CHROMOSPHERIC AND CORONAL MAGNETIC FIELDS

Eric Priest

Mathematics Institute, St Andrews University, St Andrews KY16 8QR, UK

ABSTRACT

A summary is given of the main results that have beenpresented at the conference, together with comments onthem and suggestions for future work. In particular, thiscovers the structure of the magnetic field (in the pho-tosphere, chromosphere and corona) and the dynamicsof the magnetic field (in coronal heating, prominences,emerging flux, eruptive instability and waves).

1. INTRODUCTION

This has been an unusually fine conference, with an out-standing series of talks and a series of important advancesannounced. It is quite clear from the presentations ofyoung people here that European solar physics is in ex-cellent shape and that the future bodes well for them. Thepresence of a number of key American and Japanese sci-entists at the meeting has also been very positive.

Life was simple when we were young and naive! – whenthe atmosphere of the Sun was static and spherically sym-metric, so that a corona lay above spherical shells of tran-sition region, chromosphere and photosphere – and alsowhen there was no magnetic field outside sunspots. Nowthere is magnetic field everywhere in the form of loopsand all is dynamic.

In this conference summary I plan to structure my com-ments by first discussing the structure of the magneticfield in the various parts of the solar atmosphere and thenfocussing on the many ways in which the magnetic fieldis interacting in a dynamic way with solar plasma. Butfirst let me remind you of a few of the memorable com-ments that were made during the presentations, namely:

• “This is certainly the lousiest talk” (Sami Solanki)

• “If you have heard this before, you can doze for afew minutes” (Gene Parker)

• “There are also problems with dynamo theory - ifyou have another hour· · ·” (Gene Parker)

• “The Sun with no magnetic field would be a starwith no spirit” (Nour-Edine Raouafi)

• “You build a polarimeter, put it into space - it willtake you 10 years· · ·, but then I will have solved allthe theoretical problems !!” (Javier Trujillo)

• “Most of us come from flatland” (Stephen White)

• “God blesses radio astronomers” (the anthropora-diomorphic principle)” (Stephen White)

• “I know everything about bald patches” (ThomasNeukirch)

• “The canopy is like a wineglass” (Andreas Lagg)

• “In a dextral filament you are on a highway and go-ing to the exit” (Brigitte Schmieder)

• “As chairman of this session, I will allow you onlyone final question, since I am hungry” (Javier Tru-jillo)

• “Our talks in this session are having trouble with thereferees” (Spiro Antiochos)

• “Im not so sure I like kink instability” (Spiro Antio-chos)

• “I find myself agreeing with Spiro - which is mostdisheartening” (Jon Linker)

• “I like chewy nougat” (Yuhang Fan)

• “The black stuff in the image is just chromosphericjunk” (Jorrit Leenaarts)

• “I can talk or see but not do both” (Cristina Man-drini)

• “It may be a good idea for me to speak now, so thatthe audience can cool down after Spiro” (Ineke de-Moortel)

• “This nice formula did not survive translation fromlaptop to computer” (Alfred de Wijn)

• “I sent my family to China for this meeting” (DavinaInnes)

• “You may not realise that the Sun is not an infiniteplane” (Sami Solanki)

Figure 1. A photospheric magnetogram of a supergran-ule cell, showing network field and tiny mixed polarityfragments in the interior of the cell (from H Navarro).

Figure 2. A radiative-MHD simulation of the chromo-sphere, showing the temperature colour-coded (from .SWedermeyer-Bohm).

2. STRUCTURE OF THE MAGNETIC FIELD

2.1. The Photospheric Magnetic Field

Hector Navarro (ably impersonated by Arturo Lopez)stressed that the quiet Sun is not-so-quiet, as indicatedin Figure 1. The key questions for the future here are:what is the ratio of the magnetic flux in a supergranulecell to the flux in the network? What is the intrinsicfield strength and the probability distribution function ina pixel? What is the origin of these fields?

Horst Balthasar gave a fascinating description of his mea-surements of the vertical current in a sunspot, showingthem to vary between +100 mA/m2 and−100 mA/m2.The resulting values ofα = j/B vary by a factor of 110in a sunspot and so the magnetic field is certainly not alinear force-free field!

Sven Wedermeyer-Bohm and Oskar Steiner describedtheir simulations of CO and magnetic fields in the quietSun with a radiative MHD code that was able to resolvediscontinuities very well. The resulting chromosphereis very dynamic with many filaments formed by shock

Figure 3. The magnetic flux in an active region as a func-tion of time (from V Martinez).

waves (see Figure 2).

Jorrit Leenaarts discovered that bright points in the Hαwing coincide with intergranular kilogauss magnetic con-centrations. Looking in white light, Eberhard Wiehrfound a gap in flux between the largest G-band brightpoints and the smallest dark pores, so it would be inter-esting to understand what is happening in between, wherepresumably the radiation from the walls of a thin flux tubeis insufficient to brighten the tube as a whole.

A very interesting study of the decay of active regions byValentin Martinez (Figure 3) showed that 70% of the fluxof an active region is lost by cancellation of magnetic fluxin the photosphere and the remaining 30% can diffuseaway from the active region site. However, only a smallfraction of this 30% reaches the poles to reverse the polarflux.

2.2. Connection between the Photosphere and Chro-mosphere

Mei Zhang reminded us of the traditional model of a mag-netic canopy put forward by Ron Giovanelli and AlanGabriel as a sharp discontinuity between the expandedmagnetic flux from the network and the underlying field-free region of the centre of a supergranule cell. This viewclearly needs to be modified, but can it be retained at allor should it be disgarded?

Mei Zhang pointed out that magnetic elements in thechromosphere above the network are not very muchlarger than those in the photosphere, in contradiction topredictions of the original model. She also mentioned(Figure 4) that many TRACE loops extend up from theirfootpoints without expanding very much and not givingany suggestion of a canopy. Confinement of such loops isnot a problem at all, since the corona is filled with an am-bient magnetic field which can easily confine such loops.

Figure 4. TRACE loops near the limb with their photo-spheric footpoints shown by + signs (from M Zhang).

-6 -4 -2 0 2 4 6x (Mm)

01234567

h (M

m)

Figure 5. Model of the magnetic field in a supergranulecell due to a network source and random small-scale cellflux (from K Schrijver).

However, it is puzzling as to why such loops are fairlyvertical and why their cross-sections are fairly constant(varying by at most a factor of 1.5). We must bear inmind that TRACE is imaging only a particular set of coro-nal field lines, namely only those that have temperaturesin the particular TRACE passband. In particular, whenimaging an active region such as that of Figure 4, sincethe core of the active region is much hotter, TRACE isshowing up mainly the cooler loops at the edge of the ac-tive region. So a possible explanation of the verticalityof these loops that Alan Title is considering is that theyare lying along a separatrix surface bounding the activeregion. As to the constancy of the cross-section, thereis an urgent need for a sophisticated modelling of an ac-tive region magnetic field following the approach of JimKilmchuk in order to see whether the model gives a quasi-constant cross section or not.

Karel Schrijver gave a magnificent review of the Mag-netic Carpet, pointing out that it is topologically verycomplex and that the coronal magnetic field reconnectsevery hour-and-a-half according to the recent analysisof Close, Parnell, Longcope and Priest (2004). Indeed,if one includes the sub-resolution small-scale cell flux,

Figure 6. Model of a coronal funnel acting as a sourcefor the fast solar wind (from E Marsch).

the coronal reconnection time may only be a few min-utes. He stressed that most of the heating seen in TRACEis in small-scale loops in the network and that muchof the corona over the quiet Sun is not force-free sincethe plasma beta is of order unity. Then he turned tothe intranetwork field and suggested that there may bemuch more magnetic flux in the cell than in the net-work (according to the ideas of, for example, Trujilloand Sanchez-Almeida) – certainly much more than wethought before. This intranetwork field is probably gen-erated by a small-scale dynamo, as suggested by the sim-ulations of Cataneo and it is probably heating the chro-mosphere (see Carlsson’s talk later). He proposed an en-lightening model (Figure 5) in which only30 − 70% ofthe open or large-scale magnetic flux coming down to thesolar surface ends in the network, rather than the 95% thatGabriel had suggested.

Next, Eckart Marsch talked about the coupling of thephotosphere to the fast solar wind by means of coronalfunnels. He compared SUMER doppler shifts with ex-trapolated magnetic fields and found examples in coronalholes where the area of a funnel expands by only a factorof 10 (Figure 6), which is very much less that one wouldexpect in a Gabriel model. It will be interesting to seewhat a similar analysis shows for the quiet Sun outsidecoronal holes – will it give a network of tiny funnels act-ing as the source of the slow solar wind or not?

So, does a canopy exist or not? Is the concept still corrector useful? This is related to the question about the ratioof the network to intranetwork flux, which may well varyover the surface of the Sun. Also, what is the effect of thecell flux on the canopy if it does exist? Clearly, more ob-servations and interpretations are needed to answer thesequestions, but some qualitative points may be made.

First of all, it is no longer thought that the cell centre isfree of magnetic field, so the old definition of a canopyno longer holds. However, perhaps in some situationsthe majority of coronal the flux still goes down throughthe surface in the network, in which case there would bea “canopy” dividing that flux from most of the intranet-work flux – although that canopy could have small-scaleholes in it, punctured by small amounts of intranetworkflux that extend upwards. Another definition of a canopycould be the boundary of the flux that goes up from small

z [M

m]

y [Mm]

x [Mm]

Figure 7. The structure of a magnetic flux tube in anemerging flux region (from A Lagg).

magnetic elements to the corona from, say, just part ofa superganule cell or from the boundary of a granule.Yet another definition could be the surface where theplasma beta is unity, separating low-lying regions wherethe plasma pressure dominates the dynamics from over-lying regions where the magnetic field dominates. Sucha surface could be smoothly varying or it could be highlycorrugated.

If the intranetwork flux is weak compared with the net-work flux or if it is small-scale and confined to low layers,then the overall canopy over a supergranule cell would bepreserved; for example, this could be the case in remnantactive regions where clear Hα fibril structures could beindicating fairly horizontal field structures of a canopy.But, if the intranetwork flux is larger or is clumped onlarger scales, then it could disrupt parts of the canopy andbreak through or it could destroy the notion of a canopyaltogether. The whole structure is in any case likely to bevery much more complex and dynamic than in Gabriel’smodel, as for example revealed in Hansteen and Carls-son’s simulations (see Section 3.6).

2.3. The Chromospheric Magnetic Field

A comprehensive review of the ways of measuring chro-mospheric and coronal magnetic fields was presented byNour-Edine Raouafi, including Zeeman, Hanle, radio andextrapolation. Particularly interesting was an observationof a coronal hole with SUMER (O VI 1032A) in a po-lar coronal hole at about 0.3 solar radii above the limb,implying a magnetic field strength of 3 Gauss. Also,Achim Gandorfer suggested that UV polarimetry fromthe ground is the key to measuring chromospheric mag-netic fields, in particular with CaI 4227.

Andreas Lagg continued this topic with an exceptionallyclear review of the observations of the canopy and ofspicules. He also presented in detail an analysis of themagnetic field and vertical velocity in an emerging flux

Figure 8. The best-fit nonlinear force-free magnetic fieldto the observed structure of Figure 7 (from T Wiegel-mann).

region using He 10830, which was one of the highlightsof the meeting. The left-hand panel of Figure 7 indi-cates the magnetic field strength and the right-hand panelshows the vertical velocity along the loop. This exampleshows the huge potential of Stokes polarimetry and I hopethat many similar examples of other atmospheric featurescan be analysed in future. Of course, it is very importantto compare such observations with models and a goodstart has been made by Thomas Wiegelmann, who foundthat a nonlinear force-free magnetic field model not sur-prisingly gives a much better fit with the observed loopsthan a linear-force free or potential model (Figure 8).

2.4. The Coronal Magnetic Field

Steve Tomczyk showed how to use coronal emission linesto measure Stokes parameters, pointing out that the bestlines are in the infra-red, especially Fe XIII (an examplebeing shown in Figure 9). For this a dedicated large (1metre) coronagraph would be invaluable.

Stephen White gave a superb review of radio techniques,stressing that they can be used to determine active re-gion coronal fields on the disc larger than 300 G (Figure10). The advantage here is that 3D information about themagnetic field can be deduced, since the radiation is op-tically thick. Together with magnetic extrapolations, thiscan in turn determine the heights of the emission. Theradio therefore complements infra-red measurements onthe limb of fields less than 20 G.

This was followed by a masterly case from Javier Tru-jillo for spectropolarimetry using the Hanle effect tomeasure the magnetic field in the transition region and

Figure 9. The coronal magnetic field from Fe XIII (fromS Tomczyk).

-250

-200

-150

-100

arcs

ec

Soft X-ray image (Yohkoh SXT)

Big Bear photospheric magnetogram

-750 -700 -650 -600arcsec

-250

-200

-150

-100

arcs

ec

1.6 GHz VLA image

-750 -700 -650 -600arcsec

4.5 GHz VLA image

Figure 10. The coronal magnetic field from radio abovean active region (from S White).

Figure 11. The importance of polarised light (from J Tru-jillo).

corona (Figure 11). He made a strong case for putting ahigh-sensitivity UV/EUV polarimeter in space. In addi-tion, Maxim Kramer suggested that the Maxwell equation∇.B = 0 can be used to resolve the ambiguity in coronalHanle or Zeeman data and so construct the non-potentialcomponent of the coronal magnetic field.

2.5. Coronal Magnetic Field Theory

In his usual crystal clear style, Thomas Neukirch gave awell-balanced and comprehensive overview of the differ-ent techniques for calculating nonlinear force-free mag-netic fields. There are of course different aims of sucha process. One may be to follow the slow evolution ofa magnetic configuration through a series of force-freestates in response to footpoint motions. Another maybe to reconstruct the coronal magnetic field that corre-sponds to an observed vector magnetic field measured inthe photosphere. However, in the latter case it is not obvi-ous what boundary conditions to take, since although youcan impose the normal component of the magnetic fieldeverywhere you can only impose the transverse compo-nents (and therefore the normal current and so the alphavalue) at one end of each field line. Of course, if thereare no measurement errors and the magnetic field is in-deed everywhere force-free, then the normal current (andso the alpha value) that you find at the other end of thefield line should agree exactly with the observed value –but life is not so simple, so what should you do when theydisagree?

The three families of methods are: the Grad-Rubinmethod (used for example by Stephane Regnier), whichgives extremely accurate solutions, represents a well-posed problem and satisfies∇.B = 0 very well whenbased on the vector potential; relaxation methods thatslowly relax towards a force-free state while preservingthe topology, which is a good approach if the connectiv-ity of the field is known; and minimisation methods (asdeveloped by Thomas Wiegelmann). In a recent com-parison of the methods on a model problem in which thevector magnetic field on a plane was imposed, the methodof Wiegelmann performed best.

In future, more accurate measurements of vector mag-netic fields are needed in the photosphere, for which So-larB and the Solar Dynamics Observatory (SDO) will beinvaluable. Also, the theory needs to advance more bythe development of fast and robust methods that convergemuch more quickly than the present codes. In addition,we need to be able to deal better with noise in the dataand to understand and model the non-force-free nature ofthe photosphere.

Stephane Regnier followed with a nonlinear force-freecode the evolution of an active region (Figure 12) andshowed how photospheric motions and complex topologyare precursors of flaring.

A superb review of the elements of coronal magnetictopology was then delivered by Pascal Demoulin. First

Figure 12. A nonlinear force-free model of a flaring ac-tive region (from S Regnier).

Figure 13. A force-free model of a flaring active region(from P Demoulin).

of all, he showed how the photospheric magnetic fieldcan be modelled in terms of discrete flux patches. Theskeletonof the field consists of a set ofseparatrixsur-faces that divides the corona up into topologically dif-ferent volumes. If two separatrices intersect, they doso in a special magnetic field line called aseparator,which joins two null points. Flux transfer then occursfrom one region to another byseparator reconnection.Secondly, he showed how to generalise these conceptsto continuous field distributions. The discontinuities inmapping of one footpoint to another become strong gra-dients in the mapping. A separatrix surface becomes aquasi-separatrix layer(QSL), while a separator becomesa quasi-separatorand the neighbouring structure ahy-perbolic flux tube. Some flares are found to occur at sep-aratrices and some at quasi-separatrix layers: Figure 13gives such an example, where (a) shows a magnetogramand theHα ribbons, (b) the QSL footprints (purple) andvertical currents (shaded), (c) two sets of connectivityfrom the outside of the nearest ribbon to the outside of thefurthest and from the inside of the nearest to the inside ofthe furthest, and (d) shows two other sets of connectivityfrom the inside of the nearest ribbon to the outside of thefurthest and from the outside of the nearest to the insideof the furthest

When modelling the magnetic field, either in numericalexperiments or for extrapolations of photospheric mag-netograms, sketching the skeleton when there are discrete

Figure 15. Magnetic configuration for a simulation of anx-ray bright point (from J Buchner).

magnetic flux patches or sources is of very great value –certainly much more useful than just plotting a few ran-dom field lines. Equally, when the photospheric magneticfield is continuous, it would be also valuable to sketchwhat one may call thequasi-skeleton, which consists ofthe quasi-separatrices. The skeleton (or quasi-skeleton)reveals the topology (or quasi-topology) of a complicatedmagnetic field, which then reveals where reconnection islikely to take place and also reveals the regions betweenwhich magnetic flux is transported during reconnection.

As an example of the usefulness of this approach and asan excellent example of how to do it in practice, recently,Haynes, Parnell, Galsgaard and Priest (2005, in prepara-tion) determined the skeleton of a 3D numerical resistiveMHD experiment that Parnell and Galsgaard had under-taken on the effect of the motions of two equal and op-posite photospheric magnetic fragments in an overlyingmagnetic field. Initially, the magnetic fragments wereunconnected; later they became connected and even latersome of the flux became disconnected again, but the mainquestion was: is the mechanism of 3D reconnection bynull reconnection, separator reconnection or non-null re-connection? Careful analysis by Andrew Haynes of theskeleton (both in 3D and by means of horizontal and ver-tical sections) and of the location of the current concen-trations relative to the skeleton revealed the surprising an-swer. The initial reconnection creating closed flux joiningthe two sources was by separator reconnection, initially attwo separators and later at one separator (Figure 14(a)),whereas the later reconnection of most of the closed fluxto open it up again was by separator reconnection, ini-tially at four new separators and later at two dominantseparators (Figure 14(b)).

Jorg Buchner has undertaken MHD simulations of an x-ray bright point, a current sheet and a coronal hole. Ineach case the response to slow footpoint motions is anevolution through a series of equilibria that are piecewisenonlinear force-free, with current sheets on separatricesor quasi-separatrix laters (Figure 15).

Figure 14. Vertical sections through the skeleton of a numerical experiment showing (a) a central separator with strongcurrent (seen in blue) at which reconnection is closing the field and (b) two more separators, one on each side, wherereconnection is opening up the field again (from A Haynes et al).

3. THE DYNAMICS OF THE MAGNETIC FIELD

3.1. Coronal Heating

Gene Parker delighted us with a fluent account of hisbraiding model for coronal heating by nanoflares or pi-coflares. This well known model suggests that the heatingcomes from the dissipation by impulsive reconnection ofnumerous current sheets formed by braiding. He pointedout that granules are the source of energy and demon-strated that waves are not effective.

The Coronal Tectonics Modelis a refinement of Parkerbraiding which produces current sheets much more ef-fectively. It includes the effect of the magnetic carpet,namely, the fact that coronal magnetic field is not an-chored uniformly in the photospheric surface but ratherin a complex set of small discrete flux patches. Thus,between the magnetic flux coming from each flux patchthere lie separatrix surfaces along which current sheetsreadily form and dissipate in response to footpoint mo-tions. Ineke de Moortel presented the results of a very in-teresting experiment on coronal tectonics that she is per-forming with Klaus Galsgaard. If a uniform magneticflux is slowly twisted, a weak current will form along thetube with negligible heating. However, if instead the fluxof the tube is anchored in two discrete flux patches at oneend of a cylinder and in two other patches at the otherend, they found quite a different result. By following theeffect of slowly twisting the ends, they found that cur-rent sheets do indeed form along separators or, if there isa weak background field, along quasi-separators, as ex-pected (Figure 16). Indeed, the subsequent current sheetstructure is highly fragmented and an extremely efficientcoronal heater.

Hardi Peter has examined Gudiksen’s 3D resistive MHDexperiment on coronal heating, which is essentially anexperiment on coronal tectonics, since it starts with a

0 10 20 30 40 50horizontal coordinate X [Mm]

0

10

20

30ve

rtic

al c

oord

inat

e Z

[M

m] Mg X (625 Å)

Figure 17. Synthetic line of sight emission from 3D tec-tonics experiment (from H Peter).

potential magnetic configuration calculated from a pho-tospheric magnetogram and follows the effect of a sim-ulated photospheric velocity field on that configuration.He deduces synthetic spectra (Figure 17) and finds a goodmatch with observed doppler shifts and emission mea-sure. In future, it would be interesting to calculate theskeleton or quasi-skeleton for this experiment and findout whether or not the resulting current sheets are alignedwith the separatrices or quasi-separatrices.

This talk was followed by interesting contributions byRekha Jain on so-called “forced reconnection” and byTohri Shimizu on the structure of the shocks in Petschekreconnection. Forced reconnection refers to the creationof a current sheet and its subsequent dissipation in re-sponse to a boundary motion that occurs on a time-scalelying in a rather narrow range, namely, one that is muchsmaller than the Alfv en travel time (so that a series ofequilibria are set up) but is much longer than the recon-nection time. Since the reconnection time is often of or-der a ten or a hundred times the Alfv en time, this leavesvery little room for this mechanism to be valid. It is only

Figure 16. A simulation of coronal tectonics showing (a) theinitial state of a single flux tube whose flux has two discretepatches at both ends of the tube and (b) the electric current structure after the tube has been twisted in a section acrossthe tube and half-way along it (from I de Moortel).

when the reconnection is inhibited for some reason, sothat the reconnection time is very much longer than nor-mal, that this mechanism is relevant.

3.2. Prominences

Prominences have long been an enigma and althoughmuch progress has been made in understanding theirglobal structure, there are still unanswered questionsabout their fine-scale structure, about the nature of barbsand feet, about their formation, about their fluxes of mass,momentum and energy, and about their eruption, all ofwhich need both observational and theoretical input inorder to advance. Furthermore, prominences are amaz-ing laboratories for studying fundamental processes suchas instability and turbulence.

Laura Merenda and Arturo Lopez presented recent resultson measuring the magnetic field in prominences, usingthe Hanle effect in He I 10830, whereby the presence ofa magnetic field reduces the polarization. Laura observeda polar crown prominence and found the abnormal resultthat the magnetic field was vertical – is this the case inother prominences or is it only in some parts of a promi-nence? Arturo, on the other hand, found a horizontal fieldwhose strength increased from 20G in the centre of theprominence to 80G at the edge. Clearly, it will be impor-tant in future to develop these kinds of measurements andto compare with theoretical models. Arturo also foundthat the magnetic field in spicules is about 40 G and is,not surprisingly, aligned with the spicules.

Aad van Ballegooijen showed us the results of his su-perb new model for the global magnetic structure of aprominence, in which he starts with a potential mag-netic field based on an observed photospheric magne-togram and then inserts a magnetic flux tube along thefilament channel and watches the whole field relax to a

Figure 18. Part of a prominence viewed on the disc to-gether with some magnetic field lines calculated from anonlinear force-free model. The light blue lines passthrough low-lying points (1.4 Mm) and the dark-blueones pass through higher altitude points (6.4 Mm). (fromA van Ballegooijen).

Figure 19. (a) a barb observed inHα at the Swedishtelescope and (b) the corresponding model magnetic field(from B Schmieder).

nonlinear force-free equilibrium. In particular, he has fo-cussed on the magnetic structure of a barb in his modelwhich consists of magnetic field lines slanting down fromthe prominence body to a parasitic polarity (i.e., a mag-netic fragment that has the opposite polarity from the nor-mal polarity on that particular side of the polarity inver-sion line. The comparison between fine structures in theprominence and barb and the computed magnetic fieldlines was very impressive (Figure 18). It remains to beseen whether other barbs can also be modelled in thisway,

Brigitte Schmieder then presented an interesting alterna-tive model of a barb in which a barb is identified with abald patch(i.e., a magnetic dip in the photospheric mag-netic field). This model has the great advantage that itprovides the support for barb plasma (Figure 19), but I forone remain puzzled about barbs. The detailed compari-son of barb structure with this model is less convincingthan with van Ballegooijen’s model, which, however, if itis valid possesses a key as yet unsolved aspect, namely,if the barb plasma is indeed aligned along the magneticfield, then how is it supported?

One possible support mechanism is by waves and anotheris that the plasma is in fact not in equilibrium but is flow-ing upwards in response to reconnection at the parasiticpolarity or is draining back down when reconnection isswitched off or is less strong. In any case, a barb’s truenature may be highly dynamic rather than being a mat-ter of static support. In future, it will be interesting tosee what a sequence of magnetograms underlying a barbreveals about the time-dependent evolution of the para-sitic polarity – for example, is it cancelling throughoutthe lifetime of a barb and what is the nature of the barb

Figure 20. A 3D numerical MHD simulation of emergingflux (from H Isobe).

flows (up or down) relative to the motion and cancellationphases of the parasitic polarity? It is also possible that thetwo apparently opposing models for barbs presented herecould be reconciled, since the barb itself could indeed bealigned along field lines joining the prominence body tothe parasitic polarity, but there may also be a nearby mag-netic dip associated with the parasitic polarity.

3.3. Emerging Flux

A state-of-the-art three-dimensional simulation of emerg-ing flux has been carried out by Hiroaki Isobe which re-vealed for the first time a filamentation in the third di-mension of the emerging flux. Such filamentation is rem-iniscent of the observation of Hα fibrils in emerging fluxregions and is created by Rayleigh-Taylor instability. Atthe same time he found a state of fast impulsive burstyreconnection.

Etienne Pariat described an observation of an emergingflux region and his modelling of it by a linear force-free magnetic field. This possessed several bald patchesas serpentine field lines went up a down. At the dipshe suggested that magnetic reconnection can get rid ofthe dense plasma that would otherwise be trapped dur-ing Ellerman bombs. Klaus Galsgaard also described asuperb numerical experiment that he has been conduct-ing with Fernando Moreno, Vasilis Archontis amd AlanHood on emerging flux. In his experiment the flux risesthrough a model convection zone and reconnects with anoverlying coronal magnetic field.

3.4. Global Corona

Jon Linker described a superb research programme thathe has been undertaking on the global structure of thelarge-scale corona with Zoran Mikic. First of all, heshowed us the steady polytropic MHD models, whichhave been used to predict and later compare with eclipse

Figure 21. A steady global MHD model of the solarcorona and comparison with an eclipse (from J Linker).

Figure 22. The process of interchange reconnection (fromJ Linker).

images of the white-light corona. In future he plans to im-prove the energy equation in the model, hoping to obtainhigher velocities and lighter coronal holes in better agree-ment with observation. Secondly, he presented some fas-cinating results from time-dependent modelling, includ-ing the effect of differential rotation. This was particu-larly useful to understand the global evolution of coro-nal holes, for which he found that normal disconnectionof large loops sometimes occurs whereby a large looppinches off, leaves behind a small loop and ejects a plas-moid. However, at other times interchange reconnectiontakes place (Figure 22), in which a large loop reconnectswith open flux to form a small loop and to make the foot-point of the open flux suddenly jump a long way.

3.5. Eruptive Instability (Flares and Coronal MassEjections)

Eruptive instability of some kind lies at the core of mostlarge flares and all eruptive prominences and coronalmass ejections. If a prominence erupts from an active re-gion, a two-ribbon solar flare occurs and the prominencelies at the core of a coronal mass ejection. If a promi-nence erupts from outside an active region, on the otherhand, where the magnetic field is much smaller, it againoccupies the core of a coronal mass ejection, but there arefew high-energy effects and no flare takes place.

Figure 24. An axisymmetric simulation of the breakoutmodel (from S Antiochos).

Lindsay Fletcher reviewed in a lively manner the lat-est results from flare observations, especially those fromRHESSI. In particular, she described the most recentideas on predicting flares and observations of weak par-ticle acceleration before flare onset. Also, many flaresoccur in a denser medium than thought before and thereremain many problems with understanding how electronsare accelerated in the corona. Alexander Nindos calcu-lated the evolution of the magnetic helicity of active re-gions using a linear force-free field with the alpha-bestmethod. He found that most active regions with a largemagnetic helicity produce CME’s, whereas most of thosewith small helicity do not. In future, when fast methodsare available, it will be interesting to repeat the analysiswith nonlinear force-free fields, so as to do so more ac-curately and also to determine whether it is the excessmagnetic energy or the excess magnetic helicity that isthe more important criterion for flare onset. This distinc-tion does nor exist for linear force-free fields, where oneis just proportional to the other.

Yuhong Fan described the results of a fascinating idealMHD experiment on the effect of emerging a flux ropeslowly into a potential arcade with an initial hydrostaticisothermal corona. If the twist in the rope is more than3.4π, it evolves slowly at first and then suddenly eruptsdue to a lack of magnetic equilibrium (Figure 23(a)).What happens is that the flux rope kinks and rotates andis thereby able to move out between the arcade field lines.This talk was followed by an interesting alternative fromTibor Torok, namely the occurrence of kink instability(Figure 23(b)). The two models differ in the nature of theoverlying magnetic field and in the details of the flux ropeequilibrium.

Spiro Antiochos continued with a stimulating and livelypresentation of a third possibility, namely his breakoutmodel. He stressed that observationally we are now con-fident that the filament begins to take off before the flare,but the relative timing of the filament eruption and the

Figure 23. Simulations of eruption by (a) magnetic catastrophe (from Y Fan) and (b) kink instability (from T Torok).

Figure 25. Simulation of the Reversed Shear Model (fromK Kusano).

CME are uncertain. Also, he mentioned that all mod-els require a nonpotential magnetic field in the filamentchannel, but they disagree as to whether the configura-tion is that of a sheared arcade or a twisted loop – in hisopinion, the former is more likely. All models also needan overlying magnetic field to help hold down the promi-nence magnetic field before eruption, but they disagreeover the way in which the eruption starts. In his modelit is reconnection between the arcade magnetic field andthe overlying field which is the cause.

Two other suggestions for eruptive behaviour were putforward. Bernhard Kliem proposed a torus instability,which has the observational advantage that the flux tubedoes not need to be initially twisted for eruption to occur.Kanya Kusano described aReversed Shear Model(Fig-ure 25), in which a 3D resistive MHD simulation showshow tearing mode instability can produce a relaxed lin-ear force-free field in the shape of a sigmoid-shaped flux

tube, which then undergoes an eruption following a sec-ond reconnection.

All of the above models are able to produce flare loops,but the key question is what initiates the eruption? In aflare, are several mechanisms possible for an eruption oris only one in operation? Now, several viable theoreticalmodels have been proposed, but which one has the essen-tials of a real flare? In order to answer this, it would beuseful to adopt more realistic initial configurations for thenumerical experiments and to focus on the observationalconsequences.

Several other aspects of flares and CME’s were coveredin four more talks. Anik de Groof and Daniel Mullerdiscussed the observations and theory of coronal rainas a thermal instability and discovered that the reasonfor the downflow being slower than freefall is compres-sion ahead of the downflowing blobs. Erwin Verwichtesuggested that tadpole waves are fast magnetoacoustickinks, while Cristina Mandrini showed that individual in-terplanetary clouds have essentially the same magneticflux and magnetic helicity as the erupting active regionsthat spawned them.

3.6. Waves

Mats Carlsson gave us a real treat with a stunningoverview of observations and theory of chromosphericwaves. He presented a landmark observation by Fos-sum and himself demonstrating that acoustic waves be-tween 5 and 50 mHz have a power that is a factor of10 too small to heat the chromosphere as a whole, al-though Ca II grains can be explained by acoustic waves.Also, 3-minute waves in the chromosphere are not differ-ent modes than exist in the photosphere, since they arepart of a broad spectrum that already exists in the photo-sphere: it is simply that the dominant 5-minute waves in

Figure 26. Simulation of magnetic photosphere, chromo-sphere and corona by Hansteen (from M Carlsson).

Figure 27. Height above the solar surface as a functionof velocity form the line-of-sight Doppler shift observedwith SUMER (from T Wang).

the photosphere are filtered out by the time they reach thechromosphere.

Nonmagnetic simulations of the chromosphere show itto be extremely dynamic, but more realistically Hansteenand he have undertaken a simulation of a magnetic chro-mosphere in two dimensions. Figure 26 shows a cou-ple of supergranule cells with a simple arched magneticstructure shown by black curves: the lowest layer isa convecting photosphere (with red representing densesinking plasma and blue light rising plasma) and aboveit lies the (brown) chromosphere and (white) corona. Thecurveβ = 1 separates the upper chromosphere wherethe magnetic pressure exceeds the plasma pressure fromthe lower chromosphere where the plasma pressure dom-inates. The transition region is the curve separating thebrown chromosphere from the white corona. The re-sponse to the slowly convecting photosphere is the gen-eration of waves which become highly nonlinear and per-vade the chromosphere so that it and the overlying coronaare highly dynamic. Mode conversions from one type toanother occur where the sound speed equals the Alfvenspeed near theβ = 1 surface.

Tongjiang Wang presented a comprehensive review ofcoronal oscillations, including transverse global kinkmodes from TRACE, standing slow modes from SUMER(Figure 27) and propagating slow modes from EIT andTRACE. In future there is a need for more realistic sim-ulations and detailed observations in this field ofcoronalseismology, which is in its infancy. In particular, we needto determine the excitation and damping mechanisms and

Figure 28. A complex 3D solar atmosphere.

ultimately the physical properties of the corona in detail.

There followed a series of short talks on various as-pects of waves. Elena Khomenko showed us an attrac-tive model for waves in a sunspot in which fast modesrefract back to the photosphere while slow modes con-tinue up to the corona. Dipankar Banerjee detected long-period magnetoacoustic waves in coronal holes at 50km/s using a wavelet analysis with CDS. Mag Sewar andTom Van Doosselaere discussed oscillations in coronalloops, while Claire Foulon described pulsations in solarflares. Finally, Thanassis Katslyannis described interest-ing SECIS observations at small periods of waves froman eclipse using a wavelet analysis: it would be highlyvaluable in future to apply the same technique to searchfor impulsive brightenings that could be a signature ofnanoflares, provided the false events could be reliably fil-tered out.

4. CONCLUSION

So, what do we have after all these stimulating talks? Athree-dimensional, multi-structured, coupled, dynamic,magnetic, photosphere, chromosphere and corona on awide range of scales, for which we need a strong couplingbetween theory and observations and a wide range of tal-ents in order to take our understanding to a new level. Inthis undertaking we can all as a community play our part.

Finally, our deep thanks go to Sami Solanki for invitingus here and to his merry gang (Andreas, Bernd, Eckart,Manfred, Jorg and especially Queen Davina for lookingafter us all so effectively. I hope that we can leave heredetermined to communicate the sense of vitality that wehave experienced to the young European scientists of thefuture.