A STUDY OF THE WHITE LIGHT FLARE RATES OF M AND L DWARFS by Rishi Paudel 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 2019 © 2019 Rishi Paudel All Rights Reserved A STUDY OF THE WHITE LIGHT FLARE RATES OF M AND L DWARFS by Rishi Paudel Approved: Edmund R. Nowak, Ph.D. Chair of the Department of Physics and Astronomy Approved: John Pelesko, Ph.D. Interim Dean of the College of Arts and Sciences Approved: Douglas J. Doren, Ph.D. Interim 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: Prof. John E. Gizis, 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: Prof. Dermott Mullan, 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: Prof. George C. Hadjipanayis, 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: Rachel Osten, Ph.D. Member of dissertation committee ACKNOWLEDGEMENTS I consider myself fortunate to have had the opportunity to work under the su- pervision of Prof. John Gizis. I cannot express how grateful I am to him for my achievement in my research. I am greatly indebted to Prof. Gizis for giving me the freedom to work in the way I wanted and to explore new research ideas, and for en- couraging me in all stages of my research. His positive feedback in every meeting were very helpful to motivate me and to grow as a scientist. I greatly value his contribution and effort in teaching research skills and his kindness in helping me to correct even the most minor errors with great patience. I would like to express my deepest gratitude to all the members of my dis- sertation committee: Prof. Dermott Mullan, Dr. Rachel Osten and Prof. George Hadjipanayis for generously providing their time and valuable feedback in making my dissertation better. Their suggestions were extremely helpful in giving a good direction to my research path. I am especially thankful to Dr. Osten for coming all the way from Baltimore during my oral candidacy exam and Ph.D. disseration defense despite her busy schedule. I greatly appreciate the support and contributions of my collaborators Prof. Dermott Mullan, Prof. Adam Burgasser, Dr. Sarah Schmidt, Dr. Peter Williams, Dr. Allison Youngblood and Dr. Keivan Stassun, which were very important in finishing my project and helped to lead to publication of the results. I benefited greatly from their expertise in their respective fields. I am deeply indebted to Prof. Dermott Mullan for teaching me the physics of the Sun as well as the flares. I am very grateful to him for the time he spent with me, teaching me the physical concepts which increased my understanding of the results of iv my project. His teaching was very important for increasing my confidence in the sub- ject matter. In addition, I am also thankful to him for helping me correct the language errors in my papers and dissertation. This work would not have been possible without support from the Department of Physics and Astronomy (DPA), University of Delaware. I am very thankful to the DPA for granting me admission and allowing me to use all the resources necessary for my research. My work would have been impossible without the financial support from the DPA. I am also thankful to the DPA for waiving the Physics-GRE requirement for my admission. My especial thanks to Prof. James MacDonald, the Chair of Graduate Admissions Committee, who had an important role for granting me admission. I grate- fully acknowledge University of Delaware Dissertation Fellowship which helped me to complete my dissertation on time, and also provided time for writing job applications. My sincere thanks also go to the staffs in the DPA IT department: Sola John- son, Sansern Somboonsong and Daniel De Marco who helped me solve many problems related to software and hardware. They were very friendly whenever I went to ask for help. My deep appreciation goes out to all my friends in the DPA and all also to all the members of UD Nepalese Student Association who were with me during the moments of my successes and failures. Their loving and caring company helped to boost my confidence when I had success, and remain strong even in the most difficult situation when I had a foot injury and had limited mobility for about three months in the summer of 2018. The coffee meetings we used to have in Brew Ha Ha are especially unforgettable, when we used to share our stories regarding research as well as life. I express my heart-felt gratitude to Prof. Binil Aryal, advisor of my Master's thesis, who showed me the initial direction to conduct research in astronomy. It is because of him I changed my mind away from becoming a condensed matter physicist, and was inspired to become involved in astronomy. Some of the results presented in this dissertation have already been published in two journals: the Astrophysical Journal (ApJ) and the Monthly Notices of the v Royal Astronomical Society (MNRAS). The material in this dissertation is based upon work supported by NASA under award Nos. NNX15AV64G, NNX16AE55G and NNX16AJ22G. Some/all of the data presented in this dissertation were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the As- sociation of Universities for Research in Astronomy, Inc., under NASA contract NAS5- 26555. This dissertation includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www. cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consor- tium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in A&AS 143, 23. This work made use of the http://gaia-kepler.fun crossmatch database created by Megan Bedell. I am beyond words to express my gratitude to my buba, my ama and my saano mama whose love, support and inspiration brought me to this stage of my life. My work would be incomplete without the support and love of my jeevan-sangini Nisha and my chhori Arinshu. I am extremely grateful to Nisha for her sacrifice, patience and company during the ups and downs of my life. Nisha had a very great role in en- couraging me as well as taking care of Arinshu and me when I was busy in my research. vi DEDICATION To my ama, Devi Paudel, my buba, Mitralal Paudel, my mama, Durga Datta Dhungana, my jeevan-sangini, Nisha Ghimire, and my chhori, Arinshu Paudel vii TABLE OF CONTENTS LIST OF TABLES :::::::::::::::::::::::::::::::: xiii LIST OF FIGURES ::::::::::::::::::::::::::::::: xvi ABSTRACT ::::::::::::::::::::::::::::::::::: xxvi Chapter 1 INTRODUCTION :::::::::::::::::::::::::::::: 1 1.1 A brief history of study of flares on M and L dwarfs :::::::::: 1 1.2 Stellar classification system ::::::::::::::::::::::: 2 1.3 M dwarfs ::::::::::::::::::::::::::::::::: 3 1.4 L dwarfs :::::::::::::::::::::::::::::::::: 4 1.5 Brown Dwarfs ::::::::::::::::::::::::::::::: 4 1.6 Ultracool dwarfs :::::::::::::::::::::::::::::: 5 1.7 Flares ::::::::::::::::::::::::::::::::::: 6 1.7.1 Flares on M/L dwarfs :::::::::::::::::::::: 7 1.8 Flare frequency distribution (FFDs) ::::::::::::::::::: 9 1.9 Importance of studying flares :::::::::::::::::::::: 13 1.9.1 Nature of the magnetic dynamo ::::::::::::::::: 13 1.9.2 Rotation-activity relations :::::::::::::::::::: 14 1.9.3 Motivation for studying flares on UCDs ::::::::::::: 16 1.10 M dwarf flares in the context of planet habitability :::::::::: 20 1.11 The Kepler mission :::::::::::::::::::::::::::: 23 1.12 The K2 mission :::::::::::::::::::::::::::::: 24 1.12.1 Kepler and K2 data ::::::::::::::::::::::: 26 1.13 Dissertation Outline ::::::::::::::::::::::::::: 26 viii 2 WHITE LIGHT FLARE RATES OF M/L DWARFS USING K2 SHORT CADENCE DATA :::::::::::::::::::::::: 30 2.1 White light flares ::::::::::::::::::::::::::::: 30 2.2 Sample ::::::::::::::::::::::::::::::::::: 33 2.3 Data Reduction and Computations ::::::::::::::::::: 46 2.3.1 K2 photometry :::::::::::::::::::::::::: 46 2.3.2 Flare detection :::::::::::::::::::::::::: 49 2.3.3 Calibration of equivalent duration and calculation of flare energy 51 2.4 Artificial flare injection and estimation of lowest detectable flare energy 56 2.5 Flare statistics and Flare energy spectrum of target UCDs :::::: 58 2.5.1 Possibility of a broken power-law or a power-law with exponential cutoff in the FFD of some UCDs :::::::::: 72 2.6 Superflares observed on two UCDs ::::::::::::::::::: 75 2.6.1 Photometry of superflare