The Topology of Magnetic Reconnection in Solar Flares

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38This example is similar to the reasoning used to explain two ribbon flares with shearedarcades. When a sheared magnetic field suddenly releases energy in the form of a tworibbon flare, domains of source pairs initially far apart and nearly empty of flux now havetoo little flux relative to a lower-energy field. In order to lower the energy state, flux isadded to the underlying deficient domains, reducing the shear in the field and increasingthe length and height of the separator. The separator current sheet moves along the spinelines, sweeping through equal areas of positive and negative photospheric flux and theflare footpoints move apart. The magnetic sources themselves don’t change–only theirconnectivity does so.In case 1 the imbalance of flux led to the growth of both center domains P1/N2 andP2/N1 (purple and orange) and case 2 led to their shrinkage. In case 3, we deal withthe final possibility of flux transfer in a quadrupolar configuration – when there is a fluximbalance in one of the center domains with respect to the other. For example, we assumethe domain P1/N2 has too much flux and it can reach a lower energy state by transferringflux from domains P1/N2 (purple) and P1/N1 (overlying) into domains P2/N1 (orange) andP2/N2 (red). In this process, the entire separator shifts along the magnetic neutral line asthe footpoints move parallel to each other towards the P1 and N2 poles. Parallel HXRfootpoint motions are often observed; for example, Bogachev et al. (2005) report that 35%of the flares they observed had HXR footpoint sources that moved in the same direction.To summarize, footpoint motion along spine lines corresponds to movement of thereconnection location. As the separator current sheet sweeps across region of flux, itschromospheric ends either move toward each other (compact flare; case 1) as the separatorshortens, the ends move away from each other (eruptive two ribbon flare; case 2) as theseparator lengthens or the ends move parallel to each other (case 3) as the separator staysapproximately the same length. The movement of the separator’s chromospheric ends, andhence the HXR footpoints, is along the spine lines. Spine lines connect two poles via a
39null which shifts during the flare toward one pole or the other. The direction the null shiftsdepends on the global configuration of the region; the underlying domain gains or losesflux in order to decrease the region’s energy state.The above explanation agrees with the observed footpoint tracks and footpoint separationspeeds of the three flares reviewed in this Chapter. Referring again to Figure 2.4,we propose the following explanation for the footpoint motions of flare A. As is indicatedby the number of light grey field lines drawn in domains P01/N14 and P01/N08, a largepercentage of P01’s flux is connected to N14 and N08. Initially, the footpoint separationdistance decreases due to the reconnection of flux out of underlying domains P01/N14 andP01/N08. The next stage of reconnection acts to release energy stored in the sheared arcade.Domains which have little connecting flux in the earlier stage of the flare (P01/N11and P01/N10) fill up as reconnection takes place on higher and longer separators, and thefootpoints move apart from one another. An in-depth analysis of separator properties beforeand after flares will be given in a subsequent paper.Our model can be compared to other models that have been proposed to explain HXRfootpoint source motions. Bogachev et al. (2005) use a sheared 2.5D model to explain theantiparallel motion of HXR footpoints along the neutral line. In their model, which cannotdistinguish between flares with increasing footpoint separation from flares with decreasingseparation, the apparent motions of HXR sources are determined by the order of reconnectionalong the sheared system of field lines. During the onset of a flare, the footpointsources move toward each other, decreasing the distance between them, until a critical pointis reached and the sources begin to move away from one another. This model is similar toother models of reconnection in sheared arcades, where reconnection starts on the mosthighly sheared field lines and progresses to the less sheared field higher in the corona. Aswas pointed out earlier in this section, case 2 of our model is analogous to these modelswhere reconnection in sheared fields leads to the antiparallel motion of HXR footpoint
Page 1 and 2: THE TOPOLOGY OF MAGNETIC RECONNECTI
Page 3 and 4: iiAPPROVALof a dissertation submitt
Page 5: ivTo Liebe -I’m the lucky one
Page 8 and 9: viiLIST OF TABLESTablePage2.1 Flare
Page 10 and 11: ix2.3 Left hand panels are GOES lig
Page 12 and 13: xiABSTRACTIn order to better unders
Page 14: 2The release of this large amount o
Page 17 and 18: 5100.000RHESSI Count Flux vs Energy
Page 19 and 20: 7excitation in the chromosphere.The
Page 21 and 22: 9one day before the two large X-cla
Page 23 and 24: 11of well-defined features like sun
Page 25 and 26: 13introduced (i.e. Titov et al., 20
Page 27 and 28: 15CHAPTER 2RECONNECTION IN THREE DI
Page 29 and 30: 17spine lines.In this Chapter, for
Page 31 and 32: 19Table 2.1: Flare properties. AR i
Page 33 and 34: 21-300A) TRACE 195, RHESSI 50-100 k
Page 35 and 36: 23Figure 2.3: Left hand panels are
Page 37 and 38: 25the same time. With a 20 s imagin
Page 39 and 40: 27sheared or twisted flux tubes, wh
Page 41 and 42: 29Figure 2.4: Top: photospheric foo
Page 43 and 44: 31track 2 to 3 and from track 3 to
Page 45 and 46: 33error. If we had simply fit the f
Page 47 and 48: 3512 23 31Figure 2.6: Upper panel:
Page 49: 37In case 1, we suppose that the do
Page 53 and 54: 41tiation and evolution. Further wo
Page 55 and 56: 43photospheric and coronal magnetic
Page 57 and 58: 45Here, B z (x,y) is the value of t
Page 59 and 60: 47been determined, several other to
Page 61 and 62: 49Figure 3.1: Simulated magnetogram
Page 63 and 64: 51Figure 3.3: Same as Figure 3.1, b
Page 65 and 66: 53MDI 6 Apr 2004, 12:51 UT-120-140-
Page 67 and 68: 55of new field and horizontal flows
Page 69 and 70: 57arators (Henoux and Somov, 1987).
Page 71 and 72: 59the line-tied nature of the photo
Page 73 and 74: 61a snapshot in time (Démoulin, 20
Page 75 and 76: 63Figure 4.1: GOES and RHESSI light
Page 77 and 78: 65order to take advantage of the av
Page 79 and 80: 67field lines or sheared or twisted
Page 81 and 82: 69Flare A, MDI 01:39 UT400438350256
Page 83 and 84: 71flux discrepancy∆Φ r = −∆t
Page 85 and 86: 73Flare A, RHESSI 30-100 keV4004383
Page 87 and 88: 75(in the form of heating and parti
Page 89 and 90: 77CHAPTER 5DISCUSSION AND CONCLUSIO
Page 91 and 92: 79separator (nulls) are along spine
Page 93 and 94: 81emission is concentrated in compa
Page 95 and 96: 83REFERENCESAulanier, G., P. Démou
Page 97 and 98: 85Meyer, S. J. Morrison, M. D. Morr
Page 99 and 100: 87Priest, E., and T. Forbes, Magnet

The Topology of Magnetic Reconnection in Solar Flares

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