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Interferometric Studies of the Sun at Microwave and Millimeter Wavelengths

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Interferometric Studies of the Sun at Microwave and Millimeter Wavelengths INTERFEROMETRIC STUDIES OF THE SUN AT MICROWAVE AND MILLIMETER WAVELENGTHS by Leila Ann Belkora B.A., Cornell University, 1987 M.Eng., Cornell University, 1988 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Astrophysical, Planetary, and Atmospheric Sciences 1995 This thesis for the Doctor of Philosophy degree by Leila Ann Belkora has been approved for the Department of Astrophysical, Planetary and Atmospheric Sciences by Alan Kiplinger ~--t- Date ~)~/ /?'?S ~ iii Belkora, Leila Ann (Ph.D., Astrophysical, Planetary, and Atmospheric Sciences) Interferometric Studies of the Sun at Microwave and Millimeter Wavelengths Thesis directed by Professor Frances Bagenal The work presented in this thesis relied mainly upon two radio inter- ferometers, the Owens Valley Solar Array and the Owens Valley Millimeter Array. I used the Owens Valley Millimeter Array during the eclipse of July 11, 1991 to observe the brightness temperature profile of the solar limb. These observations showed that photospheric-temperature gas exists at an altitude of about 5500 km above the visible photosphere, far beyond the ex- pected location of the transition region where the temperature increases to about one million degrees. I proposed that this result can be explained in terms of a two-component model of the upper chromosphere. Spicules would compose a relatively cool and dense component embedded in a hot, tenuous medium like that described by the so-called VAL model (Vernazza, Avrett, and Loeser 1981). Later I used data from the Solar Array to make a detailed investi- gation of the gyrosynchrotron spectrum of the flare of July 16 1992. The results of this investigation led me to propose a solution to a long-standing problem in solar microwave bursts, that of the constant peak frequency of the bursts as they evolve in brightness temperature, and the steep slope on the low-frequency side of the spectrum. I proposed that the Razin effect is at work, and I developed the theory of Razin suppression for solar microwave burst conditions. The Razin effect is the suppression of radiation from an iv electron in a medium in which the index of refraction is less than unity. I demonstrated that in a medium with density 2 x 10 11 em -J and magnetic field 300 Gauss, conditions not uncommon for solar microwave bursts, the gyrosynchroton spectrum can be suppressed for frequencies up to at least 10 GHz. Finally, I made use of the X-ray data from the Yohkoh spacecraft to learn more about this particular flare, and to check some of the results from the investigation of the radio spectrum. I found that the ambient density and electron spectral index inferred from the X-ray data matched those deduced from the microwave data. v ACKNOWLEDGEMENTS First I would like to thank the chairperson of my thesis committee, Fran Bagenal, for guiding the completion of this thesis. I deeply appreciate her wisdom and kindness. I thank Alan Kiplinger for generous help with computer resources, and for his friendship and support. I thank all my thesis committee members and professors, especially Dale Gary at Caltech for sharing his great expertise of solar and radio astronomy. I was fortunate also to learn solar radio astronomy from George Dulle I thank Dick McCray, Don Melrose, and Reuven Ramaty for valuable discussions about the Razin effect in solar microwave bursts. I also benefitted from exchanges with Nariaki Nitta, Mona Hagyard, and Jean-Pierre Wuelser in writing chapter 3, and with Gordon Hurford and Tony Phillips in writing the paper which consitutes chapter 4. For financial support I am grateful to the University of Colorado for providing me with a University Fellowship, the Protected Class Fellowship, a Dean's Small Grant Award, and teaching assistantships. I thank George Dulk and Dale Gary for Graduate Research Assistant funding. I also thank the Solar Physics Division of the American Astronomical Society for funds to attend one of their conferences. Finally I thank my wonderful parents (both also graduates of CU) for their large financial investment in my education. vi The technical support I received both at Colorado and at Caltech was given with much patience and humor, and for this I thank Carole Allen, Gwen Dickinson, John Albers-Mead and Nora Harrington. I appreciate the efforts Carole Allen and Professors Fran Bagenal and Scott Robertson made in securing some of my financial support. Anne Hammond helped with many a computer-related crisis. My parents gave me endless moral support during my graduate stu- dent career. I'm also grateful to many friends and family members for their hospitality in their homes during this time: Jeff and Amy Belkora, Suzanne Landale, Claire Hartman, Jeanette and Scott Moorhouse, Nora and Hoyt Et- ter, Dorothea El Mallakh, Jim and Kay Dugan, and Mohammed and Khadija Akacem. My brother Jeff helped me move from California back to Colorado. I especially thank Rose and Alan Harris and Frank and Kay Denson and their families for practically adopting me in the later stages of my graduate career. {I thank their respective dogs, Pretzel and Tootsie, for adopting me, too). I don't think I could have completed my thesis without the warm and heartening counsel of Rene Arrobio. I also needed the advice of Arnold Siegel, and the support of science writer John Travis (Science 265, 735, 1994). Working on my Ph.D. would not have been nearly as much fun without the friendship of many people, friends and officemates. They include Patri- cia Wrean at Caltech and Jim Glanz, Margaret Hanson, Patrick Morris, and Brad Henderson at Colorado. I also enjoyed the friendship of Anna New- man, Sarah Ngola, Lena Peterson, Michelle Arkin, Haosheng Lin, Jeremy Lim, Andy McLeod, Joaquim Costa, Bob Herman, Adam Showman, Nora vii Harrington, Michael Celaya, Jeff Valenti, Yosufi Tyebkhan, Harold Felton, Min Su Yun, Sarah Gibson, Terry Kucera, Isidoros Doxas, Susan Nossal and Kirstie Saltsman. I'm also happy to acknowledge the influence on my career of Ellen Zweibel, Patricia Bornmann, Carol Jo Crannell, Joan Schmelz, Sara Martin, Tony Phillips, Gordon Hurford, and Rich Goeden. Finally I'd like to reiterate my thanks to Alan Harris, friend and mentor since my first undergraduate research job at the Jet Propulsion Lab- oratory a decade ago. viii CONTENTS Chapter Page I. INTRODUCTION 1 1.1 Why Study Radio Emission from the Sun? 1 1.2 Objective of the Thesis and Important Results 3 1.3 Overview of the Solar Atmosphere 4 1.4 The Nature of Solar Flares . 8 1.5 Overview of Flare Microwave Emission 9 1.5.1 Introduction . 9 1.5.2 Gyrosynchrotron Emission 11 1.5.3 The Razin Effect: Essential Features 17 1.5.4 Bremsstrahlung . 17 1.6 Radio Interferometry Basics 20 1. 7 Overview of the Owens Valley Solar Array . 29 1.8 Origin of Data Used in this Thesis . 36 II. FLARE OF JULY 16 1992: OBSERVATIONS WITH THE OWENS VALLEY SOLAR ARRAY . 42 2.1 Introduction . 42 2.2 Observations and Analysis . 45 2.2.1 Overview of the Flare . 45 2.2.2 Distinction Between Low and High Frequency Components . 49 2.2.3 Images of the Radio Burst . 53 ix 2.2.4 Brightness Temperature Spectra and Source Size Spectra of the Radio Burst 61 2.3 Gyrosynchrotron Emission and Application of the Simplified Theory to Solar Bursts 67 2.4 Difficulty of Explaining the Spectra Using Simplified Theory 75 2.5 Numerical Modeling . 79 2.5.1 The Gyrosynchrotron Code 79 2.5.2 The Razin Effect 84 2.5.3 Modeling the Results 97 2.6 Discussion 120 III. FLARE OF JULY 16 1992: MULTISPECTRAL OBSERVATIONS 123 3.1 Introduction 123 3.2 Flare Location with Respect to Nearby Active Regions 124 3.3 Magnetograph Observations 126 3.4 Yohkoh Soft X-ray Images 133 3.5 Comparison of Microwave and Soft X-ray Images 137 3.6 Temperature and Emission Measure Determinations From Yohkoh 140 3. 7 Implications of Temperature and Emission Measure Results 143 3.8 Hard X-ray Images 148 3.9 Hard X-ray Spectrum 153 X 3.10 Hard X-ray and Radio Time Profiles 156 3.11 Summary and Conclusions . 160 IV. INTERFEROMETRY OF THE SOLAR LIMB AT 3 MM . 162 4.1 Introduction 163 4.2 Viewing Geometry and Observing Procedure 164 4.3 Analysis and Results . 168 4.3.1 The Occultation Record 168 4.3.2 The Strip Brightness Profile 17 4 4.4 Discussion 179 4.5 Summary 181 V. Concluding Remarks 185 LIST OF SYMBOLS . 190 COMPREHENSIVE REFERENCE LIST 192 xi TABLES Table Page 1.1 Characteristics of the Yohkoh Soft X-ray Telescope 39 1.2 Characteristics of the Yohkoh Hard X-ray Telescope ... 40 Characteristics of Microwave Spectra 68 2.2 Range of Index of Refraction For Which Razin Effect Occurs . 92 2.3 Results of Fits to Gyrosynchrotron Spectra 113 3.1 Region of Interest Characteristics 144 3.2 Photon Spectral Index ..... 157 xii FIGURES Figure Page 101 Temperature versus Height 7 1.2 Power Spectrum: Particle in Cyclotron Motion 14 1.3 The Two-Element Interferometer 21 1.4 Power Reception Pattern of a Two-Element Interferometer 22 1.5 Position Vectors 25 1.6 The Visibility Function 26 10 7 Components of an Interferometer .Array 32 201 Time Plot of the Flare Total Power 46 202 Total Power at the Peak of the Flare 48 203 Time Evolution of the Total Power Spectrum 50 2.4 Comparison of Total Power and Correlated Amplitude 0 0 0 o 54 205 Cleaning of Flare Images Using Frequency Synthesis o o 0 0 58 206 Comparison of LCP and RCP Maps 60 20 7 Deconvolution of the Source Size 64 208 Source Size Spectrum 0 0 o 0 65 209 Brightness Temperature Spectra 69 2010 Numerical Calculations of Gyromagnetic Emission 72 xiii 2.11 Universal Curves of Bremsstrahlung and Gyrosynchrotron Emission .
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