Linear oscillations of compact stars in the Cowling approximation [Elektronische Ressource] / vorgelegt von Erich Gaertig

Sujets

• Astronomie

Informations

• Publié par: eberhard_karls_universitat_tubingen
• Publié le: 01 janvier 2008
• Nombre de lectures: 11
• Langue: English
• Poids de l'ouvrage: 9 Mo

Extrait

Linear Oscillations of Compact Stars
in the Cowling Approximation
DISSERTATION
zur Erlangung des Grades eines Doktors
der Naturwissenschaften
der Fakult¨at fur¨ Mathematik und Physik
der Eberhard-Karls-Universit¨at zu Tubingen¨
vorgelegt von
Erich Gaertig
aus Pieˇst’any
2008Tag der mundlic¨ hen Prufung:¨ 12.12.2008
Dekan: Prof. Dr. Wolfgang Knapp
1. Berichterstatter: Prof. Dr. Kostas Kokkotas
2. Berich Prof. Dr. Hanns Ruder!"#$%&'$
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1 Introduction 7
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.1 Classical Stellar Oscillations . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.2 Relativistic Stellar . . . . . . . . . . . . . . . . . . . . . . 9
1.1.3 Gravitational Wave Asteroseismology . . . . . . . . . . . . . . . . . . 11
1.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 The Perturbation Equations 15
2.1 The 3+1 Split in General Relativity . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Linear Perturbation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 The Cowling Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 The Metric and the Energy-Momentum–Tensor . . . . . . . . . . . . . . . . . 21
2.5 Derivation of the Linearized Perturbation Equations . . . . . . . . . . . . . . 23
2.5.1 The Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5.2 Some Properties of the Equations . . . . . . . . . . . . . . . . . . . . . 26
2.5.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Numerical Implementations 31
3.1 A Brief Introduction to Spectral Methods . . . . . . . . . . . . . . . . . . . . 31
3.2 Pros and Cons of Spectral Methods . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Layout of the Computational Domain . . . . . . . . . . . . . . . . . . . . . . 36
3.4 The Time-Evolution Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Results with the Pseudospectral Approach . . . . . . . . . . . . . . . . . . . . 44
3.6 The Finite Di!erence Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.6.1 Crank-Nicholson Methods . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.7 Results with the Finite Di!erence Approach . . . . . . . . . . . . . . . . . . . 49
3.8 Artificial Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.9 Post-Processing Routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.9.1 Discrete Fourier Transforms and Data Windowing . . . . . . . . . . . 54
3.9.2 Peak Localization and Mode Recycling . . . . . . . . . . . . . . . . . . 58
4 Results 61
4.1 The Background Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 First Axisymmetric Validation Runs . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Convergence Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4 The Axisymmetric Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4.1 Polar Perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4.2 Axial P . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.