The Topology of Magnetic Reconnection in Solar Flares

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14along field lines near the separator. Upon encountering the chromosphere, the electronsundergo bremsstrahlung and non-thermal HXR are emitted. Thus, I interpret HXR footpointsources as the location of the chromospheric ends of newly reconnected field lines,which lie close to the separator.In Chapter 2, I examine the evolution of the reconnection that releases free magneticenergy by proposing a model for how the change of separators during a flare can resultin HXR source motions. In Chapter 3, I describe a new technique for representing photosphericmagnetic fields in topology calculations. In Chapter 4, I examine the location ofreconnection by relating the storage of energy to changes in separators. Finally, in Chapter5, I summarize the conclusions I reach by combining my studies of reconnection evolutionand location.Chapter 2, ’Reconnection in Three Dimensions: the Role of Spines in Three EruptiveFlares’ (Des Jardins et al., 2007a), and Chapter 4, ’Signatures of Magnetic Stress Prior toThree Flares Observed by RHESSI’ (Des Jardins et al., 2007b), are papers that have beensubmited for publication in the Astrophysical Journal. As of July, 2007, Chapter 4 has beenaccepted and Chapter 2 is still in the referee review process.
15CHAPTER 2RECONNECTION IN THREE DIMENSIONS: THE ROLE OF SPINES IN THREEERUPTIVE FLARESAbstractIn order to better understand magnetic reconnection and particle acceleration in solarflares, we compare the RHESSI hard X-ray (HXR) footpoint motions of three flares with adetailed study of the corresponding topology given by a Magnetic Charge Topology (MCT)model. We analyze the relationship between the footpoint motions and a topological featurecalled spine lines and find that the examined footpoints sources moved along the spinelines. HXR footpoint motions predicted by the standard 2.5D flare model cannot explainthis relationship. We present a 3D model in which the movement of footpoints along spinelines can be understood. Our 3D model also explains other important properties of HXRfootpoint motions that cannot be described by the standard model, such as the sense of theirrelative motions.IntroductionMagnetic reconnection is the mechanism of topological change that is thought to bringabout energy release and non-thermal electron acceleration in solar flares. By studying theradiative output of flares in association with the magnetic topology of the flaring region, wecan learn a great deal about the topological location of reconnection. Knowing the locationof reconnection is key to understanding both flare trigger and evolution processes.Since the wealth of data now available from Ramaty High Energy Solar SpectroscopicImager (RHESSI; Lin et al., 2002) exhibits many cases of hard X-ray (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: 13introduced (i.e. Titov et al., 20
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 and 50: 37In case 1, we suppose that the do
Page 51 and 52: 39null which shifts during the flar
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
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71flux discrepancy∆Φ r = −∆t
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73Flare A, RHESSI 30-100 keV4004383
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75(in the form of heating and parti
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77CHAPTER 5DISCUSSION AND CONCLUSIO
Page 91 and 92:
79separator (nulls) are along spine
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81emission is concentrated in compa
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83REFERENCESAulanier, G., P. Démou
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85Meyer, S. J. Morrison, M. D. Morr
Page 99 and 100:
87Priest, E., and T. Forbes, Magnet
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The Topology of Magnetic Reconnection in Solar Flares

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