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Solar Flares: the Onset of Am Gnetic Reconnection and the Structure of Radiative Slow-Mode Shocks Peng Xu University of New Hampshire, Durham

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University of New Hampshire University of New Hampshire Scholars' Repository Doctoral Dissertations Student Scholarship Spring 1992 Solar flares: The onset of am gnetic reconnection and the structure of radiative slow-mode shocks Peng Xu University of New Hampshire, Durham Follow this and additional works at: https://scholars.unh.edu/dissertation Recommended Citation Xu, Peng, "Solar flares: The onset of magnetic reconnection and the structure of radiative slow-mode shocks" (1992). Doctoral Dissertations. 1693. https://scholars.unh.edu/dissertation/1693 This Dissertation is brought to you for free and open access by the Student Scholarship at University of New Hampshire Scholars' Repository. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of University of New Hampshire Scholars' Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note, will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9225268 Solar flares: The onset of magnetic reconnection and the structure of radiative slow-mode shocks Xu, Peng, Ph.D. University of New Hampshire, 1992 UMI 300 N. ZeebRd. Ann Arbor, MI 48106 SOLAR FLARES: THE ONSET OF MAGNETIC RECONNECTION AND THE STRUCTURE OF RADIATIVE SLOW-MODE SHOCKS m PENG XU B. S., China University of Science and Technology, 1982 M. S., China University of Science and Technology, 1984 DISSERTATION Submitted to the University of New Hampshire in Partial Fulfillment of the Requirement for the Degree of Doctor of Philosophy in Physics MAY, 1992 This dissertation has been examined and approved. r \ Dissertationdirector, Terry. G. Forbes Research JProfessor of Physics osep . Hollweg Directed*, Solar-Terrestrial Theory roup Professor of Physics HarveySwepard ProfesSgr of Physics O&K_Q_ Richard L. Kaufmann Professor of Physics Dawn C. Meredith Assistant Professor of Phisics April 23, 1992 Date To my parents and my wife iii ACKNOWLEDGMENTS The work for this dissertation has been supported by the NSF Grant ATM-8916303 and NSF Grant ATM-8711089. I am grateful to many colleagues and friends who have assisted me in various ways during the years of my graduate studies. I thank Professors Joe Hollweg, Martin Lee, Phil Isenberg, Richard Kaufinann, Harvey Shepard, and Dawn Meredith for many discussions and suggestions which are very helpful to my studies. I am grateful to Kathy Theall, who has given me reliable assistance in many instances. I thank Dot Kittredge for handling much of the paper work associated with my studies. I am very grateful to my wife, Yumei Yin, who has supported me throughout these years in many ways. Most of my gratitude, however, is reserved for my research advisor. Professor Terry Forbes. He has given me not only the guidance and suggestions to this dissertation, but also the ways and ideas to do physical research. His encouragement and patience have helped me overcome many difficulties in physics, English language, and computer programming. iv Table of Contents Dedication ................................................................................................................................... iii Acknowledgments ..................................................................................................................... iv List of Tables .............................................................................................................................. v i List of Figures ............................................................................................................................. v ii Abstract....................................................................................................................................... x Introduction ................................................................................................................................ 1 Part One The Effect of Magnetic Reconnection on the Catastrophic Loss of Magnetic Equilibrium in Flares ....................................................................... 22 I. Overview................................................................................................................. 23 II. A Reconnection Model with a Detached Current Sheet .............................. 33 III. Solution for the Vector Potential ...................................................................... 46 IV. Evolution of the Equilibria and Eruption ....................................................... 55 Part Two The Structure of Radiative Slow-Mode Shocks ............................................. 85 V. Introduction ........................................................................................................... 86 VI. Governing Equations for MHD Shocks ........................................................... 92 VII. Radiative Gas Dynamic Shocks ......................................................................... 99 VIII. Radiative Slow-Mode MHD Shocks .................................................................. 117 Sum mary.................................................................................................................................... 137 Appendices .................................................................................................................................. 141 References .................................................................................................................................. 162 v lis t of Tables Table 1. Shock and subshock jump conditions ................................................................ 123 v i List of Figures Fig. 1. A schematic diagram of solar structure, showing a quarter of equatorial cross- section. The size of the various regions and their temperatures are indicated. The thicknesses of the atmospheres (photosphere and chromosphere) are not proportional to scale ......................................................................................................................................... 4 Fig. 2. The variation of the temperature with height In the solar atmosphere, based on Athay's model (Athay, 1976)................................................................................................... 6 Fig. 3. A schematic profile of the flare intensity in several wavelengths (after Priest, 1981) ............................................................................................................................................ 15 Fig. 4. Schematic diagram of the system evolving from a stable equilibrium state (a, b) to a non-equilibrium state (c) or an unstable state (d) ..................................................... 26 Fig. 5. A schematic diagram of the driving mechanism in the models of Van Tend and Kuperus type. The dark shaded circles designate the current filaments, and solid arrows indicate filament motions. Hollow arrows show the photospheric convection which increases the filament current by reconnecting field lines in the photosphere (light shaded region) (after Forbes and Isenberg, 1991) .............................................................. 30 Fig. 6. A schematic diagram showing magnetic field lines (solid) and streamlines (dashed) for Petschek-like reconnection ............................................................................. 39 Fig. 7. Geometry of the field configuration: (a) with no current; (b) with a detached current sheet............................................................................................................. 43 Fig. 8. A schematic diagram of field lines for Vacuum' solution. The filament motion is indicated by the thick solid arrow, while plasma motion below the photosphere is indicated by the hollow arrows .............................................................................................. 58 Fig. 9. A schematic diagram of the Vacuum’ solution: (a) in the 3-D (h, fo) space, the thick solid (dashed) curve represents the part of the solution in (out of) the h-tpi plane; (b) its projection onto the h-<pi plane. The point O is the turning point at which (pi = 01max...............................................................................................................................................................................
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