Asymptotic Representation of Low-Degree, Higher-Order g +-Modes in Stars Consisting of a Radiative Core and a Convective Envelope

Abstract

First-order asymptotic representations of low-degree, higher-order g +-modes are developed for stars consisting of a radiative core and a convective envelope. As in the previous chapter, the asymptotic representations are derived on the basis of the fourth-order system of differential equations for the divergence and the radial component of the Lagrangian displacement. The asymptotic methods applied are still two-variable expansions and boundary-layer theory. From the asymptotic theory of low-degree, higher-order p- and g +-modes, the global conclusion is drawn that the first asymptotic approximation for the divergence of the Lagrangian displacement and the eigenfrequency equation can be obtained from a single homogeneous second-order differential equation for that function, without any construction of an asymptotic representation for the radial component of the Lagrangian displacement.