UNLV Theses, Dissertations, Professional Papers, and Capstones 8-1-2017 Secular Resonances during Main-Sequence and Post-Main- Sequence Planetary System Dynamics Jeremy L. Smallwood University of Nevada, Las Vegas Follow this and additional works at: https://digitalscholarship.unlv.edu/thesesdissertations Part of the Astrophysics and Astronomy Commons Repository Citation Smallwood, Jeremy L., "Secular Resonances during Main-Sequence and Post-Main-Sequence Planetary System Dynamics" (2017). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3102. http://dx.doi.org/10.34917/11156810 This Thesis is protected by copyright and/or related rights. It has been brought to you by Digital Scholarship@UNLV with permission from the rights-holder(s). You are free to use this Thesis in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself. This Thesis has been accepted for inclusion in UNLV Theses, Dissertations, Professional Papers, and Capstones by an authorized administrator of Digital Scholarship@UNLV. For more information, please contact [email protected]. SECULAR RESONANCES DURING MAIN-SEQUENCE AND POST-MAIN-SEQUENCE PLANETARY SYSTEM DYNAMICS By Jeremy L. Smallwood Bachelor of Science – Astrophysics Baylor University 2015 A thesis submitted in partial fulfillment of the requirements for the Master of Science – Astronomy Department of Physics and Astronomy College of Sciences The Graduate College University of Nevada, Las Vegas August 2017 Thesis Approval The Graduate College The University of Nevada, Las Vegas June 13, 2017 This thesis prepared by Jeremy L. Smallwood entitled Secular Resonances during Main-Sequence and Post-Main-Sequence Planetary System Dynamics is approved in partial fulfillment of the requirements for the degree of Master of Science – Astronomy Department of Physics and Astronomy Rebecca Martin, Ph.D. Kathryn Hausbeck Korgan, Ph.D. Examination Committee Chair Graduate College Interim Dean Stephen Lepp, Ph.D. Examination Committee Member George Rhee, Ph.D. Examination Committee Member Arya Udry, Ph.D. Graduate College Faculty Representative ii ABSTRACT We investigate gravitational perturbations of an asteroid belt by secular resonances. We ap- ply analytic and numerical models to main–sequence and post–main–sequence planetary systems. First, we investigate how the asteroid impact rate on the Earth is affected by the architecture of the planetary system. We find that the ⌫6 resonance plays an important role in the asteroid collision rate with the Earth. Compared to exoplanetary systems, the solar system is somewhat special in its lack of a super–Earth mass planet in the inner solar system. We therefore consider the effects of the presence of a super–Earth in the terrestrial planet region. We find a significant effect for super–Earths with a mass of around 10 M and a separation greater than about 0.7AU. These ⊕ results have implications for the habitability of exoplanetary systems. Secondly, we model white dwarf pollution by asteroids from secular resonances. In the past few decades, observations have revealed signatures of metals polluting the atmospheres of white dwarfs that require a continu- ous accretion of asteroids. We show that secular resonances driven by two outer companions can provide a source of pollution if an inner terrestrial planet is engulfed during the red-giant branch phase. Secular resonances may be a viable mechanism for the pollution of white dwarfs in a variety of exoplanetary system architectures including systems with two giant planets and systems with one giant planet and a binary star companion. iii ACKNOWLEDGEMENTS All the simulations ran at the UNLV National Supercomputing Institute on the Cherry Creek cluster. This research made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org. iv TABLE OF CONTENTS ABSTRACT . iii ACKNOWLEDGEMENTS . iv LIST OF FIGURES . ix CHAPTER 1 INTRODUCTION . 1 Asteroid Impacts on Terrestrial Planets . 2 White Dwarf Pollution. 6 CHAPTER 2 ANALYTICAL MODELS . 10 Eigenfrequency . 10 Asteroid Precession Rates . 12 Resonance Widths . 12 CHAPTER 3 NUMERICAL MODELS . 16 Asteroid Impacts on Terrestrial Planets . 17 White Dwarf Pollution. 19 CHAPTER 4 RESULTS: ASTEROIDAL IMPACTS . 21 Total Number of Earth Collisions . 21 Evolution of the Asteroid Belt . 26 Resonances in the Asteroid Belt . 26 Collision Rate of the Earth . 28 The ⌫6 Resonance . 30 CHAPTER 5 RESULTS: WHITE DWARF POLLUTION . 38 Solar System . 38 Analytic Results. 38 Numerical Results . 42 Exoplanetary Systems . 47 CHAPTER 6 CONCLUSION . 51 BIBLIOGRAPHY . 54 CURRICULUM VITAE . 59 v LIST OF FIGURES 1.1 Planet mass and semi-major axis of observed exoplanets. The area between the two black-dotted lines contains the range of super-Earth masses (1M < Mp < ⊕ 10 M ) used in simulations described in Section 2. The transparent yellow box ⊕ denotes the observed super-Earths with a semi-major axis in the inner solar system. The data are from exoplanets.org (Han et al. 2014). 4 2.1 Forced eccentricity of a test particle near the ⌫6 secular resonance as a function of semi-major axis. 13 2.2 The transparent regions represent the libration width as a function of semi-major axis and eccentricity for a selection of Jupiter’s mean-motion resonances located within the asteroid belt. The overlapping of the libration widths denotes Jupiter’s chaotic region. 15 2.3 The transparent regions represent the libration width as a function of semi-major axis and eccentricity for a selection of Jupiter’s mean-motion resonances located within the asteroid belt. The overlapping of the libration widths denotes Jupiter’s chaotic region. The red circles represent a single asteroid within our asteroid dis- tribution. Simulation times are shown at t =0Myr(left panel) and t =90Myr (right panel). 15 3.1 A log–log plot showing how the number of asteroid collisions scales with the in- flated radius of the Earth, R. The black line shows how the total number of Earth collisions by asteroids (Nc) scales with changing radius of our simulated inflated Earth. The blue lines shows the number of Earth collisions in the presence of a 10 M super–Earth at semi–major axis 0.8 AU as a function of inflated Earth ⊕ radii. The red-dotted line represents the line N (R) R and the yellow-dotted c / line represents the line N (R) R2. ............................................. 18 c / 4.1 Left Panel: Total number of asteroid collisions with the Earth as a function of the semi–major axis of the super–Earth. The simulations with a 5M super-Earth are ⊕ denoted by hollow circles and the simulations with a 10M super-Earth are repre- ⊕ sented by the star symbols. The square represents the simulation of the standard solar system (without a super-Earth). Right Panel: Total number of asteroid col- lisions with the Earth as a function of super–Earth mass in units of Earth masses (M ) at semi-major axis aSE =0.8AU. .......................................... 24 ⊕ vi 4.2 Evolution of the asteroid distribution over a span of 10 million years. The as- teroid distribution is located in a system containing Earth, Jupiter, Saturn, and a super–Earth (except for the control simulation at top left). The asteroids are ini- tially sampled from a uniform distribution in semi-major axis values, represented at t =0Myr. Top-Left Panel: Evolution of asteroid distribution without a super- Earth. Top-Right Panel: Evolution of asteroid distribution with a 10M super- ⊕ Earth located at a semi-major axis of 0.8AU. Bottom-Left Panel: Evolution of asteroid distribution with a 10M super-Earth located at 1.2AU. Bottom-Right ⊕ Panel: Evolution of asteroid distribution with a 10M super-Earth located at 1.4AU. 25 ⊕ 4.3 The original semi-major axis of each asteroid as a function of the time when the final outcome occurred. The possible outcomes for each asteroid include Earth- impact (red) and other (blue). ”Other” refers to ejection, Juptier-impact, Saturn- impact, or colliding with central object. The inner and outer boundary of the as- teroid distribution are located at amin =1.558 AU and amax =4.138 AU. Top-left Panel: Asteroid outcomes for a system with no super–Earth. Top-Right Panel: 10 M super–Earth located at a semi-major axis of 0.8AU. Bottom-Left Panel: ⊕ 10 M super–Earth located at a semi-major axis of 1.2AU. Bottom-Right Panel: ⊕ 10 M super–Earth located at a semi-major axis of 1.4AU. The mean-motion res- ⊕ onances with Jupiter are represented with the black-dotted line, with the name of each resonance listed to the right of their respected line. The mean-motion reso- nances with the super–Earth are represented by the red-dotted lines. 27 4.4 Number of asteroid collisions towards Earth per million year for select simulations described in Table 1. Top Panel: Collision rate for simulations involving a 10M ⊕ super–Earth. Bottom Panel: Collision rate for simulations involving a 5M super– ⊕ Earth............................................................................ 29 4.5 The precession rate of a test particle as a function of semi-major axis in the inner part of the solar system. The solid horizontal line represents the gi eigenfrequency of Saturn. The intersection of the precession rate of the test particle with the eigen- frequency of Saturn denotes the location of a secular resonance. Top-Left Panel: A system with no super–Earth. In this case, the intersection located at 2AU is the location of the ⌫6 resonance within the asteroid belt. Top-Right Panel: System with a 10 M super–Earth located at a semi–major axis of a =0.8AU. Bottom- ⊕ Left Panel: System with a 10 M super–Earth located at a semi–major axis of ⊕ a =1.2AU.