Linear Isentropic Oscillations of Stars
Theoretical Foundations
(Sprache: Englisch)
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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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.
Klappentext zu „Linear Isentropic Oscillations of Stars “
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.
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.
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.
Inhaltsverzeichnis zu „Linear Isentropic Oscillations of Stars “
- Introduction1. Basic Concepts
2. The Equations governing Linear Perturbations in a quasi-Static Star
3. Deviations from the Hydrostatic and Thermal Equilibrium in a quasi-Static Star
4. Eigenvalue Problem of the Linear, Isentropic Normal Modes in a quasi-Static Star
5. Spheroidal and Toroidal Normal Modes
6. Determination of Spheroidal Normal Modes. Mathematical Aspects
7. The Eulerian Perturbation of the Gravitational Potential
8. The Variational Principle of Hamilton
9. Radial Propagation of Waves
10. Classification of the Spheroidal Normal Modes
11. Classification of the Spheroidal Normal Modes (continued)
12. Completeness of the Linear, Isentropic Normal Modes
13. N2(r) nowhere Negative as Condition for Non-Radial Modes with Real Eigenfrequencies
14. Asymptotic Representation of Low-Degree, Higher-Order p-Modes
15. Asymptotic Representation of Low- and Intermediate-Degree p-Modes
16. Asymptotic Representation of Low-Degree, Higher-Order g+-Modes in Stars containing a Convective Core
17. Asymptotic Representation of Low-Degree, Higher-Order g+-Modes in Stars consisting of a Radiative Core and a Convective Envelope
18. High-Degree, Low-Order Modes
19. Period Changes in a rapidly evolving pulsating Star
- Appendixes
- A Green's Fundamental Formula of Potential Theory
- B The Thermodynamic Isentropic Coefficients
- C Lagrange's Equations of Motion
- D Spherical Harmonics
- E Singular Perturbation Problems of the Boundary-Layer Type
- F Boundary Condition Relative to the Pressure on a Star's Surface
- G The Curl of a Vector Field
- H Eigenvalue Problem of the vibrating String
- I The Euler-Lagrange Equations of Hamilton's Variational Principle for a perturbed Star
- J Acoustic Waves
- References
- Index
Bibliographische Angaben
- Autoren: Paul Smeyers , Tim Van Hoolst
- 2010, XIV, 473 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3642130291
- ISBN-13: 9783642130298
Sprache:
Englisch
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