Astrophysics and Space Science Library

Eclipsing Variables-What They can Tell Us and What We can do with Them.- I. The Code of the Language.- I. Light Changes of Eclipsing Binary Systems: Spherical Stars.- 1. Equations of the Problem.- 2. Loss of Light During Eclipses.- A. Evaluation of the Integrals.- 3. Loss of Light as Aperture Cross-Correlation.- A. Cross-Correlation: a Definition.- B. Hankel Transforms.- C. Evaluation of the Hankel Transforms.- 4. Fourier Transform of the Light Changes.- A. Evaluation of Fourier Transforms.- B. Synthesis of the Fourier Transform.- Bibliographical Notes.- II. Light Changes of Close Eclipsing Systems.- 1. Light Changes of Distorted Stars Outside Eclipses.- A. Discussion of the Results.- 2. Light Changes of Distorted Systems Within Eclipses.- A. Theoretical Light Curves.- Bibliographical Notes.- III. Special Functions of the Theory of Light Curves.- 1. Associated Alpha-Functions and Related Integrals.- A. Literal Evaluation.- B. Discussion of the Results.- 2. Recursion Relations.- A. Recursion Relations for the ?nm-functions.- B. Recursion Relations for the Boundary Integrals.- 3. Differential Properties.- A. Differential Properties of the ?-functions.- B. Differential and Recursion Properties of the Boundary Corrections: the J-integrals.- C. Differential Properties of Hankel Transforms.- Bibliographical Notes.- II. Decoding of the Light Changes.- IV. Analysis of the Light Changes in the Time Domain.- 1. Direct Methods: Historical.- 2. Iterative Methods: Total and Annular Eclipses.- A. Formation and Weighting of the Equations of Condition.- B. Differential Corrections for ? and U.- C. Combination of Both Minima.- D. Evaluation of the Elements.- 3. Iterative Methods: Partial Eclipses.- A. Combination of the Alternate Minima.- B. Generalized Equations of Condition: Differential Corrections.- C. Evaluation of the Elements.- 4. Effects of Orbital Eccentricity.- A. Central Eclipses.- B. Inclined Orbits.- Bibliographical Notes.- V. Analysis of the Light Changes in the Frequency-Domain: Spherical Stars.- 1. Introduction: Uniformly Bright Stars.- A. Total (Annular) Eclipses.- B. Partial Eclipses.- C. Relation with Fourier Series.- 2. General Case: Limb-Darkened Stars.- A. Evaluation of the Moments A2m of Eclipses.- B. Alternative Evaluation of the Moments A2m.- C. Differential Properties of the Moments A2m.- D. Atmospheric Eclipses.- 3. Solution for the Elements.- A. Optimization of Solutions.- B. Combination of Alternate Minima.- C. Eccentric Orbits.- Bibliographical Notes.- VI. Analysis of the Light Changes in the Frequency-Domain: Distorted Stars.- 1. Modulation of the Light Curves.- A. Particular Cases.- 2. Photometric Perturbations.- A. Particular Case: Total Eclipses.- B. Summary of Procedure.- Bibliographical Notes.- VII. Error Analysis.- 1. Error Analysis in the Time-Domain.- A. Errors of Auxiliary Constants.- B. Other Combinations of Elements; Limb-Darkening.- 2. Differential Corrections.- A. Equations of the Problem.- B. Combination of Both Minima.- 3. Error Analysis in the Frequency-Domain.- A. Error Analysis by Fourier Series.- B. Relation between the Fourier Transform and Moments of the Light Curves.- C. Recursion Relations between Different Moments of the Light Curves.- D. Solution for the Moments and Their Uncertainty.- Bibliographical Notes.- Appendices.- Appendix II. Explicit Forms of Associated ?-Functions of Even Orders and Indices.- Appendix III. Definition of Hypergeometric Series.- References.- Name Index.