Abstract
An asymptotic approach for high-degree, low-order modes, developed by Christensen-Dalsgaard (1980), is presented. Besides p-, f-, and g +-modes that are trapped near the surface, g +-modes are possible that are trapped near a local maximum of the upper boundary of the G-region. The first modes are treated as oscillation modes of a plane-parallel layer with a constant gravity. A polytropic equilibrium model is used, in which a uniform temperature is introduced by means of the perfect gas law with a constant molecular weight. For the modes trapped near a local maximum of the upper boundary of the G-region, a homogeneous second-order differential equation is established, whose solutions are parabolic cylinder functions. Eigenfunctions are found that are oscillatory in a region near the maximum and have succesively no zero, one zero, two zeros …in their oscillatory region.
Keywords
- Polytropic Index
- Confluent Hypergeometric Function
- Constant Gravity
- Parabolic Cylinder Function
- Polytropic Model
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References
M. Abramowitz, I.A. Stegun (1965) Handbook of Mathematical Functions – with Formulas, Graphs, and Mathematical Tables. Dover Publications, New York
J. Christensen-Dalsgaard (1980) On adiabatic non-radial oscillations with moderate or large ℓ. Mon. Not. R. Astron. Soc. 190, 765–791
H. Lamb (1932) Hydrodynamics. The University Press, Cambridge
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Smeyers, P. (2010). High-Degree, Low-Order 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_19
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DOI: https://doi.org/10.1007/978-3-642-13030-4_19
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