Linear Isentropic Oscillations of Stars: Theoretical Foundations

ISBN-13: 9783642266126 / Angielski / Miękka / 2013 / 473 str.

Paul Smeyers; Tim Van Hoolst

Opis

This monograph attempts to provide a systematic and consistent survey of the fundamentals of the theory of free, linear, isentropic oscillations in spherically symmetric, gaseous equilibrium stars, whose structure is affected neither by axial rotation, nor by the tidal action of a companion, nor by a magnetic eld. Three parts can be distinguished. The rst part, consisting of Chaps.1-8, covers the 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, consisting of Chaps.9-13, is devotedto the possible existenceof waves propagating in the radial direction, the origin and classi cation of normal modes, the comple- ness of the normal modes, and the relation between the local stability with respect to convection and the global stability of a star. In the third part, Chaps.14-18 c- tain asymptoticrepresentationsof normalmodes. Chapter 19 deals with slow period changes in rapidly evolving pulsating stars. The theory is developed within the framework of the Newtonian theory of gr- itation and the hydrodynamics of compressible uids. It is described in its present status, with inclusion of open questions. We give preference to the use of the adjective "isentropic" above that of the adjective "adiabatic," since, from a thermodynamic point of view, these stellar - cillations are described as reversible adiabatic processes and thus as processes that take place at constant entropy.

Spis treści

Basic Concepts.- The Equations Governing Linear Perturbations in a Quasi-Static Star.- Deviations from the Hydrostatic and Thermal Equilibrium in a Quasi-Static Star.- Eigenvalue Problem of the Linear, Isentropic Normal Modes in a Quasi-Static Star.- Spheroidal and Toroidal Normal Modes.- Determination of Spheroidal Normal Modes: Mathematical Aspects.- The Eulerian Perturbation of the Gravitational Potential.- The Variational Principle of Hamilton.- Radial Propagation of Waves.- Classification of the Spheroidal Normal Modes.- Classification of the Spheroidal Normal Modes (continued).- Completeness of the Linear, Isentropic Normal Modes.- N 2(r) Nowhere Negative as Condition for Non-Radial Modes with Real Eigenfrequencies.- Asymptotic Representation of Low-Degree, Higher-Order p-Modes.- Asymptotic Representation of Low-Degree and Intermediate-Degree p-Modes.- Asymptotic Representation of Low-Degree, Higher-Order g +-Modes in Stars Containing a Convective Core.- Asymptotic Representation of Low-Degree, Higher-Order g +-Modes in Stars Consisting of a Radiative Core and a Convective Envelope.- High-Degree, Low-Order Modes.- Period Changes in a Rapidly Evolving Pulsating Star.

Blurb

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.