LONG-TERM VARIABILITY OF THE SUN IN THE CONTEXT OF SOLAR-ANALOG STARS by Ricky Alan Egeland A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics MONTANA STATE UNIVERSITY Bozeman, Montana April, 2017 c COPYRIGHT by Ricky Alan Egeland 2017 All Rights Reserved ii DEDICATION To those of our ancestors who diligently chronicled Nature. iii ACKNOWLEDGEMENTS I thank God, for His inspiration on a starry night in Brazil, for His wonderous creation, and for giving us some capacity to understand it. Thanks to my parents John and Bonnie for their care and wisdom. Thanks to my loving wife Patricia for her support, as well as her patience and confidence, which at times were greater than my own. Thanks to my daughter Emilie, for being a constant joy. Thanks to Dr. David DeMuth, who gave me the opportunity to work in physics research and computer programming at a time when I knew nothing. Thanks to my undergraduate advisor and supervisor, Dr. Roger Rusack, to my early mentor in solar physics, Dr. David McKenzie, and to my mentor and colleague Dr. Travis S. Metcalfe. Thanks to my excellent teachers in physics, Dr. Joseph Kapusta and Dr. Paul Crowell of the University of Minnesota, and Dr. Carla Riedel, Dr. Charles Kankelborg, and Dr. Dana Longcope of Montana State University. Thanks to Dr. Willie Soon, Dr. Sallie L. Baliunas, Dr. Jeffrey C. Hall, Gregory W. Henry, Dr. Alexei Pevtsov, Dr. Christoffer Karoff, and Dr. Timothy W. Henry for graciously sharing and explaining the various datasets used in this work. Thanks to Dr. Robert A. Donahue and Dr. Douglas K. Duncan for helpful conversations on the technical details and history of the Mount Wilson HK project. Thanks to my advisors Dr. Petrus C. H. Martens and Dr. Phillip G. Judge for guiding me toward a research topic that I found so stimulating, and for the many useful discussions. Funding Acknowledgment This work was kindly supported by the Gordon A. Newkirk Fellowship at the High Altitude Observatory of the National Center for Atmospheric Research in Boulder, Colorado. iv TABLE OF CONTENTS 1. INTRODUCTION ........................................................................................1 1.1 The Corrupt Sun is a Nearby Star ...........................................................1 1.2 The Solar Dynamo Problem ....................................................................7 1.2.1 Mean-Field Dynamo Models ....................................................... 10 1.2.2 Global Convective MHD Dynamo Models.................................... 13 1.3 Stellar \Dynamo Experiments".............................................................. 18 1.3.1 Indices of Chromospheric Activity............................................... 22 1.3.2 The Solar-Stellar Connection ...................................................... 24 1.3.3 The Vaughan-Preston Gap ......................................................... 25 1.3.4 Rotation and Differential Rotation .............................................. 25 1.3.5 Rotation-Activity-Age Relationships ........................................... 27 1.3.6 Patterns of Long-term Variability................................................ 30 1.3.7 \Maunder Minimum" Stars ........................................................ 32 1.3.8 Search for \Solar Twins" ............................................................ 33 1.3.9 Variations in Visible Bands......................................................... 35 1.3.10 Cycle Period Patterns and Dynamo Theory ................................. 36 1.3.11 Second-Generation Stellar Activity Surveys ................................. 40 1.4 Organization of this Work ..................................................................... 42 1.4.1 Related Publications and Contributions....................................... 43 2. THE SUN AS A STAR: THE SOLAR S-INDEX TIME SERIES ...................45 2.1 The S-index Scale ................................................................................. 45 2.2 Previous Solar S Proxies ....................................................................... 47 2.3 Observations ........................................................................................ 51 2.3.1 Mount Wilson Observatory HKP-1 and HKP-2............................ 51 2.3.2 NSO Sacramento Peak K-line Program........................................ 52 2.3.3 Kodaikanal Observatory Ca K Spectroheliograms......................... 53 2.3.4 Lowell Observatory Solar Stellar Spectrograph............................. 54 2.4 Analysis............................................................................................... 57 2.4.1 Cycle 23 Direct Measurements .................................................... 57 2.4.2 Cycle Shape Model Fit for Cycle 23 ............................................ 58 2.4.3 S(K) Proxy Using NSO/SP K Emission Index ............................ 62 2.4.4 Comparison with SSS Solar Data ................................................ 64 2.4.5 Calibrating HKP-1 Measurements............................................... 66 2.4.6 Composite MWO and NSO/SP S(K) Time Series........................ 69 0 2.4.7 Conversion to log(RHK) .............................................................. 72 2.5 Linearity of S with K ........................................................................... 72 2.6 Discussion ............................................................................................ 76 v TABLE OF CONTENTS | CONTINUED 3. CASE STUDY: THE YOUNG SOLAR ANALOG HD 30495.........................81 3.1 Solar and Stellar Short-Period Variations ............................................... 81 3.2 HD 30495 Properties and Previous Observations..................................... 82 3.3 Activity Analysis .................................................................................. 85 3.4 Simple Cycle Model .............................................................................. 94 3.5 Short-Period Time-Frequency Analysis................................................... 98 3.6 Rotation ............................................................................................ 102 3.7 Discussion .......................................................................................... 105 4. LONG-TERM VARIABILITY OF SOLAR-ANALOG STARS..................... 109 4.1 Sample Selection and Characterization................................................. 110 4.1.1 Binary Stars and Characterizing HD 81809................................ 110 4.1.2 Properties of the Sample .......................................................... 113 4.2 SSS Calibration to the MWO S-index Scale ......................................... 118 4.3 Activity of 18 Sco Compared to the Sun .............................................. 123 4.4 Amplitude of Variability...................................................................... 124 4.5 A New Cycle Quality Metric ............................................................... 134 4.6 Analysis of Cyclic Variability............................................................... 141 4.7 Cycle Period and Rotation Period........................................................ 146 5. THE SOLAR CYCLE IN CONTEXT ........................................................ 151 5.1 Variability Classes and FAP Grade Cycle Quality................................. 151 5.2 Binaries in the B95 Sample ................................................................. 154 5.3 Properties of the MWO Sample........................................................... 156 5.4 Variability Class by Spectral Group and Activity.................................. 160 5.5 Variability Class by Rotation and Rossby Number................................ 166 5.6 Hypotheses on the Properties Resulting in Sun-like Cycles .................... 170 5.6.1 Hypothesis Testing with the Solar Analog Ensemble................... 178 5.7 FAP Grade and Cycle Period .............................................................. 180 5.8 Summary of Results............................................................................ 181 6. CONCLUSION......................................................................................... 185 REFERENCES CITED.................................................................................. 193 APPENDICES .............................................................................................. 217 APPENDIX A: Cycle Model Monte Carlo Experiments ............................ 218 vi TABLE OF CONTENTS | CONTINUED APPENDIX B: Ensemble Time Series and Periodograms .......................... 224 vii LIST OF TABLES Table Page 2.1 S(K) Transformations ...................................................................... 48 2.2 Solar Cycle Shape Parameters and S-index Measurements .................. 71 0 2.3 Solar Cycle Measurements in log(RHK) .............................................. 73 3.1 HD 30495 Properties ......................................................................... 84 3.2 HD 30495 Cycle Properties................................................................ 96 4.1 Solar Analog Ensemble Properties.................................................... 115 4.2 Solar Analog Ensemble Statistics ..................................................... 127 4.3 Cycle Quality Metric Test Cases ...................................................... 140 4.4 Solar Analog Ensemble Variability Periods ....................................... 142 4.5 Solar