On the Cowling Approximation: A Verification of Ansatz via Methods of Functional and Asymptotic Analysis

TL;DR

This paper analytically investigates the Cowling approximation in stellar pulsation models, using asymptotic and functional analysis to verify its validity across different regimes.

Contribution

It provides a rigorous asymptotic analysis and estimates to verify the Cowling approximation's accuracy in non-radial stellar pulsation models.

Findings

Asymptotic estimates confirm the validity of the Cowling approximation in high harmonic degree regimes.

Reformulation into an integro-differential equation enables application of Hilbert-space methods.

Results extend to fundamental solution sets with boundary-value problem characterizations.

Abstract

We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic degree and high oscillation frequency. Our methods involve a reformulation of the system in terms of an integro-differential equation for which certain Hilbert-space methods apply. By way of a more complete asymptotic study, we extend our results to certain fundamental solution sets, characterized according to certain multi-point boundary-value problems: Such asymptotics further enable us to produce sharp estimates as confirmation of our general results.