Introduction to Advanced Astrophysics

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.