Helioseismology, theory; Oscillations, solar; Turbulence; Waves, acoustic; Astronomy and Astrophysics; Space and Planetary Science
Abstract :
[en] Solar gravity modes are considered the Rosetta Stone for probing and subsequently deciphering the physical properties of the solar inner-most layers. Recent claims of positive detection therefore shed some new light on the long-standing issue of estimating solar gravity mode amplitudes. In this article, our objective is to review the theoretical efforts intended to predict solar gravity-mode amplitudes. Because most of these studies assume analogous driving and damping properties to those of the observed acoustic modes, we also provide a short overview of our current knowledge for these modes in the Sun and solar-type stars (which show solar-like oscillations) before diving into the specific problem of solar gravity modes. Finally, taking recent estimates into account, we conclude and confirm that the low-frequency domain (typically between 10μHz and 100μHz) is certainly best suited to focus on for detecting solar gravity modes. More precisely, around 60μHz (approximately four-hour period), the theoretical estimates are only slightly lower than the observational detection threshold as provided by the GOLF (Global Oscillations at Low Frequencies) instrument by about a factor of two. This is typically within the current uncertainties associated with theoretical estimates and should motivate us to improve our knowledge on turbulence in the whole solar convective region, which is key to improving the accuracy of g-mode amplitude estimates. The recent detection of solar inertial modes (Gizon et al., Astron. Astrophys.652, L6, 2021) combined with the continuous development of numerical simulations provide interesting prospects for future studies.
Disciplines :
Space science, astronomy & astrophysics
Author, co-author :
Belkacem, K. ; LESIA, Observatoire de Paris, CNRS, Université PSL, Sorbonne Université, Université Paris Cité, Meudon, France
Pinçon, C. ; LERMA, Observatoire de Paris, PSL University, CNRS, Sorbonne University, Paris, France
Buldgen, Gaël ; Université de Liège - ULiège > Département d'astrophysique, géophysique et océanographie (AGO) > Astrophysique stellaire théorique et astérosismologie ; Astronomy Department, University of Geneva, Versoix, Switzerland
Sorbonne University FNS - Fonds National Suisse de la Recherche scientifique
Funding text :
AS was primary investigator and performed this examination. HA, ME, AF, YN, NM, MY, and HS. planned and performed this study. KM performed the statistical analysis. YF designed this study and he is a head of the department supervisor. All the authors read and approved the final manuscript. We are grateful to the members of the Japan Medical Association of Ukiha, the elected officials and residents of Tanushimaru, and the team of cooperating physicians for their help in performing the health examinations. This study was supported in part by the Kimura Memorial Heart Foundation (Fukuoka, Japan). SNF AMBIZIONE
Alvan, L., Brun, A.S., Mathis, S.: 2014, Theoretical seismology in 3D: nonlinear simulations of internal gravity waves in solar-like stars. Astron. Astrophys. 565, A42. DOI. ADS. DOI: 10.1051/0004-6361/201323253
Andersen, B.N.: 1996, Theoretical amplitudes of solar g-modes. Astron. Astrophys. 312, 610. ADS.
Ando, H., Osaki, Y.: 1975, Nonadiabatic nonradial oscillations – an application to the five-minute oscillation of the Sun. Publ. Astron. Soc. Japan 27, 581. ADS.
Antia, H.M., Chitre, S.M., Narasimha, D.: 1982, Overstability of acoustic modes and the solar five-minute oscillations. Solar Phys. 77, 303. DOI. ADS. DOI: 10.1007/BF00156114
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. DOI: 10.1051/0004-6361/201935196
Appourchaux, T., Fröhlich, C., Andersen, B., Berthomieu, G., Chaplin, W.J., Elsworth, Y., Finsterle, W., Gough, D.O., Hoeksema, J.T., Isaak, G.R., Kosovichev, A.G., Provost, J., Scherrer, P.H., Sekii, T., Toutain, T.: 2000, Observational upper limits to low-degree solar g-modes. Astrophys. J. 538, 401. DOI. ADS. DOI: 10.1086/309124
Appourchaux, T., Belkacem, K., Broomhall, A.-M., Chaplin, W.J., Gough, D.O., Houdek, G., Provost, J., Baudin, F., Boumier, P., Elsworth, Y., García, R.A., Andersen, B.N., Finsterle, W., Fröhlich, C., Gabriel, A., Grec, G., Jiménez, A., Kosovichev, A., Sekii, T., Toutain, T., Turck-Chièze, S.: 2010, The quest for the solar g modes. Astron. Astrophys. Rev. 18, 197. DOI. ADS. DOI: 10.1007/s00159-009-0027-z
Baglin, A., Auvergne, M., Boisnard, L., Lam-Trong, T., Barge, P., Catala, C., Deleuil, M., Michel, E., Weiss, W.: 2006a, CoRoT: a high precision photometer for stellar ecolution and exoplanet finding. In: 36th COSPAR Sci. Assembly, 3749. ADS.
Baglin, A., Auvergne, M., Barge, P., Deleuil, M., Catala, C., Michel, E., Weiss, W., COROT Team: 2006b, Scientific objectives for a minisat: CoRoT. In: Fridlund, M., Baglin, A., Lochard, J., Conroy, L. (eds.) The CoRoT Mission Pre-Launch Status - Stellar Seismology and Planet Finding SP-1306, ESA, Noordwijk, 33. ADS.
Bahcall, J.N., Brown, L.S., Gruzinov, A., Sawyer, R.F.: 2002, The Salpeter plasma correction for solar fusion reactions. Astron. Astrophys. 383, 291. DOI. ADS. DOI: 10.1051/0004-6361:20011715
Balmforth, N.J.: 1992a, Solar pulsational stability – part three – acoustical excitation by turbulent convection. Mon. Not. Roy. Astron. Soc. 255, 639. ADS. DOI: 10.1093/mnras/255.4.639
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. DOI: 10.1051/0004-6361/202140441
Belkacem, K.: 2019, Red giant stars: from mixed modes to angular momentum. In: Brun, A.S., Mathis, S., Charbonnel, C., Dubrulle, B. (eds.) Astro Fluid 2016 PS-82, EAS, Les Ulis, 189. DOI. ADS. DOI: 10.1051/eas/1982019
Belkacem, K., Samadi, R.: 2013, Connections between stellar oscillations and turbulent convection. In: Goupil, M., Belkacem, K., Neiner, C., Lignières, F., Green, J.J. (eds.) Lecture Notes in Physics 865, Springer, Berlin, 179. DOI. ADS. DOI: 10.1007/978-3-642-33380-4_9
Belkacem, K., Samadi, R., Goupil, M.J., Kupka, F., Baudin, F.: 2006, A closure model with plumes. II. Application to the stochastic excitation of solar p modes. Astron. Astrophys. 460, 183. DOI. ADS. DOI: 10.1051/0004-6361:20065370
Belkacem, K., Samadi, R., Goupil, M.-J., Dupret, M.-A.: 2008, Stochastic excitation of non-radial modes. I. High-angular-degree p modes. Astron. Astrophys. 478, 163. DOI. ADS. DOI: 10.1051/0004-6361:20077775
Belkacem, K., Samadi, R., Goupil, M.J., Dupret, M.A., Brun, A.S., Baudin, F.: 2009, Stochastic excitation of nonradial modes. II. Are solar asymptotic gravity modes detectable? Astron. Astrophys. 494, 191. DOI. ADS. DOI: 10.1051/0004-6361:200810827
Belkacem, K., Samadi, R., Goupil, M.J., Baudin, F., Salabert, D., Appourchaux, T.: 2010, Turbulent eddy-time-correlation in the solar convective zone. Astron. Astrophys. 522, L2. DOI. ADS. DOI: 10.1051/0004-6361/201015706
Belkacem, K., Dupret, M.A., Baudin, F., Appourchaux, T., Marques, J.P., Samadi, R.: 2012, Damping rates of solar-like oscillations across the HR diagram. Theoretical calculations confronted to CoRoT and Kepler observations. Astron. Astrophys. 540, L7. DOI. ADS. DOI: 10.1051/0004-6361/201218890
Belkacem, K., Marques, J.P., Goupil, M.J., Sonoi, T., Ouazzani, R.M., Dupret, M.A., Mathis, S., Mosser, B., Grosjean, M.: 2015, Angular momentum redistribution by mixed modes in evolved low-mass stars. I. Theoretical formalism. Astron. Astrophys. 579, A30. DOI. ADS. DOI: 10.1051/0004-6361/201526042
Belkacem, K., Kupka, F., Samadi, R., Grimm-Strele, H.: 2019, Solar p-mode damping rates: insight from a 3D hydrodynamical simulation. Astron. Astrophys. 625, A20. DOI. ADS. DOI: 10.1051/0004-6361/201834223
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. DOI: 10.1051/0004-6361/201935434
Borucki, W.J., Koch, D., Basri, G., Batalha, N., Brown, T., Caldwell, D., Caldwell, J., Christensen-Dalsgaard, J., Cochran, W.D., DeVore, E., Dunham, E.W., Dupree, A.K., Gautier, T.N., Geary, J.C., Gilliland, R., Gould, A., Howell, S.B., Jenkins, J.M., Kondo, Y., Latham, D.W., Marcy, G.W., Meibom, S., Kjeldsen, H., Lissauer, J.J., Monet, D.G., Morrison, D., Sasselov, D., Tarter, J., Boss, A., Brownlee, D., Owen, T., Buzasi, D., Charbonneau, D., Doyle, L., Fortney, J., Ford, E.B., Holman, M.J., Seager, S., Steffen, J.H., Welsh, W.F., Rowe, J., Anderson, H., Buchhave, L., Ciardi, D., Walkowicz, L., Sherry, W., Horch, E., Isaacson, H., Everett, M.E., Fischer, D., Torres, G., Johnson, J.A., Endl, M., MacQueen, P., Bryson, S.T., Dotson, J., Haas, M., Kolodziejczak, J., Van Cleve, J., Chandrasekaran, H., Twicken, J.D., Quintana, E.V., Clarke, B.D., Allen, C., Li, J., Wu, H., Tenenbaum, P., Verner, E., Bruhweiler, F., Barnes, J., Prsa, A.: 2010, Kepler Planet-Detection mission: introduction and first results. Science 327, 977. DOI. ADS. DOI: 10.1126/science.1185402
Brookes, J.R., Isaak, G.R., van der Raay, H.B.: 1976, Observation of free oscillations of the Sun. Nature 259, 92. DOI. ADS. DOI: 10.1038/259092a0
Buldgen, G., Eggenberger, P., Baturin, V.A., Corbard, T., Christensen-Dalsgaard, J., Salmon, S.J.A.J., Noels, A., Oreshina, A.V., Scuflaire, R.: 2020, Seismic solar models from Ledoux discriminant inversions. Astron. Astrophys. 642, A36. DOI. ADS. DOI: 10.1051/0004-6361/202037980
Chaplin, W.J., Miglio, A.: 2013, Asteroseismology of solar-type and red-giant stars. arXiv. ADS.
Chaplin, W.J., Houdek, G., Elsworth, Y., Gough, D.O., Isaak, G.R., New, R.: 2005, On model predictions of the power spectral density of radial solar p modes. Mon. Not. Roy. Astron. Soc. 360, 859. DOI. ADS. DOI: 10.1111/j.1365-2966.2005.09041.x
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. DOI: 10.1126/science.1116849
Christensen-Dalsgaard, J.: 2004, Physics of solar-like oscillations. Solar Phys. 220, 137. DOI. ADS. DOI: 10.1023/B:SOLA.0000031392.43227.7d
Christensen-Dalsgaard, J.: 2021, Solar structure and evolution. Liv. Rev. Solar Phys. 18, 2. DOI. ADS. DOI: 10.1007/s41116-020-00028-3
Corbard, T., Di Mauro, M.P., Sekii, T., GOLF Team: 1998, The solar internal rotation from GOLF splittings. In: Korzennik, S. (ed.) Structure and Dynamics of the Interior of the Sun and Sun-Like Stars SP-418, ESA, Noordwijk, 741. ADS.
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. Not. Roy. Astron. Soc. 439, 2025. DOI. ADS. DOI: 10.1093/mnras/stu080
Dintrans, B., Brandenburg, A., Nordlund, Å., Stein, R.F.: 2005a, Spectrum and amplitudes of internal gravity waves excited by penetrative convection in solar-type stars. Astron. Astrophys. 438, 365. DOI. ADS. DOI: 10.1051/0004-6361:20052831
Dintrans, B., Brandenburg, A., Nordlund, Å., Stein, R.F.: 2005b, Spectrum and amplitudes of internal gravity waves excited by penetrative convection in solar-type stars. Astron. Astrophys. 438, 365. DOI. ADS. DOI: 10.1051/0004-6361:20052831
Dupret, M.A., Barban, C., Goupil, M.-J., Samadi, R., Grigahcène, A., Gabriel, M.: 2006, Theoretical damping rates and phase-lags for solar-like oscillations. In: Fletcher, K., Thompson, M. (eds.) Proc. SOHO 18/GONG 2006/HELAS I, Beyond the Spherical Sun SP-624, ESA, Noordwijk. ADS.
Dupret, M.-A., Belkacem, K., Samadi, R., Montalban, J., Moreira, O., Miglio, A., Godart, M., Ventura, P., Ludwig, H.-G., Grigahcène, A., Goupil, M.-J., Noels, A., Caffau, E.: 2009, Theoretical amplitudes and lifetimes of non-radial solar-like oscillations in red giants. Astron. Astrophys. 506, 57. DOI. ADS. DOI: 10.1051/0004-6361/200911713
Dziembowski, W.A.: 1971, Nonradial oscillations of evolved stars. I. Quasiadiabatic approximation. Acta Astron. 21, 289. ADS.
Dziembowski, W.: 1983, Resonant coupling between solar gravity modes. Solar Phys. 82, 259. DOI. ADS. DOI: 10.1007/BF00145568
Dziembowski, W.A.: 2012, Dipolar modes in luminous red giants. Astron. Astrophys. 539, A83. DOI. ADS. DOI: 10.1051/0004-6361/201117733
Dziembowski, W.A., Paterno, L., Ventura, R.: 1985, Excitation of solar oscillation gravity modes by magnetic torque. Astron. Astrophys. 151, 47. ADS.
Dziembowski, W.A., Gough, D.O., Houdek, G., Sienkiewicz, R.: 2001, Oscillations of α UMa and other red giants. Mon. Not. Roy. Astron. Soc. 328, 601. DOI. ADS. DOI: 10.1046/j.1365-8711.2001.04894.x
Edelmann, P.V.F., Ratnasingam, R.P., Pedersen, M.G., Bowman, D.M., Prat, V., Rogers, T.M.: 2019, Three-dimensional simulations of massive stars. I. Wave generation and propagation. Astrophys. J. 876, 4. DOI. ADS. DOI: 10.3847/1538-4357/ab12df
Eggenberger, P., Maeder, A., Meynet, G.: 2005, Stellar evolution with rotation and magnetic fields. IV. The solar rotation profile. Astron. Astrophys. 440, L9. DOI. ADS. DOI: 10.1051/0004-6361:200500156
Evans, J.W., Michard, R.: 1962, Observational study of macroscopic inhomogeneities in the solar atmosphere. III. Vertical oscillatory motions in the solar photosphere. Astrophys. J. 136, 493. DOI. ADS. DOI: 10.1086/147403
Fossat, E., Schmider, F.X.: 2018, More about solar g modes. Astron. Astrophys. 612, L1. DOI. ADS. DOI: 10.1051/0004-6361/201832626
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. DOI: 10.1051/0004-6361/201730460
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, 5831. DOI. ADS. DOI: 10.1126/science.1140598
Goldreich, P., Keeley, D.A.: 1977a, Solar seismology. I – The stability of the solar p-modes. Astrophys. J. 211, 934. DOI. ADS. DOI: 10.1086/155005
Goldreich, P., Keeley, D.A.: 1977b, Solar seismology. II – The stochastic excitation of the solar p-modes by turbulent convection. Astrophys. J. 212, 243. ADS. DOI: 10.1086/155043
Goldreich, P., Kumar, P.: 1991, Thermal and mechanical damping of solar p-modes. Astrophys. J. 374, 366. DOI. ADS. DOI: 10.1086/170126
Goldreich, P., Murray, N., Kumar, P.: 1994, Excitation of solar p-modes. Astrophys. J. 424, 466. DOI. ADS. DOI: 10.1086/173904
Gough, D.: 1980, Some theoretical remarks on solar oscillations. In: Hill, H.A., Dziembowski, W.A. (eds.) Nonradial and Nonlinear Stellar Pulsation, Lecture Notes in Physics 125, Springer, Berlin, 273. DOI. ADS. DOI: 10.1007/3-540-09994-8_27
Gough, D.O.: 1985, Theory of solar oscillations. In: Rolfe, E., Battrick, B. (eds.) Future Missions in Solar, Heliospheric & Space Plasma Physics SP-235, ESA, Noordwijk, 183. ADS.
Gough, D.O., McIntyre, M.E.: 1998, Inevitability of a magnetic field in the Sun’s radiative interior. Nature 394, 755. DOI. ADS. DOI: 10.1038/29472
Grigahcène, A., Dupret, M.-A., Gabriel, M., Garrido, R., Scuflaire, R.: 2005, Convection-pulsation coupling. I. A mixing-length perturbative theory. Astron. Astrophys. 434, 1055. DOI. ADS. DOI: 10.1051/0004-6361:20041816
Grosjean, M., Dupret, M.-A., Belkacem, K., Montalban, J., Samadi, R., Mosser, B.: 2014, Theoretical power spectra of mixed modes in low-mass red giant stars. Astron. Astrophys. 572, A11. DOI. ADS. DOI: 10.1051/0004-6361/201423827
Komm, R.W., Howe, R., Hill, F.: 2000, Width and energy of solar p-modes observed by global oscillation network group. Astrophys. J. 543, 472. DOI. ADS. DOI: 10.1086/317101
Kumar, P., Goldreich, P.: 1989, Nonlinear interactions among solar acoustic modes. Astrophys. J. 342, 558. DOI. ADS. DOI: 10.1086/167616
Kumar, P., Quataert, E.J., Bahcall, J.N.: 1996, Observational searches for solar g-modes: some theoretical considerations. Astrophys. J. Lett. 458, L83. DOI. ADS. DOI: 10.1086/309926
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. DOI: 10.1051/0004-6361/202142569
Leibacher, J.W., Stein, R.F.: 1971, A new description of the solar five-minute oscillation. Astrophys. Lett. 7, 191. ADS.
Leighton, R.B., Noyes, R.W., Simon, G.W.: 1962, Velocity fields in the solar atmosphere. I. Preliminary report. Astrophys. J. 135, 474. DOI: 10.1086/147285
Lighthill, M.J.: 1952, On sound generated aerodynamically. I. General theory. Proc. Roy. Soc. London Ser. A 211, 564. DOI. ADS. DOI: 10.1098/rspa.1952.0060
Miesch, M.S., Brun, A.S., DeRosa, M.L., Toomre, J.: 2008, Structure and evolution of giant cells in global models of solar convection. Astrophys. J. 673, 557. DOI. ADS. DOI: 10.1086/523838
Mosser, B., Miglio, A., CoRoT Team: 2016, IV.2 Pulsating red giant stars. In: Baglin, A. (ed.) The CoRoT Legacy Book: The Adventure of the Ultra High Precision Photometry from Space, EDP Sci., Les Ulis, 197. DOI. ADS. DOI: 10.1051/978-2-7598-1876-1.c042
Mussack, K.: 2011, Dynamic screening in solar p-p reactions: is the mean-field approach applicable in solar plasma? Astrophys. Space Sci. 336, 111. DOI. ADS. DOI: 10.1007/s10509-010-0576-7
Mussack, K., Däppen, W.: 2011, Dynamic screening correction for solar p-p reaction rates. Astrophys. J. 729, 96. DOI. ADS. DOI: 10.1088/0004-637X/729/2/96
Osaki, Y.: 1990, Excitation mechanisms of solar oscillations. In: Osaki, Y., Shibahashi, H. (eds.) Lecture Notes in Physics: Progress of Seismology of the Sun and Stars, Springer, Berlin, 75. DOI: 10.1007/3-540-53091-6
Philidet, J., Belkacem, K., Goupil, M.-J.: 2021, Coupling between turbulence and solar-like oscillations: a combined Lagrangian PDF/SPH approach. I. The stochastic wave equation. Astron. Astrophys. 656, A95. DOI. ADS. DOI: 10.1051/0004-6361/202141483
Philidet, J., Belkacem, K., Goupil, M.-J.: 2022, Coupling between turbulence and solar-like oscillations: a combined Lagrangian PDF/SPH approach. II. Mode driving, damping and modal surface effect. Astron. Astrophys. 664, A164. DOI. ADS. DOI: 10.1051/0004-6361/202142947
Philidet, J., Belkacem, K., Samadi, R., Barban, C., Ludwig, H.-G.: 2020a, Modelling the asymmetries of the Sun’s radial p-mode line profiles. Astron. Astrophys. 635, A81. DOI. ADS. DOI: 10.1051/0004-6361/201936847
Philidet, J., Belkacem, K., Ludwig, H.-G., Samadi, R., Barban, C.: 2020b, Velocity-intensity asymmetry reversal of solar radial p-modes. Astron. Astrophys. 644, A171. DOI. ADS. DOI: 10.1051/0004-6361/202038222
Pinçon, C., Appourchaux, T., Buldgen, G.: 2021, Amplitude of solar gravity modes generated by penetrative plumes. Astron. Astrophys. 650, A47. DOI. ADS. DOI: 10.1051/0004-6361/202040003
Pinçon, C., Belkacem, K., Goupil, M.J.: 2016, Generation of internal gravity waves by penetrative convection. Astron. Astrophys. 588, A122. DOI. ADS. DOI: 10.1051/0004-6361/201527663
Press, W.H.: 1981, Radiative and other effects from internal waves in solar and stellar interiors. Astrophys. J. 245, 286. DOI. ADS. DOI: 10.1086/158809
Rempel, M.: 2004, Overshoot at the base of the solar convection zone: a semianalytical approach. Astrophys. J. 607, 1046. DOI. ADS. DOI: 10.1086/383605
Rieutord, M., Zahn, J.-P.: 1995, Turbulent plumes in stellar convective envelopes. Astron. Astrophys. 296, 127. ADS.
Rogers, T.M., Glatzmaier, G.A., Jones, C.A.: 2006, Numerical simulations of penetration and overshoot in the Sun. Astrophys. J. 653, 765. DOI. ADS. DOI: 10.1086/508482
Salabert, D., Leibacher, J., Appourchaux, T., Hill, F.: 2009, Measurement of low signal-to-noise ratio solar p-modes in spatially resolved helioseismic data. Astrophys. J. 696, 653. DOI. ADS. DOI: 10.1088/0004-637X/696/1/653
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. DOI: 10.1051/0004-6361/202140769
Samadi, R.: 2011, Stochastic excitation of acoustic modes in stars. In: Rozelot, J.-P., Neiner, C. (eds.) Lecture Notes in Physics 832, Springer, Berlin, 305. DOI. ADS. DOI: 10.1007/978-3-642-19928-8_11
Samadi, R., Belkacem, K., Sonoi, T.: 2015, Stellar oscillations - II - the non-adiabatic case. In: Michel, E., Charbonnel, C., Dintrans, B. (eds.) Ecole Evry Schatzman 2014: Asteroseismology and Next Generation Stellar Models SP-73-74, ESA, Noordwijk, 111. DOI. ADS. DOI: 10.1051/eas/1573003
Samadi, R., Goupil, M.-J.: 2001, Excitation of stellar p-modes by turbulent convection. I. Theoretical formulation. Astron. Astrophys. 370, 136. DOI: 10.1051/0004-6361:20010212
Samadi, R., Nordlund, Å., Stein, R.F., Goupil, M.J., Roxburgh, I.: 2003, Numerical 3D constraints on convective eddy time-correlations: Consequences for stochastic excitation of solar p modes. Astron. Astrophys. 404, 1129. ADS. DOI: 10.1051/0004-6361:20030504
Schatzman, E.: 1996, Do not forget gravity waves. Solar Phys. 169, 245. DOI. ADS. DOI: 10.1007/BF00190602
Scherrer, P.H., Gough, D.O.: 2019, A critical evaluation of recent claims concerning solar rotation. Astrophys. J. 877, 42. DOI. ADS. DOI: 10.3847/1538-4357/ab13ad
Schunker, H., Schou, J., Gaulme, P., Gizon, L.: 2018, Fragile detection of solar g-modes by Fossat et al. Solar Phys. 293, 95. DOI. ADS. DOI: 10.1007/s11207-018-1313-6
Scuflaire, R.: 1974, The non radial oscillations of condensed polytropes. Astron. Astrophys. 36, 107. ADS.
Scuflaire, R., Montalbán, J., Théado, S., Bourge, P.-O., Miglio, A., Godart, M., Thoul, A., Noels, A.: 2008, The Liège oscillation code. Astrophys. Space Sci. 316, 149. DOI. ADS. DOI: 10.1007/s10509-007-9577-6
Severnyi, A.B., Kotov, V.A., Tsap, T.T.: 1976, Observations of solar pulsations. Nature 259, 87. ADS. DOI: 10.1038/259087a0
Shaviv, G., Shaviv, N.J.: 2003, Why the Salpeter approximation is not valid in the Sun. J. Phys. A, Math. Gen. 36, 6187. DOI. ADS. DOI: 10.1088/0305-4470/36/22/347
Shibahashi, H.: 1979, Modal analysis of stellar nonradial oscillations by an asymptotic method. Publ. Astron. Soc. Japan 31, 87. ADS.
Stein, R.F.: 1967, Generation of acoustic and gravity waves by turbulence in an isothermal stratified atmosphere. Solar Phys. 2, 385. DOI: 10.1007/BF00146490
Stein, R.F., Nordlund, Å.: 1998, Simulations of solar granulation. I. General properties. Astrophys. J. 499, 914. DOI. ADS. DOI: 10.1086/305678
Stull, R.B.: 1976, Internal gravity waves generated by penetrative convection. J. Atmos. Sci. 33, 1279. DOI. ADS. DOI: 10.1175/1520-0469(1976)033
Townsend, A.A.: 1966, Internal waves produced by a convective layer. J. Fluid Mech. 24, 307. DOI. ADS. DOI: 10.1017/S0022112066000661
Turner, J.S.: 1986, Turbulent entrainment - the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431. DOI. ADS. DOI: 10.1017/S0022112086001222
Ulrich, R.K.: 1970, The five-minute oscillations on the solar surface. Astrophys. J. 162, 993. DOI: 10.1086/150731
Unno, W., Kato, S.: 1962, On the generation of acoustic noise from the turbulent atmosphere, I. Publ. Astron. Soc. Japan 14, 417.
Wolff, C.L., O’Donovan, A.E.: 2007, Coupled groups of g-modes in a Sun with a mixed core. Astrophys. J. 661, 568. DOI. ADS. DOI: 10.1086/513305
Zhou, Y., Asplund, M., Collet, R., Joyce, M.: 2020, Convective excitation and damping of solar-like oscillations. Mon. Not. Roy. Astron. Soc. 495, 4904. DOI. ADS. DOI: 10.1093/mnras/staa1445