Eclipsing Binary Stars: Modeling and Analysis (eBook)

Foreword 6
Preface to the Second Edition 8
Preface to the First Edition 10
References 12
Acknowledgments 13
Contents 15
List of Figures 24
Journal Abbreviations 27
Acronyms and Abbreviations 29
Mathematical Nomenclature and Symbols, Physical Units 30
Part I Introduction 31
to 1 Introduction 32
Eclipsing Binaries and Other Variable Stars 32
Eclipsing Variables 34
Algols 34
Lyrae 35
W Ursae Majoris or W UMa 35
Pulsating Variables 36
Eruptive Variables 37
Overview of the Problem 39
Why Binary Stars Are Important 39
Visual Double Stars 40
Spectroscopic Binaries 42
Eclipsing Binaries 43
Phenomenological Classification of Eclipsing Binary Light Curves 44
Morphological Classification of Eclipsing Binaries 47
What Can Be Derived from Eclipsing Binaries 51
Why Data Derived from Eclipsing Binaries AreImportant 51
The History of Light Curve Modeling 52
The Pioneers -- The Age of Geometry 52
The Age of Computational Astrophysics 53
Determining Astrophysical Parameters 54
Later Generations of Light Curve Models 54
Astrophysical Problems Solved by Light CurveMethods 55
EB Guide for Researchers in Other Fields 56
Eclipsing Binaries and Standard Candles 56
Eclipsing Binaries in ExtraSolar Planet Research 57
Nomenclature: Primary and Secondary Component 58
Where Are the Radii? 58
Precession and Apsidal Motion 58
Looking for Eclipsing Binary Standard Software 59
Analytic Techniques and Numerical Analysis 59
Selected Bibliography 59
References 60
to 2 The Database and Methods of Data Acquisition 66
Photometry 66
Photoelectric Photometry 66
Two-Star Photometers 68
Photoelectric Observations 70
Imaging Data 72
Photometric Data Reduction 73
Significance of Cluster Photometry 76
Spectroscopy 77
Radial Velocities 80
Spectrophotometry 82
Line-Profile Analysis 84
Polarimetry 86
Magnetometry 88
Doppler Profile Mapping 89
Advice to Observers 89
Eclipsing Binary Data from Surveys 91
Terminology: ``Primary Minimum'' and ``Primary Star'' 94
Selected Bibliography 95
References 96
Part II Modeling and Analysis 102
to 3 A General Approach to Modeling Eclipsing Binaries 103
System Geometry and Dynamics 105
Coordinates and Basic Geometrical Quantities 105
Dynamics and Orbits 110
Circular Orbits 113
Eccentric Orbits 113
Spherical Models 117
Ellipsoidal Models 120
Roche Geometry and Equipotential Surfaces 123
Circular Orbits and Synchronous Rotation 124
Circular Orbits and Asynchronous Rotation 126
Eccentric Orbits and Asynchronous Rotation 129
Approaches Including Radiation Pressure 131
Binary Star Morphology 137
Modeling Stellar Radiative Properties 142
Gravity Brightening 143
Stellar Atmosphere Models 147
Analytic Approximations for Computing Intensities 147
Center-to-Limb Variation 148
Reflection Effect 151
Integrated Monochromatic Flux 156
Modeling Aspect and Eclipses 156
Sources and Treatment of Perturbations 159
Third Light 159
Star Spots and Other Phenomena of Active Regions 160
Atmospheric Eclipses 164
Circumstellar Matter in Binaries 165
Gas Streams 167
Gas Stream in the VV Orionis System 168
Disks and Rings 170
Stellar Winds 172
Attenuating Clouds 172
Modeling Radial Velocity Curves 173
Modeling Line Profiles 178
Modeling Polarization Curves 180
Modeling Pulse Arrival Times 183
Self-Consistent Treatment of Parallaxes 184
Chromospheric and Coronal Modeling 185
Spectral Energy Distribution 186
Interstellar Extinction 187
Selected Bibliography 188
References 189
to 4 Determination of Eclipsing Binary Parameters 197
Mathematical Formulation of the Inverse Problem 197
The Inverse Problem from the Astronomer's Perspective 201
The Input Database 201
General Problems of Nonlinear Parameter Fitting 202
Special Problems of Nonlinear Parameter Fitting in Light Curve Analysis 203
On the Use of Constraints 206
Assignment of Weights 207
Simultaneous Fitting 210
A Brief Review of Nonlinear Least-Squares Problems 211
Nonlinear Unconstrained Least-Squares Methods 212
Nonlinear Constrained Least-Squares Methods 213
Least-Squares Techniques Used in Eclipsing Binary Data Analysis 214
A Classical Approach: Differential Corrections 215
Multiple Subset Method and Interactive Branching 218
Damped Differential Corrections and Levenberg--Marquard Algorithm 218
Derivative-Free Methods 219
The Simplex Algorithm 220
Powell's Direction Method 224
Simulated Annealing 225
Other Approaches 226
A Priori and A Posteriori Steps in Light Curve Analysis 226
Estimating Initial Parameters 226
Criteria for Terminating Iterations 230
The Interpretation of Errors Derived from Fitting 232
Calculating Absolute Stellar Parameters from a Light Curve Solution 233
The Complete Data Case 234
The Incomplete Data Case 237
Suggestions for Improving Performance 238
Utilizing Symmetry Properties 239
Interpolation Techniques 239
Surface Grid Design 241
Analytic Partial Derivatives 242
Accurate Finite Difference Approximation 244
Selected Bibliography 244
References 245
to 5 Advanced Topics and Techniques 249
Extended Sets of Observables and Parameters 249
Inclusion of Absolute Parameters in Light Curve Analysis 250
Determining Individual Temperatures 252
Temperature Estimations 252
Color Indices as Individual Temperature Indicators 254
Both Temperatures from Absolute Light Curves 256
Traditional Distance Estimation 258
Direct Distance Estimation 259
Main-Sequence Constraints 261
Intrinsic Variability of Eclipsing Binaries' Components 262
Multiple Star Systems and their Dynamics 262
Third-Body Effects on Light and Radial Velocity Curves 263
Ephemerides Derived from Whole Light Curves and Radial Velocity Curves 266
Analyzing Large Numbers of Light Curves 269
Techniques for Analyzing Large Numbers of Light Curves 269
The Matching Approach 270
Solving Linear Regression Problems 271
Generation and Storage of the Archive Curves 271
The Expert Rule Approach 272
Simplified Physical Models 272
Artificial Neural Networks 272
Extrasolar Planets 273
General Comments About Substellar Objects 275
Methods to Find ``Small''-Mass Companions 275
Astrometry Variations 275
Direct Imaging and Spectroscopy 276
Radial Velocity Variations of the Visible Component 277
Gravitational Lensing 277
Transit Eclipses 278
Indirect Effects: O--C Variation 278
Effects on Disks 279
Star--Planet Systems and Eclipsing Binary Models 279
Comparing Stars, Brown Dwarfs, and Planets 279
Transit Geometry and Modeling Approaches 280
Representing Planets in the WD Model 282
HD 209458b: Transit Analysis of an ExtraSolar Planet 283
The OGLE-TR-56 Star Planet System 284
Selected Bibliography 285
References 286
Part III Light Curve Programs and Software Packages 291
to 6 Light Curve Models and Software 292
Distinction Between Models and Programs 292
Synthetic Light Curve Models 293
The Russell--Merrill Model and Technique 293
The ``Eclipsing Binary Orbit Program'' EBOP 300
The Wood Model and the WINK program 304
Physical Models: Roche Geometry Based Programs 304
Binnendijk's Model 305
Hadrava's Program FOTEL 305
Hill's Model 306
Linnell's Model 306
Rucinski's Model 309
Wilson--Devinney Models 309
The 1998 Wilson--Devinney Model 309
New Features in the 1999--2007 Models 314
Cherepashchuk's Model 316
Other Approaches 322
Budding's Eclipsing Binary Model 322
Kopal's Frequency Domain Method 322
Mochnacki's General Synthesis Code, GENSYN 324
Collier--Mochnacki--Hendry GDDSYN Spotted General Synthesis Code 324
Other Spot Analysis Methods 325
Selected Bibliography 325
References 326
to 7 The Wilson--Devinney Program: Extensions and Applications 331
Current Capabilities of WDx2007 332
Atmospheric Options 333
Kurucz Atmospheres in WDx2007 333
Kurucz Atmospheres in WD 335
Applications and Extensions 336
The Eclipsing X-Ray Binary HD 77581/Vela X-1 337
The Eclipsing Binaries in NGC 5466 338
The Binary H235 in the Open Cluster NGC 752 341
The Field Binary V728 Herculis 343
The Eclipsing Binaries in M71 343
The Eclipsing Binaries in 47 Tuc 345
The Well-Studied System AI Phoenicis 346
HP Draconis 347
Fitting of Line Profiles 350
The Future 350
``The Future'' as Envisioned in 1999 350
The Future (as Seen in 2009) 352
References 353
to 8 Light Curve Software with Graphical User Interface and Visualization 357
Binary Maker 357
PHOEBE 361
NIGHTFALL 363
Graphics Packages 363
References 365
to 9 The Structure of Light Curve Programs and the Outlook for the Future 366
Structure of a General Light Curve Analysis Program 366
Framework of the Light Curve Models 367
Framework to Embed Least-Squares Solvers 368
Procedural Philosophies 369
Code Maintenance and Modification 370
Prospects and Expectations 371
References 373
Part IV Appendix 374
to A Brief Review of Mathematical Optimization 375
A.1 Unconstrained Optimization 375
A.2 Constrained Optimization 380
A.2.1 Foundations and Some Theorems 380
A.2.2 Sequential Quadratic Algorithms 383
A.3 Unconstrained Least-Squares Procedures 384
A.3.1 Linear Case: Normal Equations 385
A.3.2 The Linear Case: An Orthogonalization Method 386
A.3.3 Nonlinear Case: A Gauß–Newton Method 388
A.4 Constrained Least-Squares Procedures 391
A.5 Selected Bibliography 392
to A B Estimation of Fitted Parameter Errors:The Details 393
B.1 The Kolmogorov–Smirnov Test 393
B.2 Sensitivity Analysis and the Use of Simulated Light Curves 394
B.3 Deriving Bounds for Parameters: The Grid Approach 395
to A C Geometry and Coordinate Systems 397
C.1 Rotation of Coordinate Systems 397
C.2 Volume and Surface Elements in Spherical Coordinates 398
C.3 Roche Coordinates 402
C.4 Solving Kepler’s Equation 403
to A D The Russell–Merrill Model 404
D.1 Ellipticity Correction in the Russell–Merrill Model 404
to A E Subroutines of theWilson–Devinney Program 408
E.1 ATM – Interfacing Stellar Model ATMospheres 409
E.2 ATMx – Interfacing Stellar Model ATMospheres 409
E.3 BBL – Basic BLock 409
E.4 BinNum – A Search and Binning Utility 410
E.5 BOLO – Bolometric Corrections 410
E.6 CofPrep – Limb-Darkening Coefficient Preparation 410
E.7 CLOUD – Atmospheric Eclipse Parameters 410
E.8 CONJPH – Conjunction Phases 411
E.9 DGMPRD – Matrix–Vector Multiplication 411
E.10 DMINV – Matrix Inversion 411
E.11 DURA – Constraint on X-Ray Eclipse Duration 411
E.12 ELLONE – Lagrangian Points and Critical Potentials 411
E.13 FOUR – Representing Eclipse Horizon 413
E.14 FOURLS – Representing Eclipse Horizon 413
E.15 GABS – Polar Gravity Acceleration 414
E.16 JDPH – Conversion of Julian Date and Phase 414
E.17 KEPLER – Solving the Kepler Equation 414
E.18 LC and DC – The Main Programs 414
E.19 LCR – Aspect Independent Surface Computations 415
E.20 LEGENDRE – Legendre Polynomials 415
E.21 LIGHT – Projections, Horizon, and Eclipse Effects 416
E.22 LimbDark – Limb Darkening 417
E.23 LinPro – Line Profiles 417
E.24 LUM – Scaling of Polar Normal Intensity 417
E.25 LUMP – Modeling Multiple Reflection 417
E.26 MLRG – Computing Absolute Dimensions 419
E.27 MODLOG – Handling Constraints Efficiently 419
E.28 NEKMIN – Connecting Surface of Over-Contact Binaries 419
E.29 OLUMP – Modeling the Reflection Effect 419
E.30 OMEGA* – Computing O(r) 427
E.31 PLANCKINT – Planck Intensity 428
E.32 READLC* – Reading Program Control Parameters 428
E.33 RING – The Interface Ring of an Over-Contact Binary 428
E.34 RanGau – Generation of Gaussian Random Numbers 428
E.35 RanUni – Generation of Uniform Random Numbers 428
E.36 ROMQ – Distance Computation of Surface Points 428
E.37 ROMQSP – Distance Computation of Surface Points 429
E.38 SIMPLEX* – Simplex Algorithm 429
E.39 SinCos – Surface Grid Sine and Cosines 429
E.40 SQUARE – Building and Solving the Normal Equations 429
E.41 SPOT – Modeling Spots 429
E.42 SSR* – Computation of Curves and Residuals 430
E.43 SURFAS – Generating the Surfaces of the Components 430
E.44 VOLUME – Keeping Stellar Volume Constant 430
References 430
Appendix FGlossary of Symbols 433
Index 438