Linear Isentropic Oscillations of Stars: Theoretical Foundations (Astrophysics and Space Science Library Book 371)

The study of stellar oscillations is the preeminent way to investigate the stability of stars and to interpret their variability. The theory of the linear, isentropic oscillations of isolated gaseous stars, and thus of compressible spherically symmetric equilibrium configurations, has largely been developed from the viewpoint of the hypothesis of the physical radial pulsations of stars. Written for doctoral students and researchers, this monograph aims to provide a systematic and consistent survey of the fundamentals of the theory of free, linear, isentropic oscillations in spherically symmetric, gaseous equilibrium stars. The first part of the book presents basic concepts and equations, the distinction between spheroidal and toroidal normal modes, the solution of Poisson’s differential equation for the perturbation of the gravitational potential, and Hamilton’s variational principle. The second part is devoted to the possible existence of waves propagating in the radial direction, the origin and classification of normal modes, the completeness of the normal modes, and the relation between the local stability with respect to convection and the global stability of a star. The third part deals with asymptotic representations of normal modes and with slow period changes in rapidly evolving pulsating stars. Front Matter....Pages i-xiv Introduction....Pages 1-8 Basic Concepts....Pages 9-23 The Equations Governing Linear Perturbations in a Quasi-Static Star....Pages 25-35 Deviations from the Hydrostatic and Thermal Equilibrium in a Quasi-Static Star....Pages 37-50 Eigenvalue Problem of the Linear, Isentropic Normal Modes in a Quasi-Static Star....Pages 51-65 Spheroidal and Toroidal Normal Modes....Pages 67-96 Determination of Spheroidal Normal Modes: Mathematical Aspects....Pages 97-119 The Eulerian Perturbation of the Gravitational Potential....Pages 121-131 The Variational Principle of Hamilton....Pages 133-158 Radial Propagation of Waves....Pages 159-175 Classification of the Spheroidal Normal Modes....Pages 177-204 Classification of the Spheroidal Normal Modes (continued)....Pages 205-227 Completeness of the Linear, Isentropic Normal Modes....Pages 229-256 N 2 ( r ) Nowhere Negative as Condition for Non-Radial Modes with Real Eigenfrequencies....Pages 257-266 Asymptotic Representation of Low-Degree, Higher-Order p -Modes....Pages 267-299 Asymptotic Representation of Low-Degree and Intermediate-Degree p -Modes....Pages 301-326 Asymptotic Representation of Low-Degree, Higher-Order g + -Modes in Stars Containing a Convective Core....Pages 327-368 Asymptotic Representation of Low-Degree, Higher-Order g + -Modes in Stars Consisting of a Radiative Core and a Convective Envelope....Pages 369-381 High-Degree, Low-Order Modes....Pages 383-392 Period Changes in a Rapidly Evolving Pulsating Star....Pages 393-410 Back Matter....Pages 411-473 This book surveys the theory of free, linear, isentropic oscillations in spherically symmetric, gaseous equilibrium stars, from basic concepts to asymptotic representations of normal modes and with slow period changes in rapidly evolving pulsating stars.