The Pulsations of the Sun and the Stars

348 Pages·2011·13.633 MB·English

by  Alexander G. Kosovichev (auth.), Jean-Pierre Rozelot, Coralie Neiner (eds.)

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Jean-Pierre Rozelot Coralie Neiner
•
Editors
The Pulsations of the Sun
and the Stars
123
Editors
Dr. Jean-Pierre Rozelot Coralie Neiner
Dept.LAGRANGE Observatoire de Meudon GEPI
Observatoire de laCoted’Azur BâtimentCopernicA,PlaceJulesJanssen5
av.Copernic 92195Meudon,Cedex
06130Grasse France
France e-mail: [email protected]
e-mail: [email protected]
ISSN 0075-8450 e-ISSN1616-6361
ISBN 978-3-642-19927-1 e-ISBN978-3-642-19928-8
DOI 10.1007/978-3-642-19928-8
SpringerHeidelbergDordrechtLondonNewYork
(cid:2)Springer-VerlagBerlinHeidelberg2011
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Preface
The focus of this book is placed on the physics of pulsations and brings together
the knowledge from the Sun and the stars, with a particular emphasis on recent
observations and modelling, and on the influence of pulsations of other physical
processes.
Oscillations of the Sun have been widely used in the past to understand its
interior structure. The extension ofsimilar studies tomore distant stars has raised
many difficulties despite the strong efforts of the international community over
thepastdecades.However,wearecurrentlywitnessingacompleterenewalofthe
methods and models in the field of pulsations of stars due to a large extent to the
launchesoftheMOSTandCoRoTsatellitesin2003and2006respectively,which
have brought results of unprecedented precision on the pulsations of stars of all
types. In particular, pulsations make it possible to derive the internal structure of
thestars,whichstillremainsamajorscientificenigma.Inthiscontextandwiththe
first CoRoT results in hand, it seemed interesting to confront the experience of
solar astronomers with that of stellar ones. Transposing the results obtained from
heliosismologytoasterosismologyhasalreadybeenveryprofitable.Nodoubtthat
the Kepler satellite, launched in 2009, and future space missions for asteroseis-
mology will allow us to go even further in the study of pulsations and the mod-
elling of the internal structure of the various stars.
The General Overlook of this Book is as Follows:
A general up-to-date stand-alone introduction on helioseismology is proposed by
A.Kosovichev,followedbytwosections,onedevotedtotheSunandtheotherto
the stars, linked by a transition chapter from heliosismology to asterosismology
written by S. Vauclair.
The first section of the book on the Sun is divided into four chapters.
TheSunistheonlysolar-typestarwherethedynamicsandthemagnetismcan
bestudiedindetailandthephysicalprocessinvolvedisrelativelywellunderstood,
in particular those which occur at very small scales. This chapter albeit restricted
to the quiet solar photosphere describes the properties of the three cellular scales
v
vi Preface
of motions observed at the solar surface: granulation, mesogranulation and su-
pergranulation. The intranet work field, not yet clarified, is also tackled and the
questions are posed in a new way.
Thesecondchapterfocusesonvariationsofsolaractivitywhicharearesultofa
complex dynamo process in the convection zone. Despite the known general
properties ofthe solar cycles,a reliable forecast ofthe 11 year sunspot number is
still a problem. However, new methods that take into account the dynamics of
turbulent magnetic helicity are capable of providing a forecast of the system, and
its application permits a good prediction of the sunspot number.
Thethirdpartfocusesonsolargravitymodes,whicharemainlytrappedinside
the radiative region and consequently are able to provide information on the
properties of the solar core. Such a topic is of high interest today as we are
wonderingifthecoremayrotateatahigherratethantheouterenvelope.However,
the detection of solar gravity modes still remains a major challenge. The issue
discussed here is important since a theoretical determination of mode amplitudes
may help to design the track for gravity modes.
Thelastchapterofthissectiondealswiththerotation,andmorepreciselywith
thedifferentialrotationoftheSunandstars.Theeffectsontheoutershapeandto
firstorder,andthoseconcerningtheapparentoblatenessaretackled.Thankstothe
adventofinterferometrytechniques,thestellarshapescannowbemeasuredwitha
greataccuracy.Itisshownthatthecoredensityandthegravitationalmomentscan
be reached.
Then, the recent developments from helioseismology to asteroseismology are
presented.Thegeneralbasisforasteroseismology,theso-calledasymptotictheory
ofstellaroscillationsisdiscussed.Solar-typestarsarediscussedandexamplesfor
which it was possible to derive precise stellar parameters from seismology are
presented,focusingontheheliumabundance.Thepotentialityofasteroseismology
for a better knowledge of stellar structure and evolution is huge, and many new
results are expected in the near future.
The next section, consisting in five chapters, deals with stellar pulsations.
First, the requirements for a self-consistent interpretation of a collection of
observables related to rapidly rotating stars are explored. If the star is otherwise
static,rapidrotationthroughthecentrifugalforcewillaffecttheforcebalanceand
hencethestructureofthestar.Rotationalsochangesthesurfacefromasphericaltoa
spheroidal,andpossiblyinsomecasesanellipsoidal,shape.Suchchangeshavebeen
observedevenfortheSun,andtheconfrontationofthetheoriesareofimportance.
In the next chapter, the effects of stellar rotation on adiabatic oscillation fre-
quencies of massive stars are presented, together with methods to evaluate them
and some of the main results for four specific stars are shown.
The following chapter deals with the extension of the asymptotic theory of
stellar oscillations beyond the case of a non-rotating, non-magnetic spherically
symmetric star. A recent application to the high-frequency acoustic modes of
rapidly rotating stars is presented.
Then, the complete interaction between low-frequency internal gravity waves
and differential rotation in stably strongly stratified stellar radiation zones is
Preface vii
examined. This includes the modification of the structure of waves and of the
angular velocity.
Thelastchapterisdevotedtoexcitationofsolar-likeoscillationsthathavebeen
detected for more than 10 years. The computed mode excitation rates crucially
depend not only on the way turbulent convection is described but also on the
stratification and the metal abundance of the upper layers of the star. In turn it is
shownhowtheseismicmeasurementscollectedsofarallowustoinferproperties
of turbulent convection in stars.
Theaudiencetargetedbythisbookconsistsofresearchers,PhDstudents,post-
docs, and all scientists seeking a complementary culture or scientists evolving
toward new research topics.
This book is based on tutorials and discussions on the same topic held at a
CNRS school in Saint-Flour (France) in 2008, which has allowed us to give a
progressreportontheverylastsolardevelopments(structureofthesolarcorefor
example)andstellardevelopments(CoRoTresults,newstellarmodels)forabetter
understandingofstellarpulsationsandinternalstructureingeneral.Letusremind
thatafirstbooktitled‘‘TherotationoftheSunandStars’’(LNP765)resultedfrom
apreviousCNRSschoolheldinObernai(France)in2007.Wehopethatthisnew
book the ‘‘Pulsations of the Sun and Stars’’ willprovidean interestingsequell for
the reader.
The editors sincerely thank the authors for the great quality of their contribu-
tionspublishedhere.Theyhopethatthisnewbookwillhelptoabetterknowledge
of the wonderful world which surrounds us.
December 2010 J. P. Rozelot
C. Neiner
Contents
Part I General Overview
1 Advances in Global and Local Helioseismology:
An Introductory Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Brief History of Helioseismology. . . . . . . . . . . . . . . . . . . . 5
1.3 Basic Properties of Solar Oscillations . . . . . . . . . . . . . . . . . 11
1.3.1 Oscillation Power Spectrum. . . . . . . . . . . . . . . . . 11
1.3.2 Excitation by Turbulent Convection . . . . . . . . . . . 13
1.3.3 Line Asymmetry and Pseudo-modes . . . . . . . . . . . 14
1.3.4 Magnetic Effects: Sunspot Oscillations
and Acoustic Halos. . . . . . . . . . . . . . . . . . . . . . . 17
1.3.5 Impulsive Excitation: Sunquakes. . . . . . . . . . . . . . 20
1.4 Global Helioseismology. . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.2 JWKB Solution. . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.4.3 Dispersion Relations for p- and g-modes. . . . . . . . 31
1.4.4 Frequencies of p- and g-modes. . . . . . . . . . . . . . . 32
1.4.5 Asymptotic Ray-path Approximation. . . . . . . . . . . 34
1.4.6 Duvall’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.4.7 Asymptotic Sound–Speed Inversion. . . . . . . . . . . . 37
1.4.8 Surface Gravity Waves (f-mode). . . . . . . . . . . . . . 41
1.4.9 The Seismic Radius. . . . . . . . . . . . . . . . . . . . . . . 42
1.5 General Helioseismic Inverse Problem . . . . . . . . . . . . . . . . 44
1.5.1 Variational Principle . . . . . . . . . . . . . . . . . . . . . . 45
1.5.2 Perturbation Theory. . . . . . . . . . . . . . . . . . . . . . . 45
1.5.3 Kernel Transformations. . . . . . . . . . . . . . . . . . . . 46
1.5.4 Solution of Inverse Problem. . . . . . . . . . . . . . . . . 48
1.5.5 Optimally Localized Averages Method . . . . . . . . . 49
1.5.6 Inversion Results for Solar Structure. . . . . . . . . . . 50
ix
x Contents
1.5.7 Regularized Least-Squares Method . . . . . . . . . . . . 53
1.5.8 Inversions for Solar Rotation . . . . . . . . . . . . . . . . 54
1.5.9 Results for Solar Rotation . . . . . . . . . . . . . . . . . . 55
1.6 Local-area Helioseismology. . . . . . . . . . . . . . . . . . . . . . . . 58
1.6.1 Basic Principles . . . . . . . . . . . . . . . . . . . . . . . . . 58
1.6.2 Ring-diagram Analysis . . . . . . . . . . . . . . . . . . . . 58
1.6.3 Time–Distance Helioseismology
(Solar Tomography) . . . . . . . . . . . . . . . . . . . . . . 60
1.6.4 Acoustic Holography and Imaging . . . . . . . . . . . . 60
1.7 Solar Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
1.7.1 Time–distance Diagram. . . . . . . . . . . . . . . . . . . . 64
1.7.2 Wave Travel Times. . . . . . . . . . . . . . . . . . . . . . . 64
1.7.3 Deep- and Surface-Focus Measurement
Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1.7.4 Sensitivity Kernels: Ray-path Approximation. . . . . 67
1.7.5 Born Approximation . . . . . . . . . . . . . . . . . . . . . . 70
1.8 Inversion Results of Solar Acoustic Tomography . . . . . . . . . 71
1.8.1 Diagnostics of Supergranulation . . . . . . . . . . . . . . 72
1.8.2 Structure and Dynamics of Sunspot. . . . . . . . . . . . 72
1.8.3 Large-Scale and Meridional Flows . . . . . . . . . . . . 74
1.9 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 75
1.9.1 Global Helioseismology: Diagnostics of Global
Changes Inside the Sun. . . . . . . . . . . . . . . . . . . . 79
1.9.2 Local-Area Helioseismology: 3D Imaging of the
Solar Interior . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Part II Section 1: The Sun as a Star
2 The Quiet Solar Photosphere: Dynamics and Magnetism. . . . . . . 87
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
2.2 Solar Surface Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
2.2.1 The Solar Granulation. . . . . . . . . . . . . . . . . . . . . 88
2.2.2 The Solar Mesogranulation. . . . . . . . . . . . . . . . . . 90
2.2.3 The Solar Supergranulation . . . . . . . . . . . . . . . . . 91
2.2.4 The Power Spectrum of Photospheric Flows. . . . . . 93
2.2.5 Numerical Simulation of the Solar Convection;
Origin of the Granulation. . . . . . . . . . . . . . . . . . . 93
2.2.6 Origin of the Solar Mesogranulation . . . . . . . . . . . 96
2.2.7 Origin of the Solar Supergranulation. . . . . . . . . . . 98
2.3 Magnetic Field in the Quiet Photosphere. . . . . . . . . . . . . . . 99
2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
2.3.2 The Photospheric Network. . . . . . . . . . . . . . . . . . 101
Contents xi
2.3.3 Observation of the Photospheric Network
in the G-Band at 4,305 Å. . . . . . . . . . . . . . . . . . . 105
2.3.4 Intranetwork Magnetic Field. . . . . . . . . . . . . . . . . 106
2.3.5 Horizontal Component of the Intranetwork
Magnetic Field and Granular Magnetic Field . . . . . 108
2.3.6 Physical Properties of the Intranetwork Magnetic
Field and Comparison with the Properties of the
Network Field . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.3.7 Hidden Turbulent Flux . . . . . . . . . . . . . . . . . . . . 111
2.3.8 Numerical Simulations of Small-Scale
Magneto-Convection. . . . . . . . . . . . . . . . . . . . . . 111
2.3.9 Small-Scale Dynamo: A Possible Origin of the
Small-Scale Magnetic Field . . . . . . . . . . . . . . . . . 114
2.3.10 Origin of the Photospheric Network . . . . . . . . . . . 115
2.3.11 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3 Modeling and Prediction of Solar Cycles Using Data
Assimilation Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.2 Formulation of the Dynamo Models . . . . . . . . . . . . . . . . . . 122
3.2.1 Parker’s Migratory Dynamo. . . . . . . . . . . . . . . . . 122
3.2.2 The Kleeorin–Ruzmaikin Model. . . . . . . . . . . . . . 123
3.2.3 Periodic and Chaotic Solutions. . . . . . . . . . . . . . . 126
3.3 Data Assimilation Methods . . . . . . . . . . . . . . . . . . . . . . . . 129
3.3.1 Basic Formulation. . . . . . . . . . . . . . . . . . . . . . . . 129
3.3.2 Implementation of the Data Assimilation
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3.4 Reproducing and Predicting Observational Data by
the Ensemble Kalman Filter. . . . . . . . . . . . . . . . . . . . . . . . 131
3.4.1 Application Data Assimilation to Early
Sunspot Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
3.4.2 Prediction of the Last Solar Cycles. . . . . . . . . . . . 133
3.5 Discussion and Conclusions. . . . . . . . . . . . . . . . . . . . . . . . 135
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4 Amplitudes of Solar Gravity Modes . . . . . . . . . . . . . . . . . . . . . . 139
4.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.2 Basic Properties of Solar Gravity Modes. . . . . . . . . . . . . . . 140
4.2.1 Dispersion Relation of Gravito-Acoustic Modes . . . 140
4.2.2 Some g Mode Properties Near the Sun Surface . . . 142
4.3 Energetic of Gravity Modes: Driving and
Damping Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.3.1 Principle: Forced and Damped Oscillator. . . . . . . . 144