Analysis of Angular Momentum in Planetary Systems and Host Stars

201 Pages·2015·1.65 MB·English

by  Stacy Ann Irwin

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
(cid:13)
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
primarypowerlawofstellarmass, J Mα, excludingstarsof<2solarmasses. Lowermass
∝
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
andcharacterization,theangularmomentaofexoplanetarysystemscannowbedetermined.
A method is developed to calculate planetary system angular momenta from the spin and
orbitalangularmomentaofasampleincluding426hoststarsand532planets. Tomaximize
the size of the working sample, systems discovered by both the transit and radial velocity
methodsareincluded,andthebiasesofbothtechniquesareidentified. Self-consistentstellar
moment of inertia parameters are interpolated from grids of stellar evolutionary models.
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Main Sequence host stars range from 0.6 to 1.7 solar masses, and their angular mo-
mentaareshowntoagreewellwithpreviousstudiesofstellarangularmomentum, 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.
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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
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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
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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
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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
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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´on et 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
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