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Analysis of Angular Momentum in Planetary Systems and Host Stars by Stacy Ann Irwin Bachelor of Science, Computer Science University of Houston 2000 Master of Science, Space Sciences Florida Institute of Technology 2009 A dissertation submitted to the College of Science at Florida Institute of Technology in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Space Sciences Melbourne, Florida July 2015 c Copyright 2015 Stacy Ann Irwin All Rights Reserved The author grants permission to make single copies We the undersigned committee hereby recommend that the attached document be accepted as fulfilling in part the requirements for the degree of Doctor of Philosophy in Space Sciences. \Analysis of Angular Momentum in Planetary Systems and Host Stars," a dissertation by Stacy Ann Irwin Samuel T. Durrance, Ph.D. Professor, Physics and Space Sciences Major Advisor Daniel Batcheldor, Ph.D. Associate Professor, Physics and Space Sciences Committee Member Darin Ragozzine, Ph.D. Assistant Professor, Physics and Space Sciences Committee Member Semen Koksal, Ph.D. Professor, Mathematical Sciences Outside Committee Member Daniel Batcheldor, Ph.D. Professor, Physics and Space Sciences Department Head Abstract Analysis of Angular Momentum in Planetary Systems and Host Stars by Stacy Ann Irwin Dissertation Advisor: Samuel T. Durrance, Ph.D. The spin angular momentum of single Main Sequence stars has long been shown to follow a primary power law of stellar mass, J M α, excluding stars of <2 solar masses. Lower mass / stars rotate more slowly with and have smaller moments of inertia, and as a result they contain much less spin angular momentum. A secondary power law describes the upper bound of angular momenta of these less massive stars with a steeper slope. The Solar System's orbital angular momentum, however, is of the same order of magnitude as the primary law, whereas the Sun's spin angular momentum is consistent with the secondary relationship. This suggests that planets are an important clue to answering questions about stellar angular momentum loss and transfer. With recent advances in exoplanet discovery and characterization, the angular momenta of exoplanetary systems can now be determined. A method is developed to calculate planetary system angular momenta from the spin and orbital angular momenta of a sample including 426 host stars and 532 planets. To maximize the size of the working sample, systems discovered by both the transit and radial velocity methods are included, and the biases of both techniques are identified. Self-consistent stellar moment of inertia parameters are interpolated from grids of stellar evolutionary models. iii Main Sequence host stars range from 0.6 to 1.7 solar masses, and their angular mo- menta are shown to agree well with previous studies of stellar angular momentum, generally falling on or below the appropriate power law, and exhibiting detection method biases. The systems' angular momenta, including both the planetary orbital and stellar spin compo- nents, are widely spread above and below the primary power law, but on average agree well with the primary relationship. The results indicate that the primary power law describes angular momenta of stars of <2 solar masses well, when planetary angular momentum is included. This relationship also holds across host star evolutionary classifications. For 90% of the systems, the angular momentum contained in the planets is greater than the spin angular momentum of the host star, a characteristic shared by the Solar System. Undetected planets contribute significant bias to the system angular momentum as well as to the proportion of angular momentum contained in the planets. This bias is used to identify systems which are likely to harbor additional planets in already known planetary systems, assuming the Solar System's proportions are typical. iv Contents List of Figures ix List of Tables xi List of Symbols, Constants, and Abbreviations xii Acknowledgements xv 1 Introduction 1 1.1 Stellar Mass, Rotation, and Angular Momentum . 1 1.1.1 An Angular Momentum Puzzle . 2 1.1.2 The Kraft Curve . 6 1.1.3 Commonalities . 8 1.2 Star Formation and Angular Momentum Loss . 13 1.3 The Solar System and Exoplanetary Systems . 18 1.4 Motivations and Goals . 24 2 Method 27 v 2.1 Angular Momentum Defined . 27 2.2 Angular Momentum and Specific Angular Momentum . 29 2.3 Stars and Spin Angular Momentum . 32 2.3.1 Angular Velocity . 33 2.3.2 Moment of Inertia . 36 2.4 Planets and Orbital Angular Momentum . 41 2.5 Planetary Systems . 44 2.6 Biases . 47 3 Data 49 3.1 Planet Discovery Techniques . 49 3.1.1 Overview . 49 3.1.2 Detection Method Biases: RV and Transit . 54 3.2 Sources and Selection . 54 3.3 The Exoplanet Orbit Database . 58 3.4 Data Cleaning . 60 3.4.1 Inclusions and Exclusions . 61 3.4.2 Corrections and Conflicts . 61 3.4.3 Missing Data . 63 3.4.4 Other Adjustments . 65 3.5 Stellar Classification . 66 3.6 Stellar Properties . 71 3.7 Planetary Properties . 74 vi 4 Results and Discussion 78 4.1 Quantified Angular Momentum . 78 4.1.1 About the Plots . 78 4.1.2 Stars . 81 4.1.3 System Totals . 85 4.1.4 Fitting the Kraft Relation . 88 4.1.5 Discussion . 92 4.2 System Distribution of J ............................. 98 4.2.1 and K .................................. 98 L 4.2.2 Toward Determination of System Completeness . 103 4.3 Biases . 107 5 Summary, Conclusions, and Suggestions for Future Work 112 5.1 Summary . 113 5.2 Conclusions . 115 5.3 Suggestions for Future Work . 117 A Appendix A: Stellar Inertial Models 120 A.1 PKD Models . 121 A.2 CG Models . 125 A.3 Comparison of PKD and CG Models . 129 A.4 Claret (2004) Models . 131 vii B Appendix B: Treatment of Uncertainties and Error Propagation 134 C Appendix C: Stellar Properties 137 D Appendix D: Planetary Properties 148 E Appendix E: System Properties 162 viii List of Figures 1.1 Rotation of Low-mass Stars . 2 1.2 McNally j-M Plot . 4 1.3 Carrasco et al. j-M Plot . 6 1.4 Kraft j-M Plot . 8 1.5 Kawaler J-M Plot . 9 1.6 McNally and Kawaler J-M Plot . 10 1.7 Wolff et al. Plots . 12 1.8 Alves et al. Plots . 21 1.9 Paz-Chinch´onet al. Plots . 23 2.1 CG logm and logβ ................................ 39 3.1 Planet Discoveries by Year . 53 3.2 Planet Mass and Semi-major Axis . 55 3.3 HR Diagrams . 70 3.4 Stellar Mass Distribution . 72 3.5 Host Star Metalicity Distributions . 73 ix 3.6 Planet Mass Distribution . 75 4.1 J-M Model . 79 4.2 J∗ Sample Histogram . 81 4.3 J∗ Histograms . 82 4.4 J∗ Results: MS and Non-MS . 83 4.5 J∗ Results: RV and Transit . 84 4.6 Jsys Results: MS and Non-MS . 86 4.7 Jsys Results: RV and Transit . 88 4.8 Binned Results: All Systems . 96 4.9 Binned Results: Main Sequence . 97 4.10 Histograms . 98 L 4.11 Histogram: Detection Methods . 99 L 4.12 K Histograms . 100 4.13 Logarithmic K Histogram . 101 4.14 Angular Momentum of High-K MS Systems . 104 A.1 PKD Inertial Evolution . 123 A.2 PKD Interpolation Equation . 126 A.3 CG Inertial Evolution . 127 A.4 CG log m and log β ................................ 128 A.5 Plot of MS Interpolation Equation from Model Data . 133 A.6 Evolution of γ for Selected Masses . 133 x List of Tables 1.1 Angular Momentum Distribution of the Solar System . 19 3.1 EOD Downloaded Fields . 60 3.2 Summary of Host Star and System Classifications . 71 3.3 Summary of System Type and Discovery Methods . 71 4.1 Kraft Relations for Sample Subgroups . 102 4.2 K Values of Solar System Planets . 105 4.3 K Values of HD 10180 Planets . 105 A.1 PKD Model Ages at ZAMS and Mid-MS log I . 124 A.2 Interpolated Inertial Coefficient Equations . 132 C.1 Stellar Parameters . 138 D.1 Planetary Parameters . 149 E.1 System Parameters . ..
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