Pulsating Stars

Márcio Catelan holds a full professorship at the Catholic University of Chile. Previous assignments were with the University of Virginia and with NASA's Goddard Space Flight Center. He is the author of over 130 journal papers and numerous review articles, and presents an impressive record of institutional service and awards, including Hubble and Guggenheim fellowships. Horace Smith is Professor Emeritus in the Department of Physics and Astronomy at Michigan State University. He received his Master's degree and PhD from Yale and his research is focused on variable stars and what we can learn from them about the evolution of stars and galaxies. He has published extensively in astronomical journals and is the author of a book on RR Lyrae stars. He has served on numerous scientific committees and as a reviewer for several astronomical journals.

• Preface XI1 Historical Overview 11.1 Discovery of the First Pulsating Variable Stars 11.1.1 Nomenclature 51.2 The Recognition of Pulsation as a Cause of Variability 82 Fundamentals of Stellar Variability Observations 112.1 Definitions 112.1.1 Time and Julian Dates 112.1.2 Light Curves 142.2 Photometric Bandpasses 162.3 Period Determination 162.4 Common Observational Techniques 202.4.1 Visual Methods 202.4.2 Photographic Methods 222.4.3 Photoelectric Methods 242.4.4 CCD Surveys 252.5 Space-Based Versus Ground Observations 273 Classification of Variable Stars 293.1 Regular, Semi-Regular, and Irregular Variables 293.2 Variability: Intrinsic and/or Extrinsic 303.3 Extrinsic Variables 303.3.1 Algol-Type Eclipsing Binaries (EAs) 303.3.2 𝛽 Lyrae-Type Eclipsing Binaries (EBs) 323.3.3 WUMa-Type Eclipsing Binaries (EWs) 323.3.4 R-Type Binaries 323.3.5 Planetary Transits and Asteroid Occultations 333.4 Intrinsic Variables 343.4.1 Rotational Variables 343.4.1.1 Ap Stars (𝛼2 CVn Stars) 343.4.1.2 SpottedWUMa, 𝛽 Lyr, and Algol Systems 363.4.1.3 RS Canum Venaticorum Stars 363.4.1.4 BY Dra Stars 373.4.1.5 FK Com Stars 383.4.1.6 Ellipsoidal Variables 383.4.2 Eruptive Variables 393.4.2.1 UV Ceti Stars 393.4.2.2 FU Orionis (FUor) Stars 393.4.2.3 EX Lupi (EXor) Stars 403.4.2.4 T Tauri Stars 403.4.2.5 Herbig Ae/Be Stars 403.4.2.6 Luminous Blue Variables 413.4.2.7 Wolf–Rayet Stars 413.4.2.8 R Coronae Borealis (R CrB) Variables 423.4.2.9 𝛾 Cassiopeiae (Be) Stars 433.4.3 Explosive and Novalike Variables 443.4.3.1 Cataclysmic Variables 443.4.3.2 Symbiotic Stars 473.4.3.3 Supernovae 483.4.4 Pulsating Variables and the Scope of this Book 504 Stellar Structure and Evolution Theory 534.1 The Basic Equations of Stellar Structure and Evolution 534.2 The Evolution of Low-Mass Stars 574.3 The Evolution of Intermediate-Mass Stars 664.4 The Evolution of High-Mass Stars 705 Stellar Pulsation Theory 735.1 Timescales 735.2 Ritter’s (Period–Mean Density) Relation 765.3 Basic Equations of (Radial) Stellar Pulsation Theory 785.3.1 Generalization of the Energy Conservation Equation 785.3.2 Summary 815.4 Linearization of the Stellar Pulsation Equations 815.4.1 PerturbationTheory 825.4.2 The Continuity Equation 835.4.3 The Conservation of Momentum Equation 845.4.4 The Energy Conservation Equation 855.4.5 The Energy Transfer Equation 865.4.6 Constitutive Equations 865.5 Linear Adiabatic Oscillations: The LAWE 875.5.1 Justification of the Adiabatic Approximation 885.5.2 The LAWE 905.5.3 Boundary Conditions 925.6 Eigenvalues and Eigenfunctions of the LAWE 955.6.1 Examples 985.6.1.1 The Homologous Case 995.6.1.2 The Polytropic Case 995.6.1.3 An Actual RR Lyrae Model 1025.7 Non-Adiabatic Theory: Conditions for Stability 1055.8 The Linear Non-Adiabatic Wave Equation 1095.9 Driving Mechanisms 1135.9.1 The 𝜖 Mechanism 1145.9.2 The 𝜅 and 𝛾 Mechanisms 1175.9.3 The “Opacity Bump” Mechanism 1205.10 Stability Conditions and Instability Strip Edges 1235.10.1 Other Instability Mechanisms 1245.10.1.1 Convective Blocking Mechanism 1245.10.1.2 Convective Driving (𝛿 Mechanism) 1245.10.1.3 Stochastically Excited Pulsations 1255.10.1.4 Tidally Excited Pulsations 1295.10.1.5 GravitationalWaves 1295.10.1.6 Stellar Mergers 1305.10.1.7 Sunquakes and Starquakes: Flare-Driven Oscillations 1305.11 Non-Radial Pulsations 1305.11.1 Theoretical Framework; Helio- and Asteroseismological Applications 1315.12 Nonlinear Effects 1536 RR Lyrae Stars 1576.1 RR Lyrae Stars as a Class of Pulsating Variable Star 1576.2 RR Lyrae Stars as Standard Candles 1646.3 Evolution of RR Lyrae Stars 1676.4 Pulsation 1686.5 The Blazhko Effect 1696.6 RR Lyrae Stars in Globular Clusters 1726.7 The Oosterhoff Groups 1736.8 Period Changes 1776.9 RR Lyrae Stars beyond the MilkyWay 1817 Cepheid and Related Variable Stars 1837.1 Classical Cepheids 1837.1.1 Cepheid Light Curves 1857.1.2 The Period Luminosity Relation: Leavitt’s Law 1897.1.3 Evolution and Period Changes 1927.1.4 Polaris 1957.2 Type II Cepheids 1967.2.1 Light Curves 2007.2.2 Spectra and Chemical Composition 2037.2.3 Period–Luminosity Relation 2047.2.4 Evolution and Period Changes 2067.3 BL Boo Stars or Anomalous Cepheids 2087.4 RV Tauri Stars 2118 Red Variable Stars 2158.1 Convection and Pulsation 2178.2 Mira and Related Long-Period Variables 2198.3 Semi-Regular Variables 2298.4 Irregular Variables 2319 Pulsating Stars Close to the Lower Main Sequence in the H-R Diagram 2339.1 𝛿 Scuti and SX Phoenicis Stars 2339.2 𝛾 Doradus Stars 2409.3 roAp Stars 24210 Pulsating Stars Close to the Upper Main Sequence in theH-R Diagram 24510.1 𝛽 Cephei Stars 24810.2 SPB (53 Per) Stars 25111 Pulsating Supergiant Stars 25311.1 SPBsg Variables 25311.2 PV Telescopii, V652 Herculis, and R CrB Stars 25611.3 𝛼 Cygni, S Dor, and Wolf-Rayet Stars 25812 Hot Subdwarf Pulsators 26312.1 EC 14026 (V361 Hya, sdBV, sdBVp, sdBVr) Variables 26812.2 PG 1716+426 (V1093 Her, “Betsy,” sdBVg, sdBVs) Variables 26912.3 sdOV (V499 Ser) Variables 27012.4 He-sdBV Stars 27213 Pulsating Degenerate Stars 27513.1 GWVir Stars 28513.2 DBV (V777 Her) Stars 28713.3 DQV Stars 29013.4 DAV Stars 29213.4.1 ELM-DAV Stars 29413.4.2 Hot DAV Stars 29613.5 ELM-HeV Stars 29813.6 GWLibrae Stars: AccretingWD Pulsators 30013.7 Pulsations in Neutron Stars and Black Holes 302Glossary 305References 311Index 411