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Zahn’s theory of dynamical tides and its application to stars

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Abstract

Zahn’s theory of dynamical tides is analyzed critically. We compare the results of this theory with our numerical calculations for stars with a convective core and a radiative envelope and with masses of one and a half and two solar masses. We show that for a binary system consisting of stars of one and a half or two solar masses and a point object with a mass equal to the solar mass and with an orbital period of one day under the assumption of a dense spectrum and moderately rapid dissipation, the evolution time scales of the semimajor axis will be shorter than those in Zahn’s theory by several orders of magnitude.

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References

  1. E. Bolmont and S. Mathis, Celest. Mech. Dyn. Astron. 126, 275 (2016).

    Article  ADS  Google Scholar 

  2. P. Brassard, G. Fontaine, F. Wesemael, S. D. Kawaler, and M. Tassoul, Astrophys. J. 367, 601 (1991).

    Article  ADS  Google Scholar 

  3. S. V. Chernov, Astron. Lett. 43(3), 186 (2017).

    Article  ADS  Google Scholar 

  4. S. V. Chernov, J. C. B. Papaloizou, and P. B. Ivanov, Mon. Not. R. Astron. Soc. 434, 1079 (2013).

    Article  ADS  Google Scholar 

  5. J. Christensen-Dalsgaard, Lecture Notes on Stellar Oscillations, 4th ed. (Inst. Fys. Astron., Aarhus Univ., Denmark, 1998).

    Google Scholar 

  6. A. Claret and N. C. S. Cunha, Astron. Astrophys. 318, 187 (1997).

    ADS  Google Scholar 

  7. T. G. Cowling, Mon. Not. R. Astron. Soc. 101, 367 (1941).

    Article  ADS  Google Scholar 

  8. R. Essick and N. N. Weinberg, Astrophys. J. 816, 21 (2016).

    Article  ADS  Google Scholar 

  9. J. Goodman and E. Dicksun, Astrophys. J. 507, 938 (1998).

    Article  ADS  Google Scholar 

  10. P. B. Ivanov, J. C. B. Papaloizou, and S. V. Chernov, Mon. Not. R. Astron. Soc. 432, 2339 (2013).

    Article  ADS  Google Scholar 

  11. P. B. Ivanov and J. C. B. Papaloizou, Mon. Not. R. Astron. Soc. 347, 437 (2004).

    Article  ADS  Google Scholar 

  12. P. B. Ivanov and J. C. B. Papaloizou, Mon. Not. R. Astron. Soc. 353, 1161 (2004).

    Article  ADS  Google Scholar 

  13. P. B. Ivanov and J. C. B. Papaloizou, Mon. Not. R. Astron. Soc. 376, 682 (2007).

    Article  ADS  Google Scholar 

  14. P. B. Ivanov and J. C. B. Papaloizou, Mon. Not. R. Astron. Soc. 407, 1609 (2010).

    Article  ADS  Google Scholar 

  15. D. Kushnir, M. Zaldarriaga, J. Kollmeier, and R. Waldman, arXiv:1605. 03810v1[astro-ph] (2016).

  16. A. F. Lanza and S. Mathis, Celest. Mech. Dyn. Astron. 126, 249 (2016).

    Article  ADS  Google Scholar 

  17. G. Ogilvie, Ann. Rev. Astron. Astrophys. 52, 171 (2014).

    Article  ADS  Google Scholar 

  18. F. W. J. Olver, Phil. Trans. R. Soc. London, Ser. A 247, 307 (1954).

    Article  ADS  Google Scholar 

  19. F. W. J. Olver, Phil. Trans. R. Soc. London, Ser. A 249, 65 (1956).

    Article  ADS  Google Scholar 

  20. F. W. J. Olver, Asymptotics and Special Functions (Academic, London, 1974).

    MATH  Google Scholar 

  21. J. C. B. Papaloizou and P. B. Ivanov, Mon. Not. R. Astron. Soc. 364, L66 (2005).

    Article  ADS  Google Scholar 

  22. J. C. B. Papaloizou and P. B. Ivanov, Mon. Not. R. Astron. Soc. 407, 1631 (2010).

    Article  ADS  Google Scholar 

  23. B. Paxton et al., Astrophys. J. Supp. Ser. 192, 3 (2011).

    Article  ADS  Google Scholar 

  24. B. Paxton et al., Astrophys. J. Supp. Ser. 208, 4 (2013).

    Article  ADS  Google Scholar 

  25. B. Paxton et al., Astrophys. J. Supp. Ser. 220, 15 (2015).

    Article  ADS  Google Scholar 

  26. W. H. Press and S. A. Teukolsky, Astrophys. J. 213, 183 (1977).

    Article  ADS  Google Scholar 

  27. A. Rocca, Astron. Astrophys. 175, 81 (1987).

    ADS  Google Scholar 

  28. P. Smeyers and M. Tassoul, Astrophys. J. Suppl. Ser. 65, 429 (1987).

    Article  ADS  Google Scholar 

  29. M. Steffen, Astron. Astrophys. 239, 443 (1990).

    ADS  Google Scholar 

  30. M. Tassoul, Astrophys. J. Suppl. Ser. 43, 469 (1980).

    Article  ADS  Google Scholar 

  31. N. N. Weinberg, P. Arras, E. Quataert, and J. Burkart, Astrophys. J. 751, 136 (2012).

    Article  ADS  Google Scholar 

  32. J.-P. Zahn, Astron. Astrophys. 4, 452 (1970).

    ADS  Google Scholar 

  33. J.-P. Zahn, Astron. Astrophys. 41, 329 (1975).

    ADS  Google Scholar 

  34. J.-P. Zahn, Astron. Astrophys. 57, 383 (1977).

    ADS  Google Scholar 

Download references

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Correspondence to S. V. Chernov.

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Original Russian Text © S.V. Chernov, 2017, published in Pis’ma v Astronomicheskii Zhurnal, 2017, Vol. 43, No. 6, pp. 474–482.

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Chernov, S.V. Zahn’s theory of dynamical tides and its application to stars. Astron. Lett. 43, 429–437 (2017). https://doi.org/10.1134/S1063773717060020

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