The Topology of Magnetic Reconnection in Solar Flares

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12Figure 1.4: Quadrupolar diagram with key topological features. P2 and P1 (+) are arepositive poles while N1 and N2 are negative poles (×). The triangles are null points,one positive (▽) and one negative (△). The orange, purple and red field lines lie on theseparatrix surface under which exist all of the field lines connecting P2/N1, P1/N2 andP2/N2 respectively. Above the orange and purple separatricies is the domain containing allof the field lines that connect P1 to N1. All four of these domains intersect at the separator(thick black line). The thick green lines are the spine lines.
13introduced (i.e. Titov et al., 2003; Demoulin et al., 1994; Bagala et al., 1995; Wang et al.,2002). Analyses of flares using both the source method and QSLs have shown that Hα andUV flare brightenings are located along the intersections of separatricies (source method)or QSLs with the chromosphere (Mandrini et al., 1991; Demoulin et al., 1994; Bagalaet al., 1995; Aulanier et al., 1998; Lee et al., 2003; Demoulin et al., 1997; Wang et al.,2000). These results strongly suggest that the location of energy release in flares is definedby the magnetic topology (Démoulin, 2006).One might use QSLs or the source method to examine the topological location of magneticreconnection, but the use of a magnetic charge topology (MCT) model with pointsources located on the photospheric surface has several advantages. These include: 1)Powerful mathematical tools can be used because the topological features are quantitativelydefined. This includes the ability to calculate the spine lines associated with the fieldand to calculate the magnetic flux linked by separators, both of which are employed in thisdissertation. 2) Model sources represent the fluxes and locations of strong photosphericfields, thus the photospheric boundary of the model is a quantitative representation of theobserved line of sight magnetogram. 3) Calculation of the topological features of the modelcoronal field is not computationally time consuming, so we are able to study several cases.OverviewIn this dissertation, I take the next step in the analysis of flare energy storage and releaseby combining HXR observations with a 3D quantitative model of the flaring active region’stopology. To do this, I use the following working hypothesis: In the absence of major reconnection,coronal magnetic fields become stressed as the photospheric boundary slowlyevolves due to the emergence of new field and horizontal flows. When a critical point isreached, this energy is released by the rapid reconnection of magnetic field lines near theseparator. As a result, electrons are accelerated near the reconnection region and stream
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: 11of well-defined features like sun
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 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
Page 83 and 84:
71flux discrepancy∆Φ r = −∆t
Page 85 and 86:
73Flare A, RHESSI 30-100 keV4004383
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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
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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
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The Topology of Magnetic Reconnection in Solar Flares

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