The Topology of Magnetic Reconnection in Solar Flares

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8this 2D standard flare model. Also, the footpoint separation velocity predicted in the standardmodel is a only few km s −1 (Somov et al., 1998). Actual observed apparent velocitiesare much larger, on the order of 50 km s −1 . To account for the observed directions andspeeds of HXR footpoint sources, and thus the evolution of reconnection, a 3D model isneeded.Flare Energy StorageAfter the standard model for the release of energy in a solar flare was developed, thenext question became how so much energy is made available to fuel a flare. Current evidencepoints to the build-up of energy over days as the photospheric magnetic field shiftscontinuously prior to a flare. Changes in the field at the photospheric boundary (almostcertainly driven by sub-photospheric phenomona) drive the chromospheric and coronalplasma. The coronal field may remain nearly potential (current-free), but accumulates anon-potential component related to current layers that separate interacting magnetic fluxesand thus prevent coronal flux changes (Henoux and Somov, 1987). In other words, energyis stored in the corona due to changes in the photospheric boundary because no reconnectiontakes place and the magnetic configuration becomes stressed. The field becomes moreand more non-potential until some critical point is reached and a flare occurs.Past research on energy storage prior to a flare has concentrated on non-potential signaturesin the photospheric fields as observed by vector magnetograms (i.e.Gary et al.,1987; Wang et al., 1996; Moon et al., 2000; Deng et al., 2001; Tian et al., 2002; Falconeret al., 2006; Dun et al., 2007). These yield maps of not only the magnitude of the field butalso the its direction. For example, Dun et al. (2007) calculated the daily average valuesof three non-potential parameters from vector magnetograms of selected regions along themain neutral lines of active region 10486. They found that the three non-potentiality parametersincreased at the impulsively brightening flare sites from values measured at least
9one day before the two large X-class flares of 28 and 29 October, 2003. While most of themeasured parameters decreased after the flares, as expected due to the relaxation of nonpotentiality,some continued to increase. This and other, similar studies indicate that moreresearch is required to fully understand the relationship between observational signaturesof nonptentiality and the build-up and release of energy in flaring active regions.The CSHKP model is useful for explaining energy release in a simple two dimensionalconfiguration, but it does not give us any information on how or where the coronal fieldbecomes stressed. Also, while the studies of non-potential fields from photospheric vectormagnetograms cited above significantly advance our understanding of energy storage, thesestudies do not deal with coronal fields. A fully three dimensional topology model thatdefines the locations of energy storage and release is needed.Observations and AnalysisHard X-ray ImagesThe RHESSI telescope observes solar X-rays and gamma-rays from 3 keV to 17 MeVwith energy resolution of ~1 keV, time resolution of ~2 s and spatial resolution as high as2.3 ′′ . Instead of focusing optics, imaging is based on rotating modulation collimators thattime-modulate the incident flux as spacecraft rotation causes the field of view of the collimatorsto sweep across the Sun. Ground based software then uses the modulated signals toreconstruct images of HXR sources (Hurford et al., 2002).The RHESSI telescope consists of a set of nine bi-grid subcollimators, each consistingof a pair of widely separated grids in front of a corresponding non-imaging detector. Eachgrid consists of an array of equally-spaced, X-ray-opaque slats separated by transparentslits. Within each subcollimator, the slits of the two grids are parallel and their pitches areidentical. The transmission through the grid pair depends on the direction of the incidentX-rays. If the direction of incidence is changed as a function of time, the transmission of
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: 7excitation in the chromosphere.The
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 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
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
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The Topology of Magnetic Reconnection in Solar Flares

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