Pulsating Stars

Preface XI

1 Historical Overview 1

1.1 Discovery of the First Pulsating Variable Stars 1

1.1.1 Nomenclature 5

1.2 The Recognition of Pulsation as a Cause of Variability 8

2 Fundamentals of Stellar Variability Observations 11

2.1 Definitions 11

2.1.1 Time and Julian Dates 11

2.1.2 Light Curves 14

2.2 Photometric Bandpasses 16

2.3 Period Determination 16

2.4 Common Observational Techniques 20

2.4.1 Visual Methods 20

2.4.2 Photographic Methods 22

2.4.3 Photoelectric Methods 24

2.4.4 CCD Surveys 25

2.5 Space-Based Versus Ground Observations 27

3 Classification of Variable Stars 29

3.1 Regular, Semi-Regular, and Irregular Variables 29

3.2 Variability: Intrinsic and/or Extrinsic 30

3.3 Extrinsic Variables 30

3.3.1 Algol-Type Eclipsing Binaries (EAs) 30

3.3.2 𝛽 Lyrae-Type Eclipsing Binaries (EBs) 32

3.3.3 WUMa-Type Eclipsing Binaries (EWs) 32

3.3.4 R-Type Binaries 32

3.3.5 Planetary Transits and Asteroid Occultations 33

3.4 Intrinsic Variables 34

3.4.1 Rotational Variables 34

3.4.1.1 Ap Stars (𝛼² CVn Stars) 34

3.4.1.2 SpottedWUMa, 𝛽 Lyr, and Algol Systems 36

3.4.1.3 RS Canum Venaticorum Stars 36

3.4.1.4 BY Dra Stars 37

3.4.1.5 FK Com Stars 38

3.4.1.6 Ellipsoidal Variables 38

3.4.2 Eruptive Variables 39

3.4.2.1 UV Ceti Stars 39

3.4.2.2 FU Orionis (FUor) Stars 39

3.4.2.3 EX Lupi (EXor) Stars 40

3.4.2.4 T Tauri Stars 40

3.4.2.5 Herbig Ae/Be Stars 40

3.4.2.6 Luminous Blue Variables 41

3.4.2.7 Wolf–Rayet Stars 41

3.4.2.8 R Coronae Borealis (R CrB) Variables 42

3.4.2.9 𝛾 Cassiopeiae (Be) Stars 43

3.4.3 Explosive and Novalike Variables 44

3.4.3.1 Cataclysmic Variables 44

3.4.3.2 Symbiotic Stars 47

3.4.3.3 Supernovae 48

3.4.4 Pulsating Variables and the Scope of this Book 50

4 Stellar Structure and Evolution Theory 53

4.1 The Basic Equations of Stellar Structure and Evolution 53

4.2 The Evolution of Low-Mass Stars 57

4.3 The Evolution of Intermediate-Mass Stars 66

4.4 The Evolution of High-Mass Stars 70

5 Stellar Pulsation Theory 73

5.1 Timescales 73

5.2 Ritter’s (Period–Mean Density) Relation 76

5.3 Basic Equations of (Radial) Stellar Pulsation Theory 78

5.3.1 Generalization of the Energy Conservation Equation 78

5.3.2 Summary 81

5.4 Linearization of the Stellar Pulsation Equations 81

5.4.1 PerturbationTheory 82

5.4.2 The Continuity Equation 83

5.4.3 The Conservation of Momentum Equation 84

5.4.4 The Energy Conservation Equation 85

5.4.5 The Energy Transfer Equation 86

5.4.6 Constitutive Equations 86

5.5 Linear Adiabatic Oscillations: The LAWE 87

5.5.1 Justification of the Adiabatic Approximation 88

5.5.2 The LAWE 90

5.5.3 Boundary Conditions 92

5.6 Eigenvalues and Eigenfunctions of the LAWE 95

5.6.1 Examples 98

5.6.1.1 The Homologous Case 99

5.6.1.2 The Polytropic Case 99

5.6.1.3 An Actual RR Lyrae Model 102

5.7 Non-Adiabatic Theory: Conditions for Stability 105

5.8 The Linear Non-Adiabatic Wave Equation 109

5.9 Driving Mechanisms 113

5.9.1 The 𝜖 Mechanism 114

5.9.2 The 𝜅 and 𝛾 Mechanisms 117

5.9.3 The “Opacity Bump” Mechanism 120

5.10 Stability Conditions and Instability Strip Edges 123

5.10.1 Other Instability Mechanisms 124

5.10.1.1 Convective Blocking Mechanism 124

5.10.1.2 Convective Driving (𝛿 Mechanism) 124

5.10.1.3 Stochastically Excited Pulsations 125

5.10.1.4 Tidally Excited Pulsations 129

5.10.1.5 GravitationalWaves 129

5.10.1.6 Stellar Mergers 130

5.10.1.7 Sunquakes and Starquakes: Flare-Driven Oscillations 130

5.11 Non-Radial Pulsations 130

5.11.1 Theoretical Framework; Helio- and Asteroseismological Applications 131

5.12 Nonlinear Effects 153

6 RR Lyrae Stars 157

6.1 RR Lyrae Stars as a Class of Pulsating Variable Star 157

6.2 RR Lyrae Stars as Standard Candles 164

6.3 Evolution of RR Lyrae Stars 167

6.4 Pulsation 168

6.5 The Blazhko Effect 169

6.6 RR Lyrae Stars in Globular Clusters 172

6.7 The Oosterhoff Groups 173

6.8 Period Changes 177

6.9 RR Lyrae Stars beyond the MilkyWay 181

7 Cepheid and Related Variable Stars 183

7.1 Classical Cepheids 183

7.1.1 Cepheid Light Curves 185

7.1.2 The Period Luminosity Relation: Leavitt’s Law 189

7.1.3 Evolution and Period Changes 192

7.1.4 Polaris 195

7.2 Type II Cepheids 196

7.2.1 Light Curves 200

7.2.2 Spectra and Chemical Composition 203

7.2.3 Period–Luminosity Relation 204

7.2.4 Evolution and Period Changes 206

7.3 BL Boo Stars or Anomalous Cepheids 208

7.4 RV Tauri Stars 211

8 Red Variable Stars 215

8.1 Convection and Pulsation 217

8.2 Mira and Related Long-Period Variables 219

8.3 Semi-Regular Variables 229

8.4 Irregular Variables 231

9 Pulsating Stars Close to the Lower Main Sequence in the H-R Diagram 233

9.1 𝛿 Scuti and SX Phoenicis Stars 233

9.2 𝛾 Doradus Stars 240

9.3 roAp Stars 242

10 Pulsating Stars Close to the Upper Main Sequence in the

H-R Diagram 245

10.1 𝛽 Cephei Stars 248

10.2 SPB (53 Per) Stars 251

11 Pulsating Supergiant Stars 253

11.1 SPBsg Variables 253

11.2 PV Telescopii, V652 Herculis, and R CrB Stars 256

11.3 𝛼 Cygni, S Dor, and Wolf-Rayet Stars 258

12 Hot Subdwarf Pulsators 263

12.1 EC 14026 (V361 Hya, sdBV, sdBV_p, sdBV_r) Variables 268

12.2 PG 1716+426 (V1093 Her, “Betsy,” sdBV_g, sdBV_s) Variables 269

12.3 sdOV (V499 Ser) Variables 270

12.4 He-sdBV Stars 272

13 Pulsating Degenerate Stars 275

13.1 GWVir Stars 285

13.2 DBV (V777 Her) Stars 287

13.3 DQV Stars 290

13.4 DAV Stars 292

13.4.1 ELM-DAV Stars 294

13.4.2 Hot DAV Stars 296

13.5 ELM-HeV Stars 298

13.6 GWLibrae Stars: AccretingWD Pulsators 300

13.7 Pulsations in Neutron Stars and Black Holes 302

Glossary 305

References 311

Index 411

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