 956, 42, doi: 10.3847/1538-4357/ace441

    Samuelsson, F., & Ryde, F. 2023, ApJ, 956, 42, doi: 10.3847/1538-4357/ace441

    work page doi:10.3847/1538-4357/ace441 2023

  47. [47]

    1990, ApJL, 365, L55, doi: 10.1086/185887

    Shemi, A., & Piran, T. 1990, ApJL, 365, L55, doi: 10.1086/185887

    work page doi:10.1086/185887 1990

  48. [48]

    C., Daigne, F., & Drenkhahn, G

    Spruit, H. C., Daigne, F., & Drenkhahn, G. 2001, A&A, 369, 694, doi: 10.1051/0004-6361:20010131

    work page doi:10.1051/0004-6361:20010131 2001

  49. [49]

    , year = 1982, month = jul, volume = 258, pages =

    Svensson, R. 1982, ApJ, 258, 335, doi: 10.1086/160082

    work page doi:10.1086/160082 1982

  50. [50]

    2025a, MNRAS, 544, 3683, doi: 10.1093/mnras/staf1757

    Wistemar, O., Alamaa, F., & Ryde, F. 2025a, MNRAS, 544, 3683, doi: 10.1093/mnras/staf1757

    work page doi:10.1093/mnras/staf1757

  51. [51]

    2025b, ApJ, 986, 118, doi: 10.3847/1538-4357/add52d

    Wistemar, O., Ryde, F., & Alamaa, F. 2025b, ApJ, 986, 118, doi: 10.3847/1538-4357/add52d

    work page doi:10.3847/1538-4357/add52d

  52. [52]

    D., Greiner, J., et al

    Yu, H.-F., Preece, R. D., Greiner, J., et al. 2016, A&A, 588, A135, doi: 10.1051/0004-6361/201527509

    work page doi:10.1051/0004-6361/201527509 2016