Linear Isentropic Oscillations of Stars: Theoretical Foundations

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Springer Science & Business Media, Jan 18, 2011 - Science - 473 pages
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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.

 

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Contents

Introduction
1
Basic Concepts
9
The Equations Governing Linear Perturbations in a QuasiStatic Star
25
Deviations from the Hydrostatic and Thermal Equilibrium in a QuasiStatic Star
36
Eigenvalue Problem of the Linear Isentropic Normal Modes in a QuasiStatic Star
51
Spheroidal and Toroidal Normal Modes
67
Determination of Spheroidal Normal Modes Mathematical Aspects
97
The Eulerian Perturbation of the Gravitational Potential
120
Asymptotic Representation of LowDegree HigherOrder g+Modes in Stars Consisting of a Radiative Core and a Convective Envelope
369
HighDegree LowOrder Modes
383
Period Changes in a Rapidly Evolving Pulsating Star
393
Greens Fundamental Formula of Potential Theory
411
The Thermodynamic Isentropic Coefficients
415
Lagranges Equations of Motion
421
Spherical Harmonics
427
Appendix E Singular Perturbation Problems of the BoundaryLayer Type
429

The Variational Principle of Hamilton
133
Radial Propagation of Waves
159
Classification of the Spheroidal Normal Modes
176
Classification of the Spheroidal Normal Modes continued
205
Completeness of the Linear Isentropic Normal Modes
229
N2r Nowhere Negative as Condition for NonRadial Modes with Real Eigenfrequencies
257
Chapter 14 Asymptotic Representation of LowDegree HigherOrder pModes
267
Asymptotic Representation of LowDegree and IntermediateDegree pModes
300
Asymptotic Representation of LowDegree HigherOrder g+Modes in Stars Containing a Convective Core
327
Boundary Condition Relative to the Pressure on a Stars Surface
433
The Curl of a Vector Field
437
Eigenvalue Problem of the Vibrating String
441
The EulerLagrange Equations of Hamiltons Variational Principle for a Perturbed Star
445
Acoustic Waves
447
List of Symbols
451
References
455
Index
467
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About the author (2011)

Paul Smeyers is Professor at the Katholieke Universiteit Leuven in Belgium.

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