Kallrath / Milone Eclipsing Binary Stars: Modeling and Analysis

2. Auflage 2009
ISBN: 978-1-4419-0699-1
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 420 Seiten

Reihe: Astronomy and Astrophysics Library

Astronomers learn much of what they know about the mass, brightness, and size of stars by observing binary systems, in which two stars orbit each other, periodically cutting off the others light. This book provides astronomers with a guide to specifying an astrophysical model for a set of observations, selecting an algorithm to determine the parameters of the model, and estimating the errors of the parameters.

Autoren/Hrsg.

Kallrath, Josef

Milone, Eugene F.

Inhaltsverzeichnis

1;Foreword;6
2;Preface to the Second Edition;8
3;Preface to the First Edition;10
3.1;References;12
4;Acknowledgments;13
5;Contents;15
6;List of Figures;24
7;Journal Abbreviations;27
8;Acronyms and Abbreviations;29
9;Mathematical Nomenclature and Symbols, Physical Units;30
10;Part I Introduction;31
10.1;to 1 Introduction ;32
10.1.1; Eclipsing Binaries and Other Variable Stars;32
10.1.1.1; Eclipsing Variables;34
10.1.1.1.1; Algols;34
10.1.1.1.2; Lyrae;35
10.1.1.1.3; W Ursae Majoris or W UMa;35
10.1.1.2; Pulsating Variables;36
10.1.1.3; Eruptive Variables;37
10.1.2; Overview of the Problem;39
10.1.2.1; Why Binary Stars Are Important;39
10.1.2.1.1; Visual Double Stars;40
10.1.2.1.2; Spectroscopic Binaries;42
10.1.2.1.3; Eclipsing Binaries;43
10.1.2.2; Phenomenological Classification of Eclipsing Binary Light Curves;44
10.1.2.3; Morphological Classification of Eclipsing Binaries;47
10.1.2.4; What Can Be Derived from Eclipsing Binaries;51
10.1.2.5; Why Data Derived from Eclipsing Binaries AreImportant;51
10.1.2.6; The History of Light Curve Modeling;52
10.1.2.6.1; The Pioneers -- The Age of Geometry;52
10.1.2.6.2; The Age of Computational Astrophysics;53
10.1.2.6.3; Determining Astrophysical Parameters;54
10.1.2.6.4; Later Generations of Light Curve Models;54
10.1.2.6.5; Astrophysical Problems Solved by Light CurveMethods;55
10.1.2.6.6; EB Guide for Researchers in Other Fields;56
10.1.2.6.6.1; Eclipsing Binaries and Standard Candles;56
10.1.2.6.6.2; Eclipsing Binaries in ExtraSolar Planet Research;57
10.1.2.6.6.3; Nomenclature: Primary and Secondary Component;58
10.1.2.6.6.4; Where Are the Radii?;58
10.1.2.6.6.5; Precession and Apsidal Motion;58
10.1.2.6.6.6; Looking for Eclipsing Binary Standard Software;59
10.1.2.6.6.7; Analytic Techniques and Numerical Analysis;59
10.1.2.6.7; Selected Bibliography;59
10.1.2.6.8;References;60
10.2;to 2 The Database and Methods of Data Acquisition ;66
10.2.1; Photometry;66
10.2.1.1; Photoelectric Photometry;66
10.2.1.2; Two-Star Photometers;68
10.2.1.3; Photoelectric Observations;70
10.2.1.4; Imaging Data;72
10.2.1.5; Photometric Data Reduction;73
10.2.1.6; Significance of Cluster Photometry;76
10.2.2; Spectroscopy;77
10.2.2.1; Radial Velocities;80
10.2.2.2; Spectrophotometry;82
10.2.2.3; Line-Profile Analysis;84
10.2.3; Polarimetry;86
10.2.4; Magnetometry;88
10.2.5; Doppler Profile Mapping;89
10.2.6; Advice to Observers;89
10.2.7; Eclipsing Binary Data from Surveys;91
10.2.8; Terminology: ``Primary Minimum'' and ``Primary Star'';94
10.2.9; Selected Bibliography;95
10.2.10;References;96
11;Part II Modeling and Analysis;102
11.1;to 3 A General Approach to Modeling Eclipsing Binaries ;103
11.1.1; System Geometry and Dynamics;105
11.1.1.1; Coordinates and Basic Geometrical Quantities;105
11.1.1.2; Dynamics and Orbits;110
11.1.1.2.1; Circular Orbits;113
11.1.1.2.2; Eccentric Orbits;113
11.1.1.3; Spherical Models;117
11.1.1.4; Ellipsoidal Models;120
11.1.1.5; Roche Geometry and Equipotential Surfaces;123
11.1.1.5.1; Circular Orbits and Synchronous Rotation;124
11.1.1.5.2; Circular Orbits and Asynchronous Rotation;126
11.1.1.5.3; Eccentric Orbits and Asynchronous Rotation;129
11.1.1.5.4; Approaches Including Radiation Pressure;131
11.1.1.6; Binary Star Morphology;137
11.1.2; Modeling Stellar Radiative Properties;142
11.1.2.1; Gravity Brightening;143
11.1.2.2; Stellar Atmosphere Models;147
11.1.2.3; Analytic Approximations for Computing Intensities;147
11.1.2.4; Center-to-Limb Variation;148
11.1.2.5; Reflection Effect;151
11.1.2.6; Integrated Monochromatic Flux;156
11.1.3; Modeling Aspect and Eclipses;156
11.1.4; Sources and Treatment of Perturbations;159
11.1.4.1; Third Light;159
11.1.4.2; Star Spots and Other Phenomena of Active Regions;160
11.1.4.3; Atmospheric Eclipses;164
11.1.4.4; Circumstellar Matter in Binaries;165
11.1.4.4.1; Gas Streams;167
11.1.4.4.2; Gas Stream in the VV Orionis System;168
11.1.4.4.3; Disks and Rings;170
11.1.4.4.4; Stellar Winds;172
11.1.4.4.5; Attenuating Clouds;172
11.1.5; Modeling Radial Velocity Curves;173
11.1.6; Modeling Line Profiles;178
11.1.7; Modeling Polarization Curves;180
11.1.8; Modeling Pulse Arrival Times;183
11.1.9; Self-Consistent Treatment of Parallaxes;184
11.1.10; Chromospheric and Coronal Modeling;185
11.1.11; Spectral Energy Distribution;186
11.1.12; Interstellar Extinction;187
11.1.13; Selected Bibliography;188
11.1.14;References;189
11.2;to 4 Determination of Eclipsing Binary Parameters ;197
11.2.1; Mathematical Formulation of the Inverse Problem;197
11.2.1.1; The Inverse Problem from the Astronomer's Perspective;201
11.2.1.1.1; The Input Database;201
11.2.1.1.2; General Problems of Nonlinear Parameter Fitting;202
11.2.1.1.3; Special Problems of Nonlinear Parameter Fitting in Light Curve Analysis;203
11.2.1.1.4; On the Use of Constraints;206
11.2.1.1.5; Assignment of Weights;207
11.2.1.1.6; Simultaneous Fitting;210
11.2.2; A Brief Review of Nonlinear Least-Squares Problems;211
11.2.2.1; Nonlinear Unconstrained Least-Squares Methods;212
11.2.2.2; Nonlinear Constrained Least-Squares Methods;213
11.2.3; Least-Squares Techniques Used in Eclipsing Binary Data Analysis;214
11.2.3.1; A Classical Approach: Differential Corrections;215
11.2.3.2; Multiple Subset Method and Interactive Branching;218
11.2.3.3; Damped Differential Corrections and Levenberg--Marquard Algorithm;218
11.2.3.4; Derivative-Free Methods;219
11.2.3.4.1; The Simplex Algorithm;220
11.2.3.4.2; Powell's Direction Method;224
11.2.3.4.3; Simulated Annealing;225
11.2.3.5; Other Approaches;226
11.2.4; A Priori and A Posteriori Steps in Light Curve Analysis;226
11.2.4.1; Estimating Initial Parameters;226
11.2.4.2; Criteria for Terminating Iterations;230
11.2.4.3; The Interpretation of Errors Derived from Fitting;232
11.2.4.4; Calculating Absolute Stellar Parameters from a Light Curve Solution;233
11.2.4.4.1; The Complete Data Case;234
11.2.4.4.2; The Incomplete Data Case;237
11.2.5; Suggestions for Improving Performance;238
11.2.5.1; Utilizing Symmetry Properties;239
11.2.5.2; Interpolation Techniques;239
11.2.5.3; Surface Grid Design;241
11.2.5.4; Analytic Partial Derivatives;242
11.2.5.5; Accurate Finite Difference Approximation;244
11.2.6; Selected Bibliography;244
11.2.7;References;245
11.3;to 5 Advanced Topics and Techniques ;249
11.3.1; Extended Sets of Observables and Parameters;249
11.3.1.1; Inclusion of Absolute Parameters in Light Curve Analysis;250
11.3.1.2; Determining Individual Temperatures;252
11.3.1.2.1; Temperature Estimations;252
11.3.1.2.2; Color Indices as Individual Temperature Indicators;254
11.3.1.2.3; Both Temperatures from Absolute Light Curves;256
11.3.1.3; Traditional Distance Estimation;258
11.3.1.4; Direct Distance Estimation;259
11.3.1.5; Main-Sequence Constraints;261
11.3.1.6; Intrinsic Variability of Eclipsing Binaries' Components;262
11.3.2; Multiple Star Systems and their Dynamics;262
11.3.2.1; Third-Body Effects on Light and Radial Velocity Curves;263
11.3.2.2; Ephemerides Derived from Whole Light Curves and Radial Velocity Curves;266
11.3.3; Analyzing Large Numbers of Light Curves;269
11.3.3.1; Techniques for Analyzing Large Numbers of Light Curves;269
11.3.3.2; The Matching Approach;270
11.3.3.2.1; Solving Linear Regression Problems;271
11.3.3.2.2; Generation and Storage of the Archive Curves;271
11.3.3.3; The Expert Rule Approach;272
11.3.3.4; Simplified Physical Models;272
11.3.3.5; Artificial Neural Networks;272
11.3.4; Extrasolar Planets;273
11.3.4.1; General Comments About Substellar Objects;275
11.3.4.2; Methods to Find ``Small''-Mass Companions;275
11.3.4.2.1; Astrometry Variations;275
11.3.4.2.2; Direct Imaging and Spectroscopy;276
11.3.4.2.3; Radial Velocity Variations of the Visible Component;277
11.3.4.2.4; Gravitational Lensing;277
11.3.4.2.5; Transit Eclipses;278
11.3.4.2.6; Indirect Effects: O--C Variation;278
11.3.4.2.7; Effects on Disks;279
11.3.4.3; Star--Planet Systems and Eclipsing Binary Models;279
11.3.4.3.1; Comparing Stars, Brown Dwarfs, and Planets;279
11.3.4.3.2; Transit Geometry and Modeling Approaches;280
11.3.4.3.3; Representing Planets in the WD Model;282
11.3.4.3.4; HD 209458b: Transit Analysis of an ExtraSolar Planet;283
11.3.4.3.5; The OGLE-TR-56 Star Planet System;284
11.3.5; Selected Bibliography;285
11.3.6;References;286
12;Part III Light Curve Programs and Software Packages;291
12.1;to 6 Light Curve Models and Software ;292
12.1.1; Distinction Between Models and Programs;292
12.1.2; Synthetic Light Curve Models;293
12.1.2.1; The Russell--Merrill Model and Technique;293
12.1.2.2; The ``Eclipsing Binary Orbit Program'' EBOP;300
12.1.2.3; The Wood Model and the WINK program;304
12.1.3; Physical Models: Roche Geometry Based Programs;304
12.1.3.1; Binnendijk's Model;305
12.1.3.2; Hadrava's Program FOTEL;305
12.1.3.3; Hill's Model;306
12.1.3.4; Linnell's Model;306
12.1.3.5; Rucinski's Model;309
12.1.3.6; Wilson--Devinney Models;309
12.1.3.6.1; The 1998 Wilson--Devinney Model;309
12.1.3.6.2; New Features in the 1999--2007 Models;314
12.1.4; Cherepashchuk's Model;316
12.1.5; Other Approaches;322
12.1.5.1; Budding's Eclipsing Binary Model;322
12.1.5.2; Kopal's Frequency Domain Method;322
12.1.5.3; Mochnacki's General Synthesis Code, GENSYN;324
12.1.5.4; Collier--Mochnacki--Hendry GDDSYN Spotted General Synthesis Code;324
12.1.5.5; Other Spot Analysis Methods;325
12.1.6; Selected Bibliography;325
12.1.7;References;326
12.2;to 7 The Wilson--Devinney Program: Extensions and Applications ;331
12.2.1; Current Capabilities of WDx2007;332
12.2.2; Atmospheric Options;333
12.2.2.1; Kurucz Atmospheres in WDx2007;333
12.2.2.2; Kurucz Atmospheres in WD;335
12.2.3; Applications and Extensions;336
12.2.3.1; The Eclipsing X-Ray Binary HD 77581/Vela X-1;337
12.2.3.2; The Eclipsing Binaries in NGC 5466;338
12.2.3.3; The Binary H235 in the Open Cluster NGC 752;341
12.2.3.4; The Field Binary V728 Herculis;343
12.2.3.5; The Eclipsing Binaries in M71;343
12.2.3.6; The Eclipsing Binaries in 47 Tuc;345
12.2.3.7; The Well-Studied System AI Phoenicis;346
12.2.3.8; HP Draconis;347
12.2.3.9; Fitting of Line Profiles;350
12.2.4; The Future;350
12.2.4.1; ``The Future'' as Envisioned in 1999;350
12.2.4.2; The Future (as Seen in 2009);352
12.2.5;References;353
12.3;to 8 Light Curve Software with Graphical User Interface and Visualization ;357
12.3.1; Binary Maker;357
12.3.2; PHOEBE;361
12.3.3; NIGHTFALL;363
12.3.4; Graphics Packages;363
12.3.5;References;365
12.4;to 9 The Structure of Light Curve Programs and the Outlook for the Future ;366
12.4.1; Structure of a General Light Curve Analysis Program;366
12.4.1.1; Framework of the Light Curve Models;367
12.4.1.2; Framework to Embed Least-Squares Solvers;368
12.4.2; Procedural Philosophies;369
12.4.3; Code Maintenance and Modification;370
12.4.4; Prospects and Expectations;371
12.4.5;References;373
13;Part IV Appendix;374
13.1;to A Brief Review of Mathematical Optimization;375
13.1.1;A.1 Unconstrained Optimization;375
13.1.2;A.2 Constrained Optimization;380
13.1.2.1;A.2.1 Foundations and Some Theorems;380
13.1.2.2;A.2.2 Sequential Quadratic Algorithms;383
13.1.3;A.3 Unconstrained Least-Squares Procedures;384
13.1.3.1;A.3.1 Linear Case: Normal Equations;385
13.1.3.2;A.3.2 The Linear Case: An Orthogonalization Method;386
13.1.3.3;A.3.3 Nonlinear Case: A Gauß–Newton Method;388
13.1.4;A.4 Constrained Least-Squares Procedures;391
13.1.5;A.5 Selected Bibliography;392
14;to A B Estimation of Fitted Parameter Errors:The Details;393
14.1;B.1 The Kolmogorov–Smirnov Test;393
14.2;B.2 Sensitivity Analysis and the Use of Simulated Light Curves;394
14.3;B.3 Deriving Bounds for Parameters: The Grid Approach;395
15;to A C Geometry and Coordinate Systems;397
15.1;C.1 Rotation of Coordinate Systems;397
15.2;C.2 Volume and Surface Elements in Spherical Coordinates;398
15.3;C.3 Roche Coordinates;402
15.4;C.4 Solving Kepler’s Equation;403
16;to A D The Russell–Merrill Model;404
16.1;D.1 Ellipticity Correction in the Russell–Merrill Model;404
17;to A E Subroutines of theWilson–Devinney Program;408
17.1;E.1 ATM – Interfacing Stellar Model ATMospheres;409
17.2;E.2 ATMx – Interfacing Stellar Model ATMospheres;409
17.3;E.3 BBL – Basic BLock;409
17.4;E.4 BinNum – A Search and Binning Utility;410
17.5;E.5 BOLO – Bolometric Corrections;410
17.6;E.6 CofPrep – Limb-Darkening Coefficient Preparation;410
17.7;E.7 CLOUD – Atmospheric Eclipse Parameters;410
17.8;E.8 CONJPH – Conjunction Phases;411
17.9;E.9 DGMPRD – Matrix–Vector Multiplication;411
17.10;E.10 DMINV – Matrix Inversion;411
17.11;E.11 DURA – Constraint on X-Ray Eclipse Duration;411
17.12;E.12 ELLONE – Lagrangian Points and Critical Potentials;411
17.13;E.13 FOUR – Representing Eclipse Horizon;413
17.14;E.14 FOURLS – Representing Eclipse Horizon;413
17.15;E.15 GABS – Polar Gravity Acceleration;414
17.16;E.16 JDPH – Conversion of Julian Date and Phase;414
17.17;E.17 KEPLER – Solving the Kepler Equation;414
17.18;E.18 LC and DC – The Main Programs;414
17.19;E.19 LCR – Aspect Independent Surface Computations;415
17.20;E.20 LEGENDRE – Legendre Polynomials;415
17.21;E.21 LIGHT – Projections, Horizon, and Eclipse Effects;416
17.22;E.22 LimbDark – Limb Darkening;417
17.23;E.23 LinPro – Line Profiles;417
17.24;E.24 LUM – Scaling of Polar Normal Intensity;417
17.25;E.25 LUMP – Modeling Multiple Reflection;417
17.26;E.26 MLRG – Computing Absolute Dimensions;419
17.27;E.27 MODLOG – Handling Constraints Efficiently;419
17.28;E.28 NEKMIN – Connecting Surface of Over-Contact Binaries;419
17.29;E.29 OLUMP – Modeling the Reflection Effect;419
17.30;E.30 OMEGA* – Computing O(r);427
17.31;E.31 PLANCKINT – Planck Intensity;428
17.32;E.32 READLC* – Reading Program Control Parameters;428
17.33;E.33 RING – The Interface Ring of an Over-Contact Binary;428
17.34;E.34 RanGau – Generation of Gaussian Random Numbers;428
17.35;E.35 RanUni – Generation of Uniform Random Numbers;428
17.36;E.36 ROMQ – Distance Computation of Surface Points;428
17.37;E.37 ROMQSP – Distance Computation of Surface Points;429
17.38;E.38 SIMPLEX* – Simplex Algorithm;429
17.39;E.39 SinCos – Surface Grid Sine and Cosines;429
17.40;E.40 SQUARE – Building and Solving the Normal Equations;429
17.41;E.41 SPOT – Modeling Spots;429
17.42;E.42 SSR* – Computation of Curves and Residuals;430
17.43;E.43 SURFAS – Generating the Surfaces of the Components;430
17.44;E.44 VOLUME – Keeping Stellar Volume Constant;430
17.45;References;430
18;Appendix FGlossary of Symbols;433
19;Index;438