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The Future of Solar Modelling: Requirements for a New Generation of Solar Models

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Abstract

Helioseismology and solar modelling have enjoyed a golden era thanks to decades-long surveys from ground-based networks such as for example GONG, BiSON, IRIS and the SOHO and SDO space missions which have provided high-quality helioseismic observations that supplemented photometric, gravitational, size and shape, limb-darkening and spectroscopic constraints as well as measurements of neutrino fluxes. However, the success of solar models is also deeply rooted in progress in fundamental physics (equation of state of the solar plasma, high-quality atomic physics computations and opacities, description of convection and the role of macroscopic transport processes of angular momentum and chemicals, such as for example meridional circulation, internal gravity waves, shear-induced turbulence or even convection. In this paper, we briefly outline some key areas of research that deserve particular attention in solar modelling. We discuss the current uncertainties that need to be addressed, how these limit our predictions from solar models and their impact on stellar evolution in general. We outline potential strategies to mitigate them and how multidisciplinary approaches will be needed in the future to tackle them.

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References

  • Acharya, B., Aliotta, M., Balantekin, A.B., Bemmerer, D., Bertulani, C.A., Best, A., Brune, C.R., Buompane, R., Cavanna, F., Chen, J.W., Colgan, J., Czarnecki, A., Davids, B., deBoer, R.J., Delahaye, F., Depalo, R., García, A., Gatu Johnson, M., Gazit, D., Gialanella, L., Greife, U., Guffanti, D., Guglielmetti, A., Hambleton, K., Haxton, W.C., Herrera, Y., Huang, M., Iliadis, C., Kravvaris, K., La Cognata, M., Langanke, K., Marcucci, L.E., Nagayama, T., Nollett, K.M., Odell, D., Orebi Gann, G.D., Piatti, D., Pinsonneault, M., Platter, L., Robertson, R.G.H., Rupak, G., Serenelli, A., Sferrazza, M., Szücs, T., Tang, X., Tumino, A., Villante, F.L., Walker-Loud, A., Zhang, X., Zuber, K.: 2024, Solar fusion III: New data and theory for hydrogen-burning stars. arXiv e-prints. arXiv.

  • Aerts, C., Mathis, S., Rogers, T.M.: 2019, Angular momentum transport in stellar interiors. Annu. Rev. Astron. Astrophys. 57, 35. DOI. ADS.

    Article  Google Scholar 

  • Amarsi, A.M., Barklem, P.S., Asplund, M., Collet, R., Zatsarinny, O.: 2018, Inelastic O+H collisions and the O I 777 nm solar centre-to-limb variation. Astron. Astrophys. 616, A89. DOI. ADS.

    Article  Google Scholar 

  • Amarsi, A.M., Grevesse, N., Asplund, M., Collet, R.: 2021, The solar carbon, nitrogen, and oxygen abundances from a 3D LTE analysis of molecular lines. Astron. Astrophys. 656, A113. DOI. ADS.

    Article  Google Scholar 

  • Amarsi, A.M., Ogneva, D., Buldgen, G., Grevesse, N., Zhou, Y., Barklem, P.S.: 2024, The solar beryllium abundance revisited with 3D non-LTE models. Astron. Astrophys. 690, A128. DOI. ADS.

    Article  Google Scholar 

  • Anders, E.H., Lecoanet, D., Brown, B.P.: 2019, Entropy rain: dilution and compression of thermals in stratified domains. Astrophys. J. 884, 65. DOI. ADS.

    Article  Google Scholar 

  • Appel, S., Bagdasarian, Z., Basilico, D., Bellini, G., Benziger, J., Biondi, R., Caccianiga, B., Calaprice, F., Caminata, A., Cavalcante, P., Chepurnov, A., D’Angelo, D., Derbin, A., Di Giacinto, A., Di Marcello, V., Ding, X.F., Di Ludovico, A., Di Noto, L., Drachnev, I., Franco, D., Galbiati, C., Ghiano, C., Giammarchi, M., Goretti, A., Göttel, A.S., Gromov, M., Guffanti, D., Ianni, A., Ianni, A., Jany, A., Kobychev, V., Korga, G., Kumaran, S., Laubenstein, M., Litvinovich, E., Lombardi, P., Lomskaya, I., Ludhova, L., Lukyanchenko, G., Machulin, I., Martyn, J., Meroni, E., Miramonti, L., Misiaszek, M., Muratova, V., Nugmanov, R., Oberauer, L., Orekhov, V., Ortica, F., Pallavicini, M., Papp, L., Pelicci, L., Penek, Ö., Pietrofaccia, L., Pilipenko, N., Pocar, A., Raikov, G., Ranalli, M.T., Ranucci, G., Razeto, A., Re, A., Redchuk, M., Rossi, N., Schönert, S., Semenov, D., Settanta, G., Skorokhvatov, M., Singhal, A., Smirnov, O., Sotnikov, A., Tartaglia, R., Testera, G., Unzhakov, E., Villante, F.L., Vishneva, A., Vogelaar, R.B., von Feilitzsch, F., Wojcik, M., Wurm, M., Zavatarelli, S., Zuber, K., Zuzel, G., Borexino Collaboration: 2022, Improved measurement of solar neutrinos from the carbon-nitrogen-oxygen cycle by Borexino and its implications for the standard solar model. Phys. Rev. Lett. 129, 252701. DOI. ADS.

    Article  Google Scholar 

  • Appourchaux, T., Corbard, T.: 2019, Searching for g modes. II. Unconfirmed g-mode detection in the power spectrum of the time series of round-trip travel time. Astron. Astrophys. 624, A106. DOI. ADS.

    Article  Google Scholar 

  • Appourchaux, T., Pallé, P.L.: 2013, The history of the g-mode quest. In: Jain, K., Tripathy, S.C., Hill, F., Leibacher, J.W., Pevtsov, A.A. (eds.) Fifty Years of Seismology of the Sun and Stars, Astronomical Society of the Pacific Conference Series 478, 125. DOI. ADS.

    Chapter  Google Scholar 

  • Appourchaux, T., Burston, R., Chen, Y., Cruise, M., Dittus, H., Foulon, B., Gill, P., Gizon, L., Klein, H., Klioner, S., Kopeikin, S., Krüger, H., Lämmerzahl, C., Lobo, A., Luo, X., Margolis, H., Ni, W.-T., Patón, A.P., Peng, Q., Peters, A., Rasel, E., Rüdiger, A., Samain, É., Selig, H., Shaul, D., Sumner, T., Theil, S., Touboul, P., Turyshev, S., Wang, H., Wang, L., Wen, L., Wicht, A., Wu, J., Zhang, X., Zhao, C.: 2009, Astrodynamical Space Test of Relativity using Optical Devices I (ASTROD I)—a class-M fundamental physics mission proposal for Cosmic Vision 2015 – 2025. Exp. Astron. 23, 491. DOI. ADS.

    Article  Google Scholar 

  • Asplund, M., Amarsi, A.M., Grevesse, N.: 2021, The chemical make-up of the Sun: a 2020 vision. Astron. Astrophys. 653, A141. DOI. ADS.

    Article  Google Scholar 

  • Asplund, M., Grevesse, N., Sauval, A.J.: 2005, The solar chemical composition. In: Barnes, T.G. III, Bash, F.N. (eds.) Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis, Astronomical Society of the Pacific Conference Series 336, 25. ADS.

    Google Scholar 

  • Ayres, T.R., Wiedemann, G.R.: 1989, Non–LTE CO revisited. Astrophys. J. 338, 1033. DOI. ADS.

    Article  Google Scholar 

  • Backus, G., Gilbert, F.: 1968, The resolving power of Gross Earth data. Geophys. J. 16, 169. DOI. ADS.

    Article  Google Scholar 

  • Backus, G., Gilbert, F.: 1970, Uniqueness in the inversion of inaccurate Gross Earth data. Philos. Trans. R. Soc. Lond. Ser. A 266, 123. DOI. ADS.

    Article  MathSciNet  Google Scholar 

  • Bailey, J.E., Nagayama, T., Loisel, G.P., Rochau, G.A., Blancard, C., Colgan, J., Cossé, P., Faussurier, G., Fontes, C.J., Gilleron, F., Golovkin, I., Hansen, S.B., Iglesias, C.A., Kilcrease, D.P., MacFarlane, J.J., Mancini, R.C., Nahar, S.N., Orban, C., Pain, J.C., Pradhan, A.K., Sherrill, M., Wilson, B.G.: 2015, A higher-than-predicted measurement of iron opacity at solar interior temperatures. Nature 517, 3.

    Article  Google Scholar 

  • Ball, W.H., Beeck, B., Cameron, R.H., Gizon, L.: 2016, MESA meets MURaM: surface effects in main-sequence solar-like oscillators computed using three-dimensional radiation hydrodynamics simulations. Astron. Astrophys. 592, A159. ADS.

    Article  Google Scholar 

  • Baraffe, I., Pratt, J., Vlaykov, D.G., Guillet, T., Goffrey, T., Le Saux, A., Constantino, T.: 2021, Two-dimensional simulations of solar-like models with artificially enhanced luminosity. I. Impact on convective penetration. Astron. Astrophys. 654, A126. DOI. ADS.

    Article  Google Scholar 

  • Baraffe, I., Constantino, T., Clarke, J., Le Saux, A., Goffrey, T., Guillet, T., Pratt, J., Vlaykov, D.G.: 2022, Local heating due to convective overshooting and the solar modelling problem. Astron. Astrophys. 659, A53. DOI. ADS.

    Article  Google Scholar 

  • Barklem, P.S., Amarsi, A.M.: 2024, Revisiting the statistical equilibrium of H in stellar atmospheres. arXiv e-prints. arXiv. ADS.

  • Basilico, D., Bellini, G., Benziger, J., Biondi, R., Caccianiga, B., Calaprice, F., Caminata, A., Chepurnov, A., D’Angelo, D., Derbin, A., Di Giacinto, A., Di Marcello, V., Ding, X.F., Di Ludovico, A., Di Noto, L., Drachnev, I., Franco, D., Galbiati, C., Ghiano, C., Giammarchi, M., Goretti, A., Gromov, M., Guffanti, D., Ianni, A., Ianni, A., Jany, A., Kobychev, V., Korga, G., Kumaran, S., Laubenstein, M., Litvinovich, E., Lombardi, P., Lomskaya, I., Ludhova, L., Machulin, I., Martyn, J., Meroni, E., Miramonti, L., Misiaszek, M., Muratova, V., Nugmanov, R., Oberauer, L., Orekhov, V., Ortica, F., Pallavicini, M., Pelicci, L., Penek, Ö., Pietrofaccia, L., Pilipenko, N., Pocar, A., Raikov, G., Ranalli, M.T., Ranucci, G., Razeto, A., Re, A., Rossi, N., Schönert, S., Semenov, D., Settanta, G., Skorokhvatov, M., Singhal, A., Smirnov, O., Sotnikov, A., Tartaglia, R., Testera, G., Unzhakov, E., Villante, F.L., Vishneva, A., Vogelaar, R.B., von Feilitzsch, F., Wojcik, M., Wurm, M., Zavatarelli, S., Zuber, K., Zuzel, G., Borexino Collaboration: 2023, Final results of Borexino on CNO solar neutrinos. Phys. Rev. D 108, 102005. DOI. ADS.

    Article  Google Scholar 

  • Basinger, C., Pinsonneault, M., Bastelberger, S.T., Gaudi, B.S., Domagal-Goldman, S.D.: 2024, Constraints on the early luminosity history of the Sun: applications to the faint young Sun problem. Mon. Not. R. Astron. Soc. 534, 2968. DOI. ADS.

    Article  Google Scholar 

  • Basu, S., Christensen-Dalsgaard, J.: 1997, Equation of state and helioseismic inversions. Astron. Astrophys. 322, L5. DOI. ADS.

    Article  Google Scholar 

  • Baturin, V.A., Däppen, W., Morel, P., Oreshina, A.V., Thévenin, F., Gryaznov, V.K., Iosilevskiy, I.L., Starostin, A.N., Fortov, V.E.: 2017, Equation of state SAHA-S meets stellar evolution code CESAM2k. Astron. Astrophys. 606, A129. DOI. ADS.

    Article  Google Scholar 

  • Baturin, V.A., Oreshina, A.V., Däppen, W., Ayukov, S.V., Gorshkov, A.B., Gryaznov, V.K., Iosilevskiy, I.L.: 2022, Ionization of heavy elements and the adiabatic exponent in the solar plasma. Astron. Astrophys. 660, A125. DOI. ADS.

    Article  Google Scholar 

  • Baturin, V.A., Oreshina, A.V., Buldgen, G., Ayukov, S.V., Gryaznov, V.K., Iosilevskiy, I.L., Noels, A., Scuflaire, R.: 2024, Heavy elements abundances inferred from the first adiabatic exponent in the solar envelope. Sol. Phys. 299, 142. DOI. ADS.

    Article  Google Scholar 

  • Baturin, V.A., Ayukov, S.V., Oreshina, A.V., Gorshkov, A.B., Gryaznov, V.K., Iosilevskiy, I.L., Däppen, W.: 2025, Hydrogen ionization inside the Sun. Sol. Phys. 300, 3. DOI. ADS.

    Article  Google Scholar 

  • Bedding, T.R., Mosser, B., Huber, D., Montalbán, J., Beck, P., Christensen-Dalsgaard, J., Elsworth, Y.P., García, R.A., Miglio, A., Stello, D., White, T.R., De Ridder, J., Hekker, S., Aerts, C., Barban, C., Belkacem, K., Broomhall, A.-M., Brown, T.M., Buzasi, D.L., Carrier, F., Chaplin, W.J., di Mauro, M.P., Dupret, M.-A., Frandsen, S., Gilliland, R.L., Goupil, M.-J., Jenkins, J.M., Kallinger, T., Kawaler, S., Kjeldsen, H., Mathur, S., Noels, A., Silva Aguirre, V., Ventura, P.: 2011, Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars. Nature 471, 608. DOI. ADS.

    Article  Google Scholar 

  • Bergström, J., Gonzalez-Garcia, M.C., Maltoni, M., Peña-Garay, C., Serenelli, A.M., Song, N.: 2016, Updated determination of the solar neutrino fluxes from solar neutrino data. J. High Energy Phys. 2016, 132. DOI. ADS.

    Article  Google Scholar 

  • Bétrisey, J., Farnir, M., Breton, S.N., García, R.A., Broomhall, A.-M., Amarsi, A.M., Kochukhov, O.: 2024, Imprint of the magnetic activity cycle on solar asteroseismic characterisation based on 26 years of GOLF and BiSON data. Astron. Astrophys. 688, L17. DOI. ADS.

    Article  Google Scholar 

  • Böning, V.G.A., Hu, H., Gizon, L.: 2019, Signature of solar g modes in first-order p-mode frequency shifts. Astron. Astrophys. 629, A26. DOI. ADS.

    Article  Google Scholar 

  • Boothroyd, A.I., Sackmann, I.-J.: 2003, Our Sun. IV. The standard model and helioseismology: consequences of uncertainties in input physics and in observed solar parameters. Astrophys. J. 583, 1004. DOI. ADS.

    Article  Google Scholar 

  • Borexino Collaboration, Agostini, M., Altenmüller, K., Appel, S., Atroshchenko, V., Bagdasarian, Z., Basilico, D., Bellini, G., Benziger, J., Bick, D., Bonfini, G., Bravo, D., Caccianiga, B., Calaprice, F., Caminata, A., Caprioli, S., Carlini, M., Cavalcante, P., Chepurnov, A., Choi, K., Collica, L., D’Angelo, D., Davini, S., Derbin, A., Ding, X.F., Di Ludovico, A., Di Noto, L., Drachnev, I., Fomenko, K., Formozov, A., Franco, D., Gabriele, F., Galbiati, C., Ghiano, C., Giammarchi, M., Goretti, A., Gromov, M., Guffanti, D., Hagner, C., Houdy, T., Hungerford, E., Ianni, A., Ianni, A., Jany, A., Jeschke, D., Kobychev, V., Korablev, D., Korga, G., Kryn, D., Laubenstein, M., Litvinovich, E., Lombardi, F., Lombardi, P., Ludhova, L., Lukyanchenko, G., Lukyanchenko, L., Machulin, I., Manuzio, G., Marcocci, S., Martyn, J., Meroni, E., Meyer, M., Miramonti, L., Misiaszek, M., Muratova, V., Neumair, B., Oberauer, L., Opitz, B., Orekhov, V., Ortica, F., Pallavicini, M., Papp, L., Penek, Ö., Pilipenko, N., Pocar, A., Porcelli, A., Raikov, G., Ranucci, G., Razeto, A., Re, A., Redchuk, M., Romani, A., Roncin, R., Rossi, N., Schönert, S., Semenov, D., Skorokhvatov, M., Smirnov, O., Sotnikov, A., Stokes, L.F.F., Suvorov, Y., Tartaglia, R., Testera, G., Thurn, J., Toropova, M., Unzhakov, E., Villante, F.L., Vishneva, A., Vogelaar, R.B., von Feilitzsch, F., Wang, H., Weinz, S., Wojcik, M., Wurm, M., Yokley, Z., Zaimidoroga, O., Zavatarelli, S., Zuber, K., Zuzel, G.: 2018, Comprehensive measurement of pp-chain solar neutrinos. Nature 562, 505. DOI. ADS.

    Article  Google Scholar 

  • Borexino Collaboration, Agostini, M., Altenmüller, K., Appel, S., Atroshchenko, V., Bagdasarian, Z., Basilico, D., Bellini, G., Benziger, J., Biondi, R., Bravo, D., Caccianiga, B., Calaprice, F., Caminata, A., Cavalcante, P., Chepurnov, A., D’Angelo, D., Davini, S., Derbin, A., Di Giacinto, A., Di Marcello, V., Ding, X.F., Di Ludovico, A., Di Noto, L., Drachnev, I., Formozov, A., Franco, D., Galbiati, C., Ghiano, C., Giammarchi, M., Goretti, A., Göttel, A.S., Gromov, M., Guffanti, D., Ianni, A., Ianni, A., Jany, A., Jeschke, D., Kobychev, V., Korga, G., Kumaran, S., Laubenstein, M., Litvinovich, E., Lombardi, P., Lomskaya, I., Ludhova, L., Lukyanchenko, G., Lukyanchenko, L., Machulin, I., Martyn, J., Meroni, E., Meyer, M., Miramonti, L., Misiaszek, M., Muratova, V., Neumair, B., Nieslony, M., Nugmanov, R., Oberauer, L., Orekhov, V., Ortica, F., Pallavicini, M., Papp, L., Pelicci, L., Penek, Ö., Pietrofaccia, L., Pilipenko, N., Pocar, A., Raikov, G., Ranalli, M.T., Ranucci, G., Razeto, A., Re, A., Redchuk, M., Romani, A., Rossi, N., Schönert, S., Semenov, D., Settanta, G., Skorokhvatov, M., Singhal, A., Smirnov, O., Sotnikov, A., Suvorov, Y., Tartaglia, R., Testera, G., Thurn, J., Unzhakov, E., Villante, F.L., Vishneva, A., Vogelaar, R.B., von Feilitzsch, F., Wojcik, M., Wurm, M., Zavatarelli, S., Zuber, K., Zuzel, G.: 2020, Experimental evidence of neutrinos produced in the CNO fusion cycle in the Sun. Nature 587, 577. DOI. ADS.

    Article  Google Scholar 

  • Bouvier, J., Matt, S.P., Mohanty, S., Scholz, A., Stassun, K.G., Zanni, C.: 2014, Angular momentum evolution of young low-mass stars and Brown dwarfs: observations and theory. In: Protostars and Planets VI 433. DOI. ADS.

    Chapter  Google Scholar 

  • Brandenburg, A.: 2016, Stellar mixing length theory with entropy rain. Astrophys. J. 832, 6. DOI. ADS.

    Article  Google Scholar 

  • Broomhall, A.-M., Nakariakov, V.M.: 2015, A comparison between global proxies of the Sun’s magnetic activity cycle: inferences from helioseismology. Sol. Phys. 290, 3095. DOI. ADS.

    Article  Google Scholar 

  • Broomhall, A.-M., Chaplin, W.J., Elsworth, Y., New, R.: 2011, Solar-cycle variations of large frequency separations of acoustic modes: implications for asteroseismology. Mon. Not. R. Astron. Soc. 413, 2978. DOI. ADS.

    Article  Google Scholar 

  • Brun, A.S., Miesch, M.S., Toomre, J.: 2011, Modeling the dynamical coupling of solar convection with the radiative interior. Astrophys. J. 742, 79. DOI. ADS.

    Article  Google Scholar 

  • Buldgen, G., Salmon, S.J.A.J., Noels, A., Scuflaire, R., Dupret, M.A., Reese, D.R.: 2017, Determining the metallicity of the solar envelope using seismic inversion techniques. Mon. Not. R. Astron. Soc. 472, 751. DOI. ADS.

    Article  Google Scholar 

  • Buldgen, G., Bétrisey, J., Roxburgh, I.W., Vorontsov, S.V., Reese, D.R.: 2022, Inversions of stellar structure from asteroseismic data. Front. Astron. Space Sci. 9, 942373. DOI. ADS.

    Article  Google Scholar 

  • Buldgen, G., Fellay, L., Bétrisey, J., Deheuvels, S., Farnir, M., Farrell, E.: 2024b, Markov chain Monte Carlo inversions of the internal rotation of Kepler subgiants. Astron. Astrophys. 689, A307. DOI. ADS.

    Article  Google Scholar 

  • Buldgen, G., Noels, A., Baturin, V.A., Oreshina, A.V., Ayukov, S.V., Scuflaire, R., Amarsi, A.M., Grevesse, N.: 2024a, Helioseismic determination of the solar metal mass fraction. Astron. Astrophys. 681, A57. DOI. ADS.

    Article  Google Scholar 

  • Burnett, D.S., Jurewicz, A.J.G., Woolum, D.S.: 2019, The future of genesis science. Meteorit. Planet. Sci. 54, 1092. DOI. ADS.

    Article  Google Scholar 

  • Caffau, E., Ludwig, H.-G., Steffen, M., Freytag, B., Bonifacio, P.: 2011, Solar chemical abundances determined with a CO5BOLD 3D model atmosphere. Sol. Phys. 268, 255. DOI. ADS.

    Article  Google Scholar 

  • Caffau, E., Ludwig, H.-G., Malherbe, J.-M., Bonifacio, P., Steffen, M., Monaco, L.: 2013, The photospheric solar oxygen project. II. Non-concordance of the oxygen abundance derived from two forbidden lines. Astron. Astrophys. 554, A126. DOI. ADS.

    Article  Google Scholar 

  • Caliskan, S., Grumer, J., Amarsi, A.M.: 2024, Targeted optimization in small-scale atomic structure calculations: application to Au I. J. Phys. B, At. Mol. Phys. 57, 055003. DOI. ADS.

    Article  Google Scholar 

  • Canocchi, G., Lind, K., Lagae, C., Pietrow, A.G.M., Amarsi, A.M., Kiselman, D., Andriienko, O., Hoeijmakers, H.J.: 2024, 3D non-LTE modeling of the stellar center-to-limb variation for transmission spectroscopy studies. Na I D and K I resonance lines in the Sun. Astron. Astrophys. 683, A242. DOI. ADS.

    Article  Google Scholar 

  • Cantiello, M., Mankovich, C., Bildsten, L., Christensen-Dalsgaard, J., Paxton, B.: 2014, Angular momentum transport within evolved low-mass stars. Astrophys. J. 788, 93. DOI. ADS.

    Article  Google Scholar 

  • Chaplin, W.J., Miglio, A.: 2013, Asteroseismology of solar-type and red-giant stars. Annu. Rev. Astron. Astrophys. 51, 353. DOI. ADS.

    Article  Google Scholar 

  • Chaplin, W.J., Elsworth, Y., Howe, R., Isaak, G.R., McLeod, C.P., Miller, B.A., van der Raay, H.B., Wheeler, S.J., New, R.: 1996, BiSON performance. Sol. Phys. 168, 1. DOI. ADS.

    Article  Google Scholar 

  • Charbonnel, C., Talon, S.: 2005, Influence of gravity waves on the internal rotation and Li abundance of solar-type stars. Science 309, 2189. DOI. ADS.

    Article  Google Scholar 

  • Christensen-Dalsgaard, J.: 2009, On the opacity change required to compensate for the revised solar composition. Astron. Astrophys. 494, 205.

    Article  Google Scholar 

  • Christensen-Dalsgaard, J.: 2021, Solar structure and evolution. Living Rev. Sol. Phys. 18, 2. DOI. ADS.

    Article  Google Scholar 

  • Christensen-Dalsgaard, J., Däppen, W.: 1992, Solar oscillations and the equation of state. Astron. Astrophys. Rev. 4, 267. DOI. ADS.

    Article  Google Scholar 

  • Christensen-Dalsgaard, J., Proffitt, C.R., Thompson, M.J.: 1993, Effects of diffusion on solar models and their oscillation frequencies. Astrophys. J. Lett. 403, L75. DOI. ADS.

    Article  Google Scholar 

  • Christensen-Dalsgaard, J., Schou, J., Thompson, M.J.: 1990, A comparison of methods for inverting helioseismic data. Mon. Not. R. Astron. Soc. 242, 353. DOI. ADS.

    Article  Google Scholar 

  • Christensen-Dalsgaard, J., Däppen, W., Ajukov, S.V., Anderson, E.R., Antia, H.M., Basu, S., Baturin, V.A., Berthomieu, G., Chaboyer, B., Chitre, S.M., Cox, A.N., Demarque, P., Donatowicz, J., Dziembowski, W.A., Gabriel, M., Gough, D.O., Guenther, D.B., Guzik, J.A., Harvey, J.W., Hill, F., Houdek, G., Iglesias, C.A., Kosovichev, A.G., Leibacher, J.W., Morel, P., Proffitt, C.R., Provost, J., Reiter, J., Rhodes, J.E.J., Rogers, F.J., Roxburgh, I.W., Thompson, M.J., Ulrich, R.K.: 1996, The current state of solar modeling. Science 272, 1286. DOI. ADS.

    Article  Google Scholar 

  • Christensen-Dalsgaard, J., Monteiro, M.J.P.F.G., Rempel, M., Thompson, M.J.: 2011, A more realistic representation of overshoot at the base of the solar convective envelope as seen by helioseismology. Mon. Not. R. Astron. Soc. 414, 1158. DOI. ADS.

    Article  Google Scholar 

  • Colgan, J., Kilcrease, D.P., Magee, N.H., Sherrill, M.E., Abdallah, J. Jr., Hakel, P., Fontes, C.J., Guzik, J.A., Mussack, K.A.: 2016, A new generation of Los Alamos opacity tables. Astrophys. J. 817, 116.

    Article  Google Scholar 

  • Corbard, T., Blanc-Féraud, L., Berthomieu, G., Provost, J.: 1999, Non linear regularization for helioseismic inversions. Application for the study of the solar tachocline. Astron. Astrophys. 344, 696. DOI. ADS.

    Article  Google Scholar 

  • Cranmer, S.R.: 2017, Mass-loss rates from coronal mass ejections: a predictive theoretical model for solar-type stars. Astrophys. J. 840, 114. DOI. ADS.

    Article  Google Scholar 

  • Cranmer, S.R., Saar, S.H.: 2011, Testing a predictive theoretical model for the mass loss rates of cool stars. Astrophys. J. 741, 54. DOI. ADS.

    Article  Google Scholar 

  • Cunha, M.S., Aerts, C., Christensen-Dalsgaard, J., Baglin, A., Bigot, L., Brown, T.M., Catala, C., Creevey, O.L., Domiciano de Souza, A., Eggenberger, P., Garcia, P.J.V., Grundahl, F., Kervella, P., Kurtz, D.W., Mathias, P., Miglio, A., Monteiro, M.J.P.F.G., Perrin, G., Pijpers, F.P., Pourbaix, D., Quirrenbach, A., Rousselet-Perraut, K., Teixeira, T.C., Thévenin, F., Thompson, M.J.: 2007, Asteroseismology and interferometry. Astron. Astrophys. Rev. 14, 217. DOI. ADS.

    Article  Google Scholar 

  • Da Silva, L.B., MacGowan, B.J., Kania, D.R., Hammel, B.A., Back, C.A., Hsieh, E., Doyas, R., Iglesias, C.A., Rogers, F.J., Lee, R.W.: 1992, Absorption measurements demonstrating the importance of \(\Delta \)n= 0 transitions in the opacity of iron. Phys. Rev. Lett. 69, 438. DOI.

    Article  Google Scholar 

  • Deheuvels, S., Doğan, G., Goupil, M.J., Appourchaux, T., Benomar, O., Bruntt, H., Campante, T.L., Casagrande, L., Ceillier, T., Davies, G.R., De Cat, P., Fu, J.N., García, R.A., Lobel, A., Mosser, B., Reese, D.R., Regulo, C., Schou, J., Stahn, T., Thygesen, A.O., Yang, X.H., Chaplin, W.J., Christensen-Dalsgaard, J., Eggenberger, P., Gizon, L., Mathis, S., Molenda-Żakowicz, J., Pinsonneault, M.: 2014, Seismic constraints on the radial dependence of the internal rotation profiles of six Kepler subgiants and young red giants. Astron. Astrophys. 564, A27. DOI. ADS.

    Article  Google Scholar 

  • Deheuvels, S., Ballot, J., Eggenberger, P., Spada, F., Noll, A., den Hartogh, J.W.: 2020, Seismic evidence for near solid-body rotation in two Kepler subgiants and implications for angular momentum transport. Astron. Astrophys. 641, A117. DOI. ADS.

    Article  Google Scholar 

  • Delbouille, L., Roland, G., Neven, L.: 1973, Atlas Photometrique du Spectre Solaire de [Lambda] 3000 a [Lambda] 10000. ADS.

    Google Scholar 

  • Dias, E.W.B., Chakraborty, H.S., Deshmukh, P.C., Manson, S.T., Hemmers, O., Glans, P., Hansen, D.L., Wang, H., Whitfield, S.B., Lindle, D.W., Wehlitz, R., Levin, J.C., Sellin, I.A., Perera, R.C.C.: 1997, Breakdown of the independent particle approximation in high-energy photoionization. Phys. Rev. Lett. 78, 4553. DOI.

    Article  Google Scholar 

  • Drążkowska, J., Bitsch, B., Lambrechts, M., Mulders, G.D., Harsono, D., Vazan, A., Liu, B., Ormel, C.W., Kretke, K., Morbidelli, A.: 2023, Planet formation theory in the era of ALMA and Kepler: from pebbles to exoplanets. In: Inutsuka, S., Aikawa, Y., Muto, T., Tomida, K., Tamura, M. (eds.) Protostars and Planets VII, Astronomical Society of the Pacific Conference Series 534, 717. DOI. ADS.

    Chapter  Google Scholar 

  • Eggenberger, P., Buldgen, G., Salmon, S.J.A.J., Noels, A., Grevesse, N., Asplund, M.: 2022, The internal rotation of the Sun and its link to the solar Li and He surface abundances. Nat. Astron. 6, 788. DOI. ADS.

    Article  Google Scholar 

  • Elliott, J.R.: 1996, Equation of state in the solar convection zone and the implications of helioseismology. Mon. Not. R. Astron. Soc. 280, 1244. DOI. ADS.

    Article  Google Scholar 

  • Elliott, J.R., Kosovichev, A.G.: 1998, The adiabatic exponent in the solar core. Astrophys. J. Lett. 500, L199. DOI. ADS.

    Article  Google Scholar 

  • Ellwarth, M., Ehmann, B., Schäfer, S., Reiners, A.: 2023, Convective characteristics of Fe I lines across the solar disc. Astron. Astrophys. 680, A62. DOI. ADS.

    Article  Google Scholar 

  • Fabbian, D., Khomenko, E., Moreno-Insertis, F., Nordlund, Å.: 2010, Solar abundance corrections derived through three-dimensional magnetoconvection simulations. Astrophys. J. 724, 1536.

    Article  Google Scholar 

  • Fellay, L., Buldgen, G., Eggenberger, P., Khan, S., Salmon, S.J.A.J., Miglio, A., Montalbán, J.: 2021, Asteroseismology of evolved stars to constrain the internal transport of angular momentum. IV. Internal rotation of Kepler-56 from an MCMC analysis of the rotational splittings. Astron. Astrophys. 654, A133. DOI. ADS.

    Article  Google Scholar 

  • Fossat, E.: 1991, The IRIS network for full disk helioseismology - present status of the programme. Sol. Phys. 133, 1. DOI. ADS.

    Article  Google Scholar 

  • Fossat, E., Boumier, P., Corbard, T., Provost, J., Salabert, D., Schmider, F.X., Gabriel, A.H., Grec, G., Renaud, C., Robillot, J.M., Roca-Cortés, T., Turck-Chièze, S., Ulrich, R.K., Lazrek, M.: 2017, Asymptotic g modes: evidence for a rapid rotation of the solar core. Astron. Astrophys. 604, A40. DOI. ADS.

    Article  Google Scholar 

  • Freytag, B., Ludwig, H.-G., Steffen, M.: 1996, Hydrodynamical models of stellar convection. The role of overshoot in DA white dwarfs, A-type stars and the Sun. Astron. Astrophys. 313, 497. ADS.

    Google Scholar 

  • Freytag, B., Steffen, M., Ludwig, H.-G., Wedemeyer-Böhm, S., Schaffenberger, W., Steiner, O.: 2012, Simulations of stellar convection with CO5BOLD. J. Comput. Phys. 231, 919. DOI. ADS.

    Article  Google Scholar 

  • Fröhlich, C., Romero, J., Roth, H., Wehrli, C., Andersen, B.N., Appourchaux, T., Domingo, V., Telljohann, U., Berthomieu, G., Delache, P., Provost, J., Toutain, T., Crommelynck, D.A., Chevalier, A., Fichot, A., Däppen, W., Gough, D., Hoeksema, T., Jiménez, A., Gómez, M.F., Herreros, J.M., Cortés, T.R., Jones, A.R., Pap, J.M., Willson, R.C.: 1995, VIRGO: experiment for helioseismology and solar irradiance monitoring. Sol. Phys. 162, 101. DOI. ADS.

    Article  Google Scholar 

  • Fuller, J., Piro, A.L., Jermyn, A.S.: 2019, Slowing the spins of stellar cores. Mon. Not. R. Astron. Soc. 485, 3661. DOI. ADS.

    Article  Google Scholar 

  • Gabriel, A.H., Charra, J., Grec, G., Robillot, J.-M., Roca Cortés, T., Turck-Chièze, S., Ulrich, R., Basu, S., Baudin, F., Bertello, L., Boumier, P., Charra, M., Christensen-Dalsgaard, J., Decaudin, M., Dzitko, H., Foglizzo, T., Fossat, E., García, R.A., Herreros, J.M., Lazrek, M., Pallé, P.L., Pétrou, N., Renaud, C., Régulo, C.: 1997, Performance and early results from the GOLF instrument flown on the SOHO mission. Sol. Phys. 175, 207. DOI. ADS.

    Article  Google Scholar 

  • Gallet, F., Zanni, C., Amard, L.: 2019, Rotational evolution of solar-type protostars during the star-disk interaction phase. Astron. Astrophys. 632, A6. DOI. ADS.

    Article  Google Scholar 

  • García, R.A., Ballot, J.: 2019, Asteroseismology of solar-type stars. Living Rev. Sol. Phys. 16, 4. DOI. ADS.

    Article  Google Scholar 

  • García, R.A., Turck-Chièze, S., Jiménez-Reyes, S.J., Ballot, J., Pallé, P.L., Eff-Darwich, A., Mathur, S., Provost, J.: 2007, Tracking solar gravity modes: the dynamics of the solar core. Science 316, 1591. DOI. ADS.

    Article  Google Scholar 

  • Gough, D.O., McIntyre, M.E.: 1998, Inevitability of a magnetic field in the Sun’s radiative interior. Nature 394, 755. DOI. ADS.

    Article  Google Scholar 

  • Goupil, M.J., Catala, C., Samadi, R., Belkacem, K., Ouazzani, R.M., Reese, D.R., Appourchaux, T., Mathur, S., Cabrera, J., Börner, A., Paproth, C., Moedas, N., Verma, K., Lebreton, Y., Deal, M., Ballot, J., Chaplin, W.J., Christensen-Dalsgaard, J., Cunha, M., Lanza, A.F., Miglio, A., Morel, T., Serenelli, A., Mosser, B., Creevey, O., Moya, A., Garcia, R.A., Nielsen, M.B., Hatt, E.: 2024, Predicted asteroseismic detection yield for solar-like oscillating stars with PLATO. Astron. Astrophys. 683, A78. DOI. ADS.

    Article  Google Scholar 

  • Graboske, H.C., Harwood, D.J., Rogers, F.J.: 1969, Thermodynamic properties of nonideal gases. I. Free-energy minimization method. Phys. Rev. 186, 210. ADS.

    Article  Google Scholar 

  • Grumer, J., Eklund, G., Amarsi, A.M., Barklem, P.S., Rosén, S., Ji, M., Simonsson, A., Cederquist, H., Zettergren, H., Schmidt, H.T.: 2022, State-resolved mutual neutralization of Mg+ and D. Phys. Rev. Lett. 128, 033401. DOI. ADS.

    Article  Google Scholar 

  • Gryaznov, V.K., Ayukov, S.V., Baturin, V.A., Iosilevskiy, I.L., Starostin, A.N., Fortov, V.E.: 2004, SAHA-S model: equation of state and thermodynamic functions of solar plasma. In: Celebonovic, V., Gough, D., Däppen, W. (eds.) Equation-of-State and Phase-Transition in Models of Ordinary Astrophysical Matter, American Institute of Physics Conference Series 731, 147. DOI. AIP. ADS.

    Chapter  Google Scholar 

  • Gryaznov, V.K., Ayukov, S.V., Baturin, V.A., Iosilevskiy, I.L., Starostin, A.N., Fortov, V.E.: 2006, Solar plasma: calculation of thermodynamic functions and equation of state. J. Phys. A, Math. Gen. 39, 4459. DOI. ADS.

    Article  Google Scholar 

  • Guillot, T., Hueso, R.: 2006, The composition of Jupiter: sign of a (relatively) late formation in a chemically evolved protosolar disc. Mon. Not. R. Astron. Soc. 367, L47. DOI.

    Article  Google Scholar 

  • Guillot, T., Ida, S., Ormel, C.W.: 2014, On the filtering and processing of dust by planetesimals. I. Derivation of collision probabilities for non-drifting planetesimals. Astron. Astrophys. 572, A72. DOI. ADS.

    Article  Google Scholar 

  • Guzik, J.A., Mussack, K.: 2010, Exploring mass loss, low-Z accretion, and convective overshoot in solar models to mitigate the solar abundance problem. Astrophys. J. 713, 1108. DOI. ADS.

    Article  Google Scholar 

  • Hakel, P., Kilcrease, D.P.: 2004, CHEMEOS: A New Chemical-Picture-Based Model for Plasma Equation-of-State Calculations, AIP Conference Proceedings 730, American Institute of Physics, 190.

    Google Scholar 

  • Hale, S.J., Howe, R., Chaplin, W.J., Davies, G.R., Elsworth, Y.P.: 2016, Performance of the Birmingham Solar-Oscillations Network (BiSON). Sol. Phys. 291, 1. DOI. ADS.

    Article  Google Scholar 

  • Hansen, S.B., More, R., Bailey, J., Pain, J.-C., Nagayama, T.: 2020, Two-photon absorption in plasmas. In: APS Division of Plasma Physics Meeting Abstracts, APS Meeting Abstracts 2020, GO08.010. ADS.

    Google Scholar 

  • Harvey, J.W., Hill, F., Hubbard, R.P., Kennedy, J.R., Leibacher, J.W., Pintar, J.A., Gilman, P.A., Noyes, R.W., Title, A.M., Toomre, J., Ulrich, R.K., Bhatnagar, A., Kennewell, J.A., Marquette, W., Patron, J., Saa, O., Yasukawa, E.: 1996, The Global Oscillation Network Group (GONG) project. Science 272, 1284. DOI. ADS.

    Article  Google Scholar 

  • Heber, V.S., Wieler, R., Baur, H., Olinger, C., Friedmann, T.A., Burnett, D.S.: 2009, Noble gas composition of the solar wind as collected by the Genesis mission. Geochim. Cosmochim. Acta 73, 7414. DOI. ADS.

    Article  Google Scholar 

  • Hinkle, K.H., Lambert, D.L.: 1975, Formation of molecular lines in stellar atmospheres. Mon. Not. R. Astron. Soc. 170, 447. DOI. ADS.

    Article  Google Scholar 

  • Hoarty, D.J., Morton, J., Rougier, J.C., Rubery, M., Opachich, Y.P., Swatton, D., Richardson, S., Heeter, R.F., McLean, K., Rose, S.J., Perry, T.S., Remington, B.: 2023, Radiation burnthrough measurements to infer opacity at conditions close to the solar radiative zone–convective zone boundary. Phys. Plasmas 30, 063302. DOI.

    Article  Google Scholar 

  • Hoeksema, J.T., Baldner, C.S., Bush, R.I., Schou, J., Scherrer, P.H.: 2018, On-orbit performance of the Helioseismic and Magnetic Imager instrument onboard the Solar Dynamics Observatory. Sol. Phys. 293, 45. DOI. ADS.

    Article  Google Scholar 

  • Hotta, H., Kusano, K., Shimada, R.: 2022, Generation of solar-like differential rotation. Astrophys. J. 933, 199. DOI. ADS.

    Article  Google Scholar 

  • Hotta, H., Bekki, Y., Gizon, L., Noraz, Q., Rast, M.: 2023, Dynamics of large-scale solar flows. Space Sci. Rev. 219, 77. DOI. ADS.

    Article  Google Scholar 

  • Houdek, G., Trampedach, R., Aarslev, M.J., Christensen-Dalsgaard, J.: 2017, On the surface physics affecting solar oscillation frequencies. Mon. Not. R. Astron. Soc. 464, L124. DOI. ADS.

    Article  Google Scholar 

  • Howe, R., Chaplin, W.J., Basu, S., Ball, W.H., Davies, G.R., Elsworth, Y., Hale, S.J., Miglio, A., Nielsen, M.B., Viani, L.S.: 2020, Solar cycle variation of \(\nu \)max in helioseismic data and its implications for asteroseismology. Mon. Not. R. Astron. Soc. 493, L49. DOI. ADS.

    Article  Google Scholar 

  • Hummer, D.G., Mihalas, D.: 1988, The equation of state for stellar envelopes. I. An occupation probability formalism for the truncation of internal partitition functions. Astrophys. J. 331, 794. ADS.

    Article  Google Scholar 

  • Iglesias, C.A., Rogers, F.J.: 1996, Updated opal opacities. Astrophys. J. 464, 943.

    Article  Google Scholar 

  • Inutsuka, S.-i.: 2012, Present-day star formation: from molecular cloud cores to protostars and protoplanetary disks. Prog. Theor. Exp. Phys. 2012, 01A307. DOI. ADS.

    Article  Google Scholar 

  • Irwin, A.W.: 2012, FreeEOS: Equation of State for stellar interiors calculations. Astrophysics Source Code Library.

  • Jones, S., Andrassy, R., Sandalski, S., Davis, A., Woodward, P., Herwig, F.: 2017, Idealized hydrodynamic simulations of turbulent oxygen-burning shell convection in 4\(\pi \) geometry. Mon. Not. R. Astron. Soc. 465, 2991. DOI. ADS.

    Article  Google Scholar 

  • Jørgensen, A.C.S., Mosumgaard, J.R., Weiss, A., Silva Aguirre, V., Christensen-Dalsgaard, J.: 2018, Coupling 1D stellar evolution with 3D-hydrodynamical simulations on the fly - I. A new standard solar model. Mon. Not. R. Astron. Soc. 481, L35. DOI. ADS.

    Article  Google Scholar 

  • Kilcrease, D.P., Colgan, J., Hakel, P., Fontes, C.J., Sherrill, M.E.: 2015, An equation of state for partially ionized plasmas: the Coulomb contribution to the free energy. High Energy Density Phys. 16, 36. http://www.sciencedirect.com/science/article/pii/S1574181815000531.

    Article  Google Scholar 

  • Korre, L., Garaud, P., Brummell, N.H.: 2019, Convective overshooting and penetration in a Boussinesq spherical shell. Mon. Not. R. Astron. Soc. 484, 1220. DOI. ADS.

    Article  Google Scholar 

  • Korzennik, S.G.: 2005, A mode-fitting methodology optimized for very long helioseismic time series. Astrophys. J. 626, 585. DOI. ADS.

    Article  Google Scholar 

  • Korzennik, S.G.: 2008a, YAOPBM - yet another peak bagging method. Astron. Nachr. 329, 453. DOI. ADS.

    Article  Google Scholar 

  • Korzennik, S.G.: 2008b, YAOPBM—II: extension to higher degrees and to shorter time series. J. Phys. Conf. Ser. 118, 012082. DOI. ADS.

    Article  Google Scholar 

  • Kosovichev, A.G.: 1999, Inversion methods in helioseismology and solar tomography. J. Comput. Appl. Math. 109, 1. ADS.

    Article  Google Scholar 

  • Kostogryz, N.M., Shapiro, A.I., Witzke, V., Cameron, R.H., Gizon, L., Krivova, N.A., Ludwig, H.-G., Maxted, P.F.L., Seager, S., Solanki, S.K., Valenti, J.: 2024, Magnetic origin of the discrepancy between stellar limb-darkening models and observations. Nat. Astron. 8, 929. DOI. ADS.

    Article  Google Scholar 

  • Kruijer, T.S., Kleine, T., Borg, L.E.: 2020, The great isotopic dichotomy of the early Solar System. Nat. Astron. 4, 32. DOI. ADS.

    Article  Google Scholar 

  • Kruse, M.K.G., Iglesias, C.A.: 2019, Two-photon absorption framework for plasma transmission experiments. High Energy Density Phys. 31, 38. DOI. https://www.sciencedirect.com/science/article/pii/S1574181818300600.

    Article  Google Scholar 

  • Kruse, M.K.G., Iglesias, C.A.: 2021, Two-photon ionization in solar opacity experiments. High Energy Density Phys. 41, 100976. DOI. https://www.sciencedirect.com/science/article/pii/S1574181822000027.

    Article  Google Scholar 

  • Kunitomo, M., Guillot, T.: 2021, Imprint of planet formation in the deep interior of the Sun. Astron. Astrophys. 655, A51. DOI. ADS.

    Article  Google Scholar 

  • Kunitomo, M., Guillot, T., Buldgen, G.: 2022, Evidence of a signature of planet formation processes from solar neutrino fluxes. Astron. Astrophys. 667, L2. DOI. ADS.

    Article  Google Scholar 

  • Kunitomo, M., Suzuki, T.K., Inutsuka, S.-i.: 2020, Dispersal of protoplanetary discs by the combination of magnetically driven and photoevaporative winds. Mon. Not. R. Astron. Soc. 492, 3849. DOI. ADS.

    Article  Google Scholar 

  • Kunitomo, M., Guillot, T., Takeuchi, T., Ida, S.: 2017, Revisiting the pre-main-sequence evolution of stars. I. Importance of accretion efficiency and deuterium abundance. Astron. Astrophys. 599, A49. DOI. ADS.

    Article  Google Scholar 

  • Kupka, F., Muthsam, H.J.: 2017, Modelling of stellar convection. Living Rev. Comput. Astrophys. 3, 1. DOI. ADS.

    Article  Google Scholar 

  • Kurucz, R.L.: 2005, New atlases for solar flux, irradiance, central intensity, and limb intensity. Mem. Soc. Astron. Ital. Suppl. 8, 189. ADS.

    Google Scholar 

  • Kurucz, R.L., Furenlid, I., Brault, J., Testerman, L.: 1984, Solar Flux Atlas from 296 to 1300 nm. ADS.

    Google Scholar 

  • Laming, J.M.: 2015, The FIP and inverse FIP effects in solar and stellar coronae. Living Rev. Sol. Phys. 12, 2. DOI. ADS.

    Article  Google Scholar 

  • Landi, E., Testa, P.: 2015, Neon and oxygen abundances and abundance ratio in the solar corona. Astrophys. J. 800, 110. DOI. ADS.

    Article  Google Scholar 

  • Larson, R.B.: 1969, Numerical calculations of the dynamics of collapsing proto-star. Mon. Not. R. Astron. Soc. 145, 271. ADS.

    Article  Google Scholar 

  • Larson, T.P., Schou, J.: 2015, Improved helioseismic analysis of medium-\(\ell \) data from the Michelson Doppler Imager. Sol. Phys. 290, 3221. DOI. ADS.

    Article  Google Scholar 

  • Le Saux, A., Guillet, T., Baraffe, I., Vlaykov, D.G., Constantino, T., Pratt, J., Goffrey, T., Sylvain, M., Réville, V., Brun, A.S.: 2022, Two-dimensional simulations of solar-like models with artificially enhanced luminosity. II. Impact on internal gravity waves. Astron. Astrophys. 660, A51. DOI. ADS.

    Article  Google Scholar 

  • Lecoanet, D., Schwab, J., Quataert, E., Bildsten, L., Timmes, F.X., Burns, K.J., Vasil, G.M., Oishi, J.S., Brown, B.P.: 2016, Turbulent chemical diffusion in convectively bounded carbon flames. Astrophys. J. 832, 71. DOI. ADS.

    Article  Google Scholar 

  • Li, G., Gordon, I.E., Rothman, L.S., Tan, Y., Hu, S.-M., Kassi, S., Campargue, A., Medvedev, E.S.: 2015, Rovibrational line lists for nine isotopologues of the CO molecule in the X1\(\Sigma \)+ ground electronic state. Astrophys. J. Suppl. Ser. 216, 15. DOI. ADS.

    Article  Google Scholar 

  • Li, W., Jönsson, P., Amarsi, A.M., Li, M.C., Grumer, J.: 2023, Extended atomic data for oxygen abundance analyses. Astron. Astrophys. 674, A54. DOI. ADS.

    Article  Google Scholar 

  • Likalter, A.A.: 1969, Interaction of atoms with electrons and ions in a plasma. J. Exp. Theor. Phys. 29, 133.

    Google Scholar 

  • Lind, K., Amarsi, A.M.: 2024, 3D non-LTE abundance analyses of late-type stars. arXiv e-prints. arXiv. ADS.

  • Ludwig, H.-G., Kučinskas, A.: 2012, Three-dimensional hydrodynamical CO5BOLD model atmospheres of red giant stars. I. Atmospheric structure of a giant located near the RGB tip. Astron. Astrophys. 547, A118. DOI. ADS.

    Article  Google Scholar 

  • Ludwig, H.-G., Steffen, M., Freytag, B.: 2023, Effects of magnetic fields on the center-to-limb variation in solar-type stars. Astron. Astrophys. 679, A65. DOI. ADS.

    Article  Google Scholar 

  • Ma, M., Li, Y., Godefroid, M., Gaigalas, G., Li, J., Bieroń, J., Chen, C., Wang, J., Jönsson, P.: 2024, Natural orbitals and targeted non-orthogonal orbital sets for atomic hyperfine structure multiconfiguration calculations. Atoms 12, 30. DOI. https://www.mdpi.com/2218-2004/12/6/30.

    Article  Google Scholar 

  • Magg, E., Bergemann, M., Serenelli, A., Bautista, M., Plez, B., Heiter, U., Gerber, J.M., Ludwig, H.-G., Basu, S., Ferguson, J.W., Gallego, H.C., Gamrath, S., Palmeri, P., Quinet, P.: 2022, Observational constraints on the origin of the elements. IV. Standard composition of the Sun. Astron. Astrophys. 661, A140. DOI. ADS.

    Article  Google Scholar 

  • Magic, Z., Collet, R., Asplund, M., Trampedach, R., Hayek, W., Chiavassa, A., Stein, R.F., Nordlund, Å.: 2013, The stagger-grid: a grid of 3D stellar atmosphere models. I. Methods and general properties. Astron. Astrophys. 557, A26. DOI. ADS.

    Article  Google Scholar 

  • Manchon, L., Deal, M., Goupil, M.-J., Serenelli, A., Lebreton, Y., Klevas, J., Kučinskas, A., Ludwig, H.-G., Montalbán, J., Gizon, L.: 2024, Entropy-calibrated stellar modeling: testing and improving the use of prescriptions for the entropy of adiabatic convection. Astron. Astrophys. 687, A146. DOI. ADS.

    Article  Google Scholar 

  • Mayes, D.C., Hobbs, B.A., Heeter, R.F., Perry, T.S., Johns, H.M., Opachich, Y.P., Hohenberger, M., Bradley, P.A., Dutra, E.C., Fontes, C.J., Gallardo-Diaz, E., Montgomery, M.H., Robey, H.F., Wallace, M.S., Winget, D.E.: 2025, Overview of oxygen opacity experiments at the National Ignition Facility and investigation of potential systematic errors. High Energy Density Phys. 55, 101177. DOI. https://www.sciencedirect.com/science/article/pii/S1574181825000059.

    Article  Google Scholar 

  • McDonald, A.B.: 2016, Nobel lecture: the Sudbury neutrino Observatory: observation of flavor change for solar neutrinos*. Rev. Mod. Phys. 88, 030502. DOI. ADS.

    Article  Google Scholar 

  • Mihalas, D., Dappen, W., Hummer, D.G.: 1988, The equation of state for stellar envelopes. II. Algorithm and selected results. Astrophys. J. 331, 815. DOI. ADS.

    Article  Google Scholar 

  • Mondet, G., Blancard, C., Cossé, P., Faussurier, G.: 2015, Opacity calculations for solar mixtures. Astrophys. J. Suppl. Ser. 220, 2.

    Article  Google Scholar 

  • Monteiro, M.J.P.F.G., Christensen-Dalsgaard, J., Thompson, M.J.: 1994, Seismic study of overshoot at the base of the solar convective envelope. Astron. Astrophys. 283, 247. ADS.

    Google Scholar 

  • More, R.M., Hansen, S.B., Nagayama, T.: 2017, Opacity from two-photon processes. High Energy Density Phys. 24, 44. DOI. https://www.sciencedirect.com/science/article/pii/S1574181817300654.

    Article  Google Scholar 

  • More, R., Pain, J.-C., Hansen, S.B., Nagayama, T., Bailey, J.E.: 2020, Free-free matrix-elements for two-photon opacity. High Energy Density Phys. 34, 100717. DOI. https://www.sciencedirect.com/science/article/pii/S1574181819300527.

    Article  Google Scholar 

  • Mosumgaard, J.R., Ball, W.H., Silva Aguirre, V., Weiss, A., Christensen-Dalsgaard, J.: 2018, Stellar models with calibrated convection and temperature stratification from 3D hydrodynamics simulations. Mon. Not. R. Astron. Soc. 478, 5650. DOI. ADS.

    Article  Google Scholar 

  • Nagayama, T., Bailey, J.E., Loisel, G.P., Dunham, G.S., Rochau, G.A., Blancard, C., Colgan, J., Cossé, P., Faussurier, G., Fontes, C.J., Gilleron, F., Hansen, S.B., Iglesias, C.A., Golovkin, I.E., Kilcrease, D.P., MacFarlane, J.J., Mancini, R.C., More, R.M., Orban, C., Pain, J.-C., Sherrill, M.E., Wilson, B.G.: 2019, Systematic study of L-shell opacity at stellar interior temperatures. Phys. Rev. Lett. 122, 235001. DOI. ADS.

    Article  Google Scholar 

  • Nahar, S.N., Zhao, L., Eissner, W., Pradhan, A.K.: 2024, R-matrix calculations for opacities: II. Photoionization and oscillator strengths of iron ions Fe XVII, Fe XVIII and Fe XIX. J. Phys. B, At. Mol. Phys. 57, 125002. DOI. ADS.

    Article  Google Scholar 

  • Namekata, K., Maehara, H., Honda, S., Notsu, Y., Okamoto, S., Takahashi, J., Takayama, M., Ohshima, T., Saito, T., Katoh, N., Tozuka, M., Murata, K.L., Ogawa, F., Niwano, M., Adachi, R., Oeda, M., Shiraishi, K., Isogai, K., Seki, D., Ishii, T.T., Ichimoto, K., Nogami, D., Shibata, K.: 2022, Probable detection of an eruptive filament from a superflare on a solar-type star. Nat. Astron. 6, 241. DOI. ADS.

    Article  Google Scholar 

  • Neckel, H., Labs, D.: 1984, The solar radiation between 3300 and 12500 Å. Sol. Phys. 90, 205. DOI. ADS.

    Article  Google Scholar 

  • Ni, W.-T.: 2013, Astrod-GW: overview and progress. Int. J. Mod. Phys. D 22, 1341004. DOI.

    Article  Google Scholar 

  • Ni, W.-T.: 2024, Space gravitational wave detection: progress and outlook. Sci. China, Ser. G, Phys. Mech. Astron. 54, 270402. DOI. ADS.

    Article  Google Scholar 

  • Nordlund, A., Galsgaard, K.: 1995, A 3D MHD Code for Parallel Computers. Tech. rep. Astronomical Observatory, Copenhagen University:.

  • Ó Fionnagáin, D., Vidotto, A.A.: 2018, The solar wind in time: a change in the behaviour of older winds? Mon. Not. R. Astron. Soc. 476, 2465. DOI. ADS.

    Article  Google Scholar 

  • Orebi Gann, G.D., Zuber, K., Bemmerer, D., Serenelli, A.: 2021, The future of solar neutrinos. Annu. Rev. Nucl. Part. Sci. 71, 491. DOI. ADS.

    Article  Google Scholar 

  • Pain, J.-C.: 2018, A note on the contribution of multi-photon processes to radiative opacity. High Energy Density Phys. 26, 23. DOI. https://www.sciencedirect.com/science/article/pii/S1574181817300885.

    Article  Google Scholar 

  • Pereira, T.M.D., Asplund, M., Collet, R., Thaler, I., Trampedach, R., Leenaarts, J.: 2013, How realistic are solar model atmospheres? Astron. Astrophys. 554, A118. DOI. ADS.

    Article  Google Scholar 

  • Petitdemange, L., Marcotte, F., Gissinger, C.: 2023, Spin-down by dynamo action in simulated radiative stellar layers. Science 379, 300. DOI. ADS.

    Article  Google Scholar 

  • Petitdemange, L., Marcotte, F., Gissinger, C., Daniel, F.: 2024, Tayler-Spruit dynamo simulations for the modeling of radiative stellar layers. Astron. Astrophys. 681, A75. DOI. ADS.

    Article  Google Scholar 

  • Phillips, D.L.: 1962, A technique for the numerical solution of certain integral equations of the first kind. J. ACM 9, 84. DOI.

    Article  MathSciNet  Google Scholar 

  • Pijpers, F.P., Thompson, M.J.: 1992, Faster formulations of the optimally localized averages method for helioseismic inversions. Astron. Astrophys. 262, L33. ADS.

    Google Scholar 

  • Pijpers, F.P., Thompson, M.J.: 1994, The SOLA method for helioseismic inversion. Astron. Astrophys. 281, 231. ADS.

    Google Scholar 

  • Pinçon, C., Belkacem, K., Goupil, M.J.: 2016, Generation of internal gravity waves by penetrative convection. Astron. Astrophys. 588, A122. DOI. ADS.

    Article  Google Scholar 

  • Pradhan, A.K.: 2024a, Interface of equation of state, atomic data, and opacities in the solar problem. Mon. Not. R. Astron. Soc. 527, L179. DOI. ADS.

    Article  Google Scholar 

  • Pradhan, A.K.: 2024b, R-matrix calculations for opacities: III. Plasma broadening of autoionizing resonances. J. Phys. B, At. Mol. Phys. 57, 125003. DOI. ADS.

    Article  Google Scholar 

  • Pradhan, A.K., Nahar, S.N., Eissner, W.: 2024, R-matrix calculations for opacities: I. Methodology and computations. J. Phys. B, At. Mol. Phys. 57, 125001. DOI. ADS.

    Article  Google Scholar 

  • Pratt, J., Baraffe, I., Goffrey, T., Constantino, T., Viallet, M., Popov, M.V., Walder, R., Folini, D.: 2017, Extreme value statistics for two-dimensional convective penetration in a pre-main sequence star. Astron. Astrophys. 604, A125. DOI. ADS.

    Article  Google Scholar 

  • Proxauf, B.: 2021, Observations of large-scale solar flows. PhD thesis, Georg August University of Gottingen, Germany. ADS.

  • Ramelli, R., Setzer, M., Engelhard, M., Bianda, M., Paglia, F., Stenflo, J.O., Küveler, G., Plewe, R.: 2017, Atlas of the solar intensity spectrum and its center to limb variation. arXiv e-prints. arXiv. ADS.

  • Ramelli, R., Bianda, M., Setzer, M., Enegelhard, M., Paglia, F., Stenflo, J.O., Küveler, G., Plewe, R.: 2019, Atlas of the solar intensity spectrum and its center-to-limb variation. In: Belluzzi, L., Casini, R., Romoli, M., Trujillo Bueno, J. (eds.) Solar Polariation Workshop 8, Astronomical Society of the Pacific Conference Series 526, 287. ADS.

    Google Scholar 

  • Rauer, H., Aerts, C., Cabrera, J., Deleuil, M., Erikson, A., Gizon, L., Goupil, M., Heras, A., Lorenzo-Alvarez, J., Marliani, F., Martin-Garcia, C., Mas-Hesse, J.M., O’Rourke, L., Osborn, H., Pagano, I., Piotto, G., Pollacco, D., Ragazzoni, R., Ramsay, G., Udry, S., Appourchaux, T., Benz, W., Brandeker, A., Güdel, M., Janot-Pacheco, E., Kabath, P., Kjeldsen, H., Min, M., Santos, N., Smith, A., Suarez, J.-C., Werner, S.C., Aboudan, A., Abreu, M., Acuña, L., Adams, M., Adibekyan, V., Affer, L., Agneray, F., Agnor, C., Aguirre Børsen-Koch, V., Ahmed, S., Aigrain, S., Al-Bahlawan, A., Alcacera Gil, M.d.l.A., Alei, E., Alencar, S., Alexander, R., Alfonso-Garzón, J., Alibert, Y., Allende Prieto, C., Almeida, L., Alonso Sobrino, R., Altavilla, G., Althaus, C., Alonso Alvarez Trujillo, L., Amarsi, A., Ammler-von Eiff, M., Amôres, E., Andrade, L., Antoniadis-Karnavas, A., António, C., Aparicio del Moral, B., Appolloni, M., Arena, C., Armstrong, D., Aroca Aliaga, J., Asplund, M., Audenaert, J., Auricchio, N., Avelino, P., Baeke, A., Baillié, K., Balado, A., Balestra, A., Ball, W., Ballans, H., Ballot, J., Barban, C., Barbary, G., Barbieri, M., Barceló Forteza, S., Barker, A., Barklem, P., Barnes, S., Barrado Navascues, D., Barragan, O., Baruteau, C., Basu, S., Baudin, F., Baumeister, P., Bayliss, D., Bazot, M., Beck, P.G., Bedding, T., Belkacem, K., Bellinger, E., Benatti, S., Benomar, O., Bérard, D., Bergemann, M., Bergomi, M., Bernardo, P., Biazzo, K., Bignamini, A., Bigot, L., Billot, N., Binet, M., Biondi, D., Biondi, F., Birch, A.C., Bitsch, B., Bluhm Ceballos, P.V., Bódi, A., Bognár, Z., Boisse, I., Bolmont, E., Bonanno, A., Bonavita, M., Bonfanti, A., Bonfils, X., Bonito, R., Bonomo, A.S., Börner, A., Boro Saikia, S., Borreguero Martín, E., Borsa, F., Borsato, L., Bossini, D., Bouchy, F., Boué, G., Boufleur, R., Boumier, P., Bourrier, V., Bowman, D.M., Bozzo, E., Bradley, L., Bray, J., Bressan, A., Breton, S., Brienza, D., Brito, A., Brogi, M., Brown, B., Brown, D., Brun, A.S., Bruno, G., Bruns, M., Buchhave, L.A., Bugnet, L., Buldgen, G., Burgess, P., Busatta, A., Busso, G., Buzasi, D., Caballero, J.A., Cabral, A., Calderone, F., Cameron, R., Cameron, A., Campante, T., Canto Martins, B.L., Cara, C., Carone, L., Carrasco, J.M., Casagrande, L., Casewell, S.L., Cassisi, S., Castellani, M., Castro, M., Catala, C., Catalán Fernández, I., Catelan, M., Cegla, H., Cerruti, C., Cessa, V., Chadid, M., Chaplin, W., Charpinet, S., Chiappini, C., Chiarucci, S., Chiavassa, A., Chinellato, S., Chirulli, G., Christensen-Dalsgaard, J., Church, R., Claret, A., Clarke, C., Claudi, R., Clermont, L., Coelho, H., Coelho, J., Cogato, F., Colomé, J., Condamin, M., Conseil, S., Corbard, T., Correia, A.C.M., Corsaro, E., Cosentino, R., Costes, J., Cottinelli, A., Covone, G., Creevey, O.L., Crida, A., Csizmadia, S., Cunha, M., Curry, P., da Costa, J., da Silva, F., Dalal, S., Damasso, M., Damiani, C., Damiani, F., Liduina das Chagas, M., Davies, M., Davies, G., Davies, B., Davison, G., de Almeida, L., de Angeli, F., Cabral de Barros, S.C., de Castro Leão, I., Brito de Freitas, D., de Freitas, M.C., De Martino, D., Renan de Medeiros, J., de Paula, L.A., de Plaa, J., De Ridder, J., Deal, M., Decin, L., Deeg, H., Degl’Innocenti, S., Deheuvels, S., del Burgo, C., Del Sordo, F., Delgado-Mena, E., Demangeon, O., Denk, T., Derekas, A., Desidera, S., Dexet, M., Di Criscienzo, M., Di Giorgio, A.M., Di Mauro, M.P., Diaz Rial, F.J., Díaz-García, J.-J., Dima, M., Dinuzzi, G., Dionatos, O., Distefano, E., do Nascimento, J.-D. Jr., Domingo, A., D’Orazi, V., Dorn, C., Doyle, L., Duarte, E., Ducellier, F., Dumaye, L., Dumusque, X., Dupret, M.-A., Eggenberger, P., Ehrenreich, D., Eigmüller, P., Eising, J., Emilio, M., Eriksson, K., Ermocida, M., Isidoro Escate Giribaldi, R., Eschen, Y., Estrela, I., Evans, D.W., Fabbian, D., Fabrizio, M., Faria, J.P., Farina, M., Farinato, J., Feliz, D., Feltzing, S., Fenouillet, T., Ferrari, L., Ferraz-Mello, S., Fialho, F., Fienga, A., Figueira, P., Fiori, L., Flaccomio, E., Focardi, M., Foley, S., Fontignie, J., Ford, D., Fornazier, K., Forveille, T., Fossati, L., de Marca Franca, R., da Silva, L.F., Frasca, A., Fridlund, M., Furlan, M., Gabler, S.-M., Gaido, M., Gallagher, A., Galli, E., Garcia, R.A., García Hernández, A., Garcia Munoz, A., García-Vázquez, H., Garrido Haba, R., Gaulme, P., Gauthier, N., Gehan, C., Gent, M., Georgieva, I., Ghigo, M., Giana, E., Gill, S., Girardi, L., Giuliatti Winter, S., Giusi, G., Gomes da Silva, J., Gómez Zazo, L.J., Gomez-Lopez, J.M., Isai González Hernández, J., Gonzalez Murillo, K., Gorius, N., Gouel, P.-V., Goulty, D., Granata, V., Grenfell, J.L., Grießbach, D., Grolleau, E., Grouffal, S., Grziwa, S., Guarcello, M.G., Gueguen, L., Guenther, E.W., Guilhem, T., Guillerot, L., Guiot, P., Guterman, P., Gutiérrez, A., Gutiérrez-Canales, F., Hagelberg, J., Haldemann, J., Hall, C., Handberg, R., Harrison, I., Harrison, D.L., Hasiba, J., Haswell, C.A., Hatalova, P., Hatzes, A., Haywood, R., Hébrard, G., Heckes, F., Heiter, U., Hekker, S., Heller, R., Helling, C., Helminiak, K., Hemsley, S., Heng, K., Hermans, A., Hermes, J., Hidalgo Torres, N., Hinkel, N., Hobbs, D., Hodgkin, S., Hofmann, K., Hojjatpanah, S., Houdek, G., Huber, D., Huesler, J., Hui-Bon-Hoa, A., Huygen, R., Huynh, D.-D., Iro, N., Irwin, J., Irwin, M., Izidoro, A., Jacquinod, S., Emborg Jannsen, N., Janson, M., Jeszenszky, H., Jiang, C., José Jimenez Mancebo, A., Jofre, P., Johansen, A., Johnston, C., Jones, G., Kallinger, T., Kálmán, S., Kanitz, T., Karjalainen, M., Karjalainen, R., Karoff, C., Kawaler, S., Kawata, D., Keereman, A., Keiderling, D., Kennedy, T., Kenworthy, M., Kerschbaum, F., Kidger, M., Kiefer, F., Kintziger, C., Kislyakova, K., Kiss, L., Klagyivik, P., Klahr, H., Klevas, J., Kochukhov, O., Köhler, U., Kolb, U., Koncz, A., Korth, J., Kostogryz, N., Kovács, G., Kovács, J., Kozhura, O., Krivova, N., Kučinskas, A., Kuhlemann, I., Kupka, F., Laauwen, W., Labiano, A., Lagarde, N., Laget, P., Laky, G., Lam, K.W.F., Lambrechts, M., Lammer, H., Lanza, A.F., Lanzafame, A., Lares Martiz, M., Laskar, J., Latter, H., Lavanant, T., Lawrenson, A., Lazzoni, C., Lebre, A., Lebreton, Y., Lecavelier des Etangs, A., Leinhardt, Z., Leleu, A., Lendl, M., Leto, G., Levillain, Y., Libert, A.-S., Lichtenberg, T., Ligi, R., Lignieres, F., Lillo-Box, J., Linsky, J., Scige Liu, J., Loidolt, D., Longval, Y., Lopes, I., Lorenzani, A., Ludwig, H.-G., Lund, M., Sloth Lundkvist, M., Luri, X., Maceroni, C., Madden, S., Madhusudhan, N., Maggio, A., Magliano, C., Magrin, D., Mahy, L., Maibaum, O., Malac-Allain, L., Malapert, J.-C., Malavolta, L., Maldonado, J., Mamonova, E., Manchon, L., Mann, A., Mantovan, G., Marafatto, L., Marconi, M., Mardling, R., Marigo, P., Marinoni, S., Marques, É., Marques, J.P., Marrese, P.M., Marshall, D., Martínez Perales, S., Mary, D., Marzari, F., Masana, E., Mascher, A., Mathis, S., Mathur, S., Mattiuci Figueiredo, A.C., Maxted, P.F.L., Mazeh, T., Mazevet, S., Mazzei, F., McCormac, J., McMillan, P., Menou, L., Merle, T., Meru, F., Mesa, D., Messina, S., Mészáros, S., Meunier, N., Meunier, J.-C., Micela, G., Michaelis, H., Michel, E., Michielsen, M., Michtchenko, T., Miglio, A., Miguel, Y., Milligan, D., Mirouh, G., Mitchell, M.A., Moedas, N., Molendini, F., Molnár, L., Mombarg, J., Montalban, J., Montalto, M., Monteiro, M.J.P.F.G., Morales, J.C., Morales-Calderon, M., Morbidelli, A., Mordasini, C., Moreau, C., Morel, T., Morello, G., Morin, J., Mortier, A., Mosser, B., Mourard, D., Mousis, O., Moutou, C., Mowlavi, N., Moya, A., Muehlmann, P., Muirhead, P., Munari, M., Musella, I., Mustill, A.J., Nardetto, N., Nardiello, D., Narita, N., Nascimbeni, V., Nash, A., Neiner, C., Nelson, R.P., Nettelmann, N., Nicolini, G., Nielsen, M., Niemi, S.-M., Noack, L., Noels-Grotsch, A., Noll, A., Norazman, A., Norton, A.J., Nsamba, B., Ofir, A., Ogilvie, G., Olander, T., Olivetto, C., Olofsson, G., Ong, J., Ortolani, S., Oshagh, M., Ottacher, H., Ottensamer, R., Ouazzani, R.-M., Paardekooper, S.-J., Pace, E., Pajas, M., Palacios, A., Palandri, G., Palle, E., Paproth, C., Parro, V., Parviainen, H., Granado, J.P., Passegger, V.M., Pastor-Morales, C., Pätzold, M., Gade Pedersen, M., Pena Hidalgo, D., Pepe, F., Pereira, F., Persson, C.M., Pertenais, M., Peter, G., Petit, A.C., Petit, P., Pezzuto, S., Pichierri, G., Pietrinferni, A., Pinheiro, F., Pinsonneault, M., Plachy, E., Plasson, P., Plez, B., Poppenhaeger, K., Poretti, E., Portaluri, E., Portell, J., Frederico Porto de Mello, G., Poyatos, J., Pozuelos, F.J., Prada Moroni, P.G., Pricopi, D., Prisinzano, L., Quade, M., Quirrenbach, A., Rabanal Reina, J.A., Rabello Soares, M.C., Raimondo, G., Rainer, M., Ramón Rodón, J., Ramón-Ballesta, A., Ramos Zapata, G., Rätz, S., Rauterberg, C., Redman, B., Redmer, R., Reese, D., Regibo, S., Reiners, A., Reinhold, T., Renie, C., Ribas, I., Ribeiro, S., Pereira Ricciardi, T., Rice, K., Richard, O., Riello, M., Rieutord, M., Ripepi, V., Rixon, G., Rockstein, S., Rodríguez, M.T.R., Rodríguez Díaz, L.F., Rodriguez Garcia, J.P., Rodriguez-Gomez, J., Roehlly, Y., Roig, F., Rojas-Ayala, B., Rolf, T., Lysgaard Rørsted, J., Rosado, H., Rosotti, G., Roth, O., Roth, M., Rousseau, A., Roxburgh, I., Roy, F., Royer, P., Ruane, K., Rufini Mastropasqua, S., Ruiz de Galarreta, C., Russi, A., Saar, S., Saillenfest, M., Salaris, M., Salmon, S., Saltas, I., Samadi, R., Samadi, A., Samra, D., Sanches da Silva, T., Andrés Sánchez Carrasco, M., Santerne, A., Santoli, F., Santos, Â.R.G., Sanz Mesa, R., Sarro, L.M., Scandariato, G., Schäfer, M., Schlafly, E., Schmider, F.-X., Schneider, J., Schou, J., Schunker, H., Jörg Schwarzkopf, G., Serenelli, A., Seynaeve, D., Shan, Y., Shapiro, A., Shipman, R., Sicilia, D., Sierra Sanmartin, M.A., Sigot, A., Silliman, K., Silvotti, R., Simon, A.E., Simoyama Napoli, R., Skarka, M., Smalley, B., Smiljanic, R., Smit, S., Smith, A., Smith, L., Snellen, I., Sódor, Á., Sohl, F., Solanki, S.K., Sortino, F., Sousa, S., Southworth, J., Souto, D., Sozzetti, A., Stamatellos, D., Stassun, K., Steller, M., Stello, D., Stelzer, B., Stiebeler, U., Stokholm, A., Storelvmo, T., Strassmeier, K., Strøm, P.A., Strugarek, A., Sulis, S., Švanda, M., Szabados, L., Szabó, R., Szabó, G.M., Szuszkiewicz, E., Talens, G.J., Teti, D., Theisen, T., Thévenin, F., Thoul, A., Tiphene, D., Titz-Weider, R., Tkachenko, A., Tomecki, D., Tonfat, J., Tosi, N., Trampedach, R., Traven, G., Triaud, A., Trønnes, R., Tsantaki, M., Tschentscher, M., Turin, A., Tvaruzka, A., Ulmer, B., Ulmer-Moll, S., Ulusoy, C., Umbriaco, G., Valencia, D., Valentini, M., Valio, A., Valverde Guijarro, Á.L., Van Eylen, V., Van Grootel, V., van Kempen, T.A., Van Reeth, T., Van Zelst, I., Vandenbussche, B., Vasiliou, K., Vasilyev, V., Vaz de Mascarenhas, D., Vazan, A., Vela Nunez, M., Nunes Velloso, E., Ventura, R., Ventura, P., Venturini, J., Trallero, I.V., Veras, D., Verdugo, E., Verma, K., Vibert, D., Vicanek Martinez, T., Vida, K., Vigan, A., Villacorta, A., Villaver, E., Villaverde Aparicio, M., Viotto, V., Vorobyov, E., Vorontsov, S., Wagner, F.W., Walloschek, T., Walton, N., Walton, D., Wang, H., Waters, R., Watson, C., Wedemeyer, S., Weeks, A., Weingril, J., Weiss, A., Wendler, B., West, R., Westerdorff, K., Westphal, P.-A., Wheatley, P., White, T., Whittaker, A., Wickhusen, K., Wilson, T., Windsor, J., Winter, O., Lykke Winther, M., Winton, A., Witteck, U., Witzke, V., Woitke, P., Wolter, D., Wuchterl, G., Wyatt, M., Yang, D., Yu, J., Zanmar Sanchez, R., Rosa Zapatero Osorio, M., Zechmeister, M., Zhou, Y., Ziemke, C., Zwintz, K.: 2024, The PLATO Mission. arXiv e-prints. arXiv. ADS.

  • Reiners, A., Mrotzek, N., Lemke, U., Hinrichs, J., Reinsch, K.: 2016, The IAG solar flux atlas: accurate wavelengths and absolute convective blueshift in standard solar spectra. Astron. Astrophys. 587, A65. DOI. ADS.

    Article  Google Scholar 

  • Reiter, J., Rhodes, J.E.J., Kosovichev, A.G., Scherrer, P.H., Larson, T.P., Pinkerton, S.F. II: 2020, A method for the estimation of f- and p-mode parameters and rotational splitting coefficients from un-averaged solar oscillation power spectra. Astrophys. J. 894, 80. DOI. ADS.

    Article  Google Scholar 

  • Rhodes, J.E.J., Kosovichev, A.G., Schou, J., Scherrer, P.H., Reiter, J.: 1997, Measurements of frequencies of solar oscillations from the MDI medium-l program. Sol. Phys. 175, 287. DOI. ADS.

    Article  Google Scholar 

  • Richard, O., Dziembowski, W.A., Sienkiewicz, R., Goode, P.R.: 1998, On the accuracy of helioseismic determination of solar helium abundance. Astron. Astrophys. 338, 756. ADS.

    Google Scholar 

  • Rodríguez Díaz, L.F., Lagae, C., Amarsi, A.M., Bigot, L., Zhou, Y., Aguirre Børsen-Koch, V., Lind, K., Trampedach, R., Collet, R.: 2024, An extended and refined grid of 3D STAGGER model atmospheres. Processed snapshots for stellar spectroscopy. arXiv e-prints. arXiv. ADS.

  • Rogers, F.J., DeWitt, H.E.: 1973, Statistical mechanics of reacting Coulomb gases. Phys. Rev. A 8, 1061. DOI.

    Article  Google Scholar 

  • Rogers, F.J., Nayfonov, A.: 2002, Updated and expanded OPAL equation-of-state tables: implications for helioseismology. Astrophys. J. 576, 1064. DOI. ADS.

    Article  Google Scholar 

  • Rosenthal, C.S., Christensen-Dalsgaard, J., Nordlund, Å., Stein, R.F., Trampedach, R.: 1999, Convective contributions to the frequencies of solar oscillations. Astron. Astrophys. 351, 689. ADS.

    Google Scholar 

  • Sackmann, I.-J., Boothroyd, A.I.: 2003, Our Sun. V. A bright young Sun consistent with helioseismology and warm temperatures on ancient Earth and Mars. Astrophys. J. 583, 1024. DOI. ADS.

    Article  Google Scholar 

  • Salmon, S.J.A.J., Buldgen, G., Noels, A., Eggenberger, P., Scuflaire, R., Meynet, G.: 2021, Standard solar models: perspectives from updated solar neutrino fluxes and gravity-mode period spacing. Astron. Astrophys. 651, A106. DOI. ADS.

    Article  Google Scholar 

  • Scherrer, P.H., Gough, D.O.: 2019, A critical evaluation of recent claims concerning solar rotation. Astrophys. J. 877, 42. DOI. ADS.

    Article  Google Scholar 

  • Scherrer, P.H., Bogart, R.S., Bush, R.I., Hoeksema, J.T., Kosovichev, A.G., Schou, J., Rosenberg, W., Springer, L., Tarbell, T.D., Title, A., Wolfson, C.J., Zayer, I., MDI Engineering Team: 1995, The solar oscillations investigation - Michelson Doppler Imager. Sol. Phys. 162, 129. DOI. ADS.

    Article  Google Scholar 

  • Schmelz, J.T., Reames, D.V., von Steiger, R., Basu, S.: 2012, Composition of the solar corona, solar wind, and solar energetic particles. Astrophys. J. 755, 33. DOI. ADS.

    Article  Google Scholar 

  • Schmidt-May, A.F., Barklem, P.S., Grumer, J., Amarsi, A.M., Björkhage, M., Blom, M., Dochain, A., Ji, M., Martini, P., Reinhed, P., Rosén, S., Simonsson, A., Zettergren, H., Cederquist, H., Schmidt, H.T.: 2024, State-resolved mutual neutralization of +16O with −1H and −2H at collision energies below 100 meV. Phys. Rev. A 109, 052820. DOI. ADS.

    Article  Google Scholar 

  • Schou, J., Birch, A.: 2020, Estimating the nonstructural component of the helioseismic surface term using hydrodynamic simulations. Astron. Astrophys. 638, A51. ADS.

    Article  Google Scholar 

  • Schunker, H., Schou, J., Gaulme, P., Gizon, L.: 2018, Fragile detection of solar g-modes by Fossat et al. Sol. Phys. 293, 95. DOI. ADS.

    Article  Google Scholar 

  • Seaton, M.J., Yan, Y., Mihalas, D., Pradhan, A.K.: 1994, Opacities for stellar envelopes. Mon. Not. R. Astron. Soc. 266, 805. DOI. ADS.

    Article  Google Scholar 

  • Selig, H., Lämmerzahl, C., Ni, W.-T.: 2013, Astrodynamical space test of relativity using optical devices I (astrod I) — mission overview. Int. J. Mod. Phys. D 22, 1341003. DOI. ADS.

    Article  Google Scholar 

  • Serenelli, A.M., Haxton, W.C., Peña-Garay, C.: 2011, Solar models with accretion. I. Application to the solar abundance problem. Astrophys. J. 743, 24. DOI. ADS.

    Article  Google Scholar 

  • Serenelli, A.M., Basu, S., Ferguson, J.W., Asplund, M.: 2009, New solar composition: the problem with solar models revisited. Astrophys. J. 705, L123. ADS.

    Article  Google Scholar 

  • Shchukina, N., Sukhorukov, A., Trujillo Bueno, J.: 2016, Impact of surface dynamo magnetic fields on the solar abundance of the CNO elements. Astron. Astrophys. 586, A145. DOI. ADS.

    Article  Google Scholar 

  • Shchukina, N., Trujillo Bueno, J.: 2015, The impact of surface dynamo magnetic fields on the solar iron abundance. Astron. Astrophys. 579, A112. DOI. ADS.

    Article  Google Scholar 

  • Shoda, M., Cranmer, S.R., Toriumi, S.: 2023, Formulating mass-loss rates for Sun-like stars: a hybrid model approach. Astrophys. J. 957, 71. DOI. ADS.

    Article  Google Scholar 

  • Spada, F., Demarque, P., Basu, S., Tanner, J.D.: 2018, Improved calibration of the radii of cool stars based on 3D simulations of convection: implications for the solar model. Astrophys. J. 869, 135. DOI. ADS.

    Article  Google Scholar 

  • Spruit, H.C.: 1997, Convection in stellar envelopes: a changing paradigm. Mem. Soc. Astron. Ital. 68, 397. DOI. ADS.

    Article  Google Scholar 

  • Spruit, H.C.: 2002, Dynamo action by differential rotation in a stably stratified stellar interior. Astron. Astrophys. 381, 923. DOI. ADS.

    Article  Google Scholar 

  • Starostin, A.N., Roerich, V.C.: 2006, Equation of state of weakly nonideal plasmas and electroneutrality condition. J. Phys. A, Math. Gen. 39, 4431. DOI.

    Article  Google Scholar 

  • Stein, R.F., Nordlund, Å., Collet, R., Trampedach, R.: 2024, The stagger code for accurate and efficient, radiation-coupled magnetohydrodynamic simulations. Astrophys. J. 970, 24. DOI. ADS.

    Article  Google Scholar 

  • Stenflo, J.O.: 2015, FTS atlas of the Sun’s spectrally resolved center-to-limb variation. Astron. Astrophys. 573, A74. DOI. ADS.

    Article  Google Scholar 

  • Suzuki, T.K., Imada, S., Kataoka, R., Kato, Y., Matsumoto, T., Miyahara, H., Tsuneta, S.: 2013, Saturation of stellar winds from young suns. Publ. Astron. Soc. Jpn. 65, 98. DOI. ADS.

    Article  Google Scholar 

  • Takata, M., Gough, D.O.: 2024, The acoustic size of the Sun. Mon. Not. R. Astron. Soc. 527, 1283. DOI. ADS.

    Article  Google Scholar 

  • Testi, L., Birnstiel, T., Ricci, L., Andrews, S., Blum, J., Carpenter, J., Dominik, C., Isella, A., Natta, A., Williams, J.P., Wilner, D.J.: 2014, Dust evolution in protoplanetary disks. In: Beuther, H., Klessen, R.S., Dullemond, C.P., Henning, T. (eds.) Protostars and Planets VI, 339. DOI. ADS.

    Chapter  Google Scholar 

  • The Opacity Project Team: 1995, The Opacity Project 1, Institute Of Physics Publishing, Bristol.

    Google Scholar 

  • Tikhonov, A.N.: 1963, Solution of incorrectly formulated problems and the regularization method. Sov. Math. Dokl. 4, 1035.

    Google Scholar 

  • Tomczyk, S., Streander, K., Card, G., Elmore, D., Hull, H., Cacciani, A.: 1995, An instrument to observe low-degree solar oscillations. Sol. Phys. 159, 1. DOI. ADS.

    Article  Google Scholar 

  • Trampedach, R.: 2017, An opaque Sun? The potential for future, higher opacities to solve the solar abundance problem. In: Monteiro, M.J.P.F.G., Cunha, M.S., Ferreira, J.M.T. (eds.) Seismology of the Sun and the Distant Stars 2016 - Joint TASC2 & KASC9 Workshop SPACEINN & HELAS8 Conference, Web of Conferences, EPJ, 02005:1.ADS.

    Google Scholar 

  • Trampedach, R.: 2020, Non-adiabatic helioseismology via 3D convection simulations. In: Monteiro, M., García, R., Christensen-Dalsgaard, J., McIntosh, S.W. (eds.) Dynamics of the Sun and Stars, Astrophysics and Space Science Proceedings 57, Springer, New York, 145. ADS.

    Chapter  Google Scholar 

  • Trampedach, R., Däppen, W.: 2024, Various Modifications to Debye-Hückel Interactions in Solar Equations of State 1.

  • Trampedach, R., Däppen, W., Baturin, V.A.: 2006, A synoptic comparison of the Mihalas-Hummer-Däppen and OPAL equations of state. Astrophys. J. 646, 560. ADS.

    Article  Google Scholar 

  • Trampedach, R., Christensen-Dalsgaard, J., Nordlund, Å., Asplund, M., Stein, R.F.: 2014a, Improvements to stellar structure models, based on a grid of 3D convection simulations. I. \({T}\)-\(\tau \) relations. Mon. Not. R. Astron. Soc. 442, 805. ADS.

    Article  Google Scholar 

  • Trampedach, R., Christensen-Dalsgaard, J., Nordlund, Å., Asplund, M., Stein, R.F.: 2014b, Improvements to stellar structure models, based on a grid of 3D convection simulations. II. Calibrating the mixing-length. Mon. Not. R. Astron. Soc. 445, 4366. ADS.

    Article  Google Scholar 

  • Trampedach, R., Aarslev, M.J., Houdek, G., Christensen-Dalsgaard, J., Stein, R.F., Collet, R., Asplund, M.: 2017, The asteroseismic surface effect from a grid of 3D convection simulations. I. Frequency shifts from convective expansion of stellar atmospheres. Mon. Not. R. Astron. Soc. 466, L43. ADS.

    Article  Google Scholar 

  • Turck-Chièze, S., Carton, P.-H., Ballot, J., Barrière, J.-C., Daniel-Thomas, P., Delbart, A., Desforges, D., Garcia, R.A., Granelli, R., Mathur, S., Nunio, F., Piret, Y., Pallé, P.L., Jiménez, A.J., Jiménez-Reyes, S.J., Robillot, J.M., Fossat, E., Eff-Darwich, A.M., Gelly, B.: 2006, GOLF-NG spectrometer, a space prototype for studying the dynamics of the deep solar interior. Adv. Space Res. 38, 1812. DOI. ADS.

    Article  Google Scholar 

  • Turck-Chièze, S., Le Pennec, M., Ducret, J.E., Colgan, J., Kilcrease, D.P., Fontes, C.J., Magee, N., Gilleron, F., Pain, J.C.: 2016, Detailed opacity comparison for an improved stellar modeling of the envelopes of massive stars. Astrophys. J. 823, 78. DOI. ADS.

    Article  Google Scholar 

  • Turcotte, S., Richer, J., Michaud, G., Iglesias, C.A., Rogers, F.J.: 1998, Consistent solar evolution model including diffusion and radiative acceleration effects. Astrophys. J. 504, 539. DOI. ADS.

    Article  Google Scholar 

  • Vasil, G.M., Julien, K., Featherstone, N.A.: 2021, Rotation suppresses giant-scale solar convection. Proc. Natl. Acad. Sci. USA 118, e2022518118. DOI. ADS.

    Article  MathSciNet  Google Scholar 

  • Vasil, G.M., Lecoanet, D., Augustson, K., Burns, K.J., Oishi, J.S., Brown, B.P., Brummell, N., Julien, K.: 2024, The solar dynamo begins near the surface. Nature 629, 769. DOI. ADS.

    Article  Google Scholar 

  • Vaytet, N., Haugbølle, T.: 2017, A grid of one-dimensional low-mass star formation collapse models. Astron. Astrophys. 598, A116. DOI. ADS.

    Article  Google Scholar 

  • Vidotto, A.A.: 2021, The evolution of the solar wind. Living Rev. Sol. Phys. 18, 3. DOI. ADS.

    Article  Google Scholar 

  • Villante, F.L., Ricci, B.: 2010, Linear solar models. Astrophys. J. 714, 944. DOI. ADS.

    Article  Google Scholar 

  • Villante, F.L., Serenelli, A.: 2021, The relevance of nuclear reactions for standard solar models construction. Front. Astron. Space Sci. 7, 112. DOI. ADS.

    Article  Google Scholar 

  • Vlaykov, D.G., Baraffe, I., Constantino, T., Goffrey, T., Guillet, T., Le Saux, A., Morison, A., Pratt, J.: 2022, Impact of radial truncation on global 2D hydrodynamic simulations for a Sun-like model. Mon. Not. R. Astron. Soc. 514, 715. DOI. ADS.

    Article  Google Scholar 

  • Vorontsov, S.V., Baturin, V.A., Pamiatnykh, A.A.: 1991, Seismological measurement of solar helium abundance. Nature 349, 49. DOI. ADS.

    Article  Google Scholar 

  • Vorontsov, S.V., Baturin, V.A., Ayukov, S.V., Gryaznov, V.K.: 2013, Helioseismic calibration of the equation of state and chemical composition in the solar convective envelope. Mon. Not. R. Astron. Soc. 430, 1636. DOI. ADS.

    Article  Google Scholar 

  • Vorontsov, S.V., Baturin, V.A., Ayukov, S.V., Gryaznov, V.K.: 2014, Helioseismic measurements in the solar envelope using group velocities of surface waves. Mon. Not. R. Astron. Soc. 441, 3296. DOI. ADS.

    Article  Google Scholar 

  • Wedemeyer, S., Freytag, B., Steffen, M., Ludwig, H.-G., Holweger, H.: 2004, Numerical simulation of the three-dimensional structure and dynamics of the non-magnetic solar chromosphere. Astron. Astrophys. 414, 1121. DOI. ADS.

    Article  Google Scholar 

  • Weiss, B.P., Bai, X.-N., Fu, R.R.: 2021, History of the solar nebula from meteorite paleomagnetism. Sci. Adv. 7, eaba5967. DOI. ADS.

    Article  Google Scholar 

  • Wood, B.E., Müller, H.-R., Zank, G.P., Linsky, J.L., Redfield, S.: 2005, New mass-loss measurements from astrospheric Ly\(\alpha \) absorption. Astrophys. J. Lett. 628, L143. DOI. ADS.

    Article  Google Scholar 

  • Woodard, M.F., Noyes, R.W.: 1985, Change of solar oscillation eigenfrequencies with the solar cycle. Nature 318, 449. DOI. ADS.

    Article  Google Scholar 

  • Young, P.R.: 2018, Element abundance ratios in the quiet Sun transition region. Astrophys. J. 855, 15. DOI. ADS.

    Article  Google Scholar 

  • Zangwill, A., Soven, P.: 1980, Density-functional approach to local-field effects in finite systems: photoabsorption in the rare gases. Phys. Rev. A 21, 1561. DOI.

    Article  Google Scholar 

  • Zhang, Q.-S., Li, Y., Christensen-Dalsgaard, J.: 2019, Solar models with convective overshoot, solar-wind mass loss, and PMS disk accretion: helioseismic quantities, Li depletion, and neutrino fluxes. Astrophys. J. 881, 103. DOI. ADS.

    Article  Google Scholar 

  • Zhao, L., Nahar, S.N., Pradhan, A.K.: 2024, R-matrix calculations for opacities: IV. Convergence, completeness, and comparison of relativistic R-matrix and distorted wave calculations for Fe XVII and Fe XVIII. J. Phys. B, At. Mol. Phys. 57, 125004. DOI. ADS.

    Article  Google Scholar 

  • Zhou, Y., Amarsi, A.M., Aguirre Børsen-Koch, V., Karlsmose, K.G., Collet, R., Nordlander, T.: 2023, 3D stagger model atmospheres with FreeEOS. I. Exploring the impact of microphysics on the Sun. Astron. Astrophys. 677, A98. DOI. ADS.

    Article  Google Scholar 

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Acknowledgements

We thank the referee for their careful reading of the manuscript and their constructive suggestions. We thank D. Chari for providing Figure 2. We thank Dr. A.M. Amarsi for the fruitful discussions associated with the spectroscopic determinations of the solar abundances. We acknowledge support by the ISSI team “Probing the core of the Sun and the stars” (ID 423) led by Thierry Appourchaux.

Funding

GB acknowledges fundings from the Fonds National de la Recherche Scientifique (FNRS) as a postdoctoral researcher. GC acknowledges funds from the Knut and Alice Wallenberg Foundation. RT acknowledges support from NASA grants 80NSSC20K0543 and 80NSSC-22K0829. The study by V.A.B., A.V.O , and S.V.A. is conducted under the state assignment of Lomonosov Moscow State University. R.A.G. acknowledges the support from the GOLF and PLATO Centre National D’Études Spatiales grants. J.B. acknowledges funding from the SNF Postdoc.Mobility grant no. P\(\rm 500PT\_222217\) (Impact of magnetic activity on the characterization of FGKM main-sequence host-stars). M.K. was supported by the JSPS KAKENHI (grant nos. 24K00654 and 24K07099). AP acknowledges partial support from US National Science Foundation (Astronomy). Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of US Department of Energy (Contract No. 89233218NCA000001). This research has made use of the Astrophysics Data System, funded by NASA under Cooperative Agreement 80NSSC21M00561.

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G.B. initiated, designed and coordinated the project and took care of most of the writing. G.C., V.A.B, R.T., A.L.S, A.P., J.C.P., A.O.V., M.K., T.A., R.A.G., M.D., N.G. took part in the writing of their respective section of expertise. J.C.D., A.N., T.G.,D.N., J.B., C.B., J.C., P.C., C.J.F., L.P. and C.P. provided comments on the content of the manuscript.

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Correspondence to Gaël Buldgen.

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Buldgen, G., Canocchi, G., Le Saux, A. et al. The Future of Solar Modelling: Requirements for a New Generation of Solar Models. Sol Phys 300, 97 (2025). https://doi.org/10.1007/s11207-025-02508-x

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  1. Gloria Canocchi
  2. Anna V. Oreshina
  3. Jørgen Christensen-Dalsgaard