interactions between nested sunspots - springer

Astron. Astrophys. 332, 353–366 (1998) ASTRONOMYAND

ASTROPHYSICS

Interactions between nested sunspots

II. A confined X1 flare in a delta-type sunspot

V. Gaizauskas1, C.H. Mandrini2, P. Demoulin3, M.L. Luoni2, and M.G. Rovira2

1 Herzberg Institute of Astrophysics, National Research Council of Canada, 100 Sussex Drive, Ottawa K1A 0R6, Canada([email protected])

2 Instituto de Astronomıa y Fısica del Espacio, IAFE-CONICET, CC.67, Suc.28, 1428 Buenos Aires, Argentina?

([email protected]; [email protected])3 Observatoire de Paris, DASOP, URA 2080 (CNRS), F-92195 Meudon Cedex, France ([email protected])

Received 22 August 1997 / Accepted 11 November 1997

Abstract. We study the flaring activity in a nest of sunspotsin which two bipolar regions emerge inside a third one. Thesebipolar regions belong to a large complex of activity (McMath15314) formed by five bipoles on its May 1978 rotation. Theusual spreading action during the growth of the bipoles leads tothe formation of a δ-configuration: the preceding and follow-ing spots of the two interior regions overlap (p-f collision) intoa single penumbra. While δ-configurations created in this waynormally favor strong flaring activity, only very small flares oc-cur during 5 days. Only when the following umbra in the δ-spotbreaks into pieces, accompanied by rapid photospheric motions,do intense flares occur. The largest and best observed one in thissequence, a class 1B/X1 flare on 28 May 1978, is remarkable forthe absence of ejecta and for the concentration of its emissionin three widely spaced sites, a pattern which holds in generalover two days for lesser flares. We take this pattern as evidencethat the flare is confined to the low corona. We first compute thecoronal magnetic field using subphotospheric sources to modelthe observed magnetic data and derive the location of separa-trices. In this case the magnetic field topology is defined by thelink between these discrete sources. The relevant generaliza-tion of separatrices in any kind of magnetic configuration are‘quasi-separatrix layers’ (QSLs). We calculate them using theprevious model, but also for a model obtained with a more clas-sical extrapolation technique based on the fast Fourier transformmethod. We show, with both approaches, that the plage bright-enings during the quiescent phase of the region and the flarekernels are located at the intersection of separatrices and QSLswith the photosphere. Moreover, they are magnetically linked.Bright and dark ‘post’-flare loops which form in the maximumand gradual phases of the 1B/X1 flare also highlight the loca-tion of the separatrices and the QSLs. This confirms previousstudies on the importance of the magnetic field topology for

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flares and, with this study, we further constrain the underlyingphysical mechanism. We draw some conclusions about the roleof magnetic reconnection in the solar corona; depending on thephotospheric conditions that we identify, reconnection can leadto steady heating or flaring.

Key words: magnetic fields – MHD – Sun: corona – Sun: flares– Sun: magnetic fields

1. Introduction

It is a common tendency of active regions (ARs) to emerge near,or even within, existing ones (see e.g. Gaizauskas et al. 1983).Such new flux emergence frequently leads to the formation ofcomplicated magnetic configurations (complexes of activity);they are known to be associated with enhanced activity sincethe new flux tends to reconnect with pre-existing fields. Severalobservational studies in different wavelengths show that flares,and even less intense coronal phenomena, are due to interactionsbetween coronal magnetic structures (see eg. Machado et al.1988; Shimizu et al. 1994; Hanaoka 1995; van Driel-Gesztelyiet al. 1996); while recent topological studies (see Mandrini et al.1996; Demoulin et al. 1997 and references therein) show thatthis interaction takes place via 3 dimensional (3-D) magneticreconnection at places where the field-line connectivity changesrapidly.

The energy needed to power flares, and also to heat the solarcorona, is thought to come from the coronal magnetic field andseveral flare models have been proposed. For example, it hasbeen argued that current sheets can store enough magnetic en-ergy to power a flare (Somov 1986, 1992 and references therein).At some point in the evolution, this current sheet becomes un-stable and turbulence develops increasing the plasma resistivity.

354 V. Gaizauskas et al.: Interactions between nested sunspots. II

Fig. 1. Photospheric magnetogram (NSO-KP) obtained on May 27 1978. The 8’ x 8’ box in the upper panel is seen close up below with thedifferent bipoles of the complex outlined with dashed curves. Letters designate each bipole in order of emergence, suffixes -p and -f are attachedto the letters to signify preceding and following polarity, respectively. This and all subsequent figures are oriented with North at the top, Westto the right.

Then, the stored energy is rapidly released as a flare (e.g. Hey-vaerts et al. 1977). It has instead been argued that reconnectiontends to occur at a rate imposed by the evolution of the magneticfield (e.g. Priest & Forbes 1992b). In this latter case, the currentin the sheet is always small and magnetic energy is instead storedin smooth field-aligned currents, such as a twisted flux tube, at aspatial scale (length typically 1-10 Mm) that gives a negligiblerole to the resistive term. In this evolution an ideal instabilityor non-equilibrium occurs forcing reconnection to take place atthe separator (e.g. Priest & Forbes 1990). Another possibilityis that the field-aligned currents are formed by photospheric orconvective motions and then carried towards the locations ofcurrent sheets where the stored energy can be rapidly released.This list of possible solar flare models is far from being com-plete, but it shows instead that we still need to combine a largeset of observations with adequate modeling of the magnetic fieldin a search about hints on the energy release process.

The 1B/X1 flare, which occurred on 28 May 1978 inside acollinear nest of three bipolar regions in McMath 15314 (CMP27 May 1978), is a very interesting case as the global evolutionof the region and the flare itself were well-observed. The mainobservational points that support this statement are:

1. Build-up was followed for many successive days at highspatial resolution in Hα . The complex of activity in whichthe flare occurred evolved slowly and without peculiar in-ternal motions: this makes it easier to model and to comparethe roles of emerging flux and sheared magnetic fields thanin other more complex and rapidly evolving cases. Key steps

in the energy storage and release process can be identified.A δ-spot formed when adjacent expanding bipoles, alreadyemerged, forced facing p- and f-polarity spots into contact(Gaizauskas et al. 1994; hereafter Paper I).

2. A high degree of spatial symmetry developed in the mag-netic pattern (three nested collinear bipoles). A direct testcan be made of the classic Sweet model for the formationof an X-type neutral point by approaching sunspots (Sweet1958).

3. For the 1B/X1 flare there is good evidence that pre-heatingplays a role for about 2 minutes before a very sharp flashphase. The Hα morphology suggests that the energy releasemechanism works in different ways at different stages duringthis event.

4. The 1B/X1 flare is a classic example of a confined flare (seeSect. 2.5).

5. Bright and dark ‘post’-flare loops (Schmieder 1992 and ref-erences therein), formed as transient features in the maxi-mum and gradual phases of this flare, highlight some of thefield lines belonging to the separatrices or QSLs derived forthis activity complex.

6. Three flares (two of X-ray class M1) homologous to the1B/X1 flare preceded it in a 4-hour interval; at least twomore homologues followed it in a 27-hour interval. Theseexamples (see Sect. 2.4) conflict with models proposing en-ergy storage for flares in neutral current sheets.

Therefore, the central aim of this paper is to use a large set ofphotospheric and chromospheric observations, combined with

V. Gaizauskas et al.: Interactions between nested sunspots. II 355

Fig. 2. Scheme of the splitting of Cf on May 28. The 2 fragmentshave larger velocities (≈ 100 m s−1) in the directions indicated by thearrows than the velocity of the whole spot before (≈ 30 m s−1) thesplitting. The dotted zone corresponds to the smallest cupola definedby the intersection of separatrices (see Fig. 11).

a model of the coronal field, to gain some insight to the build-up and release of energy in flares. We describe the long-termevolution and the quiescent state of McMath 15314 in Sects. 2.2and 2.3, while in Sect. 2.4 we describe in general its flaringstate. After this, we analyze in detail the different phases of thelargest flare occurring in the region (Sect. 2.5). We compute themagnetic topology of the nested bipoles using two methods:the source method (SM, Demoulin et al. 1992) and the quasi-separatrix layer method (QSLM, Demoulin et al. 1996). Bothmethods are discussed and compared in Sect. 3.1 and applied, inSects. 3.2 and 3.3, to the magnetic field observations obtainedon May 27 and 28 respectively. Our results show that the energyrelease sites, both during the quiescent and flaring phases, arerelated to the topological structures that we identify. Combiningthe observations with a magnetic field model, we discuss inSect. 4 what we have learned about the storage and release ofmagnetic energy in an active region.

2. Observational evidence

2.1. Data

The data used in this paper include daily magnetograms of theline of sight component of the field obtained at the NationalSolar Observatory at Kitt Peak (NSO-KP) and chromosphericfiltergrams photographed using a 25-cm refractor at the OttawaRiver Solar Observatory (ORSO). Filtergrams were taken every2.5 s at 15 wavelength positions across the central portion of Hαout to± 1.4 A. The data were obtained during the third passageof McMath Region 15314 across the solar disk, from 21 May to3 June 1978. In this study we will deal mainly with the eventsoccurring during 27 and 28 May 1978. More details about thecharacteristics of the data can be found in Paper I.

2.2. Evolution of the complex of activity: clues on the storageand release of magnetic energy

This so-called ‘Great Complex of Activity’ (Gaizauskas et al.1983) on its third rotation consisted of five magnetic bipoles,labeled in chronological order of emergence in Fig. 1. Bipole Asurvived from the previous rotation; B and C were formed just

before and just as the complex made its eastern limb passage,respectively. Bipoles D and E were born on the visible disk on22 and 26 May, respectively. Concerning the evolution of thenested collinear sunspot groups, the penumbra of spot Df waspartially formed on 23 May (Fig. 4b of Paper I). The formationof a δ-spot then began on 24 May with the approach of spotsCf and Dp (Figs. 4b and 6 of Paper I). It is characterized by agrowing overlap of the penumbra of these spots; they reach theirclosest approach on 27 May (see Sect. 2.3). A detailed study ofthe nested spots is presented in Paper I.

A δ-type sunspot is often associated with rapidly changing,complex magnetic patterns. Here, throughout the slow creationof this δ-spot, ordinary evolutionary processes were at work onordinary sunspots. For nearly 100 hours, until 28 May 1978,there were no twisting or shearing motions by the collidingcomponents inside the δ-spot. During this continuous approachthere was no flaring activity until 27 May when very small flareserupted over Dp and Cf (see Sect. 2.3). During this period, en-ergy was being released in the steadily compressed magneticfields of the colliding bipolar regions. The system seems a realversion of the textbook example proposed initially by Sweet(1958) in his neutral point theory of solar flares. In reality, asdescribed in the next paragraph, the big energy release does nothappen through continued steady merging of adjacent fields.Other events intervene.

On 28 May, a new relative motion of the umbrae in the δ-spot replaced the strictly converging motion of the preceding 5days. The critical events happened in a 15-hour interval whenthere were no observations at high spatial resolution. In thisperiod the Cf-umbra split into 2 fragments which flew apart innew directions shearing past the now distorted Dp-umbra at ≈100 m s−1 (see Fig. 5 of Paper I and the scheme in Fig. 2). Infact, the time of the Cf splitting can be circumscribed by a 6hour gap between a full disk white light photograph obtained atKodaikanal Observatory (7:36 UT) and the first ORSO image on28 May (13:37 UT). A possible scenario, based on observationsfrom just before to just after this blank window, was developedin Paper I to account for the disrupting f-spot. It invokes thefluting instability to drive the disruption and the suppression ofthe vertical escape of sub-surface heat flux between the collidingspots to trigger it.

There is serious flaring only after the splitting of Cf: two M-class flares and a subflare in the 4 hours preceding the 1B/X1flare. The energy build-up for the 1B/X1 event takes no longerthan 90 minutes since the peak of the preceding class SN/M flare;even then it is interrupted about mid-way by a minor energyrelease in a small subflare (Fig. 3a). The shearing motion isthen sustained for the remainder of the lifetime of the δ-spot. Itsonset coincides with flare activity on an unprecedented scale inthis activity complex during Carrington Rotation 1668. It musttherefore be a key ingredient to the energy release process. Sincefield lines are rooted in the diverging fragments of the Cf-umbra,they will slip through each other and create current sheets. Theprocess is a gradual one, because some of the kernels in thesuccession of flares early on May 28 recur close to the samelocation.


Fig. 3a–f. Stages of the 1B/X1 flare on May 28 as seen in raw (undigitized) off-band Hα images from ORSO. a Kernels of a prior subflare atits maximum phase. b Onset of the 1B/X1 flare. It coincides with the onset of GOES X-ray burst, but precedes the onset of 10 cm burst by 1minute (see Fig. 7). c Beginning of the impulsive phase of the 1B/X1 flare in Site 1. d Beginning of another impulsive phase at remote Site 2.The time delay with respect to the brightening of Site 1 is ≈ 77 s. e Beginning of a third impulsive phase at remote Site 3. Although closer toSite 1, Site 3 is energized ≈ 76 s after Site 2. f A fourth remote flaring site shows a single kernel when the other sites approach maximum sizeand brightness.


Fig. 4. Umbral dynamics (upper 6 frames, digitally enhanced to show umbral details) and miniflare activity (lower 3 frames) on 27 May 1978in the δ-spot formed by colliding p- and f-spots. Numerals in the upper left indicate the offset in Angstrom units from the center of Hα, UT isshown in the lower right of each frame. Frame size is 48”x 27”.

2.3. Flaring activity just before disruption of Cf

On the day preceding the 1X/1B flare, 27 May 1978, the ap-proaching umbrae were actually closer together than they werejust before or just after this event; at the narrowest part of thegap between umbrae the distance was ≈ 3200 km (see Table 2in Paper I). Thirteen flare-like events were observed over theδ-spot in the ORSO data for that day, they were so small thatonly one of them was noted by the flare patrols reporting to So-lar Geophysical Data (SGD) (Fig. 14c in Paper I shows one ofthese events). At the same time, and at the photospheric level,the colliding p-f umbrae were undergoing dynamic changes intheir internal structure. The 6 upper panels in Fig. 4 show thattwo bright fingers traversed the Cf-umbra in almost 2 hours,and that one corner of the Dp-umbra was covered by intrudingpenumbra in about the same time. We interpret this as evidencefor reconfiguration of the compressed sunspot fields on a smallscale. The numerous miniflares (three different ones are shownin the lower panels of Fig. 4) can be taken as evidence for theformation of current sheets during the reconfiguration. The totalenergy released by these transient events is negligible comparedto the 1B/X1 flare.

2.4. Flaring activity following disruption of Cf

2.4.1. Flares on 28 May 1978

Referring to the GOES satellite soft X-ray data (1 - 8 A channel),serious flare activity probably began around 10:47 UT on 28

May when a class M1 event was attributed to this region from anormal subflare. Another class M1 event peaked at 13:15 UT. Itwas observed in progress at ORSO at 13:37 UT to have two flarekernels, one each at the edges of the umbra of Cf and Dp (notshown). A short-lived subflare with no recorded GOES eventerupted at 14:12 UT with several kernels, again on the edgesof each of the same two umbrae and in the gap between them(Fig. 3a). The next flare, the most powerful from this region,peaked at 15:02 UT as a class 1B/X1 event (see Sect. 2.5). Thesubflare and the dying phase of the second M-class flare wereobserved at ORSO to be homologous with the X1 flare in thelocation of off-band kernels in the gap between Cf and Dp; thesame was true of the first class M1 flare observed at Catania (F.Zuccarello, private communication). A subflare erupting fivehours after the 1B/X1 flare was a much weaker homologue withHα ribbons at sites 1, 2, and 3.

2.4.2. Flares on 29 May and 30 May 1978

Two more flares (not shown) erupted in McMath 15314 duringan 8-hour interval observed at ORSO on 29 May. The earliersubflare was unrelated to any of the sites of the 1B/X1 flare; thesecond erupted 2.5 hours later as a slowly rising 1B/C1 flare withribbons occupying locations similar to sites 1, 2, and 3 of the1B/X1 flare. Despite large disparities in the speeds of onset inHα and in the magnitudes of soft X-ray flux, we infer that the 1Bflares of 28 and 29 May were triggered by similar mechanismsconfined to the polarity inversion in the δ-spot and the energy


Fig. 5a–f. Enlarged, digitally enhanced views ofthe 1B/X1 flare at Hα + 1.0 A from: a the onset, bgrowth of additional kernels, c impulsive brighten-ing of new kernel at the arrow, d filling in of ribbonsand eruption of S-shaped structure at T, e maximumphase with first sign of emitting loops crossing be-tween flare ribbons, f to further spreading apart ofthe flare ribbons and development of bright emit-ting loops. The polarity inversion line is shown asa full trace and it is calculated from the coalignedNSO/KP magnetogram for May 28. Each frame is40”x 81”.

was transported to the two remote sites over a magnetic topologywhich did not alter significantly during 27 hours.

By 30 May, however, subflares were triggered inside the δ-spot of McMath 15314 in entirely different locations (describedby Gaizauskas 1986). After two days, therefore, the magnetictopology changed significantly due to the rotation and shrinkingof the spot pair Cf-Dp and to the rapid expansion of a major newbipole on the leading edge of the activity complex comprinsingMcMath 15314.

2.5. The 1B/X1 flare on 28 May 1978

2.5.1. Characteristics of the event

The ORSO images of the flare taken in the core of the Hα lineare so close to saturation that we rely on the off-band images,mostly in the red wing, to describe important properties of theflare (see Fig. 3). During the whole event there was no filamentejection, nor any Type II, III, IV, or V radio bursts. Yet the softX-rays (GOES) reached a peak flux of 1.3 10−4 watts m−2 anda class 3 solar interplanetary disturbance was reported, makingthis a major X-ray event. The absence of any signature of ejectadisqualifies this flare from being classed as an eruptive event.‘Confined’ is a better term to apply to this flare than ‘compact’


Fig. 6. Soft X-ray flux in the 1 - 8 A channel of the GOES satellite forthe 1B/X1 flare of May 28 1978.

because its four remote flaring sites are spread over a region of100 Mm width (see below).

During the onset phase, starting at 14:56:13 UT, the flareconsists of a string of bright kernels - 2 sets of 3 kernels locatedat Site 1, one set per umbral rim of the colliding p-f pair - alignedobliquely across the polarity inversion line at the photosphere(Fig. 3b and Fig. 5a). Their number grows and the space be-tween them fills with emission; the kernels progressively trans-form to ribbons (Fig. 3c,d and Fig. 5b,c). The observations lackthe temporal resolution to decide whether the kernels light uptogether or in succession, if they move along the string or stayput. This stage lasts 2 minutes, up to the time of a very largespike in soft X-rays at 14:58:21 UT (Fig. 6). Thereafter, the mor-phological character of the emitting ribbons changes (compareFig. 5c to Fig. 5d).

The flash phase occurs at 14:58:21 UT in an interval com-parable to the 3-sec sampling time of GOES, within which theflux shoots up to 18 times the preflare threshold (Fig. 6). Theflux drops back to the rising background in 9 s. The Hα re-sponds at the same time with a brilliant flash centered on Site1 (Fig. 3e and 5d). Prior to the flash, a kernel brightens at theNorth end of Cf (Fig. 5c, at the arrow). At 13 s before the X-rayflash, the kernel grows into a S-shaped structure aligned alongthe ribbon overlaying Cf (Fig. 5d, at T). Immediately after theflash (Fig. 5d) the S-shaped structure shifts away from the flareribbon over Cf (Fig. 5e, f). The 1 - 8 A X-ray flux reaches itsmaximum at 15:02:20 UT (Fig. 6). By this time the Hα ribbonsare clearly separated, but are joined by bright strands traversingthe polarity inversion line (Fig. 5e,f). The development of thebright loops is presented in Sect. 2.5.2.

Hα emission also builds very rapidly in other kernels locatedat several remote sites spread over the activity complex: Site 2,at a plage with pores of p-polarity South of Cp and Site 3, atthe spots of f-polarity in D (Fig. 3). Finally, Site 4 appears laterbetween the colliding Cp and Bp spots (Fig. 3f). As discussed inSect. 3.3 we believe that Site 4 does not brighten as a result of the

Fig. 7. Microwave burst at 10-cm wavelength associated with the1B/X1 flare from Algonquin Radio Observatory.

same energy release process that produces the other sites, eventhough the change caused in the global magnetic configurationof the activity complex after the big flare could have causedits brightening. The surge-like feature above Cp (Figs. 3) is infact one of many episodes of downflow in a large absorbingarch spanning most of the activity complex (Paper I, Fig. 2).This episode began ≈ 14:56 UT and faded out by 15:26 UT onMay 28. It may be a signature of large-scale ‘post’flare loopsconnecting Df to Cp (see Sect. 2.5.2).

Concerning the emission in radio wavelengths during thisflare, the peak flux density of single-frequency radio events in-creased with increasing frequency (SGD, No.411, Part II, p.48).We reproduce in Fig. 7 a copy of the original record made bythe 10-cm flux patrol at Algonquin Radio Observatory. The peakemission at 15:01.3 UT is a mere 34 solar flux units (sfu), oneto two orders of magnitude smaller than many flares of simi-lar optical and X-ray radiative output. There is no signature inthis 10-cm flux record coincident with the soft X-ray spike at14:58:21 UT. Other stations with higher frequency receivers re-ported higher peak emission for this event (e.g. 378 sfu at 3.4cm wavelength). From this, we infer that energy at microwavewavelengths was released at a very low height of the atmospherein at least 6 impulsive episodes over a time span of 3 minutesor more (see Fig. 7).

2.5.2. Bright and dark ‘post’-flare loops

Several systems of loops appear during the maximum and grad-ual phases of the 1B/X1 flare. A system of short (≈ 7600 km)bright loops, visible in the red wing at Hα + 1.0 A beginning≈ 15:01 UT, links the rapidly spreading flare ribbons obliquelyacross the polarity inversion at Site 1 (Fig. 5e,f). They are ini-tially invisible in the blue wing of Hα and in the core of the linewhere small-scale features are obscured against a backgroundsaturated with flare emission. They are best seen≈ 15:06 UT inthe red wing (Fig. 5f) and then fade beginning≈ 15:09 UT, los-ing all visibility at that wavelength by≈ 15:20 UT. They remain


Fig. 8a–h. Development of hot and cool loops at Site 1 of the 1B/X1 flare of 28 May 1978. a Preflare status. b Short bright loops indicatedbetween arrows separating flare ribbons 1e and 1w. c Dark loops (between arrows) replacing bright loops between the separated flare ribbonsat Site 1. d 4.7 hours after flare onset a short dark loop connects sunspots Dp (lower left contour) and Cf (upper right contour) at Site 1. eRed-shifted loops link Sites 2 and 3 and Site 3 with spot Dp. Note enhanced absorption at the footpoints. f Cool loops blanket the entire areabetween Sites 2 and 3 and between Sites 1 and 3 as fine dark threads. g Connection of some cool loops anchored at Site 2 switched from Site3 to spot Dp at Site 1. h Cool loop anchored at Site 2 traverses spot Dp. A shorter loop system links Dp with Site 3. Figures in the upper leftcorners correspond to the offset (Angstroms) from the center of Hα. Each panel is 198”x 143”.


visible in wavelengths near the core of the line until they are re-placed entirely by dark loops≈ 15:24 UT (Fig. 8c, between thearrows), about 5500 km in length. With time the nice alignmentof the short dark loops gives way to disordered dark fine struc-ture (Fig. 8f), and then hours later to a simple dark structureconnecting Dp with Cf (Fig. 8d, between the contoured spots).Bright and dark loops at Site 1 proceed from an initially sim-ple geometry of lines linking opposite polarities (Fig. 9a) to avery complex one (Fig. 9b) before returning to a simple linkage(Fig. 9c). This suggests that the field lines in the vicinity of theseparator (Sect. 3.3) are violently perturbed during the flare andtake hours to return to a stable equilibrium.

A system of longer cool loops blankets the flaring region fora short time during the gradual phase; it is best seen in a moviemade from ORSO data in the core of Hα and kindly providedby Sara Martin. The entire episode lasts a half-hour, from ≈15:35 UT until ≈ 16:05 UT. The development can be followedin Fig. 8, where panels A, B, and C show an improving regu-larity in the alignment of fibrils between flare ribbon 1e (panelB) and ribbon 3. The alignment is most striking ≈ 15:41 UT(Fig. 8f), by which time flare ribbon 1e has faded considerably.The loops consist of many fine dark threads (≤ 1”) (Fig. 8e,g h);and since they are invisible in the blue wing of Hα, we can taketheir heavily absorbing footpoints in the red wing as evidenceof strong downflows. The visibility of different loop systemschanges quickly with time. Initially, one long set connects di-rectly from Site 2 to Site 3 (Figs. 8e,f), while another shorter setconnects Site 1e to Site 3 (Figs. 8c,e,f). Within a few minutesthe linkage between Sites 2 and 3 fade and other loops betweenSites 2 and 1e become the dominant features (Figs. 8g,h).

We take the change and the downflow in the individual loopsconnecting Site 2 to Site 3 as evidence for plasma condensingvia radiative cooling of hot loops connecting the flare ribbonsas usual in ‘post’-flare loops (Schmieder et al. 1995). They cor-respond to the second set of reconnected loops (the first onebeing the usual ‘post’-flare loops at Site 1; see Sect. 3.3). Thepresence of other loops connecting Sites 1e to 3 and 1e to 2 ismore difficult to understand because these loops seam to outlinethe initial magnetic connection (before reconnection!). A strongcompression of the plasma is unlikely to occur before the recon-nection process because the velocities are sub-Alfvenic there,and because the volume of a flux-tube going to the reconnectionregion increases (the volume per unit of magnetic flux is givenby∫ds/B which is maximum at the QSLs in such quadrupolar

configuration: see Fig. 3b of Demoulin et al. 1996). One possi-bility is that energy is transported from the reconnected loopsto the pre-reconnected loops by radiative transfer in the lower(denser) part of the configuration. This may induce a gentleevaporation in the pre-reconnected loops. This mechanism ismost efficient if the evolution is slower than the radiative-timescale, so we expect qualitatively to have it at work at the end ofthe main phase, as observed.

2.5.3. Energy transport mechanism

Prior to the 1B/X1 flare there were no signs of excess energybeing stored at Sites 2 and 3. We deduce this from the direc-tion of chromospheric fibrils that we have used in all cases asproxy tracers of the horizontal component of the field, sinceno vector magnetograms are available for these days. We thenconclude that Sites 2 and 3 result from sudden deposition ofenergy coming from a remote region that we have located ata low coronal level above Site 1 from the magnetic computa-tions (see Sect. 3.3). Assuming that just one initial release ofenergy occurs there, we can estimate the speed of the distur-bances traveling to the remote sites. We measure the delays (seeFig. 3) from the moments when impulsive brightenings of ker-nels are detected at each of the sites in red-wing filtergrams. Thetiming for these impulses are: 14:56:13 UT at Site 1; 14:57:30UT at Site 2; and 14:58:46 UT at Site 3. Due to our short sam-pling interval between photographs and the impulsiveness ofthe phenomenon, our timing estimates are in error by no morethan 20 s. We estimate the distance between these sites in twodifferent ways, what gives us a velocity range for the travel-ing disturbance. Using the projected distance on the images, wefind speeds of about 250 km s−1 for a disturbance traveling toremote Site 2, but only 140 km s−1 to the closer Site 3. On theother hand, taking a line integral along field lines connecting therelevant sites, we find speeds of 1200 km s−1 to Site 2 and 660km s−1 to Site 3. The values we have found point to a mech-anism of energy transport by a thermal-conduction front (seeBagala et al. 1995 and references therein for a justification).In the present event, the slower velocity corresponding to thedisturbance traveling to Site 3 may be due to the fact that thelower set of magnetic field lines have a cooler and denser plasmatrapped, in comparison to the higher field line connections tothe West towards Site 2 (see Sect. 3.3).

3. Model and magnetic field topology

3.1. Our view on 3-D magnetic reconnection

The 3 dimensional (3-D) characteristics of magnetic reconnec-tion are highly complex and are only just beginning to be un-derstood (Schindler et al. 1988; Priest & Forbes 1992a; Lau& Finn 1990; Priest & Titov 1996). From a classical point ofview magnetic reconnection is closely related to the existenceof separatrices or of their intersection (the separator) and, so, tomagnetic null points. That is to say, in 2-D and 2.5-D approachesmagnetic reconnection is thought to occur at places where thefield-line mapping is discontinuous.

When an observed 3-D magnetic configuration is modeledby a series of sources, the 2-D picture of magnetic reconnec-tion can be directly generalized. Separatrix surfaces divide themagnetic volume into topologically distinct regions, in the sensethat any of them contains only field lines that start at a particularsource and end up at another particular source; when magneticreconnection occurs, magnetic flux is transferred from one re-gion to another. Baum & Bratenahl (1980) were the first to cal-culate the topology of a potential configuration formed by four


Fig. 9. Close-up view of dark loops at flare Site 1 during the gradualphase. Each panel is 28” x 78”.

magnetic poles; then, Gorbachev & Somov (1988, 1989) appliedthe same idea to an observed active region (AR). The next stepwas to introduce many subphotospheric sources (Mandrini et al.1991, 1993) and to determine their positions and intensities bya least-square fitting of the computed magnetic field to the ob-served one (Demoulin et al. 1994b). Using this Source Method(SM) to determine the magnetic topology, we have found thatHα flare brightenings and photospheric current concentrationsare located on the intersection of separatrices with the photo-sphere and that they can be connected by field lines (Mandrini etal. 1991, 1993, 1995; Demoulin et al. 1993, 1994b; van Driel-Gesztelyi et al. 1994; Bagala et al. 1995). Furthermore, flarekernels do not extend all along separatrices but lie on portionsof them where the connectivity of field lines changes rapidlyfrom one side of the separatrix to the other. For some of thestudied ARs we have found a magnetic null point in the extrap-olated coronal field, mainly when an almost oppositely orientedbipole emerged between the two main polarities of a group ofspots (see Sect. 3.2). However, several ARs contain no such nullpoints (Demoulin et al. 1994a); that is to say, no discontinuityis present in the coronal linkage (see Sect. 3.3).

The so-defined SM has two main limitations: first, one needsto integrate below the photosphere along a few thousands kilo-meters, where a magnetic field model is not available; second,it cannot be used with other extrapolation techniques becauseit intrinsically needs sources to define the connectivity. Theselimitations, together with our findings described in the previousparagraph, pointed out the need for a method that could takeinto account only the field-line linkage above the photosphere.This method came together with new developments in 3-D mag-netic reconnection (Priest & Demoulin 1995). In this work we

propose that magnetic reconnection may occur in 3-D in theabsence of null points at quasi-separatrix layers (QSLs), whichare regions where there is a rapid change in the mapping of fieldlines from one boundary to another of a given magnetic volume.

QSLs are defined in terms of a dimensionless function thatwe call N . If we integrate, over a distance s in both directions,a field line passing at a point P(x, y, z) of the corona, the endpoints of coordinates (x′, y′, z′) and (x′′, y′′, z′′), define a vectorD(x, y, z) = {X1, X2, X3} = {x′′ − x′, y′′ − y′, z′′ − z′}. Arapid change in field-line linkage means that for a slight shiftof point P(x, y, z), D(x, y, z) varies greatly. In the solar case,the distance s to be used is the distance to the photosphere(z′ = z′′ = 0) and the expression for N (x, y) is:

N (x, y) =

√√√√∑i=1,2

[(∂Xi

∂x

)2

+

(∂Xi

∂y

)2]. (1)

This function is evaluated on the boundary and represents thenorm of the displacement gradient tensor defined when map-ping, by field lines, points on one boundary to the other of agiven magnetic volume; both boundaries correspond to differentsections of the photosphere in our particular case. The locationsof the high values ofN (x, y) characterize the field lines involvedin the QSLs; following these lines we can locate the coronal por-tion of these layers. QSLs are open layers that behave physicallylike separatrices when their thickness is small enough so thatthe resistive term in the induction equation becomes importantfor the magnetic field evolution. A discussion on the propertiesof N (x, y) and the basic characteristics of QSLs, together witha description of the QSLM, can be found in Demoulin et al.(1996). The QSLM requires only a model of the coronal mag-netic field. Thus, we can either use a model with sources or ex-trapolate the photospheric longitudinal field (Bl) to the corona.In the last case we use the discrete fast Fourier transform (FFT)method under the linear force-free field (∇×B = αB, with αa constant) hypothesis, as proposed by Alissandrakis (1981).

3.2. Quiescent state of McMath 15314: 27 May 1978

Fig. 10a shows a portion, centered in the δ-spot, of the NSO-KPmagnetogram obtained on 27 May at 13:47 UT. Since no vectormagnetograms are available for this and the following day, wewill model the observed Bl only in the potential approach. Theresults of the SM using a model with 32 subphotospheric sourcestogether with the plage brightenings observed at ORSO at 18:14UT, can be seen in Fig. 10b. These brightenings are locatedon or close to the computed separatrices; it is remarkable howthey follow the round shape of the small separatrix to the East.We have also derived the locations of QSLs at the photospherefor the same model of the field (not shown); comparing bothresults we have found that the sections of QSLs, where the plagebrightenings lie, are located along portions of separatrices ashappens for other studied flares (see Mandrini et al. 1997).

Fig. 10c corresponds to the QSLM for a FFT extrapolationof the observed field. This representation of the field is morerealistic than a model with sources, where we only keep the


Fig. 10a–d. Magnetic topology for McMath 15314 on 27 May 1978. a Observed longitudinal field. Three isocontour levels ofBl (± 300, 1000,1500 G) are shown with positive and negative values drawn with solid and dashed lines, respectively. All distances are in Mm. b Intersectionof the separatrices (thick lines) with the photosphere for a model with 32 magnetic sources (as shown by the Bz isocontours having the samevalues as those of Bl). Hα plage brightenings are represented as hatched regions. Local x and y point to the West and North, respectively. cIntersection of the QSLs with the photosphere (thick isocontour lines of N = 20) for a potential extrapolation of Bz using the fast Fouriertransform method. Four field lines showing the different kinds of connectivity have been added (see text). d Lateral view of Fig. 10c (viewedfrom the West). The four kinds of field lines meet in a region with a top height of ≈ 8 Mm. Each division corresponds to 2 Mm.

main flux concentrations; and the location of QSLs should bemore precise in this case and not necessarily coincident withthose derived from a model with sources. Comparing Figs. 10band c, it can be seen that QSLs and separatrices coincide or lievery close to the location of plage brightenings. In this last figurewe have also drawn four field lines, issued form both sides ofQSLs at the photospheric level, corresponding to the differentkinds of connectivities: Dp - Cf and Df - Cp are shown withcontinuous style, while Df - Dp and Cf - Cp with dotted anddash-dotted lines respectively. A lateral view of these field linesis shown in Fig. 10d, it can be seen that they meet at a heightof ≈ 8 Mm in the corona. Their shape is typical of the shape oflines around an X-type neutral point; in fact we found for themodel with sources (using the method described by Demoulin etal. 1994b) that a magnetic null point exists in the configurationat that location. With the FFT extrapolation, we found QSLsso thin (as small as the computer resolution (10−15 Mm !) –see Demoulin et al. (1996) for a definition of the thickness ofQSLs) that a null point is also present. Therefore, magnetic fieldreconnection seems to be at work at QSLs in a steady and gentleregime during this quiescent state induced by the convergence

of Dp and Cf (see Sect. 2.2); the energy release site lies towardsthe East of the polarity inversion line of the p-f colliding pairvery low in the corona (Fig. 10d). Besides, as energy releaseduring this state stays at a very low value, we do not expect tofind remote brightenings as is the case with Sites 2 and 3 for the1B/X1 flare.

3.3. Flaring state of Mc Math 15314: 28 May, 1978

We apply here the SM and the QSLM to the magnetic fieldobservations obtained at NSO-KP on 28 May 1978 at 13:38 UT.The result of the FFT extrapolation, corresponding to the portionof the magnetogram comprising the same region as in Fig. 10a,is shown in Figs. 10c and d together with QSLs. No remarkablechanges can be observed when comparing Figs. 10 and 11 at theplaces of high magnetic intensity, except an extension towardsthe West in Cf; by this time this spot had already broken. InFigs. 11a and b we show the result of the SM for a model with32 sources representing again B, C and D bipoles. The computedseparatrices have been overlaid in Fig. 11a to the off-band Hαimage obtained at flare onset, 14:57:13 UT (see Fig. 3b). It can


Fig. 11a–e. Magnetic topology for McMath 15314 on 28 May 1978.The drawing convention is the same as in Fig. 10. a, b Intersectionof separatrices (thick lines) with the photosphere for a model with32 magnetic sources overlaid with the Hα kernels at the onset andmaximum of the 1B/X1 flare corresponding respectively to Figs. 3band 3f. c, d QSLs computed at the photosphere (thick isocontour linesofN = 20) for a potential extrapolation using the fast Fourier transformmethod. The coronal linkage at the borders of QSLs is shown with fieldlines connecting Cf to Cp and Df to Dp in (c), and Dp to Cf and Df toCp in (d). e Boundaries of separatrices plotted onto image with coolflare ‘post’-flare loop visible in the gradual phase at 15:46:07 for the1B/X1 flare of 28 May 1978.

be seen that the brightest part of Hα kernels lie exactly on theboundaries of separatrices enclosing regions C and D. Fig. 11bshows the overlay of separatrices with an off-band Hα imageobtained at 15:00:03 UT (see Fig. 3f). In this case the fit is lessgood, chiefly at Site 3, and the emission has spread beyond theseparatrix boundaries. The lack of agreement is mainly due tothe fact that the magnetic modeling cannot take into accountthe shearing motions affecting the field lines during this period.Separatrices and QSLs lie also in this case very close to eachother, except at low field regions (Figs. 11c,d). Notice also that,in spite of some changes in the field between 27 and 28 May,the magnetic topology of the complex stays the same; this isbecause the locations of QSLs depend on the global propertiesof the configuration which remain the same from one day to thenext.

We have calculated the value of the thickness of QSLs at thelocation of Hα kernels, as for 27 May (see Sect. 3.2); it staysas small as the computer precision. The separator is located

Fig. 11a–e. (continued)

towards spot Dp (as for May 27, see Fig. 10d) at an estimatedheight of 10 Mm, very low in the corona. The likeliest place forreconnection to occur is along this region, since all the field linesalong QSLs, including the ones tied to the moving fragment ofthe f-umbra, thread through it. The character of the radio bursts(Sect. 2.5) is also consistent with a low height for the energyrelease site in this flare.

For the first time in a study of the influence of the magneticfield topology on flares, we can also show a close connection be-tween the location of cool ‘post’-flare loops and magnetic sepa-ratrices. As the flare evolves and the flare ribbons at Site 1 spreadapart, the ‘post’-flare loops joining them lengthen (Fig. 5). Theorientation and location of the bright strands matches the mod-eled field lines in Fig. 11c and d. We have also identified theother set of reconnected loops as the large scale dark loops with


Fig. 12a and b. Perspective view of Fig. 11 showing the coronal link-age at the borders of QSLs with field lines drawn as surfaces (foraesthetics we enhanced the vertical scale by a factor 1.5 compared tothe horizontal one and we have chosen a back-side point of view). aCorresponds to Fig. 14 c); the dark gray (light gray) ribbon shows theconnection between Cf and Cp (Df and Dp). b Corresponds to Fig. 14d); the light gray (dark gray) ribbon shows the connection between Dpand Cf (Df and Cp).

downward flows (Fig. 8). We plot the boundaries of the sepa-ratrices in Fig. 11e on the relevant portion of panel H in Fig. 8,taken in the gradual phase of the 1B/X1 flare. The prominentred-shifted loop is anchored in the photosphere on the boundaryof a separatrix; it follows the boundary so closely that we haveomitted a portion of it to avoid obscuring the loop.

4. Summary and conclusion

We have focused this study on the flares occurring in a com-plex of activity where a large set of observations is available,in particular in Hα. The long-term evolution of the region hasbeen extensively studied before (Gaizauskas et al. 1994). A δ-spot formed when adjacent expanding bipoles, already emerged,forced facing p- and f-polarity spots into contact. In the presentpaper, we computed the separatrices and QSLs using a po-tential extrapolation of the photospheric magnetogram (usingsub-photospheric sources or a FFT method). The different ap-proaches show coherently that flare kernels are located on thecomputed separatrices and QSLs. They can be linked, two bytwo, by the computed field lines. The magnetic configuration isa classical quadrupolar one with energy release on the separa-trices, that is partially conducted down to the chromosphere toform the observed Hα ribbons (Fig. 12). This confirms previousresults obtained for other flaring regions (Demoulin et al. 1997)and makes it evident that magnetic reconnection is at the originof the studied flares.

For the first time in a study of the influence of the magnetictopology on flares we can also demonstrate a close connection

between the location of cool ‘post’-flare loops and magneticseparatrices. The ‘post’-flare loops are reconnected magneticloops linking the ribbons at flaring Site 1. This indicates theway magnetic reconnection proceeds during this flare: field linesconnecting initially the two independent bipoles Df-Dp and Cf-Cp, reconnect and form the new connectivity Dp-Cf and Df-Cp.In a now classical model, the plasma is first compressed andheated, then ejected both up and below the reconnection region.The transport of energy to the chromosphere drives evapora-tion which further increases the reconnected-loop density. Theincrease of density induces enhanced radiative losses which trig-ger a thermal instability, then dense and cool loops are formed(Forbes & Malherbe 1986, 1991). This model is usually invokedto explain the observed lower reconnected loops only; the onesabove the reconnection site, while formed by the same mecha-nism, are usually not observed. The main differences betweenthe reconnected loops up and below the reconnection region aretheir lengths and volumes. Even with the same energy input,these differences imply a much lower temperature and density(in particular, because of a much smaller evaporation) for theupper loops. However, these large-scale reconnected loops havebeen observed in some X-ray events ranging from bright points(e.g. Mandrini et al. 1996) to eruptive flares (e.g. Manoharan etal. 1996). In Hα, flare observations are usually limited to thelower loops giving the false impression that magnetic configura-tions where flares occur are simple arcades. In Mc Math 15314region the large set of Hα observations allows us to observe inpart the large scale loops as elongated dark features with down-ward flows. As explained above, their formation is similar tothat of the classical ‘post’-flare loops, in particular they showthe same plasma dynamic: downward motions of the dense andcold plasma.

Because this active region was very well observed duringweeks we can infer how the build-up and release of magnetic en-ergy occurred. The usual spreading action during the growth ofthe young bipoles leads to the formation of a δ-configuration: thepreceding and following spots of the two inner regions overlap(p-f collision) into a single penumbra. While δ-configurationscreated in this way normally favor strong flaring activity, onlyvery small flares occur during 5 days. Only when the followingumbra in the δ-spot breaks into pieces, accompanied by rapidphotospheric motions, do intense flares occur. The largest andbest observed one, a class 1B/X1 flare on 28 May 1978, is a clearexample showing the need of magnetic shear before a large flarecan occur.

The computed magnetic topology shows that the flaring partof the region is quadrupolar, implying the interaction of two,nearly aligned, bipoles (called C and D). The starting configu-ration is simple: four aligned spots with a potential coronal field.With only converging motions, as observed before 28 May, anideal-MHD evolution keeps the magnetic field potential exceptat the separator location where a current sheet is formed (e.gSweet 1958). The observations show that the energy is not storedin this configuration, but that it is almost continously releasedover two days producing brightenings as homologous flares atthe chromospheric level where separatrices are located. This


study is an example against the storage of magnetic energy inneutral current-sheets (see e.g. Somov 1992). Because of thevery small scales involved in the current-sheet formed, the re-sistive term is locally important so that reconnection proceedsat the speed at which the photospheric motions drive the system(see Priest & Forbes 1992b).

When shearing motions appear, due to the splitting of spotCp, observations show that magnetic storage can then take placeand large flares occur. What are the basic differences that shear-ing motions bring compared to converging ones? First, withshearing motions, a non-neutral current sheet is formed; not thethree components of the magnetic field, but only two reversewhen crossing the current sheet. Then added magnetic shearintroduces a longitudinal component of the field to the currentsheet that may stabilize it (Somov & Titov 1985). Second, thecurrent sheet is formed, not only at the separator, but also allalong the separatrices of the 2 1

2 D configurations (e.g. Low &Wolfson 1988; Finn & Lau 1991; Vekstein & Priest 1992). Thiscan be generalized in 3-D configurations to the formation of highcurrent densities at the locations of QSLs (Demoulin et al. 1996).The results of this evolution can be a larger storage of energyand a dissipation spread along separatrices, but this needs fur-ther theoretical development. Third, shearing motions are alsoable to store magnetic energy in the whole magnetic volume.The associated electric currents are distributed in the large scaleand, therefore, they are weakly dissipated. Storage of energycan proceed until the configuration becomes globally unstable.Then, as reconnection proceeds, these currents are progressivelypushed towards the QSLs and a flare occurs. This process canrepeat itself in a series of homologous flares until the contribu-tion to the overall topology by existing flux sources vanishesor is dominated by a new bipolar source arising elsewhere in-side the activity complex. In summary, the present observationsput further constraints on the flare mechanism: neutral currentsheets are unlikely to store significant energy. They rather favorthe storage of magnetic energy distributed in the magnetic con-figuration, though non-neutral current sheets are not excludedby these observations.

Acknowledgements. We thank Dr. Karen L. Harvey for transferring themagnetic field observations to us from the data archive produced coop-eratively by NSF/NOAO, NASA/GSFC, and NOAA/SEC. We thankSara F. Martin for producing a video movie of the 1B/X1 flare, and D.Wilkinson of NOAA, Boulder, for providing the high time resolutiondata from the GOES archive. P.D., C.H.M and M.G.R. acknowledgefinancial support from the CONICET (Argentina) and CNRS (France)through their Argentina/France cooperative science program.

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