All astrophysicists are acquainted with the fundamental works ofS. Chandrasekhar [6] and M. Schwarzschild [1] concerning the internal structure of stars. Although both of these works accentuate the principal mathematical devices of the theory (and use, for this reason, notations that are rather perplexing for the non-specialist), the work of Schwarzschild is distinguished by care in demonstrating the physical meaning of the principal equations, while that of Chandrasekhar makes every effort not to skip a single step in the calculations. On the other hand, Schwarz schild , who considers his two…mehr
All astrophysicists are acquainted with the fundamental works ofS. Chandrasekhar [6] and M. Schwarzschild [1] concerning the internal structure of stars. Although both of these works accentuate the principal mathematical devices of the theory (and use, for this reason, notations that are rather perplexing for the non-specialist), the work of Schwarzschild is distinguished by care in demonstrating the physical meaning of the principal equations, while that of Chandrasekhar makes every effort not to skip a single step in the calculations. On the other hand, Schwarz schild , who considers his two introductory chapters as simple reviews of results which are already known, passes a bit rapidly over certain difficult arguments, and Chandrasekhar never goes far enough in the analysis of the physical mechanisms involved. From another point of view, the excellent review articles published in the Ency clopedia of Physics [5] by M. H. Wrubel, P. Ledoux, and others, and those published in Stars and Stellar Systems [4] by H. Reeves, B. Stromgren, R. L. Sears and R. R. Brownlee, and others, are principally intended for research workers who are already initiated into the theory of internal structure. These monographs are on a level that is clearly too high for the general physicist who is approaching these astrophysical questions for the first time, and more particularly for the post-graduate student.
I. General Considerations Concerning the Energy Radiated by Stars.- 1. The Energy Output and Its 'Spectral Composition'.- 2. The Observational Data.- 3. Generalities Concerning the Energy Sources.- II. Mechanical Equilibrium: The Equilibrium between the Gravitational Force Per Unit Volume and the Gradient of the Total Pressure.- 1. Introduction.- 2. The Equilibrium between the Gradient of the Total Pressure and the Gravitational Force per Unit Volume.- 2.1. Newton's Theorem. The Gravitational Force per Unit Volume.- 2.2. The Force per Unit Volume Produced by the Pressure Gradient.- 2.3. The Equation Expressing the Mechanical Equilibrium of (dV).- 3. The Relation between Mrand 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 µ of a Particle of the Mixture in Units of mH (where mHis the Mass in Grams of a 'Real' Microscopic Hydrogen Atom).- 6. A Model of the Sun at 'Constant Density' ? = ??.- 7. The 'Homologous' Model. Expressions for Pc and Tcin Terms of M and R.- Exercises.- III. The Determination of the Internal Structure by the Density Distribution ?(r).- 1. Introduction.- 2. The Determination of the Distribution of the Mass Mr Contained in a Sphere of Radius r.- 3. The Determination of the Distribution of the Total Pressure P as a Function of r.- 4. The Determination of the Distribution of the Temperature T as a Function of r.- 5. Summary. The Empirical Representation of the Functions g (r'),?(r'), P(r'), and T(r'). The Polytropic Index n.- 6. The (Superficial) 'Convective Zone' of the Sun.- Exercises.- IV. Energy Equilibrium and Nuclear Reactions.- 1. The Equation of Energy Equilibrium.- 2. The p-p Chain and the C-N Cycle.- 2.1. Introduction.- 2.2. An Explicit Schematic Representation of the Composition of Nuclei.- 2.3. The Details of the Reactions in the p-p Chain (Bethe, 1938).- 2.4. The Details of the C-N Cycle (Bethe, 1938).- 3. Calculation of the Energy ?. Generalities.- 3.1. Calculation of R12 for a Given Reaction.- 4. The 'Mean Lifetime' of a Given Nucleus with Respect to an Isolated Reaction (R).- 4.1. Generalities.- 4.2. The Physical Meaning of ?p(c).- 4.3. ?p(c)as the 'Mean Duration of an Isolated Reaction (R)'.- 4.4. ?p(c)as an 'Exponential Decrement'.- 4.5. The Transition Probability pcaper Reaction (R).- 5. The Convergence of Cyclic Reactions to a Stationary ('Equilibrium') State.- 6. The 'Mean Duration of a Cycle'. The Calculation of the Energy ? when Cyclic Reactions Are Present.- 7. The Empirical Representation of ?pp and ?CN.- 8. Application to the Sun. The 'Final Test'.- 8.1. Review of the Principal Results.- 8.2. The Region in which ?Is Negligible.- 8.3. The 'Central' Region (r' 0.40), where L'rand X Vary.- 8.4. The 'Final Test'.- Exercises.- V. Evolutionary Models. The Actual Determination of Structure.- 1. Introduction.- 1.1. The Advantage of Studying 'Evolutionary Sequences'.- 1.2. The 'Fossilized' Composition.- 2. The Evolution of the Distributions X(r)and Y(r).- 3. Discussion.- 4. The Mathematical Structure of the Problem. Principles of the Integration Methods.- 5. The Age of a Star.- 6. The Relations between P, T, L, R, and Parameters such as M, k0, ?0, and µ for 'Homologous' Models. The 'Mass-Luminosity' and 'Mass-Radius' Relations.- Conclusion.- Solutions for the Exercises.- Index of Subjects.
I. General Considerations Concerning the Energy Radiated by Stars.- 1. The Energy Output and Its 'Spectral Composition'.- 2. The Observational Data.- 3. Generalities Concerning the Energy Sources.- II. Mechanical Equilibrium: The Equilibrium between the Gravitational Force Per Unit Volume and the Gradient of the Total Pressure.- 1. Introduction.- 2. The Equilibrium between the Gradient of the Total Pressure and the Gravitational Force per Unit Volume.- 2.1. Newton's Theorem. The Gravitational Force per Unit Volume.- 2.2. The Force per Unit Volume Produced by the Pressure Gradient.- 2.3. The Equation Expressing the Mechanical Equilibrium of (dV).- 3. The Relation between Mrand 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 µ of a Particle of the Mixture in Units of mH (where mHis the Mass in Grams of a 'Real' Microscopic Hydrogen Atom).- 6. A Model of the Sun at 'Constant Density' ? = ??.- 7. The 'Homologous' Model. Expressions for Pc and Tcin Terms of M and R.- Exercises.- III. The Determination of the Internal Structure by the Density Distribution ?(r).- 1. Introduction.- 2. The Determination of the Distribution of the Mass Mr Contained in a Sphere of Radius r.- 3. The Determination of the Distribution of the Total Pressure P as a Function of r.- 4. The Determination of the Distribution of the Temperature T as a Function of r.- 5. Summary. The Empirical Representation of the Functions g (r'),?(r'), P(r'), and T(r'). The Polytropic Index n.- 6. The (Superficial) 'Convective Zone' of the Sun.- Exercises.- IV. Energy Equilibrium and Nuclear Reactions.- 1. The Equation of Energy Equilibrium.- 2. The p-p Chain and the C-N Cycle.- 2.1. Introduction.- 2.2. An Explicit Schematic Representation of the Composition of Nuclei.- 2.3. The Details of the Reactions in the p-p Chain (Bethe, 1938).- 2.4. The Details of the C-N Cycle (Bethe, 1938).- 3. Calculation of the Energy ?. Generalities.- 3.1. Calculation of R12 for a Given Reaction.- 4. The 'Mean Lifetime' of a Given Nucleus with Respect to an Isolated Reaction (R).- 4.1. Generalities.- 4.2. The Physical Meaning of ?p(c).- 4.3. ?p(c)as the 'Mean Duration of an Isolated Reaction (R)'.- 4.4. ?p(c)as an 'Exponential Decrement'.- 4.5. The Transition Probability pcaper Reaction (R).- 5. The Convergence of Cyclic Reactions to a Stationary ('Equilibrium') State.- 6. The 'Mean Duration of a Cycle'. The Calculation of the Energy ? when Cyclic Reactions Are Present.- 7. The Empirical Representation of ?pp and ?CN.- 8. Application to the Sun. The 'Final Test'.- 8.1. Review of the Principal Results.- 8.2. The Region in which ?Is Negligible.- 8.3. The 'Central' Region (r' 0.40), where L'rand X Vary.- 8.4. The 'Final Test'.- Exercises.- V. Evolutionary Models. The Actual Determination of Structure.- 1. Introduction.- 1.1. The Advantage of Studying 'Evolutionary Sequences'.- 1.2. The 'Fossilized' Composition.- 2. The Evolution of the Distributions X(r)and Y(r).- 3. Discussion.- 4. The Mathematical Structure of the Problem. Principles of the Integration Methods.- 5. The Age of a Star.- 6. The Relations between P, T, L, R, and Parameters such as M, k0, ?0, and µ for 'Homologous' Models. The 'Mass-Luminosity' and 'Mass-Radius' Relations.- Conclusion.- Solutions for the Exercises.- Index of Subjects.
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