PECULIAR VARIATIONS OF WHITE DWARF PULSATION FREQUENCIES AND MAESTRO by James Ruland Dalessio A dissertation submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Spring 2013 c 2013 James Ruland Dalessio All Rights Reserved PECULIAR VARIATIONS OF WHITE DWARF PULSATION FREQUENCIES AND MAESTRO by James Ruland Dalessio Approved: Edmund R. Novak, Ph.D. Chair of the Department of Physics and Astronomy Approved: George H. Watson, Ph.D. Dean of the College of Arts and Sciences Approved: James G. Richards, Ph.D. Vice Provost for Graduate and Professional Education I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Henry L. Shipman, Ph.D. Professor in charge of dissertation I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Judith L. Provencal, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: James MacDonald, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Donald E. Winget, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Stephen M. Barr, Ph.D. Member of dissertation committee ACKNOWLEDGEMENTS Firstly, I thank Judi Provencal, who has put up with my antics for over 6 years. For all practical purposes, Judi served as my research advisor throughout my graduate career. Judi found the perfect balance of guidance and freedom for me to grow throughout graduate school and we've had a lot fun along the way. I'd also like to thank Harry Shipman, who served as my official advisor. Harry was always there to mentor me in both my teaching and my research. The data used for this research would not have been obtained if it weren't for the diligent work of Denis Sullivan, Fergal Mullally, and JJ Hermes. To them, I am forever indebted for the many hours they spent observing and reducing data. I'd also like to thank Roy Østensen for his work searching for a DB in the Kepler field and spearheading Kepler observations of KIC 8626021. Whenever I had a tough theoretical question, Mike Montgomery was always happy to help whether it was through email or Skype. Fergal Mullally offered extremely helpful suggestions and discussion as referee of my first major publication. I learned a lot about computers from Staszek Zola, and we had a lot of laughs. I also enjoyed time spent with members of the WET team, including Susan Thompson, Kepler, Agnes Kim, Denis Sullivan, Don Winget, and the many many others. In the early years of graduate school, I spent many hours studying with fellow graduate students including Josh Wickman, Dana Saxson, and Mary Oksala. Thanks to you folks for keeping me sane in the first few years. The Final Countdown will forever remind me of the qualifiers. I also met many graduate students in my field at other institutions. I always look forward to seeing JJ Hermes, Ross Falcon, Brad Barlow, Paul Chote, Bart Dunlap, and others. I have greatly enjoyed our conversations over the last few years. iv I've had the opportunity to TA, instruct several courses, and develop lab cur- riculum. I enjoyed TA'ing for Peter Georgopolus and working with Almas Khan, Abby Pillitteri, and Mary Oksala along the way. I thank Dermott Mullan and those at the Delaware Space Grant Consortium for two full years of funding. I also thank Mount Cuba/Crystal Trust for funding me for the first few semesters. Without some physical activity I would have gone (completely) crazy. Special thanks to Mark Poindexter and the folks at Wilbur for organizing our weekly basketball games and to Joe Wiseman, Lori Marinucci, and the New Castle county softball crew for organizing the many years of softball. I've recently also enjoyed playing softball (and post-game activities) with the Honey Badgers, despite our incredibly terrible performance on the field. In last few years, John Meyer and I have become good friends and have had many epic physics and philosophy conversations over lunch. I've also enjoyed our mini video game marathons. Its been a blast and I look forward to starting a software company with John in the very near future. Thanks to my mom, my in-laws Art and Diane, and my sister in-law Amanda, who all took turns taking care of Aria while I worked on the final stretch of my Ph.D. Extra thanks to my mom, who has always supported me, even in those years when I was especially “difficult”. A special thanks to my step-father for his helpful advice and diligent proof-reading, and for keeping me in touch with mainstream astronomy. My father did not get to see me finish graduate school, but no doubt he would be very proud. Lastly and most of all, I thank my wife, who is as patient as she is beautiful. During the course of graduate school Lindsay and I were engaged, married, and wel- comed our first child. Lindsay has supported me during every step of this long process and I wouldn't have made it without her. v To my wife vi TABLE OF CONTENTS LIST OF TABLES :::::::::::::::::::::::::::::::: x LIST OF FIGURES ::::::::::::::::::::::::::::::: xi ABSTRACT ::::::::::::::::::::::::::::::::::: xvii PART I PECULIAR VARIATIONS OF WHITE DWARF PULSATION FREQUENCIES :::::::::::::::::::::::: 1 Chapter 1 BACKGROUND, FORMALISM, AND METHODOLOGY :::: 2 1.1 White Dwarf Asteroseismology :::::::::::::::::::::: 2 1.1.1 Introduction :::::::::::::::::::::::::::: 2 1.1.2 Cooling Processes ::::::::::::::::::::::::: 5 1.1.3 Rotation and Magnetic Fields :::::::::::::::::: 6 1.1.4 Pulsation Timing Based Planet Detection ::::::::::: 7 1.1.5 Combination and Harmonic Modes ::::::::::::::: 8 1.2 Miscellaneous Considerations :::::::::::::::::::::: 9 1.2.1 Creating a Lightcurve :::::::::::::::::::::: 9 1.2.2 Linearizing a Non-Linear Model ::::::::::::::::: 10 1.3 Fourier Analysis :::::::::::::::::::::::::::::: 10 1.3.1 The Fourier Transform :::::::::::::::::::::: 10 1.3.1.1 Definition :::::::::::::::::::::::: 10 vii 1.3.1.2 Properties :::::::::::::::::::::::: 11 1.3.2 Identifying Sinusoidal Variations in a Lightcurve :::::::: 12 1.3.3 Frequency Bootstrapping ::::::::::::::::::::: 13 1.4 The O − C Method :::::::::::::::::::::::::::: 14 1.4.1 Introduction :::::::::::::::::::::::::::: 14 1.4.2 Mathematical Description :::::::::::::::::::: 15 1.4.3 Causes of Perturbations to O − C:::::::::::::::: 18 1.4.3.1 Error in the Frequency ::::::::::::::::: 18 1.4.3.2 Movement of the Source :::::::::::::::: 18 1.4.3.3 Intrinsic Frequency Perturbations ::::::::::: 21 1.4.3.4 Indistinguishable Processes :::::::::::::: 21 1.4.4 Calculating O − C:::::::::::::::::::::::: 22 1.4.5 Phase Ambiguity ::::::::::::::::::::::::: 23 2 EC 20058-5234 :::::::::::::::::::::::::::::::: 25 2.1 Observations and Data Preparation ::::::::::::::::::: 25 2.2 Fourier Analysis :::::::::::::::::::::::::::::: 27 2.3 O − C Analysis :::::::::::::::::::::::::::::: 34 2.4 Amplitude Modulation :::::::::::::::::::::::::: 46 3 KIC 8626021 ::::::::::::::::::::::::::::::::: 58 3.1 Observations and Data Preparation ::::::::::::::::::: 58 3.2 Fourier Analysis :::::::::::::::::::::::::::::: 61 3.3 O − C Analysis :::::::::::::::::::::::::::::: 61 3.4 Amplitude Modulation :::::::::::::::::::::::::: 83 4 GD 66 ::::::::::::::::::::::::::::::::::::: 104 4.1 Observations and Data Preparation ::::::::::::::::::: 104 4.2 Fourier Analysis :::::::::::::::::::::::::::::: 106 4.3 O − C Analysis :::::::::::::::::::::::::::::: 115 4.4 Amplitude Modulation :::::::::::::::::::::::::: 148 5 DISCUSSION ::::::::::::::::::::::::::::::::: 175 5.1 Pulsation Timing Based White Dwarf Planet Detection :::::::: 175 viii 5.2 Cooling and Secular Processes :::::::::::::::::::::: 176 5.3 Combination and Harmonic Modes ::::::::::::::::::: 176 5.4 Model Validation and the Reliability of the Results :::::::::: 177 5.5 Characterization of the Frequency and Amplitude Variations ::::: 178 PART II MAESTRO ::::::::::::::::::::::::::::: 181 6 THE MAESTRO FRAMEWORK :::::::::::::::::::: 182 6.1 Introduction :::::::::::::::::::::::::::::::: 182 6.2 Installation :::::::::::::::::::::::::::::::: 182 6.3 File Organization ::::::::::::::::::::::::::::: 183 6.4 Using MAESTRO ::::::::::::::::::::::::::::: 184 6.5 Configuration ::::::::::::::::::::::::::::::: 186 6.6 Creating a New Directive ::::::::::::::::::::::::: 186 6.6.1 The Manifest ::::::::::::::::::::::::::: 186 6.6.2 Argument Configuration ::::::::::::::::::::: 187 6.6.3 Flag Configuration :::::::::::::::::::::::: 187 6.6.4 Help Text Configuration ::::::::::::::::::::: 188 6.6.5 Creating the MatLab Code for a Directive ::::::::::: 188 7 THE MAESTRO REDUCTION ALGORITHM ::::::::::: 190 7.1 Introduction :::::::::::::::::::::::::::::::: 190 7.2 Preparation :::::::::::::::::::::::::::::::: 193 7.3 Calibration :::::::::::::::::::::::::::::::: 194 7.4 Star Finding ::::::::::::::::::::::::::::::::