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Radiation Recoil Effects on the Dynamical Evolution of Asteroids A Radiation Recoil Effects on the Dynamical Evolution of Asteroids A dissertation presented to the faculty of the College of Arts and Sciences of Ohio University In partial fulfillment of the requirements for the degree Doctor of Philosophy Desire´e Cotto-Figueroa December 2013 c 2013 Desire´e Cotto-Figueroa. All Rights Reserved. ! 2 This dissertation titled Radiation Recoil Effects on the Dynamical Evolution of Asteroids by DESIREE´ COTTO-FIGUEROA has been approved for the Department of Physics and Astronomy and the College of Arts and Sciences by Thomas S. Statler Professor of Physics and Astronomy Robert Frank Dean, College of Arts and Sciences 3 A COTTO-FIGUEROA, DESIREE,´ Ph.D., December 2013, Physics and Astronomy Radiation Recoil Effects on the Dynamical Evolution of Asteroids (111 pp.) Director of Dissertation: Thomas S. Statler The Yarkovsky effect is a radiation recoil force that results in a semimajor axis drift in the orbit that can cause Main Belt asteroids to be delivered to powerful resonances from which they could be transported to Earth-crossing orbits. This force depends on the spin state of the object, which is modified by the YORP effect, a variation of the Yarkovsky effect that results in a torque that changes the spin rate and the obliquity. Extensive analyses of the basic behavior of the YORP effect have been previously conducted in the context of the classical spin state evolution of rigid bodies (YORP cycle). However, the YORP effect has an extreme sensitivity to the topography of the asteroids and a minor change in the shape of an aggregate asteroid can stochastically change the YORP torques. Here we present the results of the first simulations that self-consistently model the YORP effect on the spin states of dynamically evolving aggregates. For these simulations we have developed several algorithms and combined them with two codes, TACO and pkdgrav. TACO is a thermophysical asteroid code that models the surface of an asteroid using a triangular facet representation and which can compute the YORP torques. The code pkdgrav is a cosmological N-body tree code modified to simulate the dynamical evolution of asteroids represented as aggregates of spheres using gravity and collisions. The continuous changes in the shape of an aggregate result in a different evolution of the YORP torques and therefore aggregates do not evolve through the YORP cycle as a rigid body would. Instead of having a spin evolution ruled by long periods of rotational acceleration and deceleration as predicted by the classical YORP cycle, the YORP effect is self-limiting and stochastic on aggregate asteroids. We provide a statistical description of the spin state evolution which lays out the foundation for new simulations of a coupled 4 Yarkovsky/YORP evolution. Both self-limiting YORP and to a lesser degree a stochastic YORP provide a viable means to explain why the Near-Earth Asteroid (NEA) population seems to remember their initial spin states at the time of delivery from the Main Belt. The YORP effect drives the obliquity of most objects that follow the YORP cycle to the values of 0, 90 and 180 degrees. NEAs could complete a YORP cycle on timescales much shorter than their typical dynamical lifetime. Therefore, one should expect the obliquity distribution of the population of NEAs to be concentrated about those values if they follow the YORP cycle. But to obtain a direct measurement of the obliquity distribution will require radar observations or multiple lightcurves at different illumination and orbital phases for each NEA. Instead of obtaining a direct measurement, the obliquity distribution can be inferred if the distribution of semimajor axis drift rates due to the Yarkovsky effect can be measured. From the linear heat diffusion theory for a spherical body, the semimajor axis drift rate varies linearly with cosine obliquity. Previous studies have attempted to infer the obliquity distribution taking advantage of this simple dependence. However, those results should be considered only approximate because of the neglect of the dependence of the semimajor axis drift rate on density, thermal properties, and shape. Here we seek to obtain the obliquity distribution of NEAs using a better approach based on Bayesian inference that takes into account our prior knowledge of the distributions of the physical parameters on which the semimajor axis drift rates depend. A preliminary obliquity distribution of the NEA population has been estimated to be a V-shaped model that lacks a concentration of objects at an obliquity of 90 degrees and which suggests that the most probable value of the fraction of retrograde rotators is 70.0%. Once the obliquity distribution is obtained, it can in turn be used to test YORP predictions and constrain YORP evolution. 5 To my parents, who have always believed in me. 6 A First, I would like to gratefully acknowledge support from the NASA Harriet F. Jenkins Predoctoral Fellowship Program (JPFP), the NASA Ohio Space Grant Consortium (OSGC) Fellowship and the NASA Planetary Geology & Geophysics Program. I would also like to acknowledge and express my sincere appreciation and gratitude to my advisor, Thomas S. Statler, for all of his support and advice during the completion of this dissertation. I am also grateful to the other members of my dissertation committee, Markus Boettcher, Keith Milam and Joseph C. Shields for their helpful suggestions. A special thanks to our collaborators Derek C. Richardson, Paolo Tanga, Steven R. Chesley and Davide Farnocchia for their contributions to this research. Furthermore, I would like to thank everyone who have supported me or helped me in any way not forgetting my dear friends, who were always there for me. Finally, I am deeply grateful to my daughter Iadara Nicole, my husband Jos´e, and our families for their endless love, support, and encouragement. 7 T C Page Abstract ......................................... 3 Dedication ........................................ 5 Acknowledgments .................................... 6 List of Tables ...................................... 9 List of Figures ...................................... 10 1 General Introduction ................................ 13 1.1 Near-Earth Asteroids ............................. 13 1.2 Aggregate Asteroids ............................. 17 1.3 Yarkovsky effect ............................... 20 1.4 YORP effect .................................. 24 1.5 Open Questions ................................ 32 2 Obliquity Distribution of NEAs ........................... 37 2.1 Introduction .................................. 37 2.2 Bayesian Approach .............................. 40 2.3 Results ..................................... 44 2.4 Discussion ................................... 49 3 Aggregate Dynamics ................................ 51 3.1 Introduction .................................. 51 3.2 Code Development .............................. 52 3.2.1 Tiling ................................. 52 3.2.2 Sensitivity .............................. 54 3.2.3 Transformation ............................ 59 3.2.4 The Spin State Evolution ....................... 61 3.2.5 Simulations .............................. 66 3.3 Aggregate Objects .............................. 70 3.4 Choice of Simulation Parameters ....................... 73 3.5 Results and Discussions ............................ 74 3.5.1 End States .............................. 79 8 3.5.2 Stochastic and Self-Limiting YORP Effect . 81 3.5.3 Mass Loss and Binary Formation . 85 3.5.4 Axis Ratio Evolution ......................... 94 3.5.5 The Statistical Spin and Obliquity Evolutions . 95 4 Conclusions and Future Work ............................102 References ........................................106 9 L T Table Page 1.1 Classes of NEAs. ................................. 14 2.1 Taxonomic Types. ................................. 42 3.1 Aggregate Objects. ................................ 71 3.2 Comparison of End States. ............................ 80 3.3 Mass Loss Episodes. ............................... 86 3.4 Mass Loss Spin Rates. .............................. 88 10 L F Figure Page 1.1 The orbits of the three classes of NEAs: Amors, Apollos and Atens. 14 1.2 The orbits of the major planets and the location of asteroids. 16 1.3 The aggregate asteroid 25143 Itokawa ...................... 18 1.4 The rotation rate distribution for asteroids and trans-Neptunian objects. 19 1.5 The Yarkovsky Effect. ............................... 21 1.6 Detection of the Yarkovsky effect. ........................ 23 1.7 The YORP effect. ................................. 25 1.8 The radiation forces on the wedges. ....................... 25 1.9 The YORP torques for Pseudo-gaspra ...................... 26 1.10 The spin state evolution for Pseudo-gaspra. ................... 27 1.11 Predicted Obliquity Distribution ......................... 29 1.12 Detection of the YORP Effect. .......................... 30 1.13 Typical variation in the YORP torques caused by an identical single boulder randomly placed on an identical object. ..................... 31 1.14 Identical views of the two objects from Figure 1.13 with the most positive and most negative spin torques. ............................ 32 1.15 The de-biased Fast-Rotator Fraction F plotted against absolute magnitude H and nominal diameter. ............................... 35 1.16 Snapshots of a simulation where changes in the shape and mass loss of an aggregate asteroid can be observed as a result of applying constant YORP torque. 36 2.1 Inferred obliquity
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