Linear Isentropic Oscillations of Stars: Theoretical Foundations

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.