Linearized Analysis of Adiabatic Oscillations of Rotating Gaseous Stars

TL;DR

This paper rigorously analyzes adiabatic oscillations in rotating gaseous stars, addressing the mathematical challenges of free boundary problems and stability in a complex astrophysical setting.

Contribution

It introduces a novel mathematical framework for the linearized analysis of oscillations and stability in rotating gaseous stars with non-barotropic equations of state.

Findings

Existence of solutions to the linearized oscillation equations.

Development of a new concept of stability for rotating stars.

Formulation of the eigenvalue problem as a quadratic pencil of operators.

Abstract

We study adiabatic oscillations of rotating self-gravitating gaseous stars in mathematically rigorous manner. The internal motion of the star is supposed to be governed by the Euler-Poisson equations with rotation of constant angular velocity under the equation of state of the ideal gas. The motion is supposed to be adiabatic, but not to be barotropic in general. This causes a free boundary problem to gas-vacuum interface. Existence of solutions to the linearized equation in the Lagrange coordinates of the perturbations around a fixed stationary solution, the eigenvalue problem with concept of quadratic pencil of operators, and the stability problem with a new concept of stability introduced in this article are discussed.