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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Bolmont and S. Mathis, Celest. Mech. Dyn. Astron. 126, 275 (2016).
P. Brassard, G. Fontaine, F. Wesemael, S. D. Kawaler, and M. Tassoul, Astrophys. J. 367, 601 (1991).
S. V. Chernov, Astron. Lett. 43(3), 186 (2017).
S. V. Chernov, J. C. B. Papaloizou, and P. B. Ivanov, Mon. Not. R. Astron. Soc. 434, 1079 (2013).
J. Christensen-Dalsgaard, Lecture Notes on Stellar Oscillations, 4th ed. (Inst. Fys. Astron., Aarhus Univ., Denmark, 1998).
A. Claret and N. C. S. Cunha, Astron. Astrophys. 318, 187 (1997).
T. G. Cowling, Mon. Not. R. Astron. Soc. 101, 367 (1941).
R. Essick and N. N. Weinberg, Astrophys. J. 816, 21 (2016).
J. Goodman and E. Dicksun, Astrophys. J. 507, 938 (1998).
P. B. Ivanov, J. C. B. Papaloizou, and S. V. Chernov, Mon. Not. R. Astron. Soc. 432, 2339 (2013).
P. B. Ivanov and J. C. B. Papaloizou, Mon. Not. R. Astron. Soc. 347, 437 (2004).
P. B. Ivanov and J. C. B. Papaloizou, Mon. Not. R. Astron. Soc. 353, 1161 (2004).
P. B. Ivanov and J. C. B. Papaloizou, Mon. Not. R. Astron. Soc. 376, 682 (2007).
P. B. Ivanov and J. C. B. Papaloizou, Mon. Not. R. Astron. Soc. 407, 1609 (2010).
D. Kushnir, M. Zaldarriaga, J. Kollmeier, and R. Waldman, arXiv:1605. 03810v1[astro-ph] (2016).
A. F. Lanza and S. Mathis, Celest. Mech. Dyn. Astron. 126, 249 (2016).
G. Ogilvie, Ann. Rev. Astron. Astrophys. 52, 171 (2014).
F. W. J. Olver, Phil. Trans. R. Soc. London, Ser. A 247, 307 (1954).
F. W. J. Olver, Phil. Trans. R. Soc. London, Ser. A 249, 65 (1956).
F. W. J. Olver, Asymptotics and Special Functions (Academic, London, 1974).
J. C. B. Papaloizou and P. B. Ivanov, Mon. Not. R. Astron. Soc. 364, L66 (2005).
J. C. B. Papaloizou and P. B. Ivanov, Mon. Not. R. Astron. Soc. 407, 1631 (2010).
B. Paxton et al., Astrophys. J. Supp. Ser. 192, 3 (2011).
B. Paxton et al., Astrophys. J. Supp. Ser. 208, 4 (2013).
B. Paxton et al., Astrophys. J. Supp. Ser. 220, 15 (2015).
W. H. Press and S. A. Teukolsky, Astrophys. J. 213, 183 (1977).
A. Rocca, Astron. Astrophys. 175, 81 (1987).
P. Smeyers and M. Tassoul, Astrophys. J. Suppl. Ser. 65, 429 (1987).
M. Steffen, Astron. Astrophys. 239, 443 (1990).
M. Tassoul, Astrophys. J. Suppl. Ser. 43, 469 (1980).
N. N. Weinberg, P. Arras, E. Quataert, and J. Burkart, Astrophys. J. 751, 136 (2012).
J.-P. Zahn, Astron. Astrophys. 4, 452 (1970).
J.-P. Zahn, Astron. Astrophys. 41, 329 (1975).
J.-P. Zahn, Astron. Astrophys. 57, 383 (1977).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.V. Chernov, 2017, published in Pis’ma v Astronomicheskii Zhurnal, 2017, Vol. 43, No. 6, pp. 474–482.
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063773717060020