ASTRONOMY AND ASTROPHYSICS LIBRARY

Transcription

1 ASTRONOMY AND ASTROPHYSICS LIBRARY Series Editors: G. Borner, Garching, Germany A. Burkert, München, Germany W. B. Burton, Charlottesville, VA, USA and Leiden, The Netherlands M. A. Dopita, Canberra, Australia A. Eckart, Köln, Germany E. K. Grebel, Heidelberg, Germany B. Leibundgut, Garching, Germany A. Maeder, Sauverny, Switzerland V. Trimble, College Park, MD, and Irvine, CA, USA For further volumes:

2 C. Aerts J. Christensen-Dalsgaard D.W. Kurtz Asteroseismology ABC

3 Conny Aerts K.U. Leuven Instituut voor Sterrenkunde Celestijnenlaan 200D 3001 Leuven Belgium and Radboud Universiteit Nijmegen Department of Astrophysics (IMAPP) Heyendaalseweg AJ Nijmegen The Netherlands Jørgen Christensen-Dalsgaard Aarhus University Department of Physics and Astronomy Building 1520, Ny Munkegade 8000 Aarhus C Denmark jcd@phys.au.dk Donald W. Kurtz University of Central Lancashire Centre for Astrophysics Preston PR1 2HE United Kingdom dwkurtz@uclan.ac.uk ISSN ISBN e-isbn DOI / Springer Dordrecht Heidelberg London New York Library of Congress Control Number: c Springer Science+Business Media B.V No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: estudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (

4 Dedication To Geert, An, and Jasper (CA) To Birte, Karen, Signe, Clara, and Anna (JCD) To June (DWK)

5 Preface Understanding the stars is the bedrock of modern astrophysics. Stars are the source of life. The chemical enrichment of our Milky Way and of the Universe with all elements heavier than lithium originates in the interiors of stars. Stars are the tracers of the dynamics of the Universe, gravitationally implying much more than meets the eye. Stars ionize the interstellar medium and re-ionized the early intergalactic medium. Understanding stellar structure and evolution is fundamental. While stellar structure and evolution are understood in general terms, we lack important physical ingredients, despite extensive research during recent decades. Classical spectroscopy, photometry, astrometry and interferometry of stars have traditionally been used as observational constraints to deduce the internal stellar physics. Unfortunately, these types of observations only allow the tuning of the basic common physics laws under stellar conditions with relatively poor precision. The situation is even more worrisome for unknown aspects of the physics and dynamics in stars. These are usually dealt with by using parameterised descriptions of, e.g., the treatments of convection, rotation, angular momentum transport, the equation of state, atomic diffusion and settling of elements, magneto-hydrodynamical processes, and more. There is a dearth of observational constraints on these processes, thus solar values are often assigned to them. Yet it is hard to imagine that one set of parameters is appropriate for the vast range of stars. Helioseismology led to a large step forward in the precision of the internal structural model of the Sun. Asteroseismology aims to obtain similar improvements for different types of stars by means of their oscillations. Stellar oscillations indeed offer a unique opportunity to probe the internal properties and processes, because these affect the observable frequencies. Moreover, stellar rotation and magnetic fields also modify the frequencies of a star s modes of oscillation. The confrontation between the measured oscillation frequencies and those predicted by models improves the input physics of models to a precision that cannot be reached by any other method, as we have learned from helioseismology.

6 VIII Preface Stellar oscillations are the only diagnostic known that allows us to improve the stellar structure and evolution models by at least an order of magnitude. This book, the first dedicated to this research field, explains how this can be achieved. As such, it encompasses all aspects of the field: we treat raw data gathering and reduction (Chapter 4), oscillation frequency determination through time series analysis (Chapter 5), techniques for the identification of the spherical wavenumbers of the oscillation modes from data (Chapter 6), as well as the theory of stellar oscillations with specific emphasis on the aspects of the physics that can be improved by asteroseismology (Chapter 3). The book begins with an intuitive descriptive introduction into the topic for the nonexpert by comparing stellar oscillations with musical sound waves (Chapter 1), then provides an overview of all the various classes of stars in which oscillations have been discovered (Chapter 2). Having introduced all the methodology, Chapter 7 is dedicated to some selected case studies of successful applications of asteroseismology, including a brief overview of helioseismology. Up to now, the best applications of asteroseismology, i.e., those that have led to improved values of the input physics, have relied dominantly on groundbased data sets. This will change dramatically when the results of the presently operational CoRoT and Kepler missions and other future space missions become available, while ground-based spectroscopic measurements will remain a requirement for a full asteroseismic analysis. We look into the future of this booming research field in Chapter 8 where we emphasize the immense progress that is being made in the quality and quantity of asteroseismic data from ongoing and future space missions, as well as from ground-based instrumentation.

7 Acknowledgements It is a pleasure to thank all the scientists and students whose paths we have crossed during conferences, meetings, schools, observing trips, scientific visits, etc., for the interesting discussions and debates and for the education we received. This book could not have been accomplished without considerable help and advice from many colleagues. We are very grateful to the numerous scientists who gave us permission to use figures from their original publications and for providing us with the electronic files to reproduce them in this monograph. We have included the reference to the original source for each reproduced figure. We acknowledge the copyright holders: Acta Astronomica, Astronomy and Astrophysics, Astronomy and Astrophysics Review, Cambridge University Press, Monthly Notices of the Royal Astronomical Society published by Wiley-Blackwell, Cambridge University Press, Memorie della Societa Astronomica Italiana, and The Astronomical Journal and The Astrophysical journal published by the American Astronomical Society, for granting us the kind permission to reprint the figures from their publications. We thank the BiSON and GOLF teams for the use of figures from their project website and the American Association of Variable Star Observers (AAVSO) for the production of several figures for us. The preparation of this book has been a memorable period of fruitful and enjoyable collaboration for us. 31 March 2009 Conny Aerts K.U.Leuven, Belgium Radboud University Nijmegen, the Netherlands Jørgen Christensen-Dalsgaard Aarhus University, Denmark Donald W. Kurtz University of Central Lancashire, United Kingdom

8 Contents 1 Introducing Asteroseismology Introduction The Music of the Spheres Seeing with Sound Can we Hear the Stars? Pressure Modes and Gravity Modes D Oscillations D Oscillations on a String D Oscillations in an Organ Pipe D Oscillations in a Drum Head D Oscillations in Stars Radial Modes Nonradial Modes The Effect of Rotation So how does Asteroseismology Work? p Modes and g Modes An Asteroseismic HR Diagram for p-mode Pulsators A Pulsation HR Diagram How do Stars Pulsate: The Relevant Time Scales Why do Stars Pulsate: Driving Mechanisms What Selects the Modes of Pulsation in Stars? Stellar Oscillations across the Hertzsprung-Russell Diagram Stellar Evolution in a Nutshell Variability Studies from Large-Scale Surveys Hipparcos Ground-Based Surveys Oscillations Near the Main Sequence Solar-Like Oscillations in Solar-Like Stars γ Dor Stars δ Sct Stars... 49

9 XII Contents SX Phe Stars Rapidly Oscillating Ap Stars Slowly Pulsating B Stars β Cep Stars Pulsating Be Stars Oscillations in Pre-Main-Sequence Stars Pulsations in Evolved Stars with M 9M RR Lyrae Stars Cepheids RV Tauri Stars Mira and Semi-Regular Variables Solar-Like Oscillations in Red Giants Pulsations in Evolved Stars with M 9M Periodically Variable B and A Supergiants Wolf-Rayet Stars The Role of Core g Modes in Supernova Explosions Compact Oscillators Variable Subdwarf B Stars White Dwarf Stars Neutron Stars Pulsations in Binaries Tidal Perturbations of Free Oscillations Tidally Induced Oscillations Are the SX Phe Stars all Blue Stragglers? Are all Dusty RV Tauri Stars Binaries? Hydrogen-Deficient Carbon Stars and Extreme HeliumStars Pulsating sdb Primaries Pulsating Cataclysmic Variables X-Ray Burst Oscillations Conclusions Theory of Stellar Oscillations General Hydrodynamics Equations of Hydrodynamics The Adiabatic Approximation Equilibrium States and Perturbation Analysis Simple Waves Equilibrium Stellar Structure Basic Properties of Stellar Evolution Microphysics of Stellar Interiors Standard Stellar Evolution Complications Equations of Linear Stellar Oscillations The Oscillation Equations...188

10 Contents XIII Linear, Adiabatic Oscillations The Dependence of the Frequencies on the Equilibrium Structure Asymptotic Theory of Stellar Oscillations The Cowling Approximation Trapping of p and g Modes Asymptotic Properties of Frequencies andeigenfunctions Computed Properties of Modes of Oscillation Results for the Present Sun The Classification of Modes Results for the Models with Convective Cores Variational Properties of Stellar Adiabatic Oscillations The Oscillation Equations as Linear Eigenvalue ProblemsinaHilbertSpace Effects on Frequencies of a Change in the Model Driving Mechanisms The Work Integral The Condition for Instability Effects of Convection on Stellar Stability Excitation of High-Order g Modes Stochastic Excitation of Oscillations Effects of Rotation A Simplified Description of the Effect of Rotation The Effect of Large-Scale Velocities on the Oscillation Frequencies The Effect of Pure Rotation Properties of Rotational Splitting Effects of Rotation on Low-Frequency Modes Higher-Order Rotational Effects Effect of Rotation on the Excitation of Oscillations Observational Techniques Duty Cycle Time Photometry Sources of Error in Photometry Differential Photometry High-Speed Photometry (Non-differential Photometry) Filters Spectroscopy Wavelength Stability and Low Frequency Noise inspectroscopy High-Resolution Spectroscopy and Line Profile Variations Requirements of Spectroscopy for Asteroseismology...322

11 XIV Contents Observational Line Diagnostics Increasing the Signal-to-Noise Ratio of the Line Profile Variations Increasing the Radial Velocity Precision in the Context of Exoplanet Finding and Solar-Like Oscillations Disentangling Spectra to Interpret the Oscillations ofdouble-linedbinaries Frequency Analysis Harmonic Analysis by Least Squares Searching for a Single Frequency Searching for Multiple Frequencies Non-parametric Frequency Analysis Methods String Length Methods Phase Dispersion Minimization Parametric Frequency Analysis Methods The Continuous Fourier Transform of an Infinite TimeSeries The Continuous Fourier Transform of a Finite TimeSeries Real Life: The Discrete Fourier Transform The Classical Periodogram The Lomb-Scargle Periodogram Significance Criteria Error Estimation of the Derived Frequencies Data without Alias Problems Data suffering from Aliasing The use of Weights in Merging different Data Sets forfrequencyanalysis Damped Oscillations Eliminating Aliases Conclusions Mode Identification Mode Identification from Multicolour Photometry General Considerations Detailed Description Mode Identification Schemes Mode Identification from High-Resolution Spectroscopy Calculation of Theoretical Line-Profile Variations Line Profile Fitting The Moment Method The Pixel-by-Pixel Method Mode Identification from Combined Photometry andspectroscopy...440

12 Contents XV 6.4 Towards Mode Identification from Combined Interferometry andspectroscopy? Towards Mode Identification from Eclipse Mapping? Applications of Asteroseismology Helioseismology Introduction Analysis of Solar-Oscillation Observations Observational Results on Solar Oscillations Properties of Solar Oscillations Principles of Inverse Analysis Inversion for Solar Structure Results on Solar Structure Results for Solar Rotation Temporal Variations of the Solar Interior Solar-Like Pulsators Observational Aspects Asteroseismic Diagnostics The Binary α Centauri A and B The Subgiant η Bootis The Red Giant ε Ophiuchi Heat Driven Main Sequence Stars The β Cep Star V836 Centauri The β Cep Star ν Eridani The β Cep Binary θ Ophiuchi HR 1217 among the roap Stars Compact Pulsators The GW Vir Star PG , GW Vir itself The DB White Dwarf GD 358, V777 Her The Subdwarf B Star PG The Subdwarf B Eclipsing Binary PG , NYVir The Future Space Missions CoRoT The Kepler Mission BRITE PLATO Solar Missions Ground-Based Networks and Antarctica SONG: A Ground-Based Radial Velocity Network Antarctic Asteroseismology A Summary of the Different Classes of Stellar Pulsators...679

13 XVI Contents B C Properties of Legendre Functions and Spherical Harmonics B.1 Properties of Legendre Functions B.2 Properties of Spherical Harmonics Mathematical Preliminaries C.1 Formulation of Oscillation Equations in Complex Form C.2 Vector Operators in Spherical Polar Coordinates D Adiabatic Oscillations in an Isothermal Atmosphere D.1 Equilibrium Structure D.2 Oscillation Properties D.3 Boundary Conditions in a Stellar Atmosphere E Asymptotic Theory of Stellar Oscillations E.1 A General Asymptotic Expression E.2 JWKB Analysis E.3 The Duvall Law for p-mode Frequencies E.3.1 Frequencies in Polytropic Envelopes E.3.2 Frequencies of Low-Degree Modes E.4 Asymptotic Properties of Eigenfunctions E.4.1 Asymptotic Properties of the p-mode Eigenfunctions E.4.2 Asymptotic Properties of the g-mode Eigenfunctions Bibliography Subject Index Object Index Acronym Definition Index...865