A Dissertation entitled Kepler Planet Occurrence Rates for Mid-Type M Dwarfs as a Function of Spectral Type by Kevin K. Hardegree-Ullman Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics Dr. Michael C. Cushing, Committee Chair Dr. Jon E. Bjorkman, Committee Member Dr. Rupali Chandar, Committee Member Dr. Philip S. Muirhead, Committee Member Dr. Nikolas J. Podraza, Committee Member Dr. Amanda C. Bryant-Friedrich, Dean College of Graduate Studies The University of Toledo August 2018 Copyright 2018, Kevin K. Hardegree-Ullman This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of Kepler Planet Occurrence Rates for Mid-Type M Dwarfs as a Function of Spectral Type by Kevin K. Hardegree-Ullman Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics The University of Toledo August 2018 Previous studies of planet occurrence rates largely relied on photometric stellar characterizations. We present spectroscopic observations of 337 out of 561 probable mid-type M dwarfs in the primary Kepler field. Our observations have allowed us to constrain spectral type, temperatures, and in some cases metallicities for these stars. We use a random forest classifier to spectral type the remaining 224 targets. Combining our data with Gaia parallaxes, we have computed precise (∼3%) stellar radii, which we use to update planet parameters and planet occurrence rates for Kepler mid-type M dwarfs. Within the Kepler field, there are seven M3 V to M5 V stars which host a total of 13 confirmed planets between 0.5 and 2.5 Earth radii and at orbital periods between 0.5 and 10 days. For this population, we compute a +0:14 planet occurrence rate of 1:27−0:28 planets per star. With our spectral classifications, +0:53 we compute planet occurrence rates for each spectral sub-type which yields 0:78−0:40, +1:14 +2:87 1:23−0:75, and 2:51−1:51 planets per star for M3 V, M4 V, and M5 V, respectively. Our updated planet parameters show Kepler-1649 b to be an Earth sized planet receiving insolation flux similar to Earth. We also use our data to compute stellar mass, identify active stars with Hα emission, and identify binary candidates. Our observations with the multi-object spectrograph Hydra on the WIYN telescope allowed us to observe 1,083 other Kepler stars, which will be useful in future studies. iii For Emily, Kelly, Michael, Melody, and Angelina. Acknowledgments I would like to thank my advisor Mike Cushing, who has allowed me to pursue my scientific interests while keeping me from meandering too far off track. My disser- tation would not have been possible without the guidance and help developing this project from Phil Muirhead. I am lucky to have been able to take a majority of my graduate courses with Jon Bjorkman, who has the unique talent of making Jackson electrodynamics understandable. I am also grateful to my committee members Rupali Chandar and Nik Podraza for bringing in additional perspectives to my work. My graduate experience was immeasurably enriched during my IPAC Visiting Graduate Fellowship, and I am thankful to Jessie Christiansen for guiding me down the rabbit hole of exoplanet research. I would also like to thank my fellow graduate students at the University of Toledo, and members of the Ritter observing team for making our department scientifically fruitful. Finally, a special thank you to Rick Irving and Mike Brown for keeping everything working behind the scenes. v Contents Abstract iii Acknowledgments v Contents vi List of Tables ix List of Figures xii List of Abbreviations xviii List of Symbols xix 1 Introduction 1 1.1 A Brief History of Exoplanet Discovery . .2 1.1.1 Early Exoplanet Claims . .2 1.1.2 The Radial Velocity Method . .2 1.1.3 The First Exoplanets . .6 1.1.4 The Transit Method . .7 1.1.5 Direct Imaging . .8 1.2 Kepler . 10 1.3 Planet Occurrence Rates . 12 1.4 M Dwarf Pros and Cons . 12 1.5 Accurate Stellar Properties for Occurrence Rate Calculations . 16 vi 2 Mid-Type M Dwarf Planet Occurrence Rates 19 2.1 Target Selection, Observations, and Data Reduction . 19 2.1.1 WIYN . 20 2.1.2 Discovery Channel Telescope . 24 2.1.3 IRTF . 24 2.1.4 LAMOST . 25 2.1.5 Gaia . 25 2.2 Stellar Properties . 26 2.2.1 Absolute Magnitudes . 27 2.2.2 Spectral Type . 27 2.2.3 Effective Temperature . 30 2.2.4 Metallicity . 31 2.2.5 Radius . 32 2.3 Refining the Sample . 35 2.3.1 Giants . 35 2.3.2 Eclipsing and Spectroscopic Binaries . 36 2.3.3 Gaia Color Cuts and Binaries . 38 2.4 Mid-Type M Dwarf Planets . 40 2.5 Planet Occurrence Rate . 45 2.5.1 Monte Carlo Analysis . 47 2.6 Discussion . 49 3 Additional Information from Spectra 52 3.1 Stellar Properties from Spectra . 52 3.1.1 Mass . 52 3.1.2 Stellar Activity . 53 3.1.3 BY Draconis Binaries . 57 vii 3.2 Kepler Spectroscopic Library . 58 3.2.1 Optimizing Hydra Observations . 58 4 Conclusions 63 4.1 Planet Occurrence Rates . 63 4.2 Future Directions . 65 A Additional Acknowledgements 68 B Data Reduction for DCT/DeVeny Spectra 71 B.1 Rotate images and add a dispersion axis . 72 B.2 Bias subtract and flat field . 72 B.3 Extract spectra . 77 B.4 Calibrate wavelengths . 83 B.5 Combine spectra . 89 B.6 Flux calibrate spectra . 92 C Stellar Property Tables 96 viii List of Tables 2.1 Kepler Mid-Type M Dwarf Planets . 44 2.2 Planet occurrence rates per spectral type. 49 4.1 Planet occurrence rates per planet radius bin. 64 B.1 DeVeny Spectrograph Atomic Line List . 85 B.1 DeVeny Spectrograph Atomic Line List . 86 C.1 Stellar parameters for spectroscopically classified targets. 97 C.1 Stellar parameters for spectroscopically classified targets. 98 C.1 Stellar parameters for spectroscopically classified targets. 99 C.1 Stellar parameters for spectroscopically classified targets. 100 C.1 Stellar parameters for spectroscopically classified targets. 101 C.1 Stellar parameters for spectroscopically classified targets. 102 C.1 Stellar parameters for spectroscopically classified targets. 103 C.1 Stellar parameters for spectroscopically classified targets. 104 C.1 Stellar parameters for spectroscopically classified targets. 105 C.1 Stellar parameters for spectroscopically classified targets. 106 C.1 Stellar parameters for spectroscopically classified targets. 107 C.1 Stellar parameters for spectroscopically classified targets. 108 C.1 Stellar parameters for spectroscopically classified targets. 109 C.1 Stellar parameters for spectroscopically classified targets. 110 C.1 Stellar parameters for spectroscopically classified targets. 111 ix C.1 Stellar parameters for spectroscopically classified targets. 112 C.1 Stellar parameters for spectroscopically classified targets. 113 C.1 Stellar parameters for spectroscopically classified targets. 114 C.1 Stellar parameters for spectroscopically classified targets. 115 C.1 Stellar parameters for spectroscopically classified targets. 116 C.1 Stellar parameters for spectroscopically classified targets. 117 C.1 Stellar parameters for spectroscopically classified targets. 118 C.1 Stellar parameters for spectroscopically classified targets. 119 C.1 Stellar parameters for spectroscopically classified targets. 120 C.1 Stellar parameters for spectroscopically classified targets. 121 C.1 Stellar parameters for spectroscopically classified targets. 122 C.1 Stellar parameters for spectroscopically classified targets. 123 C.1 Stellar parameters for spectroscopically classified targets. 124 C.2 Stellar parameters for photometrically classified targets. 125 C.2 Stellar parameters for photometrically classified targets. 126 C.2 Stellar parameters for photometrically classified targets. 127 C.2 Stellar parameters for photometrically classified targets. 128 C.2 Stellar parameters for photometrically classified targets. 129 C.2 Stellar parameters for photometrically classified targets. 130 C.2 Stellar parameters for photometrically classified targets. 131 C.2 Stellar parameters for photometrically classified targets. 132 C.2 Stellar parameters for photometrically classified targets. 133 C.2 Stellar parameters for photometrically classified targets. 134 C.2 Stellar parameters for photometrically classified targets. 135 C.2 Stellar parameters for photometrically classified targets. 136 C.2 Stellar parameters for photometrically classified targets. 137 C.2 Stellar parameters for photometrically classified targets. 138 x C.2 Stellar parameters for photometrically classified targets. 139 C.2 Stellar parameters for photometrically classified targets. 140 C.2 Stellar parameters for photometrically classified targets. 141 C.2 Stellar parameters for photometrically classified targets. 142 C.2 Stellar parameters for photometrically classified targets. 143 C.3 Other Kepler stars. 144 C.3 Other Kepler stars. 145 C.3 Other Kepler stars. 146 C.3 Other Kepler stars. 147 C.3 Other Kepler stars. 148 C.3 Other Kepler stars. 149 C.3 Other Kepler stars. 150 C.3 Other Kepler stars. 151 C.3 Other Kepler stars. 152 C.3 Other Kepler stars. 153 C.3 Other Kepler stars. 154 C.3 Other Kepler stars. 155 C.3 Other Kepler stars. 156 C.3 Other Kepler stars. 157 C.3 Other Kepler stars. 158 C.3 Other Kepler stars. 159 C.3 Other Kepler stars. 160 C.3 Other Kepler stars. 161 xi List of Figures 1-1 The reference frame where the center of mass is at rest for a single planet star system. .3 1-2 The reference frame where the star is at rest. .4 1-3 A plot of the cumulative number of unique planet detections per year, color coded by discovery method (NASA Exoplanet Archive). .9 1-4 A plot of planet detections per.