Kurth Dimensional Analysis and Group Theory in Astrophysics

1. Auflage 2013
ISBN: 978-1-4832-8020-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 250 Seiten, Web PDF

Dimensional Analysis and Group Theory in Astrophysics describes how dimensional analysis, refined by mathematical regularity hypotheses, can be applied to purely qualitative physical assumptions. The book focuses on the continuous spectral of the stars and the mass-luminosity relationship. The text discusses the technique of dimensional analysis, covering both relativistic phenomena and the stellar systems. The book also explains the fundamental conclusion of dimensional analysis, wherein the unknown functions shall be given certain specified forms. The Wien and Stefan-Boltzmann Laws can be significant in the systematic application of dimensional analysis to the physics of a single star. The text also discusses group-theoretical reduction of ordinary differential equations and the reductions of the differential equations of stellar structure. The structure of a stellar envelope requires three hypotheses: (1) thermo-nuclear reactions as source of energy of stellar; (2) thermo-nuclear reactions occur at the star's core; and (3) that an envelope surrounding the core exists where no radiation is generated. To complete the model of a star, the investigator should have further assumptions such as the pressure is made-up of gas, radiation, or both. The book can prove helpful for astronomers, astro-physicists, cosmologists, and students of general physics.

Autoren/Hrsg.

Kurth, Rudolf

Inhaltsverzeichnis

1;Front Cover;1
2;Dimensional Analysis and Group Theory in Astrophysics;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;14
6;Part I: Dimensional Analysis;16
6.1;Chapter 1. The Technique of Dimensional Analysis;18
6.1.1;§ 1. Relativistic Phenomena;18
6.1.2;§ 2. Stellar Systems;34
6.2;Chapter 2. Foundations of Dimensional Analysis;48
6.2.1;§ 3. Postulates of Dimensional Analysis;48
6.2.2;§ 4. The Pi Theorem;52
6.3;Chapter 3. Applications of Dimensional Analysis to Problems of Stellar Radiation;60
6.3.1;§ 5. The Wien and Stefan–Boltzmann Laws;60
6.3.2;§ 6. Normal Forms of Spectral Densities;71
6.3.3;§ 7. Limb Darkening;82
6.3.4;§ 8. Two–colour Relations;94
6.3.5;§ 9. Interstellar Absorption;105
6.3.6;§ 10. Photometric Relations;117
6.4;Chapter 4. Applications of Dimensional Analysis to Problems of Stellar Structure;121
6.4.1;§ 11. Mass–luminosity Relations;121
6.4.2;§ 12. Asymptotic Photometric Relations;140
6.4.3;§ 13. Period-luminosity Relations;142
6.4.4;§ 14. Proto-stars;145
7;Part II: Applications of Group Theory;150
7.1;Chapter 5. Group-theoretical Reduction of Ordinary Differential Equations;152
7.1.1;§ 15. Local Lie Groups;152
7.1.2;§ 16. Group-theoretical Reduction of Ordinary Differential Equations;159
7.1.3;§ 17. Autonomous Monomial Differential Equations;168
7.1.4;§ 18. Non-autonomous Monomial Differential Equations;176
7.2;Chapter 6. Reductions of the Differential Equations of Stellar Structure;184
7.2.1;§ 19. Polytropic Gas Balls;184
7.2.2;§ 20. Isothermal Gas Balls;189
7.2.3;§ 21. Stellar Envelopes;191
7.2.4;§ 22. Stellar Interiors;201
7.2.5;§ 23. Stellar Interiors With Convective Cores;212
8;Appendices;216
8.1;Appendix 1: The Law of Titius and Bode (cf. § 1);216
8.2;Appendix 2: Note on the Temperatures and Atmospheres of the Planets (cf. § 5);219
8.2.1;Notes and References;223
8.3;Appendix 3: The Mass-radius Relation of the Major Planets (cf. § 11);225
8.4;Appendix 4: The Concept of a Group;228
8.4.1;Notes and References;230
8.5;Appendix 5: Methodological Reflections;231
8.5.1;Notes and References;238
8.6;Appendix 6: Some Data and Dimensions;240
9;References;242
10;Index;248