Improving the asymptotic approximations of higher-order radial oscillations in stars
Since the initial work of Ledoux (1962) on the asymptotic representation of higher-order radial oscillation modes, it has been customary to use the square of the angular frequency as the large parameter in the governing second-order differential equation. In the present investigation, the introduction of a different large parameter is shown to improve the accuracy of the first and second asymptotic approximations of the eigenfrequencies of the radial oscillation modes, for the equilibrium sphere with uniform mass density and the polytropes with index n = 2 and n = 3. The definition of the new large parameter is based on the use of the second-order differential equation in the divergence of the radial displacement.
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- Ledoux, P. 1962, Bull. Acad. Roy. Belg., Cl. Sci., 5e Série, 48, 240.Google Scholar
- Mullan, D.J., and Ulrich, R.K. 1988, Astrophys. J. 331, 1013.Google Scholar
- Olver, F.W.J. 1974, Asymptotics and Special Functions (Academic Press, New York).)Google Scholar
- Pallé, P.L., Pérez Hernández, P.L., Roca Cortés, T., and Isaak, G.R. 1989, Astron. Astrophys. 216, 253.Google Scholar
- Tassoul, M., and Tassoul, J.-L. 1968, Astrophys. J. 153, 127.Google Scholar