Asteroseismic Data Analysis

Sarbani Basu is a professor in the Department of Astronomy at Yale University. William J. Chaplin is a professor in the School of Physics and Astronomy at the University of Birmingham. He is the author of The Music of the Sun: The Story of Helioseismology.

Preface and Acknowledgments ix

1 Introduction 1

1.1 The Different Types of Pulsators 1

1.2 A Brief History of the Study of Solar-Type Oscillations 5

1.3 Overview of the Data 7

1.4 Scope of This Book 13

1.5 Further Reading 14

1.6 Exercises 15

2 Theoretical Underpinnings: Modeling Stars 16

2.1 The Equations of Stellar Structure and Evolution 16

2.2 The Question of â 19

2.3 Other Physical Processes 22

2.4 Boundary Conditions 22

2.5 Inputs to Stellar Models 25

2.6 Modeling a Star 26

2.7 Constructing Solar Models 27

2.8 Constructing Stellar Models of a Given Mass, Radius, and Teff 28

2.9 Further Reading 29

2.10 Exercises 31

3 Theoretical Underpinnings: Stellar Oscillations 33

3.1 The Equations of Stellar Oscillations 33

3.2 Properties of Stellar Oscillations 40

3.3 Changes in Frequencies in Response to Changes in Stellar Structure 58

3.4 The Effects of Acoustic Glitches 63

3.5 The Effects of Rotation 66

3.6 Mode Excitation 70

3.7 Further Reading 74

3.8 Exercises 76

4 Observational Data: Overview and Fundamentals 78

4.1 Spatial Response of the Observations 78

4.2 Photometric and Doppler Velocity Observations 83

4.3 Other Contributions to the Observed Data 89

4.4 Further Reading 98

4.5 Exercises 99

5 Observational Data: Detailed Characteristics in the Frequency Domain 100

5.1 Power Spectrum Estimation 101

5.2 Statistics of the Power Spectrum 111

5.3 Solar-Like Oscillations in the Frequency Domain 113

5.4 Global Properties of the Oscillation Spectrum 127

5.5 Frequency Spectrum of Granulation and Active-Region Signal 134

5.6 Harmonic Structure from Transits, Eclipses, and Stellar Rotation 137

5.7 Super-Nyquist Asteroseismology 145

5.8 Further Reading 150

5.9 Exercises 152

6 Observational Data: Analysis of the Frequency Spectrum 153

6.1 Statistical Tests: Example of Detection of Signatures of Individual Modes 154

6.2 Automated Detection of Oscillation Spectra 162

6.3 Fundamentals of Peak-Bagging: Extraction of Individual Mode Parameters 181

6.4 Peak-Bagging: Practicalities and Challenges 187

6.5 Challenges for Peak-Bagging Posed by Mixed Modes 207

6.6 Further Reading 220

6.7 Exercises 221

7 Drawing Inferences from Average Seismic Parameters 223

7.1 The Direct Method 223

7.2 Grid-Based Modeling 227

7.3 Further Reading 234

7.4 Exercises 235

8 Interpreting Frequencies of Individual Modes: Comparing Frequencies 237

8.1 Choosing the Physics of Models 237

8.2 Effects of Different Model Parameters 239

8.3 A Complicating Factor: The Surface Term 243

8.4 Common Ways of Constructing Models to Fit Frequencies 249

8.5 Dealing with Avoided Crossings in Subgiants 257

8.6 Modeling Red Giants 258

8.7 Alternative Methods for Fitting Frequencies 259

8.8 Analysis of Rotation 265

8.9 Further Reading 268

8.10 Exercises 269

9 Interpreting Frequencies of Individual Modes: Other Diagnostics 271

9.1 Learning from Combinations of Frequencies 271

9.2 Fitting and Interpreting the Signature of Acoustic Glitches 276

9.3 Analysis of Red Giants 281

9.4 Further Reading 293

9.5 Exercises 295

10 Inverting Mode Frequencies 297

10.1 The Inversion Equation 297

10.2 The Regularized Least Squares Technique 299

10.3 The Method of Forming Optimally Localized Averages 306

10.4 Applying Inversions to Stars 315

10.5 Inversions for Global Quantities 320

10.6 Alternative Methods 325

10.7 Inversions for Rotation 327

10.8 Further Reading 329

10.9 Exercises 331

Index 333