The Topology of Magnetic Reconnection in Solar Flares

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74the second largest 〈E b 〉.In order to quantify the significance of this result, we found the probability of havingone of the top two best outcomes in the relationship between flaring NGP and the valueof〈E b 〉, the best outcome being that the flaring NGPs had the largest 〈E b 〉in all three flares.Our result is the second best outcome, with two of the flares having the largest 〈E b 〉 andthe third flare having the second largest. Out of 144 possible outcomes (6 × 4 × 6 NGPsfor flares A, B and C, respectively), there is one way of having the best outcome and threeways of having the second best. Thus, there is a 4/144 or ~2.8% chance of having oneof the top two best outcomes. Therefore, we find that the statistical significance of thisresult is ~97.2%. The actual situation, however, is more clear-cut than the 97% confidenceimplies. In the two cases where the flaring NGP has the largest 〈E b 〉, this value is a clearoutlier; it is larger than the next highest value by 46 and 30% for flares B and C.Discussion and ConclusionsWe conclude that we are able to understand the location of HXR sources observed inflares in terms of a physical and mathematical model of the topology of the flaring activeregion. In this Chapter, we have calculated the fluxes and lengths of the separators presentin three flaring active regions based on MDI magnetograms and a MCT model. We studiedthe change in average separator flux per unit length, 〈E b 〉, where the average was over theseparators belonging to the same null group pair. The function 〈E b 〉 is proportional to theself current that acts to prevent flux changes in the coronal field and is thus a signatureof non-potentiality and energy storage. We find that the separator stress, 〈E b 〉, is largestfor the flaring null group pair in two of the flares and is second largest in the third flare.Thus, we have shown that separators connecting the HXR sources of these flares are highlystressed.This conclusion supports the hypothesis that the energy associated with reconnecion
75(in the form of heating and particle acceleration) is released near separators. Prior to aflare, energy is built up in the stressed coronal field due to motions in the photosphericfield. During a flare, this energy is released via reconnection at separators, resulting in theacceleration of electrons on field lines near the separator. The electrons stream along thesefield lines until they encounter the chromosphere and emit HXR.In this Chapter, we implicitly assume that the numerical technique we use to calculateseparators locates them all each time. When we attempted to follow each individual separatorby matching their nulls from one time to the next, we found that a majority of theseparators could not be followed. This means that either there are many separator bifurcationsor our assumption about the separator locating method is not correct. We are notsure what percentage of the currently observed separator bifurcations are real and not anartifact of noise. Work is currently being done to better understand the separator locatingtechnique.As an example of what we consider to be real separator bifurcation, we consider thetopology shown in Figure 4.3 for flare C. This topology does not have a separator connectingfrom the middle HXR source to the third footpoint (located in NG 2) which is presentin the second half of flare C’s impulsive phase. Several separators, however, connect thetwo sources in the previous and following times (at 21:15 and 23:15 UT). The bifucationof these separators suggests a major change taking place in this area of the photosphericfield, which causes the build up of stress in the coronal field above it. These connectingseparators are linked to a common null (shown by the arrow) shared by the northern mostflaring separator in NGP 3,7. We suggest that the third footpoint appeared because thereconnection which started on the NGP 3,7 separators triggered a secondary reconnectionevent, via the common null, to release energy stored at the NGP 2,7 separators.We also conclude that the relative value of separator stress, measured for a period oftime as short as 2 hours, can be used as an indicator of where within an active region
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THE TOPOLOGY OF MAGNETIC RECONNECTI
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iiAPPROVALof a dissertation submitt
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ivTo Liebe -I’m the lucky one
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viiLIST OF TABLESTablePage2.1 Flare
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ix2.3 Left hand panels are GOES lig
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xiABSTRACTIn order to better unders
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2The release of this large amount o
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5100.000RHESSI Count Flux vs Energy
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7excitation in the chromosphere.The
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9one day before the two large X-cla
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11of well-defined features like sun
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13introduced (i.e. Titov et al., 20
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15CHAPTER 2RECONNECTION IN THREE DI
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17spine lines.In this Chapter, for
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19Table 2.1: Flare properties. AR i
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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: 73Flare A, RHESSI 30-100 keV4004383
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
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The Topology of Magnetic Reconnection in Solar Flares

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