Skip to main content
SpringerLink
Log in

Connections Between Stellar Oscillations and Turbulent Convection

  • Chapter
Studying Stellar Rotation and Convection

Part of the book series: Lecture Notes in Physics ((LNP,volume 865))

Abstract

Since the advent of space asteroseismology, enabled by the CoRoT and Kepler space-craft, solar-like oscillations have appeared to be a common feature of low-mass stars from the main-sequence to the red-giant phases. In this context, scaling relations that relate asteroseismological quantities and stellar parameters are an essential tool in the study a large class of stars. Most of these relations concern the connection between pulsations and turbulent convection. Therefore, a deep investigation of this connection is necessary to obtain insight into the processes underlying mode driving and damping and consequently to improve our knowledge of the scaling relations. This is a key step that will permit us to perform a leap forward in our understanding of stellar interiors.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A Lorentzian profile in the Fourier time domain corresponds to an exponentially damped oscillation in the time domain.

  2. 2.

    A detailed derivation can be found in [61].

  3. 3.

    This characteristic size can be determined from the kinetic E(k) or by default using some prescriptions (for more details, see Sect. 11.5.1 in [60]).

  4. 4.

    Note that mode inertia also scales with the dynamical time scale \(\sqrt{(}GM/R^{3})\) with almost the same dispersion as for the surface gravity.

  5. 5.

    A more sophisticated quasi-adiabatic approach has been proposed by [69]. These authors go beyond the approximation of isothermal atmosphere by taking into account the temperature gradient and the fact that the intensity is measured at constant instantaneous optical depth. Both effects are taken into account by the non-adiabatic pulsation code MAD.

  6. 6.

    This scaling is only valid for sub- and red-giant stars.

References

  1. Ando, H., Osaki, Y.: Nonadiabatic nonradial oscillations: an application to the five-minute oscillation of the Sun. Publ. Astron. Soc. Jpn. 27, 581–603 (1975)

    ADS  Google Scholar 

  2. Antia, H.M., Chitre, S.M., Narasimha, D.: Overstability of acoustic modes and the solar five-minute oscillations. Sol. Phys. 77, 303–327 (1982)

    Article  ADS  Google Scholar 

  3. Appourchaux, T., Michel, E., Auvergne, M., Baglin, A., Toutain, T., Baudin, F., Benomar, O., Chaplin, W.J., Deheuvels, S., Samadi, R., Verner, G.A., Boumier, P., García, R.A., Mosser, B., Hulot, J.C., Ballot, J., Barban, C., Elsworth, Y., Jiménez-Reyes, S.J., Kjeldsen, H., Régulo, C., Roxburgh, I.W.: CoRoT sounds the stars: p-mode parameters of sun-like oscillations on HD 49933. Astron. Astrophys. 488, 705–714 (2008)

    Article  ADS  Google Scholar 

  4. Appourchaux, T., Benomar, O., Gruberbauer, M., Chaplin, W.J., García, R.A., Handberg, R., Verner, G.A., Antia, H.M., Campante, T.L., Davies, G.R., Deheuvels, S., Hekker, S., Howe, R., Salabert, D., Bedding, T.R., White, T.R., Houdek, G., Silva Aguirre, V., Elsworth, Y.P., van Cleve, J., Clarke, B.D., Hall, J.R., Kjeldsen, H.: Oscillation mode linewidths of main-sequence and subgiant stars observed by Kepler. Astron. Astrophys. 537, A134 (2012)

    Article  ADS  Google Scholar 

  5. Balmforth, N.J.: Solar pulsational stability—III. Acoustical excitation by turbulent convection. Mon. Not. R. Astron. Soc. 255, 639 (1992)

    ADS  Google Scholar 

  6. Balmforth, N.J.: Solar pulsational stability—I. Pulsation-mode thermodynamics. Mon. Not. R. Astron. Soc. 255, 603–649 (1992)

    ADS  Google Scholar 

  7. Basu, S., Chaplin, W.J., Elsworth, Y.: Determining stellar radii using large separations: an error analysis. Astrophys. Space Sci. 328, 79–82 (2010)

    Article  ADS  Google Scholar 

  8. Batchelor, G.K.: The Theory of Homogeneous Turbulence. Cambridge University Press, Cambridge (1970)

    Google Scholar 

  9. Baudin, F., Samadi, R., Goupil, M.J., Appourchaux, T., Barban, C., Boumier, P., Chaplin, W.J., Gouttebroze, P.: Inferred acoustic rates of solar p modes from several helioseismic instruments. Astron. Astrophys. 433, 349–356 (2005)

    Article  ADS  Google Scholar 

  10. Baudin, F., Barban, C., Belkacem, K., Hekker, S., Morel, T., Samadi, R., Benomar, O., Goupil, M.J., Carrier, F., Ballot, J., Deheuvels, S., De Ridder, J., Hatzes, A.P., Kallinger, T., Weiss, W.W.: Amplitudes and lifetimes of solar-like oscillations observed by CoRoT. Red-giant versus main-sequence stars. Astron. Astrophys. 529, A84 (2011)

    Article  ADS  Google Scholar 

  11. Baudin, F., Barban, C., Belkacem, K., Hekker, S., Morel, T., Samadi, R., Benomar, O., Goupil, M.J., Carrier, F., Ballot, J., Deheuvels, S., De Ridder, J., Hatzes, A.P., Kallinger, T., Weiss, W.W.: Amplitudes and lifetimes of solar-like oscillations observed by CoRoT. Red-giant versus main-sequence stars. Astron. Astrophys. 535, C1 (2011)

    Article  Google Scholar 

  12. Bedding, T.R., Kjeldsen, H.: Solar-like oscillations. Publ. Astron. Soc. Aust. 20, 203–212 (2003)

    Article  ADS  Google Scholar 

  13. Belkacem, K.: Amplitudes of solar gravity modes. In: Rozelot, J.P., Neiner, C. (eds.) Pulsation of the Sun and Stars. Lecture Notes in Physics, vol. 832, p. 139 (2011)

    Chapter  Google Scholar 

  14. Belkacem, K., Samadi, R., Goupil, M.J., Kupka, F.: A closure model with plumes. I. The solar convection. Astron. Astrophys. 460, 173–182 (2006)

    Article  ADS  Google Scholar 

  15. Belkacem, K., Samadi, R., Goupil, M.J., Kupka, F., Baudin, F.: A closure model with plumes. II. Application to the stochastic excitation of solar p modes. Astron. Astrophys. 460, 183–190 (2006)

    Article  ADS  Google Scholar 

  16. Belkacem, K., Samadi, R., Goupil, M.J., Dupret, M.A.: Stochastic excitation of non-radial modes. I. High-angular-degree p modes. Astron. Astrophys. 478, 163–174 (2008)

    Article  ADS  MATH  Google Scholar 

  17. Belkacem, K., Samadi, R., Goupil, M.J., Dupret, M.A., Brun, A.S., Baudin, F.: Stochastic excitation of nonradial modes. II. Are solar asymptotic gravity modes detectable? Astron. Astrophys. 494, 191–204 (2009)

    Article  ADS  Google Scholar 

  18. Belkacem, K., Samadi, R., Goupil, M.J., Baudin, F., Salabert, D., Appourchaux, T.: Turbulent eddy-time-correlation in the solar convective zone. Astron. Astrophys. 522, L2 (2010)

    Article  ADS  Google Scholar 

  19. Belkacem, K., Goupil, M.J., Dupret, M.A., Samadi, R., Baudin, F., Noels, A., Mosser, B.: The underlying physical meaning of the ν max−ν c relation. Astron. Astrophys. 530, A142 (2011)

    Article  ADS  Google Scholar 

  20. Belkacem, K., Samadi, R., Goupil, M.: Amplitudes of solar p modes: modelling of the eddy time-correlation function. J. Phys. Conf. Ser. 271(1), 012047 (2011)

    Article  ADS  Google Scholar 

  21. Belkacem, K., Dupret, M.A., Baudin, F., Appourchaux, T., Marques, J.P., Samadi, R.: Damping rates of solar-like oscillations across the HR diagram. Theoretical calculations confronted to CoRoT and Kepler observations. Astron. Astrophys. 540, L7 (2012)

    Article  ADS  Google Scholar 

  22. Bohm-Vitense, E.: Introduction to Stellar Astrophysics vol. 3. Cambridge University Press, Cambridge (1989)

    Book  Google Scholar 

  23. Brown, T.M., Gilliland, R.L., Noyes, R.W., Ramsey, L.W.: Detection of possible p-mode oscillations on Procyon. Astrophys. J. 368, 599–609 (1991)

    Article  ADS  Google Scholar 

  24. Canuto, V.M.: Turbulent convection with overshooting—Reynolds stress approach. Astrophys. J. 392, 218–232 (1992)

    Article  ADS  Google Scholar 

  25. Chaplin, W.J., Houdek, G., Elsworth, Y., Gough, D.O., Isaak, G.R., New, R.: On model predictions of the power spectral density of radial solar p modes. Mon. Not. R. Astron. Soc. 360, 859–868 (2005)

    Article  ADS  Google Scholar 

  26. Chaplin, W.J., Houdek, G., Appourchaux, T., Elsworth, Y., New, R., Toutain, T.: Challenges for asteroseismic analysis of Sun-like stars. Astron. Astrophys. 485, 813–822 (2008)

    Article  ADS  Google Scholar 

  27. Chaplin, W.J., Houdek, G., Karoff, C., Elsworth, Y., New, R.: Mode lifetimes of stellar oscillations. Implications for asteroseismology. Astron. Astrophys. 500, L21–L24 (2009)

    Article  ADS  Google Scholar 

  28. Christensen-Dalsgaard, J., Frandsen, S.: Stellar 5 min oscillations. Sol. Phys. 82, 469–486 (1983)

    Article  ADS  Google Scholar 

  29. Dolginov, A., Muslimov, A.: Nonradial stellar oscillations excited by turbulent convection. Astrophys. Space Sci. 98, 15–36 (1984)

    Article  ADS  MATH  Google Scholar 

  30. Dupret, M.A., Barban, C., Goupil, M.J., Samadi, R., Grigahcène, A., Gabriel, M.: Theoretical damping rates and phase-lags for solar-like oscillations. In: Proceedings of SOHO 18/GONG 2006/HELAS I, Beyond the Spherical Sun. ESA Special Publication, vol. 624 (2006)

    Google Scholar 

  31. Dziemblowski, W.: Oscillations of giants and supergiants. Acta Astron. 27, 95–126 (1977)

    ADS  Google Scholar 

  32. Evans, J.W., Michard, R.: Observational study of macroscopic inhomogeneities in the solar atmosphere. III. Vertical oscillatory motions in the solar photosphere. Astrophys. J. 136, 493 (1962)

    Article  ADS  Google Scholar 

  33. Freytag, B., Holweger, H., Steffen, M., Ludwig, H.G.: On the scale of photospheric convection. In: Paresce, F. (ed.) Science with the VLT Interferometer, p. 316 (1997)

    Google Scholar 

  34. Gabriel, A.H., Grec, G., Charra, J., Robillot, J.M., Roca Cortés, T., Turck-Chièze, S., Bocchia, R., Boumier, P., Cantin, M., Cespédes, E., Cougrand, B., Crétolle, J., Damé, L., Decaudin, M., Delache, P., Denis, N., Duc, R., Dzitko, H., Fossat, E., Fourmond, J.J., García, R.A., Gough, D., Grivel, C., Herreros, J.M., Lagardère, H., Moalic, J.P., Pallé, P.L., Pétrou, N., Sanchez, M., Ulrich, R., van der Raay, H.B.: Global oscillations at low frequency from the SOHO mission (GOLF). Sol. Phys. 162, 61–99 (1995)

    Article  ADS  Google Scholar 

  35. Gautschy, A., Saio, H.: Stellar pulsations across the HR diagram: Part 1. Annu. Rev. Astron. Astrophys. 33, 75–114 (1995)

    Article  ADS  Google Scholar 

  36. Gautschy, A., Saio, H.: Stellar pulsations across the HR diagram: Part 2. Annu. Rev. Astron. Astrophys. 34, 551–606 (1996)

    Article  ADS  Google Scholar 

  37. Goldreich, P., Keeley, D.A.: Solar seismology. I. The stability of the solar p-modes. Astrophys. J. 211, 934–942 (1977)

    Article  ADS  Google Scholar 

  38. Goldreich, P., Keeley, D.A.: Solar seismology. II. The stochastic excitation of the solar p-modes by turbulent convection. Astrophys. J. 212, 243–251 (1977)

    Article  ADS  Google Scholar 

  39. Goldreich, P., Kumar, P.: Thermal and mechanical damping of solar p-modes. Astrophys. J. 374, 366–368 (1991)

    Article  ADS  Google Scholar 

  40. Goldreich, P., Murray, N., Kumar, P.: Excitation of solar p-modes. Astrophys. J. 424, 466–479 (1994)

    Article  ADS  Google Scholar 

  41. Gough, D.: Some theoretical remarks on solar oscillations. In: Hill, H.A., Dziembowski, W.A. (eds.) Nonradial and Nonlinear Stellar Pulsation. Lecture Notes in Physics, vol. 125, pp. 273–299 (1980)

    Chapter  Google Scholar 

  42. Grigahcène, A., Dupret, M.A., Gabriel, M., Garrido, R., Scuflaire, R.: Convection-pulsation coupling. I. A mixing-length perturbative theory. Astron. Astrophys. 434, 1055–1062 (2005)

    Article  ADS  Google Scholar 

  43. Houdek, G.: The effect of convection on pulsational stability. Commun. Asteroseismol. 157, 137–143 (2008)

    ADS  Google Scholar 

  44. Houdek, G., Balmforth, N.J., Christensen-Dalsgaard, J., Gough, D.O.: Amplitudes of stochastically excited oscillations in main-sequence stars. Astron. Astrophys. 351, 582–596 (1999)

    ADS  Google Scholar 

  45. Kjeldsen, H., Bedding, T.R.: Amplitudes of stellar oscillations: the implications for asteroseismology. Astron. Astrophys. 293, 87–106 (1995)

    ADS  Google Scholar 

  46. Ledoux, P., Walraven, T.: Variable stars. Handb. Phys. 51, 353–604 (1958)

    ADS  Google Scholar 

  47. Leibacher, J.W., Stein, R.F.: A new description of the solar five-minute oscillation. Astrophys. J. Lett. 7, 191–192 (1971)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  49. Lesieur, M.: Turbulence in Fluids, 3rd edn. Kluwer Academic, Dordrecht (1997)

    Book  MATH  Google Scholar 

  50. Lighthill, M.: On sound generated aerodynamically. I. General theory. Proc. R. Soc. Lond. Ser. A 211, 564–587 (1952)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  51. Lighthill, J.: Waves in Fluids. Cambridge University Press, Cambridge (1978)

    MATH  Google Scholar 

  52. Michel, E., Baglin, A., Auvergne, M., Catala, C., Samadi, R., Baudin, F., Appourchaux, T., Barban, C., Weiss, W.W., Berthomieu, G., Boumier, P., Dupret, M.A., Garcia, R.A., Fridlund, M., Garrido, R., Goupil, M.J., Kjeldsen, H., Lebreton, Y., Mosser, B., Grotsch-Noels, A., Janot-Pacheco, E., Provost, J., Roxburgh, I.W., Thoul, A., Toutain, T., Tiphène, D., Turck-Chieze, S., Vauclair, S.D., Vauclair, G.P., Aerts, C., Alecian, G., Ballot, J., Charpinet, S., Hubert, A.M., Lignières, F., Mathias, P., Monteiro, M.J.P.F.G., Neiner, C., Poretti, E., Renan de Medeiros, J., Ribas, I., Rieutord, M.L., Cortés, T.R., Zwintz, K.: CoRoT measures solar-like oscillations and granulation in stars hotter than the Sun. Science 322, 558 (2008)

    Article  ADS  Google Scholar 

  53. Michel, E., Samadi, R., Baudin, F., Barban, C., Appourchaux, T., Auvergne, M.: Intrinsic photometric characterisation of stellar oscillations and granulation. Solar reference values and CoRoT response functions. Astron. Astrophys. 495, 979–987 (2009)

    Article  ADS  Google Scholar 

  54. Miglio, A., Montalbán, J., Baudin, F., Eggenberger, P., Noels, A., Hekker, S., de Ridder, J., Weiss, W., Baglin, A.: Probing populations of red giants in the galactic disk with CoRoT. Astron. Astrophys. 503, L21–L24 (2009)

    Article  ADS  Google Scholar 

  55. Mosser, B., Belkacem, K., Goupil, M., Miglio, A., Morel, T., Barban, C., Baudin, F., Hekker, S., Samadi, R., De Ridder, J., Weiss, W., Auvergne, M., Baglin, A.: Red-giant seismic properties analyzed with CoRoT. Astron. Astrophys. 517, A22 (2010)

    Article  ADS  Google Scholar 

  56. Osaki, Y.: Excitation mechanisms of solar oscillations. In: Osaki, Y., Shibahashi, H. (eds.) Lecture Notes in Physics: Progress of Seismology of the Sun and Stars, p. 75. Springer, Berlin (1990)

    Google Scholar 

  57. Pamyatnykh, A.A.: Pulsational instability domains in the upper main sequence. Acta Astron. 49, 119–148 (1999)

    ADS  Google Scholar 

  58. Pesnell, W.D.: Nonradial, nonadiabatic stellar pulsations. Astrophys. J. 363, 227–233 (1990)

    Article  ADS  Google Scholar 

  59. Salabert, D., Leibacher, J., Appourchaux, T., Hill, F.: Measurement of low signal-to-noise ratio solar p-modes in spatially resolved helioseismic data. Astrophys. J. 696, 653–667 (2009)

    Article  ADS  Google Scholar 

  60. Samadi, R.: Stochastic excitation of acoustic modes in stars. In: Rozelot, J.P., Neiner, C. (eds.) Pulsation of the Sun and Stars. Lecture Notes in Physics, vol. 832, p. 305. Springer, Berlin (2011)

    Chapter  Google Scholar 

  61. Samadi, R., Goupil, M.: Excitation of stellar p-modes by turbulent convection. I. Theoretical formulation. Astron. Astrophys. 370, 136–146 (2001)

    Article  ADS  Google Scholar 

  62. Samadi, R., Nordlund, Å., Stein, R.F., Goupil, M.J., Roxburgh, I.: Numerical 3D constraints on convective eddy time-correlations: consequences for stochastic excitation of solar p modes. Astron. Astrophys. 404, 1129–1137 (2003)

    Article  ADS  Google Scholar 

  63. Samadi, R., Nordlund, Å., Stein, R.F., Goupil, M.J., Roxburgh, I.: Numerical constraints on the model of stochastic excitation of solar-type oscillations. Astron. Astrophys. 403, 303–312 (2003)

    Article  ADS  Google Scholar 

  64. Samadi, R., Georgobiani, D., Trampedach, R., Goupil, M.J., Stein, R.F., Nordlund, Å.: Excitation of solar-like oscillations across the HR diagram. Astron. Astrophys. 463, 297–308 (2007)

    Article  ADS  Google Scholar 

  65. Samadi, R., Belkacem, K., Goupil, M.J., Dupret, M.A., Kupka, F.: Modeling the excitation of acoustic modes in α Centauri A. Astron. Astrophys. 489, 291–299 (2008)

    Article  ADS  Google Scholar 

  66. Samadi, R., Ludwig, H.G., Belkacem, K., Goupil, M.J., Benomar, O., Mosser, B., Dupret, M.A., Baudin, F., Appourchaux, T., Michel, E.: The CoRoT target HD 49933. II. Comparison of theoretical mode amplitudes with observations. Astron. Astrophys. 509, A16 (2010)

    Article  ADS  Google Scholar 

  67. Samadi, R., Ludwig, H.G., Belkacem, K., Goupil, M.J., Dupret, M.A.: The CoRoT target HD 49933. I. Effect of the metal abundance on the mode excitation rates. Astron. Astrophys. 509, A15 (2010)

    Article  ADS  Google Scholar 

  68. Samadi, R., Belkacem, K., Dupret, M.A., Ludwig, H.G., Baudin, F., Caffau, E., Goupil, M.J., Barban, C.: Amplitudes of solar-like oscillations in red-giant stars. Evidence for non-adiabatic effects using CoRoT observations. Astron. Astrophys. 543, A120 (2012)

    Article  ADS  Google Scholar 

  69. Severino, G., Straus, T., Steffen, M.: Velocity and intensity power and cross spectra in numerical simulations of solar convection. Sol. Phys. 251, 549–562 (2008)

    Article  ADS  Google Scholar 

  70. Stein, R.F.: Generation of acoustic and gravity waves by turbulence in an isothermal stratified atmosphere. Sol. Phys. 2, 385–432 (1967)

    Article  ADS  Google Scholar 

  71. Stello, D., Chaplin, W.J., Basu, S., Elsworth, Y., Bedding, T.R.: The relation between Δν and ν max for solar-like oscillations. Mon. Not. R. Astron. Soc. 400, L80–L84 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  73. Unno, W., Kato, S.: On the generation of acoustic noise from the turbulent atmosphere, I. Publ. Astron. Soc. Jpn. 14, 417 (1962)

    ADS  Google Scholar 

  74. White, T.R., Bedding, T.R., Stello, D., Christensen-Dalsgaard, J., Huber, D., Kjeldsen, H.: Calculating asteroseismic diagrams for solar-like oscillations. Astrophys. J. 743, 161 (2011)

    Article  ADS  Google Scholar 

  75. Xiong, D.R., Cheng, Q.L., Deng, L.: Turbulent convection and pulsational stability of variable stars: non-adiabatic oscillations of the solar p-modes. Mon. Not. R. Astron. Soc. 319, 1079–1093 (2000)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LESIA, UMR8109, Observatoire de Paris, Université Pierre et Marie Curie, Université Denis Diderot, 92195, Meudon Cedex, France

    K. Belkacem & R. Samadi

Authors
  1. K. Belkacem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Samadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Belkacem .

Editor information

Editors and Affiliations

  1. LESIA, Observatoire de Paris-Meudon, place Jules Janssen, batiment 14 5, Meudon Cedex, 92195, France

    Mariejo Goupil

  2. LESIA, Observatoire de Paris-Meudon, place Jules Janssen 5, Meudon Cedex, 92195, France

    Kévin Belkacem

  3. LESIA, Observatoire de Paris-Meudon, place Jules Janssen, batiment 14 5, Meudon Cedex, 92195, France

    Coralie Neiner

  4. Institut de Recherche en Astrophysique, et Planétologie, Observatoire Midi-Pyrénées, avenue Édouard Belin 14, Toulouse, 31400, France

    Francois Lignières

  5. Observatoire de Paris-Meudon, LESIA, Place Jules Janssen 5, Meudon, 92190, France

    John J. Green

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Belkacem, K., Samadi, R. (2013). Connections Between Stellar Oscillations and Turbulent Convection. In: Goupil, M., Belkacem, K., Neiner, C., Lignières, F., Green, J. (eds) Studying Stellar Rotation and Convection. Lecture Notes in Physics, vol 865. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33380-4_9

Download citation

Publish with us

Policies and ethics

Search

Navigation