Abstract
The second-order asymptotic theory for low-degree, higher-order p-modes is seen to be inadequate to reproduce frequency separations D n,ℓ for the low-degree p-modes in the solar 5 min-oscillations in a satisfactory way. The reason of the inadequacy is that the inner boundary of the resonant acoustic cavity in the Sun is supposed to be located close to the solar centre, while this condition is not really fulfilled for the oscillations concerned. Therefore, a first-order asymptotic theory for p-modes is developed for which the inner boundary of the resonant acoustic cavity is situated at larger distances from the star’s centre. This theory applies to low-degree p-modes of less high radial orders and to intermediate-degree p-modes as well. Its validity is verified for the compressible equilibrium sphere of uniform mass density.
Keywords
- Asymptotic Solution
- Asymptotic Approximation
- Asymptotic Representation
- Airy Function
- Frequency Separation
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Notes
- 1.
This section is a reproduction of Van Hoolst, T., Smeyers, P.: The quantities D n,ℓ as measures of small frequency separations in the Sun and their origin. Astronomy & Astrophysics 248, 647–655 (1991). With permission from Astronomy & Astrophysics, http://www.aanda.org.
- 2.
The remaining part of this chapter is partially a reproduction of Smeyers, P.: Asymptotic representation of low- and intermediate-degree p-modes in stars. Astronomy & Astrophysics 407, 643–653 (2003). With permission from Astronomy & Astrophysics, http://www.aanda.org.
References
V.V. Babikov (1976) Methods of Phase Functions in Quantum Mechanics. Nauka, Moscow
J.N. Bahcall, R.K. Ulrich (1988) Solar models, neutrino experiments, and helioseismology. Rev. Mod. Phys. 60, 297–372
M. Gabriel (1989) The D n, ℓ values and the structure of the solar core. Astron. Astrophys. 226, 278–283
D.O. Gough (1983) Our first inferences from helioseismology. Phys. Bull. 34, 502–507
J. Kevorkian, J.D. Cole (1981) Perturbation Methods in Applied Mathematics. Springer, New York
R.E. Langer (1937) On the connection formulas and the solutions of the wave equation. Phys. Rev. 51, 669–676
I.W. Roxburgh, S.V. Vorontsov (1993) Inside the Stars, ed. by W.W. Weiss, A. Baglin. Asymptotic theory of low-degree stellar acoustic oscillations. International Astronomical Union Colloquium 137, Astronomical Society of the Pacific Conference Series, vol. 40, p. 535–537
I.W. Roxburgh, S.V. Vorontsov (1996) An asymptotic description of solar acoustic oscillation of low and intermediate degree. Mon. Not. R. Astron. Soc. 278, 940–946
P. Smeyers (2003) Asymptotic representation of low- and intermediate-degree p-modes in stars. Astron. Astrophys. 407, 643–653
P. Smeyers, R. Briers, M. Tassoul, K. Degryse, R. Polfliet, T. Van Hoolst (1988) Seismology of the Sun & Sun-Like Stars, ed. by E.J. Rolfe. Asymptotic approximations of non-radial oscillation modes of the Sun. European Space Agency SP-286, Paris, pp. 623–627
M. Tassoul (1980) Asymptotic approximations for stellar nonradial pulsations. Astrophys. J. Suppl. Ser. 43, 469–490
M. Tassoul (1990) Second-order asymptotic approximations for stellar nonradial acoustic modes. Astrophys. J. 358, 313–327
T. Van Hoolst, P. Smeyers (1991) The quantities D n, ℓ as measures of small frequency separations in the Sun and their origin. Astron. Astrophys. 248, 647–655
S.V. Vorontsov (1991) Astronomicheskii Zhurnal 68, 808–824 (1991). English translation: Asymptotic theory of acoustic oscillations of the sun and stars. Soviet Astronomy 35, 400–408
S.V. Vorontsov, V.N. Zharkov (1989) Helioseismology: theory and interpretation of experimental data. Sov. Sci. Rev. E, Astrophys. Space Phys. Rev. 7, 1–103
J.H. Woodhouse (1978) Asymptotic results for elastodynamic propagator matrices in plane-stratified and spherically-stratified earth models. Geophys. J. Int. 54, 263–280
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Smeyers, P. (2010). Asymptotic Representation of Low-Degree and Intermediate-Degree p-Modes. In: Linear Isentropic Oscillations of Stars. Astrophysics and Space Science Library, vol 371. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13030-4_16
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DOI: https://doi.org/10.1007/978-3-642-13030-4_16
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