[en] Since the first observations of solar oscillations in 1962, helioseismology has probably been one of the most successful fields of astrophysics. Data of unprecedented quality were obtained through the implementation of networks of ground-based observatories such as the GONG project or the BiSON network, coupled with space-based telescopes such as SOHO, Solar Orbiter and SDO missions. Besides the improvement of observational data, solar seismologists developed sophisticated techniques to infer the internal structure of the Sun from its eigenfrequencies. These methods, then already extensively used in the field of Geophysics, are called inversion techniques. They allowed to precisely determine the position of the solar convective envelope, the helium abundance in this region and the internal radial profiles of given thermodynamic quantities. Back in 1990s these comparisons showed a very high agreement between solar models and the Sun. However, the downward revision of the CNO surface abundances in the Sun in 2005, confirmed in 2009, induced a drastic reduction of this agreement leading to the so-called solar modelling problem. More than ten years later, in the era of the space-based photometry missions which have established asteroseismology of solar-like stars as a standard approach to obtain their masses, radii and ages, the solar modelling problem still awaits a solution. In this paper, we will present the results of new helioseismic inversions, discuss the current uncertainties of solar models as well as some possible solutions to the solar modelling problem. We will show how helioseismology can help us grasp what is amiss in our solar models. We will also show that, far from being an argument about details of solar models, the solar problem has significant implications for seismology of solar-like stars, on the main sequence and beyond, impacting asteroseismology as a whole as well as the fields requiring precise and accurate knowledge of stellar masses, radii and ages, such as Galactic archaeology and exoplanetology.
Research center :
STAR - Space sciences, Technologies and Astrophysics Research - ULiège
Disciplines :
Space science, astronomy & astrophysics
Author, co-author :
Buldgen, Gaël ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Astrophysique stellaire théorique et astérosismologie
Salmon, Sébastien ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Astrophysique stellaire théorique et astérosismologie
Noels-Grötsch, Arlette ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Département d'astrophys., géophysique et océanographie (AGO)
Language :
English
Title :
Progress in Global Helioseismology: A New Light on the Solar Modeling Problem and Its Implications for Solar-Like Stars
Publication date :
02 July 2019
Journal title :
Frontiers in Astronomy and Space Sciences
eISSN :
2296-987X
Publisher :
Frontiers Research Foundation, Lausanne, Switzerland
Adelberger E. G., García A., Robertson R. G. H., Snover K. A., Balantekin A. B., Heeger K., et al. (2011). Solar fusion cross sections. II. The pp chain and CNO cycles. Rev. Mod. Phys. 83, 195–246. 10.1103/RevModPhys.83.195
Ahmad Q. R., Allen R. C., Andersen T. C., Anglin J. D., Barton J. C., Beier E. W., et al. (2002). Direct evidence for neutrino flavor transformation from neutral-current interactions in the sudbury neutrino observatory. Phys. Rev. Lett. 89:011301. 10.1103/PhysRevLett.89.01130112097025
Airapetian V. S., Glocer A., Gronoff G., Hébrard E., Danchi W., (2016). Prebiotic chemistry and atmospheric warming of early Earth by an active young Sun. Nat. Geosci. 9, 452–455. 10.1038/ngeo2719
Alecian G., LeBlanc F., (2002). New approximate formulae for radiative accelerations in stars. Mon. Notices R. Astron. Soc. 332, 891–900. 10.1046/j.1365-8711.2002.05352.x
Allende Prieto C., Lambert D. L., Asplund M., (2001). The forbidden abundance of oxygen in the Sun. Astrophys. J. Lett. 556, L63–L66. 10.1086/322874
Antia H. M., Basu S., (1994). Nonasymptotic helioseismic inversion for solar structure. Astron. Astrophys. Suppl. Ser. 107, 421–444.
Antia H. M., Basu S., (2005). The Discrepancy between Solar Abundances and Helioseismology. Astrophys. J. Lett. 620, L129–L132. 10.1086/428652
Antia H. M., Basu S., (2006). Determining solar abundances using helioseismology. Astrophys. J. 644, 1292–1298. 10.1086/503707
Appourchaux T., Antia H. M., Ball W., Creevey O., Lebreton Y., Verma K., et al. (2015). A seismic and gravitationally bound double star observed by Kepler. Implication for the presence of a convective core. Astron. Astrophys. 582:A25. 10.1051/0004-6361/201526610
Appourchaux T., Belkacem K., Broomhall A.-M., Chaplin W. J., Gough D. O., Houdek G., et al. (2010). The quest for the solar g modes. Astron. Astrophys. Rev. 18, 197–277. 10.1007/s00159-009-0027-z
Asplund M., Grevesse N., Sauval A. J., (2005a). The solar chemical composition, in Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis, Vol. 336 of Astronomical Society of the Pacific Conference Series, eds Barnes T. G., III Bash F. N., (Austin, TX: Astronomical Society of the Pacific), 25.
Asplund M., Grevesse N., Sauval A. J., Allende Prieto C., Blomme R., (2005b). Line formation in solar granulation. VI. [C I], C I, CH and C2 lines and the photospheric C abundance. Astron. Astrophys. 431, 693–705. 10.1051/0004-6361:20041951
Asplund M., Grevesse N., Sauval A. J., Allende Prieto C., Kiselman D., (2004). Line formation in solar granulation. IV. [O I], O I and OH lines and the photospheric O abundance. Astron. Astrophys. 417, 751–768. 10.1051/0004-6361:20034328
Asplund M., Grevesse N., Sauval A. J., Scott P., (2009). The chemical composition of the Sun. Annu. Rev. Astron. Astrophys. 47, 481–522. 10.1146/annurev.astro.46.060407.145222
Ayukov S. V., Baturin V. A., (2011). Low-Z solar model: sound speed profile under the convection zone. J. Phys. Conf. Ser. 271:012033. 10.1088/1742-6596/271/1/012033
Ayukov S. V., Baturin V. A., (2017). Helioseismic models of the sun with a low heavy element abundance. Astron. Rep. 61, 901–913. 10.1134/S1063772917100018
Badnell N. R., Bautista M. A., Butler K., Delahaye F., Mendoza C., Palmeri P., et al. (2005). Updated opacities from the Opacity Project. Mon. Notices R. Astron. Soc. 360, 458–464. 10.1111/j.1365-2966.2005.08991.x
Baglin A., Auvergne M., Barge P., Deleuil M., Michel E., CoRoT Exoplanet Science Team (2009). CoRoT: Description of the Mission and Early Results, in Transiting Planets, Vol. 253 of IAU Symposium, eds Pont F., Sasselov D., Holman M. J., 71–81.
Bahcall J. N., Basu S., Pinsonneault M., Serenelli A. M., (2005a). Helioseismological implications of recent solar abundance determinations. Astrophys. J. 618, 1049–1056. 10.1086/426070
Bahcall J. N., Basu S., Serenelli A. M., (2005b). What is the Neon abundance of the Sun? Astrophys. J. 631, 1281–1285. 10.1086/431926
Bahcall J. N., Huebner W. F., Lubow S. H., Parker P. D., Ulrich R. K., (1982). Standard solar models and the uncertainties in predicted capture rates of solar neutrinos. Rev. Mod. Phys. 54, 767–799. 10.1103/RevModPhys.54.767
Bahcall J. N., Peña-Garay C., (2004). Solar models and solar neutrino oscillations. New J. Phys. 6:63. 10.1088/1367-2630/6/1/063
Bahcall J. N., Serenelli A. M., Basu S., (2005c). New solar opacities, abundances, helioseismology, and neutrino fluxes. Astrophys. J. Lett. 621, L85–L88. 10.1086/428929
Bahcall J. N., Serenelli A. M., Basu S., (2006). 10,000 Standard solar models: a monte carlo simulation. Astron. Astrophys. Suppl. Ser. 165, 400–431. 10.1086/504043
Bailey J. E., Nagayama T., Loisel G. P., Rochau G. A., Blancard C., Colgan J., et al. (2015). A higher-than-predicted measurement of iron opacity at solar interior temperatures. Nature 517, 56–59. 10.1038/nature1404825557711
Basu S., Antia H. M., (1994). Effects of diffusion on the extent of overshoot below the solar convection zone. Mon. Notices R. Astron. Soc. 269:1137. 10.1093/mnras/269.4.1137
Basu S., Antia H. M., (1995). Helium abundance in the solar envelope. Mon. Notices R. Astron. Soc., 276:1402–1408.
Basu S., Antia H. M., (1997). Seismic measurement of the depth of the solar convection zone. Mon. Notices R. Astron. Soc. 287, 189–198.
Basu S., Antia H. M., (2004). Constraining solar abundances using helioseismology. Astrophys. J. Lett. 606, L85–L88. 10.1086/421110
Basu S., Antia H. M., (2008). Helioseismology and solar abundances. Phys. Rep. 457, 217–283. 10.1016/j.physrep.2007.12.002
Basu S., Chaplin W. J., Elsworth Y., New R., Serenelli A. M., (2009). Fresh insights on the structure of the solar core. Astrophys. J. 699, 1403–1417. 10.1088/0004-637X/699/2/1403
Basu S., Christensen-Dalsgaard J., (1997). Equation of state and helioseismic inversions. Astron. Astrophys. 322, L5–L8.
Basu S., Christensen-Dalsgaard J., Schou J., Thompson M. J., Tomczyk S., (1996). Solar structure as revealed by 1 year LOWL data. Bull. Astron. Soc. India 24:147.
Baturin V. A., Ayukov S. V., Gryaznov V. K., Iosilevskiy I. L., Fortov V. E., Starostin A. N., (2013). The Current Version of the SAHA-S Equation of State: Improvement and Perspective, in Progress in Physics of the Sun and Stars: A New Era in Helio- and Asteroseismology, volume 479 of Astronomical Society of the Pacific Conference Series, eds Shibahashi H., Lynas-Gray A. E., 11.
Baturin V. A., Gorshkov A. B., Oreshina A. V., (2015). Formation of a chemical-composition gradient beneath the convection zone and the early evolution of the sun. Astron. Rep. 59, 46–57. 10.1134/S1063772915010023
Bazot M., Bourguignon S., Christensen-Dalsgaard J., (2012). A Bayesian approach to the modelling of α Cen A. Mon. Notices R. Astron. Soc. 427, 1847–1866. 10.1111/j.1365-2966.2012.21818.x
Benomar O., Bazot M., Nielsen M. B., Gizon L., Sekii T., Takata M., et al. (2018). Asteroseismic detection of latitudinal differential rotation in 13 Sun-like stars. Science 361, 1231–1234. 10.1126/science.aao657130237352
Blancard C., Colgan J., Cossé P., Faussurier G., Fontes C. J., Gilleron F., et al. (2016). Comment on “large enhancement in high-energy photoionization of Fe XVII and missing continuum plasma opacity”. Phys. Rev. Lett. 117:249501. 10.1103/PhysRevLett.117.24950128009220
Blancard C., Cossé P., Faussurier G., (2012). Solar mixture opacity calculations using detailed configuration and level accounting treatments. Astrophys. J. 745:10. 10.1088/0004-637X/745/1/10
Böhm-Vitense E., (1958). Über die Wasserstoffkonvektionszone in Sternen verschiedener Effektivtemperaturen und Leuchtkräfte. Mit 5 Textabbildungen. Z. Astrophys. 46:108.
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, 1004–1023. 10.1086/345407
Borexino Collaboration Agostini M., Altenmüller K., Appel S., Atroshchenko V., Bagdasarian Z., et al. (2018). Comprehensive measurement of pp-chain solar neutrinos. Nature 562, 505–510. 10.1038/s41586-018-0624-y
Borucki W. J., Koch D., Basri G., Batalha N., Brown T., Caldwell D., et al. (2010). Kepler planet-detection mission: introduction and first results. Science 327:977. 10.1126/science.118540220056856
Boury A., Gabriel M., Noels A., Scuflaire R., Ledoux P., (1975). Vibrational instability of a 1 solar mass star towards non-radial oscillations. Astron. Astrophys. 41, 279–285.
Bristow T. F., Haberle R. M., Blake D. F., Des Marais D. J., Eigenbrode J. L., Fairén A. G., et al. (2017). Low Hesperian PCO2 constrained from in situ mineralogical analysis at Gale Crater, Mars. Proc. Natl. Acad. Sci. U.S.A. 114, 2166–2170. 10.1073/pnas.161664911428167765
Brookes J. R., Isaak G. R., van der Raay H. B., (1978). A resonant-scattering solar spectrometer. Mon. Notices R. Astron. Soc. 185, 1–18. 10.1093/mnras/185.1.1
Brown T. M., Morrow C. A., (1987). Observations of solar p-mode rotational splittings, in The Internal Solar Angular Velocity, Vol. 137 of Astrophysics and Space Science Library, eds Durney B. R., Sofia S., (Sunspot: Reidel), 7–17.
Brun A. S., Antia H. M., Chitre S. M., Zahn J.-P., (2002). Seismic tests for solar models with tachocline mixing. Astron. Astrophys. 391, 725–739. 10.1051/0004-6361:20020837
Buldgen G., Reese D., Dupret M.-A., (2017a). Asteroseismic inversions in the Kepler era: application to the Kepler Legacy sample. Euro. Phys. J. Web Conf. 160:03005. 10.1051/epjconf/201716003005
Buldgen G., Reese D. R., Dupret M. A., (2015a). Using seismic inversions to obtain an indicator of internal mixing processes in main-sequence solar-like stars. Astron. Astrophys. 583:A62. 10.1051/0004-6361/201526390
Buldgen G., Reese D. R., Dupret M. A., (2016a). Constraints on the structure of 16 Cygni A and 16 Cygni B using inversion techniques. Astron. Astrophys. 585:A109. 10.1051/0004-6361/201527032
Buldgen G., Reese D. R., Dupret M. A., (2017b). Analysis of the linear approximation of seismic inversions for various structural pairs. Astron. Astrophys. 598:A21. 10.1051/0004-6361/201629485
Buldgen G., Reese D. R., Dupret M. A., (2018). Constraining convective regions with asteroseismic linear structural inversions. Astron. Astrophys. 609:A95. 10.1051/0004-6361/201730693
Buldgen G., Reese D. R., Dupret M. A., Samadi R., (2015b). Stellar acoustic radii, mean densities, and ages from seismic inversion techniques. Astron. Astrophys. 574:A42. 10.1051/0004-6361/201424613
Buldgen G., Salmon S. J. A. J., Godart M., Noels A., Scuflaire R., Dupret M. A., et al. (2017c). Inversions of the Ledoux discriminant: a closer look at the tachocline. Mon. Notices R. Astron. Soc. 472, L70–L74. 10.1093/mnrasl/slx139
Buldgen G., Salmon S. J. A. J., Noels A., Scuflaire R., Dupret M. A., Reese D. R., (2017d). Determining the metallicity of the solar envelope using seismic inversion techniques. Mon. Notices R. Astron. Soc. 472, 751–764. 10.1093/mnras/stx2057
Buldgen G., Salmon S. J. A. J., Noels A., Scuflaire R., Reese D. R., Dupret M.-A., et al. (2017e). Seismic inversion of the solar entropy. A case for improving the standard solar model. Astron. Astrophys. 607:A58. 10.1051/0004-6361/201731354
Buldgen G., Salmon S. J. A. J., Reese D. R., Dupret M. A., (2016b). In-depth study of 16CygB using inversion techniques. Astron. Astrophys. 596:A73. 10.1051/0004-6361/201628773
Burgers J. M., (1969). Flow Equations for Composite Gases (New York, NY: Academic Press).
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, 255–269. 10.1007/s11207-010-9541-4
Castro M., Vauclair S., Richard O., (2007). Low abundances of heavy elements in the solar outer layers: comparisons of solar models with helioseismic inversions. Astron. Astrophys. 463, 755–758. 10.1051/0004-6361:20066327
Chapman S., Cowling T. G., (1970). The Mathematical Theory of Non-uniform Gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases (Cambridge: University Press).
Charbonnel C., Talon S., (2005). Influence of gravity waves on the internal rotation and Li abundance of solar-type stars. Science 309, 2189–2191. 10.1126/science.111684916195453
Charnay B., Le Hir G., Fluteau F., Forget F., Catling D. C., (2017). A warm or a cold early Earth? New insights from a 3-D climate-carbon model. Earth Planet. Sci. Lett. 474, 97–109. 10.1016/j.epsl.2017.06.029
Christensen-Dalsgaard J., Däppen W., (1992). Solar oscillations and the equation of state. Astron. Astrophys. Rev. 4, 267–361. 10.1007/BF00872687
Christensen-Dalsgaard J., Däppen W., Ajukov S. V., Anderson E. R., Antia H. M., Basu S., et al. (1996). The current state of solar modeling. Science 272, 1286–1292. 8662456
Christensen-Dalsgaard J., di Mauro M. P., Houdek G., Pijpers F., (2009). On the opacity change required to compensate for the revised solar composition. Astron. Astrophys. 494, 205–208. 10.1051/0004-6361:200810170
Christensen-Dalsgaard J., Dilke F. W. W., Gough D. O., (1974). The stability of a solar model to non-radial oscillations. Mon. Notices R. Astron. Soc. 169, 429–445.
Christensen-Dalsgaard J., Gough D. O., (1975). Nonadiabatic nonradial oscillations of a solar model. Memoir. Soc. R. Sci. Liege 8, 309–316.
Christensen-Dalsgaard J., Gough D. O., Knudstrup E., (2018). On the hydrostatic stratification of the solar tachocline. Mon. Notices R. Astron. Soc. 477, 3845–3852. 10.1093/mnras/sty752
Christensen-Dalsgaard J., Gough D. O., Thompson M. J., (1991). The depth of the solar convection zone. Astrophys. J. 378, 413–437. 10.1086/170441
Christensen-Dalsgaard J., Houdek G., (2010). Prospects for asteroseismology. Astrophys. Space Sci. 328, 51–66. 10.1007/s10509-009-0227-z
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. Notices R. Astron. Soc. 414, 1158–1174. 10.1111/j.1365-2966.2011.18460.x
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–L78. 10.1086/186725
Christensen-Dalsgaard J., Thompson M. J., (2007). Observational results and issues concerning the tachocline, in The Solar Tachocline, eds Hughes D. W., Rosner R., Weiss N. O., (Cambridge: Cambridge University Press), 53.
Colgan J., Kilcrease D. P., Magee N. H., Sherrill M. E., Abdallah J., Jr. Hakel P., et al. (2016). A new generation of Los Alamos opacity tables. Astrophys. J. 817:116. 10.3847/0004-637X/817/2/116
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, 696–708.
Cox J. P., Giuli R. T., (1968). Principles of Stellar Structure (New York, NY: Gordon and Breach).
Däppen W., Mihalas D., Hummer D. G., Mihalas B. W., (1988). The equation of state for stellar envelopes. III - Thermodynamic quantities. Astrophys. J. 332, 261–270.
Davies G. R., Broomhall A. M., Chaplin W. J., Elsworth Y., Hale S. J., (2014). Low-frequency, low-degree solar p-mode properties from 22 years of Birmingham Solar Oscillations Network data. Mon. Notices R. Astron. Soc. 439, 2025–2032. 10.1093/mnras/stu080
Davis R., Harmer D. S., Hoffman K. C., (1968). Search for neutrinos from the Sun. Phys. Rev. Lett. 20, 1205–1209.
Deal M., Alecian G., Lebreton Y., Goupil M. J., Marques J. P., LeBlanc F., et al. (2018). Impacts of radiative accelerations on solar-like oscillating main-sequence stars. Astron. Astrophys. 618:A10. 10.1051/0004-6361/201833361
Deal M., Richard O., Vauclair S., (2015). Accretion of planetary matter and the lithium problem in the 16 Cygni stellar system. Astron. Astrophys. 584:A105. 10.1051/0004-6361/201526917
Defouw R. J., (1970). Thermal-convective instability. Astrophys. J. 160:659.
Delahaye F., Pinsonneault M. H., (2006). The solar heavy-element abundances. I. Constraints from stellar interiors. Astrophys. J. 649, 529–540. 10.1086/505260
Dilke F. W. W., Gough D. O., (1972). The Solar spoon. Nature 240, 262–294.
Domingo V., Fleck B., Poland A. I., (1995). The SOHO mission: an overview. Sol. Phys. 162, 1–37.
Dziembowski W., (1982). Nonlinear mode coupling in oscillating stars. I - Second order theory of the coherent mode coupling. Acta Astron. 32, 147–171.
Dziembowski W., (1983). Resonant coupling between solar gravity modes. Sol. Phys. 82, 259–266.
Dziembowski W. A., Pamyatnykh A. A., Sienkiewicz R., (1990). Solar model from helioseismology and the neutrino flux problem. Mon. Notices R. Astron. Soc. 244, 542–550.
Eggenberger P., Deheuvels S., Miglio A., Ekström S., Georgy C., Meynet G., et al. (2019). Asteroseismology of evolved stars to constrain the internal transport of angular momentum. I. Efficiency of transport during the subgiant phase. Astron. Astrophys. 621:A66. 10.1051/0004-6361/201833447
Eggenberger P., Lagarde N., Miglio A., Montalbán J., Ekström S., Georgy C., et al. (2017). Constraining the efficiency of angular momentum transport with asteroseismology of red giants: the effect of stellar mass. Astron. Astrophys. 599:A18. 10.1051/0004-6361/201629459
Eggenberger P., Maeder A., Meynet G., (2005). Stellar evolution with rotation and magnetic fields. IV. The solar rotation profile. Astron. Astrophys. 440, L9–L12. 10.1051/0004-6361:200500156
Eggenberger P., Meynet G., Maeder A., Hirschi R., Charbonnel C., Talon S., et al. (2008). The Geneva stellar evolution code. Astrophys. Space Sci. 316, 43–54. 10.1007/s10509-007-9511-y
Eguchi K., Enomoto S., Furuno K., Goldman J., Hanada H., Ikeda H., et al. (2003). First results from KamLAND: evidence for reactor antineutrino disappearance. Phys. Rev. Lett. 90:021802. 10.1103/PhysRevLett.90.02180212570536
Elliott J. R., (1996). Equation of state in the solar convection zone and the implications of helioseismology. Mon. Notices R. Astron. Soc. 280, 1244–1256. 10.1093/mnras/280.4.1244
Elliott J. R., Gough D. O., (1999). Calibration of the thickness of the solar tachocline. Astrophys. J. 516, 475–481.
Elsworth Y., Howe R., Isaak G. R., McLeod C. P., New R., (1990). Evidence from solar seismology against non-standard solar-core models. Nature 347, 536–539.
Farnir M., Dupret M.-A., Salmon S. J. A. J., Noels A., Buldgen G., (2019). Comprehensive stellar seismic analysis. New method exploiting the glitches information in solar-like pulsators. Astron. Astrophys. 622:A98. 10.1051/0004-6361/201834044
Ferziger J. H., Kaper H. G., (eds.) (1972). Mathematical Theory of Transport Processes in Gases. Amsterdam: North-Holland Pub. Co.
Forget F., Wordsworth R., Millour E., Madeleine J.-B., Kerber L., Leconte J., et al. (2013). 3D modelling of the early martian climate under a denser CO2 atmosphere: temperatures and CO2 ice clouds. Icarus 222, 81–99. 10.1016/j.icarus.2012.10.019
Fossat E., Boumier P., Corbard T., Provost J., Salabert D., Schmider F. X., et al. (2017). Asymptotic g modes: evidence for a rapid rotation of the solar core. Astron. Astrophys. 604:A40. 10.1051/0004-6361/201730460
Fukuda Y., Hayakawa T., Ichihara E., Inoue K., Ishihara K., Ishino H., et al. (1999). Constraints on neutrino oscillation parameters from the measurement of day-night solar neutrino fluxes at super-kamiokande. Phys. Rev. Lett. 82, 1810–1814. 10.1103/PhysRevLett.82.1810
Gabriel M., (1997). Influence of heavy element and rotationally induced diffusions on the solar models. Astron. Astrophys. 327, 771–778.
Gabriel M., Noels A., Scuflaire R., Boury A., (1976). On the evolution of a one-solar-mass star with a periodically mixed core. Astron. Astrophys. 47, 137–141.
García R. A., Turck-Chièze S., Jiménez-Reyes S. J., Ballot J., Pallé P. L., Eff-Darwich A., et al. (2007). Tracking solar gravity modes: the dynamics of the Solar core. Science 316:1591. 10.1126/science.114059817478682
Gorshkov A. B., Baturin V. A., (2008). Diffusion settling of heavy elements in the solar interior. Astron. Rep. 52, 760–771. 10.1134/S1063772908090072
Gorshkov A. B., Baturin V. A., (2010). Elemental diffusion and segregation processes in partially ionized solar plasma. Astrophys. Space Sci. 328, 171–174. 10.1007/s10509-010-0277-2
Gough D. O., (2015). Some glimpses from helioseismology at the dynamics of the deep solar interior. Space Sci. Rev. 196, 15–47. 10.1007/s11214-015-0159-6
Gough D. O., (2019). Anticipating the Sun's heavy-element abundance. Mon. Notices R. Astron. Soc. 485, L114–L115. 10.1093/mnrasl/slz044
Gough D. O., Kosovichev A. G., (1993a). Initial asteroseismic inversions, in Inside the stars; Proceedings of the 137th IAU Colloquium, Vol. 40 of Astronomical Society of the Pacific Conference Series, eds Weiss W. W., Baglin A., (Vienna: University of Vienna), 541.
Gough D. O., Kosovichev A. G., (1993b). The Influence of Low-Degree P-Mode Frequencies on the Determination of the Structure of the Solar Interior. Mon. Notices R. Astron. Soc. 264:522. 10.1093/mnras/264.2.522
Gough D. O., McIntyre M. E., (1998). Inevitability of a magnetic field in the Sun's radiative interior. Nature 394, 755–757. 10.1038/29472
Gough D. O., Thompson M. J., (1991). The Inversion Problem (Tucson, AZ: University of Arizona Press), 519–561.
Graedel T. E., Sackmann I.-J., Boothroyd A. I., (1991). Early solar mass loss - A potential solution to the weak sun paradox. Geophys. Res. Lett. 18, 1881–1884. 10.1029/91GL02314
Grevesse N., Noels A., (1993). Cosmic abundances of the elements, in Origin and Evolution of the Elements, eds Prantzos N., Vangioni-Flam E., Casse M., 15–25.
Grevesse N., Sauval A. J., (1998). Standard solar composition. Space Sci. Rev. 85, 161–174.
Grevesse N., Scott P., Asplund M., Sauval A. J., (2015). The elemental composition of the Sun. III. The heavy elements Cu to Th. Astron. Astrophys. 573:A27. 10.1051/0004-6361/201424111
Gruberbauer M., Guenther D. B., Kallinger T., (2012). Toward a new kind of asteroseismic grid fitting. Astrophys. J. 749:109. 10.1088/0004-637X/749/2/109
Gryaznov V., Iosilevskiy I., Fortov V., Starostin A., Roerich V., Baturin V. A., et al. (2013). Saha's thermodynamic model of solar plasma. Contrib. Plasma Phys. 53, 392–396. 10.1002/ctpp.201200109
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 Equation-of-State and Phase-Transition in Models of Ordinary Astrophysical Matter, vol. 731 of American Institute of Physics Conference Series, eds Celebonovic V., Gough D., Däppen W., 147–161.
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. 10.1088/0305-4470/39/17/S22
Guzik J. A., (2008). Problems for the standard solar model arising from the new solar mixture. Memor. Soc. Astron. Ital. 79:481.
Guzik J. A., Fontes C. J., Walczak P., Wood S. R., Mussack K., Farag E., (2016). Sound speed and oscillation frequencies for solar models evolved with Los Alamos ATOMIC opacities. IAU Focus Meet. 29, 532–535. 10.1017/S1743921316006062
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, 1108–1119. 10.1088/0004-637X/713/2/1108
Guzik J. A., Watson L. S., Cox A. N., (2005). Can Enhanced diffusion improve helioseismic agreement for solar models with revised abundances? Astrophys. J. 627, 1049–1056. 10.1086/430438
Guzik J. A., Watson L. S., Cox A. N., (2006). Implications of revised solar abundances for helioseismology. Memor. Soc. Astron. Ital. 77:389.
Guzik J. A., Willson L. A., Brunish W. M., (1987). A comparison between mass-losing and standard solar models. Astrophys. J. 319, 957–965.
Harvey J., Abdel-Gawad K., Ball W., Boxum B., Bull F., Cole J., et al. (1988). The GONG instrument, in Seismology of the Sun and Sun-Like Stars, Vol. 286 of ESA Special Publication, ed Rolfe E. J..
Haxton W. C., Hamish Robertson R. G., Serenelli A. M., (2013). Solar neutrinos: status and prospects. Annu. Rev. Astron. Astrophys 51, 21–61. 10.1146/annurev-astro-081811-125539
Holweger H., Mueller E. A., (1974). The photospheric barium spectrum - Solar abundance and collision broadening of BA II lines by hydrogen. Sol. Phys. 39, 19–30.
Hotta H., (2017). Solar overshoot region and small-scale dynamo with realistic energy flux. Astrophys. J. 843:52. 10.3847/1538-4357/aa784b
Houdek G., Gough D. O., (2011). On the seismic age and heavy-element abundance of the Sun. Mon. Notices R. Astron. Soc. 418, 1217–1230. 10.1111/j.1365-2966.2011.19572.x
Houdek G., Rogl J., (1996). On the accuracy of opacity interpolation schemes. Bull. Astron. Soc. India 24, 317–320.
Hummer D. G., Mihalas D., (1988). The equation of state for stellar envelopes. I - an occupation probability formalism for the truncation of internal partition functions. Astrophys. J. 331, 794–814.
Iglesias C. A., (2015). Iron-group opacities for B stars. Mon. Notices R. Astron. Soc. 450, 2–9. 10.1093/mnras/stv591
Iglesias C. A., Hansen S. B., (2017). Fe XVII opacity at solar interior conditions. Astrophys. J. 835:284. 10.3847/1538-4357/835/2/284
Iglesias C. A., Rogers F. J., (1996). Updated opal opacities. Astrophys. J. 464:943.
Irwin A. W., (2012). FreeEOS: Equation of State for Stellar Interiors Calculations. Astrophysics Source Code Library.
Isaak G. R., McLeod C. P., Palle P. L., van der Raay H. B., Roca Cortes T., (1989). Solar oscillations as seen in the NaI and KI absorption lines. Astron. Astrophys. 208, 297–302.
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. Notices R. Astron. Soc. 481, L35–L39. 10.1093/mnrasl/sly152
King J. R., Deliyannis C. P., Hiltgen D. D., Stephens A., Cunha K., Boesgaard A. M., (1997). Lithium abundances in the solar twins 16 CYG A and B and the solar analog alpha CEN A, calibration of the 6707 angstrom Li region linelist, and implications. Astron. J. 113:1871. 10.1086/118399
Kosovichev A. G., (1988). The internal rotation of the sun from helioseismological data. Soviet Astron. Lett. 14:145.
Kosovichev A. G., (1999). Inversion methods in helioseismology and solar tomography. J. Comput. Appl. Math. 109, 1–39.
Kosovichev A. G., Fedorova A. V., (1991). Construction of a seismic model of the Sun. Sov. Astron. 35:507.
Kosovichev A. G., Severnyi A. B., (1985). The influence of chemical composition on the stability of solar gravity-mode oscillations. Izvestiya Ordena Trudovogo Krasnogo Znameni Krymskoj Astrofizicheskoj Observatorii 72, 188–198.
Krief M., Feigel A., Gazit D., (2016). Line broadening and the solar opacity problem. Astrophys. J. 824:98. 10.3847/0004-637X/824/2/98
Landi E., Testa P., (2015). Neon and oxygen abundances and abundance ratio in the solar corona. Astrophys. J. 800:110. 10.1088/0004-637X/800/2/110
Le Pennec M., Turck-Chièze S., Salmon S., Blancard C., Cossé P., Faussurier G., et al. (2015). First new solar models with OPAS opacity tables. Astrophys. J. Lett. 813:L42. 10.1088/2041-8205/813/2/L42
Lebreton Y., Montalbán J., Christensen-Dalsgaard J., Théado S., Hui-Bon-Hoa A., Monteiro M. J. P. F. G., et al. (2007). Microscopic Diffusion in Stellar Evolution Codes: First Comparisons Results of ESTA-Task 3, in EAS Publications Series, Vol. 26 of EAS Publications Series, eds Straka C. W., Lebreton Y., Monteiro M. J. P. F. G., 155–165.
Ledoux P., (1974). Non-radial oscillations, in Stellar Instability and Evolution, Vol. 59 of IAU Symposium, eds Ledoux P., Noels A., Rodgers A. W., (Canberra, ACT: International Astronomical Union Dordrecht; D. Reidel Publishing), 135–173.
Li Y., Yang J. Y., (2007). Testing turbulent convection theory in solar models - I. Structure of the solar convection zone. Mon. Notices R. Astron. Soc. 375, 388–402. 10.1111/j.1365-2966.2006.11319.x
Lund M. N., Silva Aguirre V., Davies G. R., Chaplin W. J., Christensen-Dalsgaard J., Houdek G., et al. (2017). Standing on the shoulders of dwarfs: the kepler asteroseismic LEGACY sample. I. oscillation mode parameters. Astrophys. J. 835:172. 10.3847/1538-4357/835/2/172
Marchenkov K., Roxburgh I., Vorontsov S., (2000). Non-linear inversion for the hydrostatic structure of the solar interior. Mon. Notices R. Astron. Soc. 312, 39–50. 10.1046/j.1365-8711.2000.03059.x
Metcalfe T. S., Creevey O. L., Davies G. R., (2015). Asteroseismic Modeling of 16 Cyg A B using the Complete Kepler Data Set. Astrophys. J. Lett. 811:L37. 10.1088/2041-8205/811/2/L37
Michaud G., Alecian G., Richer J., (2015). Atomic Diffusion in Stars. Springer International Publishing.
Michaud G., Charland Y., Vauclair S., Vauclair G., (1976). Diffusion in main-sequence stars - Radiation forces, time scales, anomalies. Astrophys. J. 210, 447–465. 10.1086/154848
Michaud G., Proffitt C. R., (1993). Particle transport processes, in Inside the Stars; Proceedings of the 137th IAU Colloquium, eds Weiss W. W., Baglin A., (Vienna: University of Vienna), 246–259.
Michaud G., Richer J. (2008). Radiative accelerations in stellar evolution. Memor. Soc. Astron. Ital. 79:592.
Mihalas D., Däppen W., Hummer D. G., (1988). The equation of state for stellar envelopes. II - Algorithm and selected results. Astrophys. J. 331, 815–825.
Mihalas D., Hummer D. G., Mihalas B. W., Däppen W., (1990). The equation of state for stellar envelopes. IV - Thermodynamic quantities and selected ionization fractions for six elemental mixes. Astrophys. J. 350, 300–308. 10.1086/168383
Minton D. A., Malhotra R., (2007). Assessing the massive young sun hypothesis to solve the warm young Earth puzzle. Astrophys. J. 660, 1700–1706. 10.1086/514331
Mondet G., Blancard C., Cossé P., Faussurier G., (2015). Opacity calculations for solar mixtures. Astron. Astrophys. Suppl. Ser. 220:2. 10.1088/0067-0049/220/1/2
Montalban J., Miglio A., Theado S., Noels A., Grevesse N., (2006). The new solar abundances - Part II: the crisis and possible solutions. Commun. Asteroseismol. 147, 80–84. 10.1553/cia147s80
Montalbán J., Théado S., Lebreton Y., (2007). Comparisons for ESTA-Task3: CLES and CESAM, in EAS Publications Series, volume 26 of EAS Publications Series, C. W. Straka, Y. Lebreton, and M. J. P. F. G. Monteiro, 167–176.
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, 247–262.
Mussack K., Däppen W., (2011). Dynamic screening correction for solar p-p reaction rates. Astrophys. J. 729:96. 10.1088/0004-637X/729/2/96
Nahar S. N., Pradhan A. K., (2016). Large enhancement in high-energy photoionization of Fe XVII and missing continuum plasma opacity. Phys. Rev. Lett. 116:235003. 10.1103/PhysRevLett.116.23500327341239
Noels A., Boury A., Gabriel M., Scuflaire R., (1976). Vibrational stability towards non-radial oscillations during central hydrogen burning. Astron. Astrophys. 49:103.
Noerdlinger P. D., (1977). Diffusion of helium in the sun. Astron. Astrophys. 57, 407–415.
Ouazzani R.-M., Marques J. P., Goupil M., Christophe S., Antoci V., Salmon S. J. A. J., (2018). {\gamma} Doradus stars as test of angular momentum transport models. arXiv e-prints.
Pain J.-C., Gilleron F., Comet M., (2018). Detailed opacity calculations for stellar models, in Workshop on Astrophysical Opacities, Vol. 515 of Astronomical Society of the Pacific Conference Series eds Mendoza C., Turck-Chiéze S., Colgan J., (Kalamazoo, MI: Astronomical Society of the Pacific), 35.
Piau L., Turck-Chièze S., (2001). Lithium burning in the early evolution of the Sun and Sun-like Stars, in From Darkness to Light: Origin and Evolution of Young Stellar Clusters, Vol. 243 of Astronomical Society of the Pacific Conference Series, eds Montmerle T., André P., (San Francisco, CA: Astronomical Society of the Pacific), 639.
Pijpers F. P., Thompson M. J., (1994). The SOLA method for helioseismic inversion. Astron. Astrophys. 281, 231–240.
Pinsonneault M. H., Delahaye F., (2009). The shoiolar heavy element abundances. II. Constraints from stellar atmospheres. Astrophys. J. 704, 1174–1188. 10.1088/0004-637X/704/2/1174
Pradhan A. K., Nahar S. N., (2018). Recalculation of astrophysical opacities: overview, methodology, and atomic calculations, in Workshop on Astrophysical Opacities, Vol. 515 of Astronomical Society of the Pacific Conference Series, 79.
Proffitt C. R., Michaud G., (1991). Gravitational settling in solar models. Astrophys. J. 380, 238–250. 10.1086/170580
Rabello-Soares M. C., Basu S., Christensen-Dalsgaard J., (1999). On the choice of parameters in solar-structure inversion. Mon. Notices R. Astron. Soc. 309, 35–47.
Rauer H., Catala C., Aerts C., Appourchaux T., Benz W., Brandeker A., et al. (2014). The PLATO 2.0 mission. Exp. Astron. 38, 249–330. 10.1007/s10686-014-9383-4
Reese D. R., Marques J. P., Goupil M. J., Thompson M. J., Deheuvels S., (2012). Estimating stellar mean density through seismic inversions. Astron. Astrophys. 539:A63. 10.1051/0004-6361/201118156
Rempel M., (2004). Overshoot at the base of the solar convection zone: a semianalytical approach. Astrophys. J. 607, 1046–1064. 10.1086/383605
Rendle B. M., Buldgen G., Miglio A., Reese D., Noels A., Davies G. R., et al. (2019). AIMS - a new tool for stellar parameter determinations using asteroseismic constraints. Mon. Notices R. Astron. Soc. 484, 771–786. 10.1093/mnras/stz031
Richard O., Dziembowski W. A., Sienkiewicz R., Goode P. R., (1998). On the accuracy of helioseismic determination of solar helium abundance. Astron. Astrophys. 338, 756–760.
Richard O., Michaud G., Richer J., (2001). Iron convection zones in B, A, and F stars. Astrophys. J. 558, 377–391. 10.1086/322264
Richard O., Michaud G., Richer J., (2002a). Models of metal-poor stars with gravitational settling and radiative accelerations. III. Metallicity dependence. Astrophys. J. 580, 1100–1117. 10.1086/343733
Richard O., Michaud G., Richer J., Turcotte S., Turck-Chièze S., VandenBerg D. A., (2002b). Models of metal-poor stars with gravitational settling and radiative accelerations. I. Evolution and abundance anomalies. Astrophys. J. 568, 979–997. 10.1086/338952
Richard O., Vauclair S., Charbonnel C., Dziembowski W. A., (1996). New solar models including helioseismological constraints and light-element depletion. Astron. Astrophys. 312, 1000–1011.
Richer J., Michaud G., Turcotte S., (2000). The Evolution of AMFM stars, abundance anomalies, and turbulent transport. Astrophys. J. 529, 338–356. 10.1086/308274
Ricker G. R., Winn J. N., Vanderspek R., Latham D. W., Bakos G. Á., Bean J. L., et al. (2015). Transiting Exoplanet Survey Satellite (TESS). J. Astron. Telesc. Instrum. Syst. 1:014003. 10.1117/1.JATIS.1.1.014003
Rogers F. J., Nayfonov A., (2002). Updated and expanded OPAL equation-of-state tables: implications for helioseismology. Astrophys. J. 576, 1064–1074. 10.1086/341894
Rogers F. J., Swenson F. J., Iglesias C. A., (1996). OPAL equation-of-state tables for astrophysical applications. Astrophys. J. 456:902.
Roxburgh I., Audard N., Basu S., Christensen-Dalsgaard J., Vorontsov S., (1998). Inversion for the internal structure of an evolved small mass star using modes with l=0-3 in proceedings, in Sounding Solar and Stellar Interiors, eds Schmider F., Provost J., (Nice: IAU Coll. 181), 245.
Roxburgh I., Vorontsov S., (2003a). Diagnostics of the internal structure of stars using the differential response technique. Astrophys. Space Sci. 284, 187–191. 10.1051/0004-6361:20031318
Roxburgh I. W., (1976). The internal structure of the Sun and solar type stars, in Basic Mechanisms of Solar Activity, Vol. 71 of IAU Symposium, eds Bumba V., Kleczek J., (Prague, Czechoslovakia), 453.
Roxburgh I. W., (1984). On turbulent mixing, in Observational Tests of the Stellar Evolution Theory, Vol. 105 of IAU Symposium, eds Maeder A., Renzini A., (Geneva: D. Reidel Publishing Company), 519.
Roxburgh I. W., (2016). Asteroseismic model fitting by comparing ϵn values. Astron. Astrophys. 585:A63. 10.1051/0004-6361/201526593
Roxburgh I. W., Vorontsov S. V., (2002). Inversion for a 0.8 Msolar star using differential-response technique, in Proceedings of the First Eddington Workshop on Stellar Structure and Habitable Planet Finding, Vol. 485 of ESA Special Publication, eds Battrick B., Favata F., Roxburgh I. W., Galadi D., (Córdoba: ESA Publications Division), 337–339.
Roxburgh I. W., Vorontsov S. V., (2003b). The ratio of small to large separations of acoustic oscillations as a diagnostic of the interior of solar-like stars. Astron. Astrophys. 411, 215–220.
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, 1024–1039. 10.1086/345408
Saio H., (1980). Stability of nonradial g/+/-mode pulsations in 1 solar mass models. Astrophys. J. 240, 685–692.
Schatten K. H., (1973). Magnetic convection. Sol. Phys. 33, 305–318.
Schlattl H., (2002). Microscopic diffusion of partly ionized metals in the Sun and metal-poor stars. Astron. Astrophys. 395, 85–95. 10.1051/0004-6361:20021212
Schlattl H., Salaris M., (2003). Quantum corrections to microscopic diffusion constants. Astron. Astrophys. 402, 29–35. 10.1051/0004-6361:20030230
Schou J., Antia H. M., Basu S., Bogart R. S., Bush R. I., Chitre S. M., et al. (1998). Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the michelson doppler imager. Astrophys. J. 505, 390–417.
Schunker H., Schou J., Gaulme P., Gizon L., (2018). Fragile detection of solar g-Modes by Fossat et al. Sol. Phys. 293:95. 10.1007/s11207-018-1313-6
Schwarzschild K., (1906). On the equilibrium of the Sun's atmosphere. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen 195, 41–53.
Scott P., Asplund M., Grevesse N., Bergemann M., Sauval A. J., (2015a). The elemental composition of the Sun. II. The iron group elements Sc to Ni. Astron. Astrophys. 573:A26. 10.1051/0004-6361/201424110
Scott P., Grevesse N., Asplund M., Sauval A. J., Lind K., Takeda Y., et al. (2015b). The elemental composition of the Sun. I. The intermediate mass elements Na to Ca. Astron. Astrophys. 573:A25. 10.1051/0004-6361/201424109
Scuflaire R., Gabriel M., Noels A., Boury A., (1975). Oscillatory periods in the sun and theoretical models with or without mixing. Astron. Astrophys. 45, 15–18.
Scuflaire R., Montalbán J., Théado S., Bourge P.-O., Miglio A., Godart M., et al. (2008a). The Liège oscillation code. Astrophys. Space Sci. 316, 149–154. 10.1007/s10509-007-9577-6
Scuflaire R., Théado S., Montalbán J., Miglio A., Bourge P.-O., Godart M., et al. (2008b). CLÉS, code liégeois d'Évolution stellaire. Astrophys. Space Sci. 316, 83–91. 10.1007/s10509-007-9650-1
Serenelli A. M., Basu S., Ferguson J. W., Asplund M., (2009). New solar composition: the problem with solar models revisited. Astrophys. J. Lett. 705, L123–L127. 10.1088/0004-637X/705/2/L123
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. 10.1088/0004-637X/743/1/24
Shibahashi H., Osaki Y., Unno W., (1975). Nonradial g-mode oscillations and the stability of the sun. Publ. Astron. Soc. Jpn 27, 401–410.
Silva Aguirre V., Lund M. N., Antia H. M., Ball W. H., Basu S., Christensen-Dalsgaard J., et al. (2017). Standing on the shoulders of dwarfs: the kepler asteroseismic LEGACY sample. II.Radii, masses, and ages. Astrophys. J. 835:173. 10.3847/1538-4357/835/2/173
Sonoi T., Shibahashi H., (2012a). Dipole low-order g-mode instability of metal-poor low-mass main-sequence stars due to the ϵ mechanism. Mon. Notices R. Astron. Soc. 422, 2642–2647. 10.1111/j.1365-2966.2012.20827.x
Sonoi T., Shibahashi H., (2012b). Fully nonadiabatic analysis of vibrational instability of population III stars due to the varepsilon-Mechanism. Publ. Astron. Soc. Jpn 64:2. 10.1093/pasj/64.1.2
Spalding C., Fischer W. W., Laughlin G., (2018). An Orbital window into the Ancient Suns Mass. Astrophys. J. Lett. 869:L19. 10.3847/2041-8213/aaf219
Spiegel E. A., Zahn J.-P., (1992). The solar tachocline. Astron. Astrophys. 265, 106–114.
Takata M., Montgomery M. H., (2002). Seismic inversions for white dwarf stars, in IAU Colloq. 185: Radial and Nonradial Pulsationsn as Probes of Stellar Physics, Vol. 259 of Astronomical Society of the Pacific Conference Series, eds Aerts C., Bedding T. R., Christensen-Dalsgaard J., (San Francisco, CA: Astronomical Society of the Pacific), 606.
Takata M., Shibahashi H., (2001). Solar metal abundance inferred from helioseismology, in Recent Insights into the Physics of the Sun and Heliosphere: Highlights from SOHO and Other Space Missions, Vol. 203 of IAU Symposium, eds Brekke P., Fleck B., Gurman J. B., 43.
Théado S., Alecian G., LeBlanc F., Vauclair S., (2012). The new Toulouse-Geneva stellar evolution code including radiative accelerations of heavy elements. Astron. Astrophys. 546:A100. 10.1051/0004-6361/201219610
Theado S., Vauclair S., (2010). Radiative accelerations, accumulation of iron and thermohaline convection inside stars. Theado 328, 209–212. 10.1007/s10509-009-0221-5
Théado S., Vauclair S., Castro M., Charpinet S., Dolez N., (2005). Asteroseismic tests of element diffusion in solar type stars. Astron. Astrophys. 437, 553–560. 10.1051/0004-6361:20042328
Thévenin F., Oreshina A. V., Baturin V. A., Gorshkov A. B., Morel P., Provost J., (2017). Evolution of lithium abundance in the Sun and solar twins. Astron. Astrophys. 598:A64. 10.1051/0004-6361/201629385
Thoul A. A., Bahcall J. N., Loeb A., (1994). Element diffusion in the solar interior. Astrophys. J. 421, 828–842.
Tucci Maia M., Meléndez J., Ramírez I., (2014). High precision abundances in the 16 Cyg binary system: a signature of the rocky core in the giant planet. Astrophys. J. Lett. 790:L25. 10.1088/2041-8205/790/2/L25
Turbet M., Forget F., Head J. W., Wordsworth R., (2017). 3D modelling of the climatic impact of outflow channel formation events on early Mars. Icarus 288, 10–36. 10.1016/j.icarus.2017.01.024
Turck-Chièze S., (2005). How does helioseismology constrain solar neutrino properties? Nucl. Phys. B Proc. Suppl. 143, 35–42. 10.1016/j.nuclphysbps.2005.01.085
Turck-Chieze S., Cahen S., Casse M., Doom C., (1988). Revisiting the standard solar model. Astrophys. J. 335, 415–424.
Turck-Chièze S., Couvidat S., (2011). Solar neutrinos, helioseismology and the solar internal dynamics. Rep. Prog. Phys. 74:086901. 10.1088/0034-4885/74/8/086901
Turck-Chièze S., Couvidat S., Piau L., Ferguson J., Lambert P., Ballot J., et al. (2004). Surprising sun: a new step towards a complete picture? Phys. Rev. Lett. 93:211102. 10.1103/PhysRevLett.93.21110215600989
Turck-Chièze S., Piau L., Couvidat S., (2011). The solar energetic balance revisited by young solar analogs, helioseismology, and neutrinos. Astrophys. J. Lett. 731:L29. 10.1088/2041-8205/731/2/L29
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, 539–558.
Ulrich R. K., (1974). Solar models with low neutrino fluxes. Astrophys. J. 188, 369–378.
Ulrich R. K., (1975). Solar neutrinos and variations in the solar luminosity. Science 190, 619–624.
Ulrich R. K., Rood R. T., (1973). Mixing in stellar models. Nat. Phys. Sci. 241, 111–112.
Unno W., (1975). On the stability of the solar core. Publ. Astron. Soc. Jpn 27, 81–99.
VandenBerg D. A., Richard O., Michaud G., Richer J., (2002). Models of metal-poor stars with gravitational settling and radiative accelerations. II. the age of the oldest stars. Astrophys. J. 571, 487–500. 10.1086/339895
Verma K., Faria J. P., Antia H. M., Basu S., Mazumdar A., Monteiro M. J. P. F. G., et al. (2014). Asteroseismic estimate of helium abundance of a solar analog binary system. Astrophys. J. 790:138. 10.1088/0004-637X/790/2/138
Vernazza J. E., Avrett E. H., Loeser R., (1976). Structure of the solar chromosphere. II - The underlying photosphere and temperature-minimum region. Astron. Astrophys. Suppl. Ser. 30, 1–60.
Viallet M., Meakin C., Prat V., Arnett D., (2015). Toward a consistent use of overshooting parametrizations in 1D stellar evolution codes. Astron. Astrophys. 580:A61. 10.1051/0004-6361/201526294
Vinyoles N., Serenelli A. M., Villante F. L., Basu S., Bergström J., Gonzalez-Garcia M. C., et al. (2017). A new generation of standard solar models. Astrophys. J. 835:202. 10.3847/1538-4357/835/2/202
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. Notices R. Astron. Soc. 430, 1636–1652. 10.1093/mnras/sts701
Vorontsov S. V., Baturin V. A., Pamiatnykh A. A., (1991). Seismological measurement of solar helium abundance. Nature 349, 49–51.
Weiss A., Heners N., (2013). Low-mass stars: Open problems all along their evolution. Eur. Phys. J. Web Conf. 43:01002. 10.1051/epjconf/20134301002
White T. R., Huber D., Maestro V., Bedding T. R., Ireland M. J., Baron F., et al. (2013). Interferometric radii of bright Kepler stars with the CHARA Array: Cygni and 16 Cygni A and B. Mon. Notices R. Astron. Soc. 433, 1262–1270. 10.1093/mnras/stt802
Winnick R. A., Demarque P., Basu S., Guenther D. B., (2002). Seismic test of solar models, solar neutrinos, and implications for metal-rich accretion. Astrophys. J. 576, 1075–1084. 10.1086/341795
Wood B. E., Müller H.-R., Zank G. P., Linsky J. L., Redfield S., (2005). New mass-loss measurements from astrospheric lyα absorption. Astrophys. J. Lett. 628, L143–L146. 10.1086/432716
Wood S. R., Mussack K., Guzik J. A., (2018). Solar models with dynamic screening and early mass loss tested by helioseismic, astrophysical, and planetary constraints. Sol. Phys. 293:111. 10.1007/s11207-018-1334-1
Wordsworth R. D., (2016). The climate of Early mars. Annu. Rev. Earth Planet. Sci. 44, 381–408. 10.1146/annurev-earth-060115-012355
Xiong D. R., Deng L., (2001). The structure of the solar convective overshooting zone. Mon. Notices R. Astron. Soc. 327, 1137–1144. 10.1046/j.1365-8711.2001.04820.x
Yang J. Y., Li Y., (2007). Testing turbulent convection theory in solar models - II. Solar p-mode oscillations. Mon. Notices R. Astron. Soc. 375, 403–414. 10.1111/j.1365-2966.2006.11320.x
Young P. R., (2018). Element abundance ratios in the quiet sun transition region. Astrophys. J. 855:15. 10.3847/1538-4357/aaab48
Zaatri A., Provost J., Berthomieu G., Morel P., Corbard T., (2007). Sensitivity of low degree oscillations to the change in solar abundances. Astron. Astrophys. 469, 1145–1149. 10.1051/0004-6361:20077212
Zhang Q. S., (2017). Numerical integral of resistance coefficients in diffusion. Astrophys. J. 834:132. 10.3847/1538-4357/834/2/132
Zhao L., Eissner W., Nahar S. N., Pradhan A. K., (2018). Converged R-matrix calculations of the photoionization of fexvii in astrophysical plasmas: from convergence to completeness, in Workshop on Astrophysical Opacities, Vol. 515 of Astronomical Society of the Pacific Conference Series, eds Mendoza C., Turck-Chiéze S., Colgan J., (Kalamazoo, MI: Astronomical Society of the Pacific), 89.