Continuum Eigenmodes in Some Linear Stellar Models

TL;DR

This paper investigates the continuous oscillation spectra of linear stellar models using advanced mathematical methods, revealing conditions for unbounded oscillations and potential instabilities in stellar structures.

Contribution

It introduces novel applications of Jacobi matrices and subordinancy theory to analyze continuum eigenmodes in stellar models, expanding understanding of their spectral properties.

Findings

Identification of pressure-density conditions for continuous spectra

Discovery of unbounded oscillations in certain stellar models

Implications for stellar stability and dynamic behavior

Abstract

We apply parallel approaches in the study of continuous spectra to adiabatic stellar models. We seek continuum eigenmodes for the LAWE formulated as both finite difference and linear differential equations. In particular, we apply methods of Jacobi matrices and methods of subordinancy theory in these respective formulations. We find certain pressure-density conditions which admit positive-measured sets of continuous oscillation spectra under plausible conditions on density and pressure. We arrive at results of unbounded oscillations and computational or, perhaps, dynamic instability.