Introduction to Advanced Astrophysics

The purpose of this textbook is to provide a basic knowledge of the main parts of modern astrophysics for all those starting their studies in this field at the undergraduate level. The reader is supposed to have only a high school training in physics and mathematics. In many respects this Introduction to Advanced Astrophysics could represent a volume of the Berkeley Physics Course. Thus, the primary audience for this work is composed of students in astronomy, physics, mathematics, physical chemistry and engineering. It also includes high school teachers of physics and mathematics. Many amateur astronomers will fmd it quite accessible. In the frame of approximations proper to an introductory textbook, the treatment is quite rigorous. Therefore, it is also expected to provide a firm background for a study of advanced astrophysics on a postgraduate level. A rather severe selection is made here among various aspects of the Universe accessible to modern astronomy. This allows us to go beyond simple information on astronomical phenomena - to be found in popular books - and to insist upon explanations based on modern general physical theories. More precisely, our selection of topics is determined by the following considerations: The study of the solar system (the Moon and the planets) has recently progressed at a tremendous rate. However, the very rich harvest of observations provided by space research is mainly purely descriptive and is perfectly presented in review papers of Scien­ tific American, Science, Physics Today and similar magazines.

I. Radiative Transfer and Internal Structure of Normal Stars.- 1. Introduction to the Theory of Radiative Transfer.- 1. Basic Concepts in the Description of a Radiation Field.- 2. Relations between Macroscopic and Microscopic Parameters Describing the Interactions between Matter and Radiation.- 3. Equation of Transfer and the Corresponding Equation of Continuity.- 4. Applications to the Physics of Stellar Interiors.- Appendix: The Relations between Einstein’s Coefficients.- 2. Elementary Introduction to the Physics of Stellar Interiors.- 1. General Conditions of Mechanical Equilibrium.- 2. The Equilibrium between the Gradient of the Total Pressure and the Gravitational Force per Unit Volume.- 3. The Relation between Mr and the Density ? at a Distance r from the Center.- 4. The Expression for div g as a Function of the Local Density ?. Poisson’s Equation.- 5. The Calculation of the Gas Pressure Pgas. The Concept of the Mean Mass ? of a Particle of the Mixture, in Units of mB (where mB is the Mass in Grams of a Baryon).- 6. A Model of the Sun at Constant Density $$\rho = \bar{\rho }$$.- 3. The Physics of Interiors of the Main Sequence Stars.- 1. Introduction.- 2. The Equation of Energy Equilibrium.- 3. The Expression for ?(r) in the Case when Energy is Produced by the p-p Chain or the C-N Cycle.- 4. The System of Differential Equations and of Boundary Conditions which Determine the Internal Structure of a Normal Star.- 5. Evolutionary Models and Solution of the Problem Concerning the Function X(r).- 6. Utilization of Boundary Conditions in the Study of Initial Models.- 7. From Initial Models to Models Corresponding to the Present State. Determination of the Age of a Star.- 8. The Present Internal Structure of the Sun.- 9. Comparison between the Present Structure of the Sun and its Structure at Age Zero.- 10. The Superficial Convective Zone of the Sun.- II. White Dwarfs, Neutron Stars and Pulsars.- 4. Elementary Properties of a Degenerate Fermi Gas.- 1. Different ‘Energy Parameters’ of an Isolated Particle. Energy Groups (NR), (UR) and (RR).- 2. The Number of Independent Identical Particles (Confined in a Macroscopic Unit of Volume) whose Momentum lies between p and (p + dp).- 3. The General Trend of the Fermi-Dirac Distribution Function. Definition of the Complete Degeneracy. The Fermi Level.- 4. Relations between the Number Density of a System of Fermions in a State of Complete Degeneracy and Energy Parameters of the Fermi Level.- 5. Energy Density (for Total and for Kinetic Energy) of a Completely Degenerate System of Independent Identical Fermions.- 6. The Mean (Total) Energy and the Mean Kinetic Energy of One Particle of a Completely Degenerate System of Independent Identical Fermions. Relations with the Fermi Level.- 7. Expressions for Partial Number Densities of Different Components of a Stellar Mixture as a Function of the Mass Density of the Mixture. Parameters µ, µe and ?e?.- 8. The Pressure Produced by a System of Independent Identical Fermions in a State of Complete Degeneracy.- 9. The Domain of Separation between the State of a Perfect Gas and the State of Complete Degeneracy. Application to the Sun.- Appendix: Establishment of the Rigorous (RR) Expressions for u(n, m) and uk(n, m).- 5. White Dwarfs.- 1. A Few Historical Remarks.- 2. Polytropes and the Virial Theorem. Application to an Elementary Theory of White Dwarfs.- 3. Polytropic White Dwarfs Studied by Means of the Emden-Lane Equation.- 4. Chandrasekhar’s ‘Rigorous’ Theory of White Dwarfs.- Appendix: The Gravitational Binding Energy of a Star.- 6. Neutron Stars.- 1. Introduction: (RZ) Reactions (Electron Captures and ?-Disintegrations).- 2. Neutronization by a Degenerate Gas of Free Electrons.- 3. (RA) Reactions Leading to an Increase of Atomic Weight of Nuclei.- 4. The Different Domains of Mass Density.- 5. Different Forms of Equilibrium Equations for (RZ) Reactions.- 6. Equilibrium Equations for (RA) Reactions.- 7. The Domain A: Determination of A and Z Corresponding to an Equilibrium with Respect to Reactions (RZ) and (RA).- 8. The Domain B: A Mixture of Free Electrons, Free Neutrons and Nuclei (A, Z).- 9. The Domain C: A Mixture of Free Electrons, Free Protons and Free Neutrons.- 10. The Structure of Neutron Stars. Their Radius as a Function of Their Mass.- 7. Pulsars.- 1. The Discovery of Pulsars.- 2. The First Investigations and the First General Properties.- 3 Pulsar Distances.- 4. Pulsar Ages.- 5. Luminosity Problems and the Pacini Model.- 6. The Problem of Association of Pulsars with Supernovae.- 7. The ‘Celibacy’ of Radio Pulsars (and Binary Character of the ‘X-ray’ Pulsars).- III. Newton’s Law, Binary Systems and Galactic X-ray Sources.- 8. Theory of Spectroscopic and Eclipsing Binaries. Stellar Masses.- 1. The Newtonian Form of Kepler’s Third Law.- 2. Elementary Interpretation of Observations.- 3. The Values of Stellar Masses. Relations between Masses, Luminosities and Spectral Classes.- Appendix A. On Keplerian Motion.- Appendix B. Inductions Leading from Kepler’s Empirical Laws to Newton’s Law of Gravitation.- 9. Galactic X-ray Sources.- 1. Introduction.- 2. The Classification Problem.- 3. A few Particularly Interesting Galactic X-ray Sources.- Appendix: A Dictionary of Abbreviations in the Field of Galactic Sources. Conversion of Names. Tables.- IV. Cosmology: Elementary Theory and Basic Observational Data.- 10. Elementary Theoretical Cosmology: The Newtonian Approach.- 1. Introduction.- 2. The Fundamental Principles.- 3. The Kinematics of a Model of Cosmic Fluid. Hubble’s law.- 4. A few Observational Data.- 5. The Friedmann Model of Universe.- 6. The Ratio of the Age of the Friedmann Universe to the ‘Hubble Time’ as a Function of ?.- 7. The Radiation Model of the Early Universe.- 11. Basic Concepts of Relativistic Cosmology.- 1. Introduction.- 2. Some Elementary Relativistic Concepts.- 3. The Characteristic Properties of Non-Euclidean Spaces.- 4. The Geodesic Principle.- 12. Relativistic Effects in Observational Cosmology. The Cosmological Redshift in Expanding Universe.- 1. A Bi-dimensional Model of an Expanding Universe. Fixity in Mobility: The Comoving Coordinates.- 2. Tri-dimensional Friedmann Relativistic Models of Expanding Universe.- 3. The Cosmological Redshift.- 4. The Metric (Mathematical) Linear Distance of a Source.- 5. The Classical Distance of a Source as a Function of its Redshift.- 6. The Relativistic Variation of the Angular Diameter, for Sources of a given Linear Diameter, as a Function of their Redshift.- 7. A Physical Interpretation of the Metric Distance.- 8. The Relativistic Variation of the Integrated (Bolometric) Brightness, for Point Sources of given Luminosity, as a Function of their Redshift.- 9. The Brightness of an Extended Source per Unit Solid Angle.- 10. The Source Counts.- Appendix: Relations between the Magnitudes, the Luminosities and the Cosmological Redshift.- 13. Basic Data in Observational Cosmology: Active Galactic Nuclei and Clusters of Galaxies.- 3. Clusters of Galaxies.- 4. Superclusters of Galaxies?.- 5. General Comments on the Confrontation of Cosmological Theories with Observational Data.- Appendix: A Dictionary of Abbreviations in the Field of Extragalactic Objects.- Table of Values.