P.Ulmschneider E.R.PriestR.Rosner (Eds.)

Mechanisms ofChromo spheric andCoronal HeatingProceedings of the International Conference,Heidelberg, 5-8 June 1990

With 260 Figures

Springer-VerlagBerlin Heidelberg New YorkLondon Paris TokyoHong Kong Barcelona

Professor Dr. Peter UlmschneiderInstitut fur Theoretische Astrophysik, 1m Neuenheimer Feld 561,D-6900 Heidelberg, Fed. Rep. of Germany

Professor Dr. Eric R. PriestUniversity of St. Andrews, The Mathematical Institute North Haugh,St. Andrews KY16 9SS, Great Britain

Professor Dr. Robert RosnerE.Fermi Institute and Dept. of Astronomy and Astrophysics, 5640 S Ellis Ave.,Chicago, IL 60637, USA

COVf!r picture: In this scenario by Chitre and Davila (see the article on p.402 of this book)acoustic waves shake coronal magnetic loops and get resonantly absorbed in the loop.

ISBN 3-540-53436-9 Springer-Verlag Berlin Heidelberg New YorkISBN 0-387-53436-9 Springer-Verlag New York Berlin Heidelberg

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Preface

The plans for the Heidelberg Conference Mechanisms of Chromospheric and Coro-nal Heating, held from June 5 to 8, 1990, materialized during several discussionsbetween Eric Priest, Robert Rosner, Peter Ulmschneider, and later Jeff Linsky atmeetings in Titisee and Tenerife in 1987 and 1988, in which we all realized that,despite the extensive work in the field, our understanding of the physics of stellarchromospheres and coronae, the sources of stellar radio, UV and X-ray emission,and stellar winds remains in a dismal state.

The principal reason for this is that the fundamental physical process - themechanical heating mechanism, which is the cause of these important stellar layers- is still largely unknown, 50 years after W. Grotrian and B. Edlen discovered thatthe solar corona is hot by identifying the source of the 6374A line as FeX, and 45years after L. Biermann proposed the first coronal heating theory. We appreciated thatthe identification of the heating mechanism is a formidable observational problembecause it involves very small spatial scales, possibly down to (for current sheets)thicknesses in the meter range, and far beyond even the most sophisticated presentinstrumentation.

This observational difficulty is complemented by severe problems on the theo-retical side. The many very complicated heating theories, most of which derive fromterrestrial plasma and MHD applications, cannot be adequately simulated at presenteven with the most advanced supercomputers. Moreover, it is not well understoodwhether these (primarily) fusion-physics-related applications are in fact suitable forstellar environments. Yet worse, there has been an apparent lack of contact betweenthe many researchers in the field of stellar atmospheric heating, who often labouredexclusively on their own favoured heating mechanism and disregarded the work oftheir colleagues or of the observers. (This sort of behaviour is of course not onlycharacteristic of stellar astronomers!)

These realizations led to the idea of organizing a meeting devoted entirely to thetopic of atmospheric heating, where for the first time a comprehensive inventory ofour knowledge of heating mechanisms could be made, and where disparate workerscould learn about the wide scope of the field and about the new observations. Thepresent book is the result of this effort. We leave it to the reader to judge how well wehave succeeded. But even if this book fails our expectations, it nevertheless revealsthe exciting new plans to use large-scale numerical simulations and fascinating newinstrumentation to attack the formidable heating problem.

Our most sincere thanks go to the other members of the Scientific OrganizingCommittee, to Lawrence Cram, Joe Hollweg, Jeff Linsky, Dan Spicer, Giuseppe

v

Vaiana, Yuzef Zhugzhda, and Cornelis Zwaan for help in the selection of the speak-ers. We also very warmly thank the Local Organizing Committee for the smoothorganization, particularly Bodo and Elke Baschek, Hans-Peter Gail, Darren Kelly,Peter Korevaar, Helgard and Katharina Ulmschneider, and Rainer Wehrse. The sup-port by the Max-Planck-Institut through Hans Elsasser, which offered to house theconference, is gratefully acknowledged. These thanks also extend to the Institut fiirTheoretische Astrophysik, where Werner Tscharnuter gave us all the support weneeded. We are especially grateful to the Deutsche Forschungsgemeinschaft, to theState of Baden-Wtirttemberg, and particularly to Dr. Theodor Mayer, Firma Bessey,for generous provision of funds.

Heidelberg,Decem ber 1990

Peter Ulmschneider, Eric Priest, Robert Rosner

VI

Contents

Introduction .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1

Chapter 1: Solar Observations

1.1 Observations of OscillationsObservations of Waves and OscillationsBy F.-L. Deubner (With 2 Figures) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6

Observations of Waves and Oscillationsin Solar Magnetic Fluxtube ConcentrationsBy B. Fleck and F.-L. Deubner (With 1 Figure) . . . . . . . . . . . . . . . . . . . . . . .. 19

The Generation of Long Period Acoustic Waves by Solar Global OscillationsBy B. Fleck and F. Schmitz (With 1 Figure) . . . . . . . . . . . . . . . . . . . . . . . . . .. 22

Measurements of I-Hz Coronal Oscillations at Total Eclipsesand Their Implications for Coronal HeatingBy 1. M. Pasachoff .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25

Short-Term Oscillations in Green and Red Coronal LinesBy V. Rusin and M. Minarovjech (With 1 Figure) 30

Height-Dependent Short-Period Oscillations in the Fe XIV (530.3 nm)Solar Corona Above a Sunspot Group Crossing the LimbBy V.N. Dermendjiev (With 2 Figures) . . . . . . . . . . . . . . . . . .. 33

1.2 Photospheric Dynamics and HeatingOn the Dynamics of Granulation in Active Regions and the Heating ProblemBy A. Nesis, A. Hanslmeier, R. Hammer, R. Komm, and W. Mattig(With 2 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36

Generation of Electric Currents and Waves on Magnetic Flux Tubesby Horizontal Velocities in the PhotosphereBy T.D. Tarbell, G.L. Slater, Z.A. Frank, R.A. Shine, and K.P. Topka(With 1 Figure) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39

On the Magnetic Field Activity in Solar Active RegionsBy 1. Linke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42

VII

1.3 Chromospheric Observations and HeatingThe Bright Points in the Can K-Line and Their Relationto the Inner Network Magnetic StructuresBy K.R. Sivaraman (With 1 Figure) 44K2V Cell Grains and Chromospheric HeatingBy RiJ, Rutten and H. Uitenbroek (With 1 Figure) 48

Wave Heating in Chromospheric Bright PointsBy W. Kalkofen 54

Do We Really Know What the Actual Chromospheric HeatingRequirements Are?By 1. Trujillo Bueno (With 1 Figure) 60The Effects of Electron Scattering on the Si II 1816 Linein the Solar ChromosphereBy K.E. Rangarajan and D.M. Rao (With 1 Figure) 63SIMURIS: a High Resolution Solar Physics Interferometric Missionin Answer to the Chromospheric and Coronal Heating ProblemBy L. Dame (With 2 Figures) 66

The Solar Ultraviolet Network (SUN)By L. Dame (With 3 Figures) 73

1.4 Chromosphere-Transition Layer Observations and ModellingHRTS Time Series Observations: Chromospheric and Coronal HeatingBy Ci-C. Cheng (With 5 Figures) , 77

High Spatial Resolution Observations of the Solar Transition Region:Spicules and MicroftaresBy 1. W. Cook (With 6 Figures) , 83

New Models of the Chromosphere and Transition RegionBy E. H. Avrett (With 2 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 97

The Role of Particle Diffusion in the Lower Transition Region:Revised Interpretation of Emission MeasuresBy E.H. Avrett and 1. M. Fontenla (With 2 Figures) 100Why Heating is Not Necessary in the Transition Regionor Upper ChromosphereBy P. S. Cally (With 3 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 103Height-Dependent Solar Plage Temperature DistributionBy A. Kucera, Z. Scherbakova, and E. Baranovsky (With 3 Figures) 109On the Temperature Inhomogeneity of the Lower Solar CoronaBy K.I. Nikolskaya . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. 113

1.5 Coronal and Solar Wind Observations and ModellingVery High Resolution Solar X-ray ImagingBy L. Golub (With 6 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 115

VIII

Spectra of MHD Turbulence in Coronal Active RegionsBy D. Gomez, P. Martens, M. Herant, F. Pardo, and L. Golub(With 3 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 124

Observations of Coronal Bright Points and Implicationsfor Coronal Heating MechanismsBy S.R. Habbal (With 3 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 127

Modelling Coronal Active Region Emission PatternsBy S.P. Brown and CiL, Durrant (With 1Figure) 132

The Fe Ionization Equilibrium in the Solar CoronaWith a Non-Maxwellian Distribution FunctionBy E. Dzifcakova (With 3 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 135

Energetics of Solar Coronal HolesBy Y.-Q. Lou ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 137

Coronal Radio EmissionBy A. O. Benz (With 7 Figures) 140

Implications of Microwaves for Heating and Particle Acceleration on the SunBy A. Kruger, J. Hildebrandt, and S. Urpo ..... . . . . . . . . . . . . . . . . . . . . .. 150

Properties of Impulsive Events in a Polar Coronal HoleBy S. Koutchmy and M.L. Loud! (With 6 Figures) 152

Explosive Instability in Solar Coronal LoopsBy M. Ryutova 159

Signatures of Coronal Structures and Turbulence in the Solar WindBy E. Marsch (With 1 Figure) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 162

Chapter 2: Stellar Observations

2.1 Chromospheric and Coronal Observations, UVWhat Can Solar and Stellar Ultraviolet Observations TellAbout Chromospheric and Coronal Heating Mechanisms?By J.L. Linsky (With 1 Figure) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 166

He I 5876 A Line As an Indicator of Chromospheric Heatingin Young F-Type MS StarsBy R.I. Garda Lopez, R. Rebolo, J. E. Beckman, and C.D. McKeith(With 1 Figure) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 179

Chromospheric Modelling of Active Regions on AU MicBy E.R. Houdebine (With 2 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 182

2.2 Chromospheres of Cool Giant Stars, InfraredNew Clues to Atmospheric Heating Processes in Luminous Cool StarsBy A.K. Dupree (With 7 Figures) . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. 185

IX

Chromospheres of Cool Non-Mira Giant StarsBy H.R. lohnson, U.G. Jorgensen. and D. G. Luttermoser(With 2 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 200

What Can Observations of Giants and Supergiant Stars Tell UsAbout Chromospheric and Coronal Heating?By M. Cuntz and R.E. Stencel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 206

Chromo spheric Activity in Late-Type Giants and Supergiants:Constraints on Heating TheoriesBy L. Pasquini, E. Brocato, and R. Pallavicini (With 1 Figure) 222

Coronal Heating and the Dividing LineBy B. Haisch (With 2 Figures) 225

An Infrared Perspective on ChromospheresBy T.R. Ayres (With 3 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 228

2.3 Activity and Magnetic FieldsMagnetic Activity Across the Hertzsprung-Russell DiagramBy C. Zwaan (With 8 Figures) 241

Relations Between Activity and Magnetic FieldsBy C.l. Schrijver (With 6 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 257

Recent Measurements of Stellar Magnetic FieldsBy S. Saar (With 3 Figures) 273

Chromo spheric/Coronal Emission Correlations in 'Quiescent'and Eruptive Phenomena in M-Dwarf StarsBy M. Mathioudakis and l. G. Doyle (With 1 Figure) 279

Global Electrodynamic Coupling in Stellar AtmospheresBy L. Cram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 282

2.4 Coronal Heating Constraints, X-rays, Hot Stars, Accretion DisksImplications for Coronal Heating Theories from Stellar X-ray ObservationsBy R. Rosner (With 5 Figures) 287

Empirical Constraints on Coronal Heating ProcessesBy C. Jordan (With 5 Figures) 300

Minimum Coronal Energy Requirements:Constraints for Heating MechanismsBy R. Hammer (With 2 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 316

Sun-Hot Star Contrast in Chromospheric/Coronal Te(r).Nonradiative Heating vs. Outflow Enhanced OpacityBy V. Doazan and R. N. Thomas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 319

Formation of Chromospheres and Coronae of Accretion Disksby Viscous DissipationBy R. Wehrse, H. Storzer, and G. Shaviv (With 2 Figures) 324

x

Chapter 3: Wave Heating Mechanisms

3.1 Acoustic Waves, PulsationsAcoustic HeatingBy P. Ulmschneider (With 9 Figures) 328

On the Intrinsic Difficulty of Producing Stellar Coronae With Acoustic WavesBy R. Hammer and P. Ulmschneider (With 1 Figure) . . . . . . . . . . . . . . . . .. 344

The Effect of Waves on Optically Thin Transition Region LinesBy V. Hansteen (With 2 Figures) 347

Heating of the Solar Atmosphere by SpiculesBy Q. Q. Cheng, P. Ulmschneider, and P. Korevaar (With 4 Figures) 350

Nonlinear Pulse Propagation in a Stratified AtmosphereBy G. Bodo, W. Kalkofen, S. Massaglia, and P. Rossi (With 1 Figure) 353

The Shock Wave Heating Mechanism of Pulsating Star ChromospheresBy S.M. Andrievsky and G.A. Garbunov (With 2 Figures) 356

Ionization PumpingBy C. Lindsey (With 3 Figures) 359Shock Amplification by RadiationBy M. Carlsson and R. Stein (With I Figure) 366

3.2 Acoustic and MHD Wave GenerationRecent Developments in Theories of Wave GenerationBy Z. E. Musielak (With 5 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 369

Generation of Acoustic Flux Derived from Numerical Simulationsof the Solar Granular ConvectionBy M. Steffen, A. Kruss, and H. Holweger (With 3 Figures) 380

3.3 Magnetoacoustic WavesMagnetoacoustic Waves and Their Generation by ConvectionBy R. F. Stein and A. Nordlund (With 15 Figures) , 386

Magnetoacoustic Heating of the Solar ChromosphereBy S.M. Chitre and I.M. Davila (With 1 Figure) 402Effects of Line-Tying and Non-Uniformities on Thermal Instabilitiesand Slow MHD ModesBy D. Hermans, A.W. Hood, L. Clifford, and A. Milne (With 2 Figures) 405

Heating in Intense Flux TubesBy S. S. Hasan (With 4 Figures) 408

Line Simulation of Solar Structures Permeated by Acoustic and MHD-WavesBy W. Rammacher (With 6 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 414

Damping of Shocks in Magnetic Flux TubesBy A. Ferriz Mas and F. Moreno Insertis . . . . . . . . . . . . . . . . . . . . . . . . . . .. 417

XI

Heating of the Solar Chromosphere by MHD- WavesBy R. Erdelyi and M. Marik (With 3 Figures) 420

3.4 Alfven WavesAlfven WavesBy J.V. Hollweg 423

Reflection of Alfven Waves and Heating in Solar Coronal HolesBy R.L. Moore, Z. E. Musielak, S. T. Suess, and C.-H. An (With 1 Figure) 435

Alfven Wave Propagation in a Solar Magnetic StructureBy P.L. Similon and S. Zargham (With 3 Figures) 438

On Propagation and Absorption of Alfven Waves in Coronal LoopsBy Y.D. Zhugzhda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 442

Magnetic Confinement, Alfven Wave Reflection, and the Origin of X-rayand Mass Loss "Dividing Lines"By C.-H. An, R. Rosner, Z.E. Musielak, R.L. Moore, and S.T. Suess 445

Heating in Stochastic Magnetic FieldsBy R.N. Sudan (With 10 Figures) 448

Resonance Absorption HeatingBy J.M. Davila (With 5 Figures) 464

Resonant Absorption of MHD Waves in Magnetic Loops in the Solar CoronaBy M. Goossens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 480

On the Time Scales and the Efficiencyof Solar Coronal Loop Heating by Resonant AbsorptionBy S.M. Poedts (With 1 Figure) 486

Line- Tying Effects on Stability and Heating of Solar Coronal LoopsBy G. Halberstadt, J.P. Goedbloed, S.M. Poedts, and R.A.M. Van der Linden(With 2 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 489

Coronal Loop Heating by Discrete Alfven WavesBy C.A. Azevedo, A.S. de Assis, H. Shigueoka, andP.H. Sakanaka 492

3.5 Magnetoacoustic and Alfven Surface WavesMagnetohydrodynamic Surface WavesBy B. Roberts (With 2 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 494

Magnetoacoustic-Gravity Surface WavesBy A.J. Miles and B. Roberts (With 1Figure) 508Properties of Non-Parallel Magnetoacoustic Surface WavesBy R. Jain and B. Roberts (With 1 Figure) . . . . . . . . . . . . . . . . . . . . . . . . . .. 511

Viscous Damping of Magnetohydrodynamic Surface WavesBy M. Ruderman 514

Coronal Loop Heating by the Fast Surface WaveBy A.S. de Assis and K.H. Tsui 517

XII

Chapter 4: Electrodynamic Heating Mechanisms

4.1 Current Sheet Formation and HeatingThe Formation of Current Sheets and Coronal HeatingBy E. R. Priest (With 12 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 520

Current Sheet Formation in Force-Free Magnetic FieldsBy G. Vekstein and E.R. Priest (With 2 Figures) . . . . . . . . . . . . . . . . . . . . .. 536Two-Dimensional Magnetic Neutral PointsBy N.R. Strachan and E.R. Priest (With 1 Figure)The Significance of Magnetic Null PointsBy K. Galsgaard and A. Nordlurul (With 1 Figure)Effect of Coronal Heating on Coronal ArcadesBy C.D.C. Steele and E.R. Priest (With 3 Figures)

539

541

544

Heating by Field Aligned DC Joule DissipationBy D.S. Spicer , 547Joule Heating in the Sun's Lower Transition RegionBy G. Roumeliotis 562Plasma Heating by Current Sheets in Solar Active RegionsBy B. Kliem and N. Seehafer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 564Chromosphere Generation in Magnetic Flux-TubesBy J. C. Henoux and B. V. Somov (With 1 Figure) 567

4.2 Heating and HelicityCoronal Magnetic Structure: the Role of Ideal MHD InvariantsBy M.A. Berger (With 4 Figures) 570Current Helicity and the Generation of Magnetic Field Aligned CurrentsBy N. Seehafer and K.-H. Radler 582

Nonlinear Evolution of a Force-Free Arcade Field Driven by Shear FlowBy N. Bekki, T. Tajima, and J.W. Van Dam (With 1 Figure) 585

4.3 Reconnection, Heating by Flux EmergenceTwo-Dimensional Magnetic ReconnectionBy M. Jardine (With 7 Figures) , 588

Magnetic Field Annihilation Within a Stagnation Point FlowBy M. Jardine, E.R. Priest, and H.R. Allen (With 2 Figures) 601Three-Dimensional Magnetic Reconnection: Basic ConceptsBy M. Hesse, K. Schindler, and 1. Birn (With 3 Figures) 604Atmospheric Heating in Emerging Flux RegionsBy K. Shibata, S. Nozawa, R. Matsumoto, T. Tajima, and A.C. Sterling(With 2 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 609

XIII

4.4 Micro/Nanofiare Coronal HeatingMicro/N anoflare Coronal HeatingBy E.N. Parker (With 8 Figures) '. 615

Numerical Simulation of Microflare Evolutionin the Solar Transition Region and CoronaBy A.C. Sterling and 1. T. Mariska (With 4 Figures) 630

Coronal Heating by Nanoflares: Plasma Dynamics of Elementary EventsBy R.A. Kopp and G. Poletto (With 2 Figures) 634

Coronal Heating by Nanoflares: Possible Evidence of Plasmoidsin Radio Occultation DataBy D.J. Mullan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 637

Author Index 641

643List of Participants

XIV

International Heidelberg Conference Mechanisms of Chromosphenc and Coronal Heating, June 5-8, 1990,in front of the Max-Planck-Hans, Berlinerstr.10

Introduction

Over the past few years it has become clear that the heating phenomenon in chromospheresand coronae very likely cannot be explained by a single process alone, but is rather due to amultitude of mechanisms. Some of these mechanisms operate globally, others only in particularphysical situations or in very special magnetic field geometries. At the present time, it is notpossible to decide which mechanisms are the important ones. This is due to the relatively primi-tive theoretical development of many mechanisms, and to the paucity of definitive observationaltests which are capable of deciding between alternative mechanisms, or of testing specific pre-dictions of particular mechanisms. This book is devoted to an exposition of the observationaland theoretical work on stellar atmospheric heating which is pursued today, as propoundedby the scientists conducting this research. As a consequence, the reader will not find here anexhaustive compendium of all possible such heating processes, but rather only discussions ofthose mechanisms which have survived the challenges of past observational tests (the interestedreader will find a more extensive review, based on the published literature up to mid-1989, inNarain and Ulmschneider, Space Science Reviews, to appear 1990).

A reader entirely unfamiliar with the subject of this book might be excused if he or sheobtains the impression that virtually nothing is known for certain in the field of chromosphericand coronal heating. For this reason, it might be useful to make some comments about the pastevolution of the field.

To begin with, the past decade has seen a dramatic change in our view of what the heat-ing problem is all about. At the end of the 1970s, solar observations had already shown thatmagnetic fields must playa significant role in (at least) coronal heating, but it was not yetclear that the solar problem was extendable to other stars. With the flight of REAO-l, andespecially the Einstein Observatory and the International Ultraviolet Explorer, it became clearby the beginning of the 1980s that mechanical heating of the outer layers of stars is a generalphenomenon. Indeed, these observations, together with data from solar observations by OSO-8,finally definitively excluded the damping of classic acoustic waves as .a viable coronal heatingprocess. This produced a profound change in the cast of theorists working on the heating prob-lem: There was a continued influx of plasma physicists trained in fusion research, who focussedtheir attention on the heating problem as yet another instance of plasma heating. The magneticfield was now seen as the key player, whereas before magnetic fields were viewed by most (notall!) researchers as a (possibly annoying) secondary complication.

This change in perspective, and in the style of carrying out the research, is very much inevidence here: Most (if not all) of the coronal heating processes discussed here are related tomagnetic fields in one way or another (but see below); and the level of sophistication with whichthe heating problems are discussed has far more the flavor of physics discussions rather thanof astronomy. A measure of the impact made by the idea that magnetic fields play the centralrole in coronal heating is that theorists interested in the chromospheric heating problem musttoday defend themselves if they do not place magnetic fields at the center of their theories -this despite the fact that observations of both the Sun and other late-type stars give abundantevidence that (at least) the "quiet" chromosphere is heated by mechanisms having little to dowith magnetic fields. In particular the acoustic wave heating has been rediscovered in the lastfew years and appears now a very likely method for heating the nonmagnetic regions of stars.

In any case, the level of sophistication that heating theories now aim for is a clear reflectionof the level of detail which observations - especially observations of the Sun - can now give us;and the prospect of yet more exacting observational constraints which the instruments on SOROand SOLAR-A, as well as on the more remote projects such as the Orbiting Solar Laboratory

(OSL), will give us, is clearly inspiring much new, detailed work. Similarly, the enormous increasein available data on stellar coronae which ROSAT is now giving us is bound to lead to newconstraints on heating processes: If nothing else, the resulting large stellar data base will containstatistically useful information about the extremes of coronal behaviour, information whicheluded us previously because of the relatively small sample sizes. Thus, while we are unlikelyto see, for example, nanoflares directly resolved within the next decade, we most likely will beable to constrain the flux of Alfven waves in the solar atmosphere, and thus at minimum tofinally provide a direct observational test of the mechanism underlying the acceleration of thesolar wind.

In order to provide somewhat more guidance to the reader, we provide below an essentiallyannotated table of contents, which gives an account of the organization of this book, and of thebasis on which this organization was carried out.

1. The observations

Observations are the prime source of our knowledge of the existence of heating processes instellar atmospheres, and ultimately must also be the means by which we distinguish amongthe various proposed mechanisms by testing their specific predictions. Because of the greatdifferences in spatial, temporal, and spectral resolution, we have classified the observations in asomewhat arbitrary manner in two broad categories: solar observations and stellar observations,corresponding to the first two chapters of this book.

The first chapter, Solar Observations is organized as follows. In Ch. 1.1 we compile theobservations of oscillations and waves, which are the signatures of the wave-like (alternatingcurrent: AC) energy input in the outer solar atmosphere. Ch. 1.2 describes the observationsof the photospheric dynamics which, through the slow (direct current: DC) footpoint motion,leads to a buildup of magnetic energy. Ch. 1.3 summarizes the chromospheric observations, withcontroversial opinions on the nature and heating of the chromospheric bright points and with adiscussion of proposed new instruments. Ch. 1.4 discusses the chromosphere-corona transitionlayer observations, including the spicule and microflare phenomena, and outlines the difficultieswhich we still have in understanding this region, which is characterized by very rapid changein temperature over small distances. Ch. 1.5 gives an overview of the coronal and solar windobservations and modeling; it also discusses the first results of the new NIXT experiment byLeon Golub, the normal incidence X-ray telescope which gave us the breathtaking photo shownas our frontispiece.

In the second chapter, Stellar Observations, we first review the heating-related chromo-spheric and coronal observations which are derived mainly from the UV. Ch. 2.2 summarizes theobservations and the modeling of cool giants, together with the infrared observations. The inti-mate relation between the chromospheric and coronal activity and the magnetic field is discussedin Ch. 2.3. Ch. 2.4 summarizes the coronal heating constraints, and particularly discusses the X-ray observations. It shows that the heating question must also be considered in the investigationof early-type stars and of accretion disks.

2. The heating mechanisms

Based on the mechanical energy input, the various chromospheric and coronal heating processescan be broadly classified as wave mechanisms and electrodynamic mechanisms, correspondingto the last two chapters of this book. The wave mechanisms comprise acoustic waves, fast andslow magnetoacoustic waves, and Alfven waves. The magnetohydrodynamic (MHD) waves canbe both body and surface waves. Waves in late-type stars are excited by fast turbulent motionsnear the top of the convection zone, by small-scale instabilities, or by mode-coupling with otherwaves. The electrodynamic mechanisms include current dissipation, both in loops and in arcadesystems resulting from large-scale magnetic flux emergence, and locally in micro/nanoflares. Here

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the energy is introduced into the magnetic field by slow convective motions of the photosphericfoot points, or by buoyancy.

The third chapter, on Wave Heating Mechanisms, is subdivided as follows. In Ch. 3.1we discuss planar acoustic waves, as well as acoustic waves in tubes (as may be relevant forthe spicule problem). Ionization pumping and radiative amplification are important effects foracoustic waves. The acoustic and MHD wave energy generation by turbulent motions in theconvection zone is summarized in Ch. 3.2 both from the general perspective as .wellas from themore specific perspective of 2D granular convection simulations. Ch. 3.3 discusses fast and slowMHD waves and longitudinal MHD tube waves. The generation, propagation, and damping ofAlfven waves are discussed in Ch. 3.4; particular emphasis is placed in the damping processes,including phase-mixing, resonant absorption and propagation in stochastic magnetic fields. Ch.3.5 is dedicated to magnetoacoustic and Alfven surface waves.

In the fourth and last chapter, Electrodynamic Heating Mechanisms, we first devotean extensive section (Ch. 4.1) to the formation of current sheets, both in large-scale arcadesystems and in loops. The relation of heating and helicity is summarized in Ch. 4.2; and inCh. 4.3 are discussed two- and three-dimensional magnetic reconnection and the heating bylarge-scale magnetic flux emergence. Finally, the micro and nanoflare heating mechanisms arediscussed in Ch. 4.4.

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