High-Degree, Low-Order Modes

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.