## Linear Isentropic Oscillations of Stars: Theoretical FoundationsThis 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

1 | |

9 | |

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 |

455 | |

467 | |

### Other editions - View all

Linear Isentropic Oscillations of Stars: Theoretical Foundations Paul Smeyers,Tim Van Hoolst No preview available - 2010 |

Linear Isentropic Oscillations of Stars: Theoretical Foundations Tim Van Hoolst,Paul Smeyers No preview available - 2011 |

Linear Isentropic Oscillations of Stars: Theoretical Foundations Tim Van Hoolst,Paul Smeyers No preview available - 2013 |

### Common terms and phrases

acoustic waves angular frequency arbitrary constants asteroseismology Astrophysics asymptotic representation asymptotic solutions avoided crossing Bessel function boundary condition boundary-layer boundary-layer expansions boundary-layer solution convective convective core convective envelope derivative dimensionless displacement field divergence eigenfrequencies eigenfrequency equation eigenfunctions eigenvalue problem energy equal to zero equilibrium star Eulerian perturbation gC-modes generalised coordinates given by Eq gravitational potential Hoolst horizontal hydrostatic equilibrium integration ıqi ıqj Lagrangian density Lagrangian displacement Lagrangian displacement field Lagrangian perturbation larger distances layer low-degree lowest-order mass element means of Eq metric tensor model with index p-modes parameter Poisson’s polytropic model pressure pulsation quasi-static star radial component radial modes radial order radiative envelope relation right-hand member scalar second-order differential equation Smeyers sphere of uniform spherical harmonics spheroidal normal modes stellar models Taylor series toroidal transformed turning point two-variable expansion two-variable solution uniform mass density uniformly valid variable variations vector field velocity wavenumber