X{ray and Radio Diagnostics of Accelerated Electrons in Solar Active Regions A dissertation submitted to the University of Dublin for the degree of Doctor of Philosophy Aidan O'Flannagain Trinity College Dublin, March 2015 School of Physics University of Dublin Trinity College ii Declaration I declare that this thesis has not been submitted as an exercise for a degree at this or any other university and it is entirely my own work. I agree to deposit this thesis in the University's open access institu- tional repository or allow the library to do so on my behalf, subject to Irish Copyright Legislation and Trinity College Library conditions of use and acknowledgement. Name: Aidan O'Flannagain Signature: ........................................ Date: .......................... Summary Solar eruptive events occur when magnetic energy stored in the at- mosphere of the Sun is released as a mixture of rapidly ejected plasma (coronal mass ejections) and radiation across the electromagnetic spec- trum (solar flares). Energy released in this way can reach as high as 1032 ergs, making these events the most powerful explosions in the solar system. Despite centuries of study since their first observation in 1859, understanding of the exact nature of the initiation of these events is still incomplete. In this thesis, I outline work which was performed in order to build upon the understanding of the initiation of solar flares, primarily through analysis of nonthermal X{ray and radio emissions. In the first two parts of this work, open questions on the motion and size of nonthermal X{ray sources in solar flare loops are addressed, and in the final part a unique observation of magnetic reconnection in the high corona and the associated radio emissions are presented and discussed. The nonthermal distribution of accelerated electrons believed to pro- duce solar hard X{ray emissions is known to evolve dramatically over the course of a solar flare, from a steep to a flat power{law spectrum as the acceleration process becomes more efficient. In the context of the commonly{used collisional thick{target model, this should pro- duce nonthermal X{ray sources which move down the flare loop as the spectrum steepens. However, this has never been observed, con- stituting a problem with the standard model. In the first part of this thesis, the analysis of an early impulsive event, which exhibits low{ energy nonthermal emission early in the flare, is presented. It is found that this downward motion is indeed present, and through modelling is shown to be consistent with the flattening of the injected electron spectrum, revealed through X{ray spectroscopy. The second piece of work outlined in this thesis includes a poten- tial solution to another outstanding problem in X{ray solar physics, namely of extended X{ray source sizes. Previously, X{ray sources were found to be far larger than the sizes predicted using the colli- sional thick{target model. This problem is addressed by incorporating a unique model of the ionisation fraction of the plasma encountered by the accelerated electron distribution in a model flare. We include a local peak ionisation, which is expected to be produced by the beam itself. This locally ionised and heated chromosphere successfully pro- duces a vertically extended X{ray source, which accounts for a large portion of the difference between observed and previously modelled X{ray emission. The final part of this thesis outlines a new observation of magnetic re- connection in progress in an active region which also exhibits a radio noise storm. The collapse of the observed X{point includes inflows and outflows of 1{5 km/s and 30{100 km/s, respectively, implying a reconnection rate of 0.05, consistent with previous observations of reconnection on the solar limb. We demonstrate that the magnetic geometry suggested by extreme ultra{violet imaging and potential magnetic field extrapolations suggests the presence of a 3D separa- tor connecting magnetic null points above the active region. In this context, the radio noise storm evolution during the collapse is then explained by the concept of long{term gradual acceleration followed by flare–related reconnection, which produces a rapid brightnening of the radio emission. For Mam and Dad. Acknowledgements Firstly I'd like to thank my supervisor, Peter Gallagher, for always knowing whether I needed motivation or a good shove. Above all, for your unstoppable, contagious enthusiasm. Similarly I'd like to extend a huge thanks to John Brown, Ryan Mil- ligan and Gordon Holman, without whom I never would have known where to start. Thank you to the stellar professors, Brian Espey and Graham Harper, for reminding me that other stars can be cool too. I am also hugely grateful for the group of ridiculous people who made the Office a truly fun place to be. My fellow students and postdocs, Shaun, Sreejith, Scullion, DVD, Jason, Larisza, Dave, Shano, Joe, Sophie, Higgo, Big Eamo, Eoin, Danny, Pietro, Neal, Mel, Diana, Lauren, Draco, Sam Badman, Aoife and Laura, have all had a unique impact on my life and my sanity. The times we've shared will be very difficult to forget. Except the Fridays. They're already gone. I'd like to thank my family, Mary, Liam K., Liam D., and Roisin, all of whom worked hard to keep reminding me what life is really about. Finally, Jen, you know how much your support and patience have helped me during the last four years. Any of the people who noticed that I was unexpectedly happy during the final months of writing this thesis would understand if they knew you. List of Publications 1. O'Flannagain, A. M. & Gallagher, P. T. \Magnetic Reconnection in a Collapsing Coronal Null{Point", Astrophysical Journal Letters, in prep., Outlined in Chapter 6 2. O'Flannagain, A. M., Brown, J. C. & Gallagher, P. T. \Solar Hard X-ray Source Sizes in a Beam-Heated and Ionised Chromo- sphere", Astrophysical Journal, in review, 2014, Outlined in Chapter 5 3. Aschwanden, M. J., O'Flannagain, A. M. et al. \A Global Survey of Solar Flare Energetics", Astronomy & Astrophysics, in prep. 4. Bloomfield, D. S., O'Flannagain, A. M. et al. \A Comprehensive Overview of the 2011 June 7 Event", Astronomy & Astrophysics, in review, 2014 5. Ryan, D. R., O'Flannagain, A. M., Aschwanden, M. J. & Gallagher, P. T. \The Compatibility of Flare Temperatures Observed with AIA, GOES, and RHESSI", Solar Physics, 289, 7, 2014 vii 0. LIST OF PUBLICATIONS 6. O'Flannagain, A. M., Gallagher, P. T., Brown, J. C., Milligan, R. O., Holman, G. D. \Solar Flare X-ray Source Motion as a Response to Electron Spectral Hard- ening", Astronomy & Astrophysics, 555, A21, 2013, Outlined in Chapter 4 viii Contents List of Publications vii List of Figures xiii List of Tables xxxv 1 Introduction 1 1.1 Solar Flares . .2 1.1.1 Morphology . .8 1.1.1.1 X{Ray Structure . 12 1.1.1.2 Structure in Other Wavelengths . 14 1.1.2 Temporal Evolution . 18 1.1.2.1 The Preflare Phase . 18 1.1.2.2 The Impulsive Phase . 18 1.1.2.3 The Gradual Phase . 22 1.2 Radio Noise Storms . 25 1.2.1 Spectral Obsevations . 26 1.2.2 Spatial Structure . 28 1.3 Thesis Outline . 31 2 Theory 33 2.1 Plasma Physics . 34 2.1.1 Maxwell's Equations . 35 2.1.2 Plasma Kinetic Theory . 36 2.1.3 Magnetohydrodynamics . 37 2.1.4 The Force{Free Approximation . 41 2.1.4.1 Potential Field Extrapolations . 42 ix CONTENTS 2.1.5 Magnetic Reconnection . 46 2.1.5.1 Sweet-Parker Reconnection . 49 2.1.5.2 Petschek Reconnection . 50 2.2 Solar Flare Models . 53 2.2.1 Particle Acceleration . 55 2.2.1.1 Acceleration in 3D Reconnection at Null Points . 56 2.2.2 Density Models and Nonuniform Ionisation . 59 2.3 Nonthermal Emission Mechanisms . 63 2.3.1 The Collisional Thick Target Model . 63 2.3.2 Plasma Emission . 65 3 Instrumentation 69 3.1 The Ramaty High Energy Solar Spectroscopic Imager (RHESSI) . 70 3.1.1 RHESSI Imaging . 70 3.1.1.1 Back Projection . 73 3.1.1.2 CLEAN . 76 3.1.1.3 Visibility Forward Fit . 77 3.1.2 RHESSI Spectroscopy . 78 3.2 The Solar Dynamics Observatory (SDO) . 81 3.2.1 The Atmospheric Imaging Assembly (AIA) . 82 3.2.2 The Helioseismic and and Magnetic Imager (HMI) . 86 3.3 The Nan¸cay Radioheliograph (NRH) . 91 3.3.1 Interferometric Imaging . 93 4 Coronal Hard X-ray Source Response to Electron Spectral Hard- ening 99 4.1 Introduction . 100 4.2 RHESSI Observations . 103 4.2.1 Spectroscopy . 105 4.2.2 Imaging . 108 4.3 Thick Target Modelling . 112 4.4 Results . 116 4.5 Discussion and Conclusion . 119 x CONTENTS 5 Hard X-ray Source Sizes in a Beam-Heated and Ionised Chro- mosphere 125 5.1 Introduction . 127 5.2 Method . 129 5.2.1 Target Density Model . 130 5.2.2 HXR Height Profile . 131 5.2.3 HXR Spectrum . 132 5.3 Generalised HXR NUI Spectrum . 132 5.4 Results . 134 5.4.1 HXR Height Profile . 134 5.4.2 Instrumental Effects . 138 5.4.3 HXR Spectrum . 141 5.5 Conclusion . 143 6 Observing Magnetic Reconnection in a Collapsing Coronal Null- Point 147 6.1 Introduction . 149 6.2 Observations . 151 6.3 Data Analysis . 154 6.3.1 Potential Field Extrapolation . 154 6.3.2 EUV and Radio Comparison . 157 6.4 Interpretation . 161 6.5 Conclusion . 162 7 Discussion and Future Work 165 7.1 Coronal Hard X-ray Source Response to Electron Spectral Hardening166 7.1.1 Expanded Dataset .