Table Of ContentINTERNATIONAL SERIES OF MONOGRAPHS
ON PHYSICS
SERIES EDITORS
J. BIRMAN CITY UNIVERSITY OF NEW YORK
S. F. EDWARDS UNIVERSITY OF CAMBRIDGE
R. FRIEND UNIVERSITY OF CAMBRIDGE
M. REES UNIVERSITY OF CAMBRIDGE
D. SHERRINGTON UNIVERSITY OF OXFORD
G. VENEZIANO CERN, GENEVA
International Series of Monographs on Physics
154.L.Mestel:Stellarmagnetism,Secondedition
153.R.A.Klemm:Layeredsuperconductors,Volume1
152.E.L.Wolf:Principlesofelectrontunnelingspectroscopy,Secondedition
151.R.Blinc:Advancedferroelectricity
150.L.Berthier,G.Biroli,J.-P.Bouchaud,W.vanSaarloos,L.Cipelletti:Dynamicalheterogeneitiesin
glasses,colloids,andgranularmedia
149.J.Wesson:Tokamaks,Fourthedition
148.H.Asada,T.Futamase,P.Hogan:Equationsofmotioningeneralrelativity
147.A.Yaouanc,P.DalmasdeR´eotier:Muonspinrotation,relaxation,andresonance
146.B.McCoy:Advancedstatisticalmechanics
145.M.Bordag,G.L.Klimchitskaya,U.Mohideen,V.M.Mostepanenko:AdvancesintheCasimireffect
144.T.R.Field:Electromagneticscatteringfromrandommedia
143.W.G¨otze:Complexdynamicsofglass-formingliquids–amode-couplingtheory
142.V.M.Agranovich:Excitationsinorganicsolids
141.W.T.Grandy:Entropyandthetimeevolutionofmacroscopicsystems
140.M.Alcubierre:Introductionto3+1numericalrelativity
139.A.L.Ivanov,S.G.Tikhodeev:Problemsofcondensedmatterphysics–quantumcoherence
phenomenainelectron-holeandcoupledmatter-lightsystems
138.I.M.Vardavas,F.W.Taylor:Radiationandclimate
137.A.F.Borghesani: Ionsandelectronsinliquidhelium
136.C.Kiefer:Quantumgravity,Secondedition
135.V.Fortov,I.Iakubov,A.Khrapak:Physicsofstronglycoupledplasma
134.G.Fredrickson:Theequilibriumtheoryofinhomogeneouspolymers
133.H.Suhl:Relaxationprocessesinmicromagnetics
132.J.Terning:Modernsupersymmetry
131.M.Marin˜o:Chern-Simonstheory,matrixmodels,andtopologicalstrings
130.V.Gantmakher:Electronsanddisorderinsolids
129.W.Barford:Electronicandopticalpropertiesofconjugatedpolymers
128.R.E.Raab,O.L.deLange:Multipoletheoryinelectromagnetism
127.A.Larkin,A.Varlamov:Theoryoffluctuationsinsuperconductors
126.P.Goldbart,N.Goldenfeld,D.Sherrington:Stealingthegold
125.S.Atzeni,J.Meyer-ter-Vehn:Thephysicsofinertialfusion
123.T.Fujimoto:Plasmaspectroscopy
122.K.Fujikawa,H.Suzuki:Pathintegralsandquantumanomalies
121.T.Giamarchi:Quantumphysicsinonedimension
120.M.Warner,E.Terentjev:Liquidcrystalelastomers
119.L.Jacak,P.Sitko,K.Wieczorek,A.Wojs:QuantumHallsystems
117.G.Volovik:TheUniverseinaheliumdroplet
116.L.Pitaevskii,S.Stringari:Bose-Einsteincondensation
115.G.Dissertori,I.G.Knowles,M.Schmelling:Quantumchromodynamics
114.B.DeWitt:Theglobalapproachtoquantumfieldtheory
113.J.Zinn-Justin:Quantumfieldtheoryandcriticalphenomena,Fourthedition
112.R.M.Mazo:Brownianmotion–fluctuations,dynamics,andapplications
111.H.Nishimori:Statisticalphysicsofspinglassesandinformationprocessing–anintroduction
110.N.B.Kopnin:Theoryofnonequilibriumsuperconductivity
109.A.Aharoni:Introductiontothetheoryofferromagnetism,Secondedition
108.R.Dobbs:Heliumthree
107.R.Wigmans:Calorimetry
106.J.Ku¨bler:Theoryofitinerantelectronmagnetism
105.Y.Kuramoto,Y.Kitaoka:Dynamicsofheavyelectrons
104.D.Bardin,G.Passarino:TheStandardModelinthemaking
103.G.C.Branco,L.Lavoura,J.P.Silva:CPViolation
102.T.C.Choy: Effectivemediumtheory
101.H.Araki:Mathematicaltheoryofquantumfields
100.L.M.Pismen:Vorticesinnonlinearfields
98.K.H.Bennemann:Nonlinearopticsinmetals
94.S.Chikazumi:Physicsofferromagnetism
91.R.A.Bertlmann:Anomaliesinquantumfieldtheory
90.P.K.Gosh:Iontraps
87.P.S.Joshi:Globalaspectsingravitationandcosmology
86.E.R.Pike,S.Sarkar:Thequantumtheoryofradiation
83.P.G.deGennes,J.Prost:Thephysicsofliquidcrystals
73.M.Doi,S.F.Edwards:Thetheoryofpolymerdynamics
69.S.Chandrasekhar:Themathematicaltheoryofblackholes
51.C.Møller:Thetheoryofrelativity
46.H.E.Stanley:Introductiontophasetransitionsandcriticalphenomena
32.A.Abragam:Principlesofnuclearmagnetism
27.P.A.M.Dirac:Principlesofquantummechanics
23.R.E.Peierls:Quantumtheoryofsolids
Stellar Magnetism
Second Edition
Leon Mestel
Emeritus Professor of Astronomy
University of Sussex
3
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In Memoriam
SOLOMON MESTEL 1886 – 1966
RACHEL MESTEL (n´ee BRODETSKY) 1891 – 1974
‘IT IS NOT THY DUTY TO COMPLETE THE LABOUR,
BUT NEITHER ART THOU FREE TO DESIST THEREFROM’
Ethics of the Fathers, II, 21.
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Preface
The response to the 1999 publication of Stellar Magnetism was gratifying. However,
alreadywhenpreparingtheverylimitedmodificationsallowedforthe2003paperback
version,Icouldseethattheadvancesbeingmadeinbothobservationalandtheoretical
work pointed towards the need for an updated version within a decade or so.
The book is designed so as to be self-contained, with the early chapters presenting
the basic physics and mathematics underlying cosmical magnetohydrodynamics,
followed by studies of the specific applications appropriate for a book devoted to
a central area in astrophysics.
There are some modest changes in Chapters 4, ‘Magnetism and convection’;
5, ‘Magnetic fields in stellar interiors’; and 11, ‘Magnetism and star formation
I’. The main changes are in Chapters 6, ‘Dynamo processes in stars’; 7, ‘Stellar
winds: magnetic braking’; 8, ‘Late-type stars’; 9, ‘The early-type magnetic stars’;
10, ‘Pre-main-sequence stars’; and 12, ‘Magnetism and star formation II’.
The now ‘classical’ twentieth-century work on dynamo theory in general and its
application to stars has yielded valuable qualitative and semi-quantitative under-
standing of both the kinematics and the dynamics of the most important active
processes. However, ongoing studies in mathematical depth—both analytical and
computational—also reveal the limitations of our knowledge. The solar dynamo,
manifested in particular by the sunspot cycle and the Maunder minimum, ‘continues
to pose a challenge to observers and theoreticians’. In particular, inferences from
‘helioseismological’ observations of the internal solar rotation have set exacting tasks
for the theorist. Our Sun has been taken as the prototype of the ‘late-type stars’;
but observations of rapidly rotating stars of solar mass show that the concept of the
‘solar–stellar connection’ must be applied with caution, as must extrapolation of our
developing picture of the Sun to stars of half a solar mass. The updated Chapters 6
and 8 present a detailed account of the advances made and the challenges awaiting
new generations of astrophysicists.
Whereas it appears that all late-type stars, with their extensive convective
envelopes, show spontaneous dynamo-built magnetic fields, only a minority of the
more massive ‘early-type’ main-sequence stars are observably magnetic. They are
well described by the phenomenological ‘oblique rotator’ model, with a quasi-steady,
‘fossil’magneticstructure‘frozen’intothehighlyconducting,non-turbulentenvelope.
The observed periodic variation in the magnetic field is due to the rotation with the
star of the magnetic field with its axis inclined to the rotation axis. The considerable
progress made towards the understanding of the theoretical problems set by this
model, complementary to those of the late-type stars, is presented in the updated
Chapter 9.
viii Preface
Chapter 7 contains new material, relevant to both late- and early-type main-
sequence stars, and also to stars that have evolved into the red-giant domain. There
is also some rearrangement, between chapters, of individual sections.
Concerning Chapters 10 and 12 ... In the words of a leading observer of pre-
main-sequence stars: ‘Normal stars show their highest degree of magnetic activity
in their pre-main-sequence period.’ The well-known strong interaction between
a magnetic field and rotating ionized gas—central to the studies in the earlier
chapters—manifests itself in the magneto-rotational instability and the magneto-
centrifugal wind that develop spontaneously in the ‘accretion disk’ surrounding the
contractingstar.Andintheearlierphasesofstarformationindensemolecularclouds,
increasingly sophisticated observational techniques point to ‘magneto-turbulence’ as
theappropriatescenarioinwhichtheorymayproduceaconvincingexplanationofthe
themassspectrumofproto-stars,andtheassociatedformationofplanetarysatellites.
The first edition of this book concluded with Chapters 13 and 14 on pulsar
electrodynamics. However, rather than making this second edition unduly long
and also further delaying its appearance, the updating of the special problems of
magnetized neutron stars is postponed for separate treatment.
Again, I acknowledge helpful interactions with colleagues over the years. Special
thanks go to Steve Balbus, Jonathan Braithwaite, Axel Brandenburg, Paul Bushby,
Nuria Calvet, Andrew Collier Cameron, Paul Charbonneau, Lee Hartmann, David
Hughes, Moira Jardine, John Landstreet, Mario Livio, Donald Lynden-Bell, Mike
McIntyre,ChrisMcKee,JimMcKenzie,JonathanMestel,MarkMiesch,DavidMoss,
Thomas Neukirch, Gordon Ogilvie, Isao Okamoto, Eve Ostriker, Eric Priest, Mike
Proctor, Frank Shu, Henk Spruit, Richard Sword, Jack Thomas, Mike Thompson,
Steve Tobias, Juri Toomre, Nigel Weiss, and Ellen Zweibel. It is also a pleasure to
acknowledge the help from the staff at Oxford University Press.
Cambridge
July 2011
Contents
Figure acknowledgements xvi
Abbreviations in Reference Lists xx
1 Introduction 1
1.1 Historical survey 1
1.2 Stellar magnetic fields 6
Bibliography 11
2 Theoretical basis 13
2.1 Maxwell’s equations and the magnetohydrodynamic approximation 13
2.2 Properties of cosmical plasmas 16
2.3 Macroscopic equations for a fully ionized gas: the two-fluid model 19
2.3.1 Equations to the flow of the whole gas 20
2.3.2 The generalized Ohm’s law 23
2.4 The energy equation of a fully ionized gas 27
2.5 Kinematic coupling 29
2.6 Dynamical coupling 33
2.7 The three-fluid model 37
2.8 ‘Anomalous’ resistivity 40
Bibliography 43
3 Applications 45
3.1 Magnetosonic waves 45
3.2 Magnetohydrodynamic shocks 47
3.3 Self-gravitating systems: the virial theorems 52
3.4 Magnetostatic equilibrium: force-free fields 58
3.5 Magnetic helicity 65
3.6 Stability 69
3.6.1 The MHD energy principle 69
3.6.2 Illustrative examples 71
3.6.3 The pinched cylindrical discharge 74
3.6.4 The Kelvin–Helmholtz instability 79
3.6.5 Stability of rotating systems 82
3.7 Effects of dissipation: reconnection 84
3.7.1 Reconnection in a medium at rest 85
3.7.2 The Sweet–Parker model 88
3.7.3 Fast reconnection 91
3.7.4 Hall reconnection 95
3.8 Macroscopic dissipation 97
Appendix: Poloidal and toroidal fields 99
Bibliography 100
