Modeling Exoplanet Interiors from Host Star Elemental Abundances A thesis presented to the faculty of the College of Arts and Sciences of Ohio University In partial fulfillment of the requirements for the degree Master of Science Brandi B. Hamilton December 2019 © 2019 Brandi B. Hamilton. All Rights Reserved. 2 This thesis titled Modeling Exoplanet Interiors from Host Star Elemental Abundances by BRANDI B. HAMILTON has been approved for the Department of Geological Sciences and the College of Arts and Sciences by Keith A. Milam Associate Professor of Geological Sciences Florenz Plassmann Dean, College of Arts and Sciences 3 ABSTRACT HAMILTON, BRANDI, M.S., December 2019, Geological Sciences Modeling Exoplanet Interiors from Host Star Elemental Abundances Director of Thesis: Keith A. Milam The overall dimensions and internal structures of potential Earth-sized rocky exoplanets are modeled based on the relative photospheric abundances of Mg, Si, and Fe in their host stars. The modeling assumes that the planet has these same relative abundances and that all iron resides in a liquid core surrounded by a magnesiosilicate mantle comprising enstatite orthopyroxene and forsterite olivine or their high-pressure transformation products. The Mg/Si ratio sets the olivine/orthopyroxene fractions of the upper mantle and the Mg-perovskite/MgO fractions of the lower mantle. The amounts of volatile elements are not considered aside from the oxygen required by the silicate and oxide minerals. The planets are assumed to have formed under conditions where silicon remained in condensed form during accretion and volatile elements such as hydrogen, nitrogen and carbon did not. The core mass fraction is determined from the amount of Fe relative to Mg, Si, and O. Following the approaches of Valencia et al. (2006) and Sotin et al. (2007), the self-compression of a planet is modeled using published experimental observations or theoretical calculations of densities, bulk moduli, and thermal expansion coefficients of the silicate and iron components. Assuming a specific planet mass and an initial estimate of radius, compression is calculated from the surface downward in increments of 1-km layers, taking into account reconstructive phase changes as pressure and temperature 4 increase. The core-mantle boundary is reached when the underlying (i.e., remaining) mass equals the core mass fraction of the planet. The self-compression is modeled iteratively, varying planet radius until the gravitational acceleration at the center converges to zero. In this research, effort is made to avoid using potentially Earth-unique assumptions regarding the core mass fraction of the planet, or the partitioning of iron into mantle silicates, instead relying primarily on data from observational astronomy. Potential terrestrial planets were modeled for fifteen F or G class stars, each with an 24 assumed mass equal to that of Earth: 5.97 x 10 kg (1 ME). The resulting planet radii varied by over 200 km due to differing elemental ratios, with the strongest influence being the core (iron) mass fraction according to R = 6980 km - 1751 km (Fe mass fraction). The Mg/Si ratio had a second-order effect, with a higher ratio producing a larger planet, as reported by Sotin et al. (2010). These radii are lower bounds in that the partitioning of Fe into the mantle (assumed to be zero here) would produce smaller cores and larger planets. 5 DEDICATION This work is dedicated to my family, and all the bright minds who vow to never stop learning. 6 ACKNOWLEDGMENTS I would like to extend my sincere thanks to Dr. Douglas Green for taking me on as a graduate student and allowing me the opportunity to pursue this area of research. He was instrumental to this project, and I hope he enjoys retirement as much as I enjoyed having him as an advisor. I would also like to acknowledge Dr. Keith Milam for stepping in as my final advisor and helping me complete this process. And finally, I would like to thank my committee members, both past and present, who have assisted me in this endeavor. 7 TABLE OF CONTENTS Page Abstract ................................................................................................................................3 Dedication ............................................................................................................................5 Acknowledgments................................................................................................................6 List of Tables .......................................................................................................................8 List of Figures ......................................................................................................................9 Chapter 1: Introduction ......................................................................................................10 Detection of Exoplanets ...............................................................................................10 Terrestrial Planet Formation ........................................................................................12 Elemental Composition ................................................................................................17 Stellar Abundances ..................................................................................................... 18 Chapter 2: Methods ........................................................................................................... 20 Mineral Assemblages and Internal Structure ...............................................................21 Geophysical Calculations............................................................................................ 24 Temperature Profile .................................................................................................... 26 Sol Model Earth Mass Trial ........................................................................................ 31 Sol Model Venus Mass Trial ...................................................................................... 35 Modeling Other Target Stars ...................................................................................... 36 Chapter 3: Results ............................................................................................................. 39 Chapter 4: Discussion ....................................................................................................... 44 References ......................................................................................................................... 50 Appendix A ....................................................................................................................... 54 Appendix B ....................................................................................................................... 56 Appendix C ....................................................................................................................... 57 8 LIST OF TABLES Page Table 1 Sol Abundance Data ............................................................................................21 Table 2 PREM vs. Sol Model Values for 1 ME Planet .....................................................32 Table 3 Target Stars ..........................................................................................................38 Table 4 Fe mass% and Resulting Core and Planet Radii for 1ME Planets .......................42 Table 5 Modeling Results for Earth-Moon System ..........................................................46 Table 6 Modeling Results for Mercury and Mars .............................................................47 9 LIST OF FIGURES Page Figure 1. Confirmed Exoplanets by Type ..........................................................................12 Figure 2. Condensation Temperatures of Elements. ..........................................................13 Figure 3. Diagram of Earth’s Differentiated Layers. .........................................................16 Figure 4. Abundances of the Solar Atmosphere and Carbonaceous Chondrites. ..............17 Figure 5. Temperature Profile Used in the Model. ............................................................29 Figure 6. Self-Compression Flow Chart. ...........................................................................30 Figure 7. Sol Model vs. PREM Density Plot. ....................................................................33 Figure 8. Sol Model vs. PREM Gravity Plot .....................................................................34 Figure 9. Hertzsprung-Russell Diagram. ...........................................................................37 Figure 10. Modeled Planet Radii vs. Mg/Si Ratio. ............................................................40 Figure 11. Modeled Planet Radii vs. Iron Mass Percent....................................................41 10 CHAPTER 1: INTRODUCTION Thousands of planets have recently been discovered, and now most (99.8%) of the planets we are aware of orbit stars other than the Sun. Few characteristics are known about these exoplanets, but missions such as the Kepler Space Telescope and the James Webb Telescope are designed to learn more (Borucki et al., 2003; Gardner et al., 2009). Given the challenges presented to even detect these small, distant bodies, it is crucial to apply our understanding of planetary accretion and layering, derived from our studies of the Solar System, to exoplanets in order forward research of these bodies which