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arxiv: 2603.22975 · v1 · submitted 2026-03-24 · 🌌 astro-ph.SR · astro-ph.EP· astro-ph.GA

Recognition: 2 theorem links

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3D NLTE Sodium abundances in late-type stars. Abundance corrections and synthetic spectra

G. Canocchi , E. X. Wang , A. M. Amarsi , K. Lind , M. Racca
Authors on Pith no claims yet

Pith reviewed 2026-05-15 00:59 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.EPastro-ph.GA
keywords sodium abundances3D NLTElate-type starsabundance correctionsstellar atmospheressodium linesGalactic chemical evolutionexoplanet atmospheres
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The pith

Three-dimensional non-LTE calculations yield sodium abundance corrections that are negative relative to 1D LTE but more positive than 1D NLTE for late-type stars.

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

This paper quantifies the impact of using three-dimensional model atmospheres and non-local thermodynamic equilibrium on derived sodium abundances from spectral lines in FGK stars. The authors post-process Stagger-grid 3D simulations with the Balder code to compute corrections for nine Na I lines across a wide range of effective temperatures, gravities, and metallicities. They find that the corrections are generally negative compared to standard 1D LTE analyses, but less negative than those from 1D NLTE, owing to stronger overionisation effects in the 3D temperature structures. A grid of these corrections is made public along with interpolation methods to support more accurate sodium measurements in Galactic archaeology and exoplanet atmosphere research.

Core claim

The central discovery is that 3D NLTE abundance corrections for Na I lines relative to 1D LTE tend to be negative and more positive than the corresponding 1D NLTE corrections. This arises because overionisation is more efficient in the steeper temperature gradients of the 3D models. The corrections are typically less severe than -0.1 dex for weak lines but can reach -0.7 dex for saturated lines in low-gravity giants, while for the D resonance lines they become slightly positive around +0.05 dex at the lowest metallicities.

What carries the argument

The 3D NLTE radiative transfer calculations performed by the Balder code on Stagger-grid radiation-hydrodynamic model atmospheres for nine Na I lines.

If this is right

  • Derived sodium abundances in metal-poor giants will be lower when using 3D NLTE instead of 1D LTE.
  • Publicly available grids enable correction of large survey data for better Galactic chemical evolution studies.
  • Exoplanet transmission spectroscopy of Na I D lines will benefit from more accurate stellar reference abundances.
  • Saturated lines require the largest adjustments, particularly in supergiants and giants with log g below 2.

Where Pith is reading between the lines

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

  • Previous sodium abundance measurements in halo stars based on 1D LTE may have been systematically too high.
  • The approach of 3D NLTE post-processing could be applied to other trace elements like lithium or potassium with similar formation physics.
  • Interpolation via neural networks may allow seamless integration into automated stellar parameter pipelines for upcoming surveys.

Load-bearing premise

The 3D radiation-hydrodynamic models from the Stagger grid accurately represent the temperature and velocity fields that affect sodium line formation, and the Balder code solves the non-LTE problem without significant unaccounted errors.

What would settle it

Comparison of sodium abundances inferred from 3D NLTE models against those from independent methods, such as sodium lines in the Sun or in stars with known abundances from other indicators, showing discrepancies larger than 0.1 dex would falsify the corrections.

Figures

Figures reproduced from arXiv: 2603.22975 by A. M. Amarsi, E. X. Wang, G. Canocchi, K. Lind, M. Racca.

Figure 1
Figure 1. Figure 1: Kiel diagram illustrating the Stagger-grid nodes at which the 3D NLTE computations have been performed, for val￾ues of [Fe/H] described by the colorbar. The models at [Fe/H] = 0.0 and +0.5 in the yellow-shaded area were previously pub￾lished in Canocchi et al. (2024b). 2. Synthetic stellar spectra 2.1. 3D hydrodynamical model atmospheres The grid of synthetic spectra for Na i presented in this work ex￾tend… view at source ↗
Figure 2
Figure 2. Figure 2: Synthetic line profiles for the Na i line at 5682 Å, computed with Balder in 1D LTE (dashed red line), 1D NLTE (dashed blue line), 3D LTE (solid red line), and 3D NLTE (solid blue line) for a cool metal-poor red giant star (left), a solar metallicity F-dwarf (middle), and a metal-rich lower main-sequence dwarf (right). 1D vmic = 1.0 km s−1 , and a sodium abundance corresponding to [Na/Fe]= +0.5 are adopted… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of interpolation models with verification models (not included in the training set) for the Na [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the REWs in 1D NLTE and 1D LTE for four selected Na [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Spatially resolved difference between the reduced equivalent width in NLTE and LTE at disc centre intensity for different Na i lines in a 3D model with Teff = 4978.17 K, log g = 2.0, [Fe/H]= −2.0 and A(Na)=4.22. Article number, page 9 of 21 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Abundance corrections for the Na i D line at 5889 Å for all models between 3D NLTE to 3D LTE, colour-coded by their [Fe/H]. The datapoints are computed at [Na/Fe]= −0.5 to +0.5 for the dwarfs, and +1.0 for the giants, in steps of 0.5 dex. (L11) and Lind et al. (2022) (L22) for four Na i lines in a turn￾off star (upper panels) and a giant (lower panels). In both L11 and L22, values below a prescribed minimu… view at source ↗
Figure 7
Figure 7. Figure 7: Abundance corrections for the Na i line at 5688 Å for all models between: 3D NLTE to 1D LTE (top left), 3D NLTE to 1D NLTE (top right), 1D NLTE to 1D LTE (bottom left) and 3D NLTE to 3D LTE (bottom right), colour-coded by their log g. The datapoints are computed at [Na/Fe]= −0.5 to +0.5 for the dwarfs, and +1.0 for the giants, in steps of 0.5 dex and, for the 1D models, at a vmic = 1.0 km s−1 . dance corre… view at source ↗
Figure 8
Figure 8. Figure 8: 3D NLTE - 1D LTE abundance corrections ( [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: 3D NLTE abundance corrections as functions of re [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Na i abundances in 1D LTE, 1D NLTE, 3D LTE, and 3D NLTE for our selected benchmark stars and the ultra metal-poor star SDSS J102915.14+172927.9. The derived A(Na) represents the weighted mean and the one sigma standard deviation of the available lines measured as in Lind et al. (2022). dance and thus behaving in the opposite direction compared to the 1D NLTE correction. 5. Conclusions In this work, we inv… view at source ↗
read the original abstract

Neutral sodium is an important tracer of the Galactic chemical evolution, a powerful diagnostic of different stellar populations, and the subject of detailed studies of exoplanet atmospheres via transmission spectroscopy. This work aims to study and quantify the errors in stellar analyses of Na I lines caused by the use of one-dimensional (1D) hydrostatic model atmospheres and the assumption of local thermodynamic equilibrium (LTE). We studied the line formation of nine Na I lines in FGK dwarfs and giants via, for the first time, 3D non-LTE (NLTE) radiative transfer post-processing with the code Balder on 3D radiation hydrodynamic stellar atmospheres from the Stagger grid spanning Teff= 4000 to 6500 K, log g = 1.5 to 5.0, and [Fe/H]=-4 to +0.5. We find that the 3D NLTE abundance corrections relative to 1D LTE tend to be negative, and more positive than the corresponding 1D NLTE corrections. This reflects more efficient overionisation in the steeper temperature gradient of the 3D models. The corrections are typically less severe than -0.1 dex for weak lines, but become much larger for saturated lines in low-gravity giants (log g < 2.0), even reaching -0.7 dex. However, for the D resonance lines, the 3D NLTE corrections relative to 1D LTE become slightly positive at the lowest metallicities in our grid, typically around +0.05 dex at [Fe/H]=-4. We make our 3D NLTE grid, together with interpolation routines based on radial basis functions and fully connected feedforward neural networks, publicly available. This will enable more accurate determination of sodium abundances in present and forthcoming stellar spectroscopic surveys, particularly for metal-poor stars, as well as a better characterisation of the Na I D lines in exoplanet atmospheres.

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

1 major / 0 minor

Summary. The manuscript presents the first 3D NLTE radiative-transfer calculations for nine Na I lines in FGK dwarfs and giants, performed with the Balder code on Stagger-grid 3D radiation-hydrodynamic models (Teff 4000–6500 K, log g 1.5–5.0, [Fe/H] −4 to +0.5). It reports that 3D NLTE abundance corrections relative to 1D LTE are generally negative but systematically more positive than the corresponding 1D NLTE corrections, with values typically < −0.1 dex for weak lines and reaching −0.7 dex for saturated lines in low-gravity giants; the D resonance lines show slightly positive corrections (~+0.05 dex) at the lowest metallicities. A public grid of corrections together with radial-basis-function and neural-network interpolation routines is released.

Significance. If the computed corrections hold, the work supplies a practical and publicly accessible improvement to sodium abundance determinations that are central to Galactic chemical-evolution studies, stellar-population diagnostics, and exoplanet transmission spectroscopy. The release of the full grid and ready-to-use interpolation tools is a clear strength that directly enhances reproducibility and usability across ongoing and future spectroscopic surveys.

major comments (1)
  1. [Abstract and results/discussion] The central interpretive claim (abstract and results section) that the 3D NLTE corrections are more positive than 1D NLTE corrections because of “more efficient overionisation in the steeper temperature gradient of the 3D models” is not accompanied by any explicit comparison of horizontally averaged T(τ) profiles, departure coefficients, or ionization balances between the 3D and 1D structures at the optical depths where the nine Na I lines form. Without such a demonstration the proposed mechanism remains an assertion rather than a demonstrated result; a figure or table showing these quantities at line-formation depths should be added.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation of minor revision. We address the single major comment below and will incorporate the requested demonstration in the revised version of the manuscript.

read point-by-point responses

  1. Referee: [Abstract and results/discussion] The central interpretive claim (abstract and results section) that the 3D NLTE corrections are more positive than 1D NLTE corrections because of “more efficient overionisation in the steeper temperature gradient of the 3D models” is not accompanied by any explicit comparison of horizontally averaged T(τ) profiles, departure coefficients, or ionization balances between the 3D and 1D structures at the optical depths where the nine Na I lines form. Without such a demonstration the proposed mechanism remains an assertion rather than a demonstrated result; a figure or table showing these quantities at line-formation depths should be added.

    Authors: We agree that an explicit comparison of the 3D and 1D temperature structures and Na I departure coefficients at line-formation depths would strengthen the physical interpretation. In the revised manuscript we will add a new figure (or expanded panel) that shows, for representative models spanning the grid (e.g., a metal-poor giant and a solar-metallicity dwarf), the horizontally averaged T(τ) profiles from the Stagger 3D models versus the corresponding 1D hydrostatic models, together with the departure coefficients b_i for the relevant Na I levels at the optical depths where the nine lines form. This will directly illustrate the steeper temperature gradient and its impact on over-ionisation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; direct computation on independent models

full rationale

The paper computes 3D NLTE abundance corrections via direct radiative transfer post-processing of Stagger-grid 3D radiation-hydrodynamic atmospheres using the Balder code. No parameters are fitted to the target Na I line data, no self-definitional loops appear in the equations, and no load-bearing claims reduce to self-citations or prior ansatzes by the same authors. The reported corrections and the overionisation interpretation follow from the numerical solution on the supplied 3D structures; the derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central results rest on established 3D stellar atmosphere models and NLTE radiative transfer codes without introducing new free parameters, ad-hoc entities, or fitted quantities beyond the input grid.

axioms (2)
  • domain assumption Stagger-grid 3D radiation-hydrodynamic models accurately represent the temperature and velocity fields in late-type stellar atmospheres
    Used as input atmospheres for the Balder radiative transfer calculations
  • domain assumption The Balder code correctly computes NLTE line formation for Na I transitions
    Post-processing tool whose accuracy is taken as given for the chosen lines

pith-pipeline@v0.9.0 · 5687 in / 1404 out tokens · 52390 ms · 2026-05-15T00:59:42.082118+00:00 · methodology

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Works this paper leans on

86 extracted references · 86 canonical work pages

  1. [1]

    Amarsi, A. M. 2015, MNRAS, 452, 1612

    work page 2015

  2. [2]

    M., Liljegren, S., & Nissen, P

    Amarsi, A. M., Liljegren, S., & Nissen, P. E. 2022, A&A, 668, A68

    work page 2022

  3. [3]

    M., Lind, K., Osorio, Y ., et al

    Amarsi, A. M., Lind, K., Osorio, Y ., et al. 2020, A&A, 642, A62

    work page 2020

  4. [4]

    M., Nissen, P

    Amarsi, A. M., Nissen, P. E., & Skúladóttir, Á. 2019, A&A, 630, A104

    work page 2019

  5. [5]

    M., Nordlander, T., Barklem, P

    Amarsi, A. M., Nordlander, T., Barklem, P. S., et al. 2018, A&A, 615, A139

    work page 2018

  6. [6]

    M., Spite, M., Korotin, S

    Andrievsky, S. M., Spite, M., Korotin, S. A., et al. 2007, A&A, 464, 1081

    work page 2007

  7. [7]

    Anstee, S. D. & O’Mara, B. J. 1995, MNRAS, 276, 859

    work page 1995

  8. [8]

    M., & Grevesse, N

    Asplund, M., Amarsi, A. M., & Grevesse, N. 2021, A&A, 653, A141

    work page 2021

  9. [9]

    J., & Scott, P

    Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481

    work page 2009

  10. [10]

    Athay, R. G. & Canfield, R. C. 1969, ApJ, 156, 695

    work page 1969

  11. [11]

    S., Belyaev, A

    Barklem, P. S., Belyaev, A. K., Dickinson, A. S., & Gadéa, F. X. 2010, A&A, 519, A20

    work page 2010

  12. [12]

    & Lardo, C

    Bastian, N. & Lardo, C. 2018, ARA&A, 56, 83

    work page 2018

  13. [13]

    K., Barklem, P

    Belyaev, A. K., Barklem, P. S., Dickinson, A. S., & Gadéa, F. X. 2010, Phys. Rev. A, 81, 032706

    work page 2010

  14. [14]

    2017, A&A, 605, A89

    Bensby, T., Feltzing, S., Gould, A., et al. 2017, A&A, 605, A89

    work page 2017

  15. [15]

    Bensby, T., Feltzing, S., & Oey, M. S. 2014, A&A, 562, A71 Bertran de Lis, S., Allende Prieto, C., Ludwig, H. G., & Koesterke, L. 2022, A&A, 661, A76 Böhm-Vitense, E. 1958, ZAp, 46, 108

    work page 2014

  16. [16]

    & Carlsson, M

    Botnen, A. & Carlsson, M. 1999, in Astrophysics and Space Science Library, V ol. 240, Numerical Astrophysics, ed. S. M. Miyama, K. Tomisaka, & T. Hanawa, 379

    work page 1999

  17. [17]

    X., et al

    Buder, S., Kos, J., Wang, E. X., et al. 2024, arXiv e-prints, arXiv:2409.19858

    work page arXiv 2024

  18. [18]

    K., et al

    Buder, S., Lind, K., Ness, M. K., et al. 2022, MNRAS, 510, 2407

    work page 2022

  19. [19]

    2021, MNRAS, 506, 150

    Buder, S., Sharma, S., Kos, J., et al. 2021, MNRAS, 506, 150

    work page 2021

  20. [20]

    Cameron, A. G. W. 1959, ApJ, 130, 429

    work page 1959

  21. [21]

    M., Nissen, P

    Carlos, M., Amarsi, A. M., Nissen, P. E., & Canocchi, G. 2025, A&A, 700, A127

    work page 2025

  22. [22]

    1992, in Astronomical Society of the Pacific Conference Series, V ol

    Carlsson, M. 1992, in Astronomical Society of the Pacific Conference Series, V ol. 26, Cool Stars, Stellar Systems, and the Sun, ed. M. S. Giampapa & J. A. Bookbinder, 499

    work page 1992

  23. [23]

    2009, A&A, 505, 139

    Carretta, E., Bragaglia, A., Gratton, R., & Lucatello, S. 2009, A&A, 505, 139

    work page 2009

  24. [24]

    2011, in Journal of Physics Conference

    Collet, R., Magic, Z., & Asplund, M. 2011, in Journal of Physics Conference

    work page 2011

  25. [25]

    & Mendoza, C

    Cunto, W. & Mendoza, C. 1992, Rev. Mexicana Astron. Astrofis., 23, 107 de Mink, S. E., Pols, O. R., Langer, N., & Izzard, R. G. 2009, A&A, 507, L1 De Silva, G. M., Freeman, K. C., Bland-Hawthorn, J., et al. 2015, MNRAS, 449, 2604

    work page 1992

  26. [26]

    2007, A&A, 464, 1029

    Decressin, T., Meynet, G., Charbonnel, C., Prantzos, N., & Ekström, S. 2007, A&A, 464, 1029

    work page 2007

  27. [27]

    Denisenkov, P. A. & Denisenkova, S. N. 1990, Soviet Astronomy Letters, 16, 275

    work page 1990

  28. [28]

    Dimitrijevic, M. S. & Sahal-Brechot, S. 1990, J. Quant. Spectr. Rad. Transf., 44, 421

    work page 1990

  29. [29]

    1981, A&A, 96, 345

    Dravins, D., Lindegren, L., & Nordlund, A. 1981, A&A, 96, 345

    work page 1981

  30. [30]

    2021, A&A, 649, A16 El Eid, M

    Dravins, D., Ludwig, H.-G., & Freytag, B. 2021, A&A, 649, A16 El Eid, M. F. & Champagne, A. E. 1995, ApJ, 451, 298

    work page 2021

  31. [31]

    & Nordlund, A

    Galsgaard, K. & Nordlund, A. 1995, A 3D MHD Code for Parallel Computers

    work page 1995

  32. [32]

    2010, Phys

    Gao, X., Han, X.-Y ., V oky, L., Feautrier, N., & Li, J.-M. 2010, Phys. Rev. A, 81, 022703

    work page 2010

  33. [33]

    2004, ARA&A, 42, 385

    Gratton, R., Sneden, C., & Carretta, E. 2004, ARA&A, 42, 385

    work page 2004

  34. [34]

    G., Bonifacio, P., Bragaglia, A., et al

    Gratton, R. G., Bonifacio, P., Bragaglia, A., et al. 2001, A&A, 369, 87

    work page 2001

  35. [35]

    G., Carretta, E., & Bragaglia, A

    Gratton, R. G., Carretta, E., & Bragaglia, A. 2012, A&A Rev., 20, 50

    work page 2012

  36. [36]

    G., Carretta, E., Eriksson, K., & Gustafsson, B

    Gratton, R. G., Carretta, E., Eriksson, K., & Gustafsson, B. 1999, A&A, 350, 955

    work page 1999

  37. [37]

    G., Lucatello, S., Carretta, E., et al

    Gratton, R. G., Lucatello, S., Carretta, E., et al. 2011, A&A, 534, A123

    work page 2011

  38. [38]

    Grevesse, N., Asplund, M., & Sauval, A. J. 2007, Space Sci. Rev., 130, 105

    work page 2007

  39. [39]

    2008, A&A, 486, 951

    Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951

    work page 2008

  40. [40]

    2015, A&A, 582, A49

    Heiter, U., Jofré, P., Gustafsson, B., et al. 2015, A&A, 582, A49

    work page 2015

  41. [41]

    Hinton, G. E. 1990, Artificial Intelligence, 46, 47

    work page 1990

  42. [42]

    2008, Atomic Data and Nuclear Data Tables, 94, 981

    Igenbergs, K., Schweinzer, J., Bray, I., Bridi, D., & Aumayr, F. 2008, Atomic Data and Nuclear Data Tables, 94, 981

    work page 2008

  43. [43]

    2013, An Introduction to Sta- tistical Learning: with Applications in R, corrected edition edn

    James, G., Witten, D., Hastie, T., & Tibshirani, R. 2013, An Introduction to Sta- tistical Learning: with Applications in R, corrected edition edn. (New York: Springer)

    work page 2013

  44. [44]

    Johnson, H. R. 1964, Annales d’Astrophysique, 27, 695

    work page 1964

  45. [45]

    Karakas, A. I. 2010, MNRAS, 403, 1413

    work page 2010

  46. [46]

    R., Nordlander, T., et al

    Karovicova, I., White, T. R., Nordlander, T., et al. 2020, A&A, 640, A25

    work page 2020

  47. [47]

    I., & Lugaro, M

    Kobayashi, C., Karakas, A. I., & Lugaro, M. 2020, ApJ, 900, 179

    work page 2020

  48. [48]

    M., & Lind, K

    Lagae, C., Amarsi, A. M., & Lind, K. 2025, A&A, 697, A60

    work page 2025

  49. [49]

    M., Rodríguez Díaz, L

    Lagae, C., Amarsi, A. M., Rodríguez Díaz, L. F., et al. 2023, A&A, 672, A90

    work page 2023

  50. [50]

    & Carlsson, M

    Leenaarts, J. & Carlsson, M. 2009, in Astronomical Society of the Pacific Conference Series, V ol. 415, The Second Hinode Science Meeting: Be- yond Discovery-Toward Understanding, ed. B. Lites, M. Cheung, T. Magara, J. Mariska, & K. Reeves, 87

    work page 2009

  51. [51]

    & Amarsi, A

    Lind, K. & Amarsi, A. M. 2024, ARA&A, 62, 475

    work page 2024

  52. [52]

    S., & Belyaev, A

    Lind, K., Asplund, M., Barklem, P. S., & Belyaev, A. K. 2011, A&A, 528, A103

    work page 2011

  53. [53]

    2013, A&A, 554, A96

    Lind, K., Melendez, J., Asplund, M., Collet, R., & Magic, Z. 2013, A&A, 554, A96

    work page 2013

  54. [54]

    2022, A&A, 665, A33

    Lind, K., Nordlander, T., Wehrhahn, A., et al. 2022, A&A, 665, A33

    work page 2022

  55. [55]

    2023, MNRAS, 526, 2378

    Loaiza-Tacuri, V ., Cunha, K., Souto, D., et al. 2023, MNRAS, 526, 2378

    work page 2023

  56. [56]

    2013, A&A, 557, A26

    Magic, Z., Collet, R., Asplund, M., et al. 2013, A&A, 557, A26

    work page 2013

  57. [57]

    F., Villanova, S., Milone, A

    Marino, A. F., Villanova, S., Milone, A. P., et al. 2011, ApJ, 730, L16

    work page 2011

  58. [58]

    2023, MNRAS, 524, 3526

    Mashonkina, L., Pakhomov, Y ., Sitnova, T., et al. 2023, MNRAS, 524, 3526

    work page 2023

  59. [59]

    I., Shimanski ˘i, V

    Mashonkina, L. I., Shimanski ˘i, V . V ., & Sakhibullin, N. A. 2000, Astronomy Reports, 44, 790

    work page 2000

  60. [60]

    M., Carlos, M., & Nissen, P

    Matsuno, T., Amarsi, A. M., Carlos, M., & Nissen, P. E. 2024, A&A, 688, A72

    work page 2024

  61. [61]

    F., et al

    McKenzie, M., Yong, D., Marino, A. F., et al. 2022, MNRAS, 516, 3515

    work page 2022

  62. [62]

    2016, PASA, 33, e040

    McWilliam, A. 2016, PASA, 33, e040

    work page 2016

  63. [63]

    Milone, A. P. & Marino, A. F. 2022, Universe, 8, 359

    work page 2022

  64. [64]

    1999, A&A, 350, 73

    Mowlavi, N. 1999, A&A, 350, 73

    work page 1999

  65. [65]

    E., Amarsi, A

    Nissen, P. E., Amarsi, A. M., Skúladóttir, Á., & Schuster, W. J. 2024, A&A, 682, A116

    work page 2024

  66. [66]

    M., Lind, K., et al

    Nordlander, T., Amarsi, A. M., Lind, K., et al. 2017, A&A, 597, A6

    work page 2017

  67. [67]

    K., Buder, S., Ruiter, A

    Owusu, E. K., Buder, S., Ruiter, A. J., Seitenzahl, I. R., & Rodriguez-Segovia, N. 2024, PASA, 41, e092

    work page 2024

  68. [68]

    2011, Journal of Machine Learning Research, 12, 2825

    Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2011, Journal of Machine Learning Research, 12, 2825

    work page 2011

  69. [69]

    2021, A&A, 645, A96 Prša, A., Harmanec, P., Torres, G., et al

    Pepe, F., Cristiani, S., Rebolo, R., et al. 2021, A&A, 645, A96 Prša, A., Harmanec, P., Torres, G., et al. 2016, AJ, 152, 41

    work page 2021

  70. [70]

    L., D’Antona, F., & Ventura, P

    Pumo, M. L., D’Antona, F., & Ventura, P. 2008, ApJ, 672, L25

    work page 2008

  71. [71]

    2005, Memorie della Societa Astronomica Italiana Supplementi, 8, 96

    Ralchenko, Y . 2005, Memorie della Societa Astronomica Italiana Supplementi, 8, 96

    work page 2005

  72. [72]

    2014, Experimental Astronomy, 38, 249 Rodríguez Díaz, L

    Rauer, H., Catala, C., Aerts, C., et al. 2014, Experimental Astronomy, 38, 249 Rodríguez Díaz, L. F., Lagae, C., Amarsi, A. M., et al. 2024, A&A, 688, A212

    work page 2014

  73. [73]

    J., Belczynski, K., Sim, S

    Ruiter, A. J., Belczynski, K., Sim, S. A., et al. 2011, MNRAS, 417, 408

    work page 2011

  74. [74]

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

    work page 2003

  75. [75]

    L., et al

    Ryabchikova, T., Piskunov, N., Kurucz, R. L., et al. 2015, Phys. Scr, 90, 054005

    work page 2015

  76. [76]

    Salpeter, E. E. 1952, ApJ, 115, 326

    work page 1952

  77. [77]

    Sansonetti, J. E. 2008, Journal of Physical and Chemical Reference Data, 37, 1659

    work page 2008

  78. [78]

    B., Bjelksjo, K., Korhonen, T

    Scharmer, G. B., Bjelksjo, K., Korhonen, T. K., Lindberg, B., & Petterson, B. 2003, in Society of Photo-Optical Instrumentation Engineers (SPIE) Confer- ence Series, V ol. 4853, Innovative Telescopes and Instrumentation for Solar Astrophysics, ed. S. L. Keil & S. V . Avakyan, 341–350

    work page 2003

  79. [79]

    R., Gehren, T., & Zhao, G

    Shi, J. R., Gehren, T., & Zhao, G. 2004, A&A, 423, 683

    work page 2004

  80. [80]

    F., Nordlund, Å., Collet, R., & Trampedach, R

    Stein, R. F., Nordlund, Å., Collet, R., & Trampedach, R. 2024, ApJ, 970, 24

    work page 2024

Showing first 80 references.