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Amplitudes of Solar Gravity Modes: A Review

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Abstract

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 \(10~\upmu \,\mbox{Hz}\) and \(100~\upmu \,\mbox{Hz}\)) is certainly best suited to focus on for detecting solar gravity modes. More precisely, around \(60~\upmu \,\mbox{Hz}\) (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.

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References

  • 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.

    Article  ADS  Google Scholar 

  • Andersen, B.N.: 1996, Theoretical amplitudes of solar g-modes. Astron. Astrophys. 312, 610. ADS.

    ADS  Google Scholar 

  • 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.

    ADS  Google Scholar 

  • 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.

    Article  ADS  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  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Balmforth, N.J.: 1992a, Solar pulsational stability – part three – acoustical excitation by turbulent convection. Mon. Not. Roy. Astron. Soc. 255, 639. ADS.

    Article  ADS  Google Scholar 

  • Balmforth, N.J.: 1992b, Solar pulsational stability - I. Pulsation-mode thermodynamics. Mon. Not. Roy. Astron. Soc. 255, 603. DOI. ADS.

    Article  ADS  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 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  MATH  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  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  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Brookes, J.R., Isaak, G.R., van der Raay, H.B.: 1976, Observation of free oscillations of the Sun. Nature 259, 92. DOI. ADS.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  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  ADS  Google Scholar 

  • Christensen-Dalsgaard, J.: 2004, Physics of solar-like oscillations. Solar Phys. 220, 137. DOI. ADS.

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Dolginov, A.Z., Muslimov, A.G.: 1984, Nonradial stellar oscillations excited by turbulent convection. Astrophys. Space Sci. 98, 15. DOI. ADS.

    Article  MATH  ADS  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Dziembowski, W.A.: 1971, Nonradial oscillations of evolved stars. I. Quasiadiabatic approximation. Acta Astron. 21, 289. ADS.

    ADS  Google Scholar 

  • Dziembowski, W.: 1983, Resonant coupling between solar gravity modes. Solar Phys. 82, 259. DOI. ADS.

    Article  ADS  Google Scholar 

  • Dziembowski, W.A.: 2012, Dipolar modes in luminous red giants. Astron. Astrophys. 539, A83. DOI. ADS.

    Article  MATH  ADS  Google Scholar 

  • Dziembowski, W.A., Paterno, L., Ventura, R.: 1985, Excitation of solar oscillation gravity modes by magnetic torque. Astron. Astrophys. 151, 47. ADS.

    ADS  Google Scholar 

  • Dziembowski, W.A., Gough, D.O., Houdek, G., Sienkiewicz, R.: 2001, Oscillations of \(\alpha\) UMa and other red giants. Mon. Not. Roy. Astron. Soc. 328, 601. DOI. ADS.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Fossat, E., Schmider, F.X.: 2018, More about solar g modes. Astron. Astrophys. 612, L1. DOI. ADS.

    Article  ADS  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 

  • 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.

    Article  Google Scholar 

  • Gizon, L., Cameron, R.H., Bekki, Y., Birch, A.C., Bogart, R.S., Brun, A.S., Damiani, C., Fournier, D., Hyest, L., Jain, K., Lekshmi, B., Liang, Z.-C., Proxauf, B.: 2021, Solar inertial modes: observations, identification, and diagnostic promise. Astron. Astrophys. 652, L6. DOI. ADS.

    Article  ADS  Google Scholar 

  • Goldreich, P., Keeley, D.A.: 1977a, Solar seismology. I – The stability of the solar p-modes. Astrophys. J. 211, 934. DOI. ADS.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Goldreich, P., Kumar, P.: 1991, Thermal and mechanical damping of solar p-modes. Astrophys. J. 374, 366. DOI. ADS.

    Article  ADS  Google Scholar 

  • Goldreich, P., Murray, N., Kumar, P.: 1994, Excitation of solar p-modes. Astrophys. J. 424, 466. DOI. ADS.

    Article  ADS  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    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  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Hekker, S., Christensen-Dalsgaard, J.: 2017, Giant star seismology. Astron. Astrophys. Rev. 25, 1. DOI. ADS.

    Article  ADS  Google Scholar 

  • Houdek, G., Dupret, M.-A.: 2015, Interaction between convection and pulsation. Liv. Rev. Solar Phys. 12, 8. DOI. ADS.

    Article  ADS  Google Scholar 

  • Houdek, G., Balmforth, N.J., Christensen-Dalsgaard, J., Gough, D.O.: 1999, Amplitudes of stochastically excited oscillations in main-sequence stars. Astron. Astrophys. 351, 582. ADS.

    ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Kumar, P., Goldreich, P.: 1989, Nonlinear interactions among solar acoustic modes. Astrophys. J. 342, 558. DOI. ADS.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  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., Quataert, E.: 2013, Internal gravity wave excitation by turbulent convection. Mon. Not. Roy. Astron. Soc. 430, 2363. DOI. ADS.

    Article  ADS  Google Scholar 

  • Ledoux, P., Walraven, T.: 1958, Variable stars. In: Astrophysics II: Stellar Structure, Handbuch der Physik 51, Springer, Heidelberg, 353. DOI. ADS.

    Chapter  Google Scholar 

  • Leibacher, J.W., Stein, R.F.: 1971, A new description of the solar five-minute oscillation. Astrophys. Lett. 7, 191. ADS.

    ADS  Google Scholar 

  • Leighton, R.B., Noyes, R.W., Simon, G.W.: 1962, Velocity fields in the solar atmosphere. I. Preliminary report. Astrophys. J. 135, 474.

    Article  ADS  Google Scholar 

  • Lighthill, M.J.: 1952, On sound generated aerodynamically. I. General theory. Proc. Roy. Soc. London Ser. A 211, 564. DOI. ADS.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Mussack, K., Däppen, W.: 2011, Dynamic screening correction for solar p-p reaction rates. Astrophys. J. 729, 96. DOI. ADS.

    Article  ADS  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Pinçon, C., Appourchaux, T., Buldgen, G.: 2021, Amplitude of solar gravity modes generated by penetrative plumes. Astron. Astrophys. 650, A47. DOI. ADS.

    Article  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  ADS  Google Scholar 

  • Press, W.H.: 1981, Radiative and other effects from internal waves in solar and stellar interiors. Astrophys. J. 245, 286. DOI. ADS.

    Article  ADS  Google Scholar 

  • Rempel, M.: 2004, Overshoot at the base of the solar convection zone: a semianalytical approach. Astrophys. J. 607, 1046. DOI. ADS.

    Article  ADS  Google Scholar 

  • Rieutord, M., Zahn, J.-P.: 1995, Turbulent plumes in stellar convective envelopes. Astron. Astrophys. 296, 127. ADS.

    ADS  Google Scholar 

  • Rogers, T.M., Glatzmaier, G.A.: 2005, Gravity waves in the Sun. Mon. Not. Roy. Astron. Soc. 364, 1135. DOI. ADS.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Rogers, T.M., Lin, D.N.C., McElwaine, J.N., Lau, H.H.B.: 2013, Internal gravity waves in massive stars: angular momentum transport. Astrophys. J. 772, 21. DOI. ADS.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  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  ADS  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Samadi, R., Goupil, M.-J.: 2001, Excitation of stellar p-modes by turbulent convection. I. Theoretical formulation. Astron. Astrophys. 370, 136.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Schatzman, E.: 1996, Do not forget gravity waves. Solar Phys. 169, 245. DOI. ADS.

    Article  ADS  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  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Scuflaire, R.: 1974, The non radial oscillations of condensed polytropes. Astron. Astrophys. 36, 107. ADS.

    ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Severnyi, A.B., Kotov, V.A., Tsap, T.T.: 1976, Observations of solar pulsations. Nature 259, 87. ADS.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Shibahashi, H.: 1979, Modal analysis of stellar nonradial oscillations by an asymptotic method. Publ. Astron. Soc. Japan 31, 87. ADS.

    ADS  Google Scholar 

  • Stein, R.F.: 1967, Generation of acoustic and gravity waves by turbulence in an isothermal stratified atmosphere. Solar Phys. 2, 385.

    Article  ADS  Google Scholar 

  • Stein, R.F., Nordlund, Å.: 1998, Simulations of solar granulation. I. General properties. Astrophys. J. 499, 914. DOI. ADS.

    Article  ADS  Google Scholar 

  • Stull, R.B.: 1976, Internal gravity waves generated by penetrative convection. J. Atmos. Sci. 33, 1279. DOI. ADS.

    Article  ADS  Google Scholar 

  • Townsend, A.A.: 1966, Internal waves produced by a convective layer. J. Fluid Mech. 24, 307. DOI. ADS.

    Article  MathSciNet  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Ulrich, R.K.: 1970, The five-minute oscillations on the solar surface. Astrophys. J. 162, 993.

    Article  ADS  Google Scholar 

  • Unno, W., Kato, S.: 1962, On the generation of acoustic noise from the turbulent atmosphere, I. Publ. Astron. Soc. Japan 14, 417.

    ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

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Acknowledgments

The authors thank the reviewer for their useful comments that helped to improve the manuscript.

Funding

During this work, C. Pinçon was financially supported by Sorbonne University (EMERGENCE project). G. Buldgen acknowledges funding from the SNF AMBIZIONE grant No 185805 (Seismic inversions and modeling of transport processes in stars).

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Authors and Affiliations

  1. LESIA, Observatoire de Paris, CNRS, Université PSL, Sorbonne Université, Université Paris Cité, 5 place Jules Janssen, 92195, Meudon, France

    K. Belkacem

  2. LERMA, Observatoire de Paris, PSL University, CNRS, Sorbonne University, Paris, France

    C. Pinçon

  3. Astronomy Department, University of Geneva, Versoix, 1290, Switzerland

    G. Buldgen

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  1. K. Belkacem
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  2. C. Pinçon
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  3. G. Buldgen
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K. Belkacem, C. Pinçon, and G. Buldgen wrote the manuscript text, prepared the figures and reviewed the manuscript.

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Belkacem, K., Pinçon, C. & Buldgen, G. Amplitudes of Solar Gravity Modes: A Review. Sol Phys 297, 147 (2022). https://doi.org/10.1007/s11207-022-02075-5

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