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Origin of the Earth and Moon

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Origin of the Earth and Moon Origin of the Earth and Moon Thesis by Miki Nakajima In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2016 (Defended Oct 30th, 2015) ii © 2016 Miki Nakajima All Rights Reserved iii I dedicate this thesis to our mysterious Moon : % iv Acknowledgements I am deeply grateful to my advisor Dave Stevenson for wonderful guidance, wisdom and humor. I have been very inspired by his attitude towards science. Dave is knowl- edgeable in any research field and his ideas are exceptionally creative and inspiring. He is willing to challenge conventional ideas including own previous research, and he really cares about young scientists and future directions of planetary science. I think that he is one the greatest samurai in academia who is loyal to science (this is the biggest compliment I can think of). I am so fortunate that I have had this opportunity to work with him through my Ph.D. career. I would like to thank Andy Ingersoll for providing this great opportunity to work with him. He is a living legend in planetary science and it has been very fun to work with him by sharing excitement about research findings, observations and ideas. I cannot wait for having discussions with you about upcoming observations by Cassini. I also would like to thank Andy for inviting us for his house on thanksgiving and July 4th. It was wonderful to spend time with you, your family, and our colleagues on these special occasions. I am thankful to Paul Asimow for providing perspectives of thermodynamics and science discussions. I have learned so much through his classes and discussions we had. v I would like thank John Eiler for teaching me geochemistry and having fun science discussions with me at PRG (petrology reading group) and other places. When I came to Caltech, I had no background in geochemistry, but now it has become an essential part of my research. I am grateful to Konstantin Batygin, Bethany Ehlmann, Yuk Yung, and Oded Aharonson for providing me with scientific and career advice. I would like to thank former graduate students we had science discussions with over SecDec lunch: Aaron Wolf, Dan Bower, June Wicks, and Clair Waller-Thomas. I am so fortunate to meet with the former graduates Kaveh Pahlevan, Kevin Lewis, Alejandro Soto, Kuai Le, and Mike Line, who have provided me science and career advice. I cannot imagine my PhD life without having my wonderful officemates Zhang Su, Cheng Li, Mike Wong, and Danielle Piskorz. It has been great fun to take classes and have fun together with my classmates, including Peter Gao, Masha Kleschcheva, Hilary Martens, Adam Waszczak, and Josh Kammer. I cannot believe it has been five years since we first met. I wish you all the best luck with the wonderful journeys ahead of you. It has been fun to spend time in the offices as well as outside with my fellow graduates students and postdoctoral scholars Hao Cao, Bjoern Benneke, Kat Deck, Leslie Rogers, Abigail Fraeman, Pushkar Kopparla, Henry Ngo, Joe O'Rourke, Lu Pan, Dana Anderson, Peter Buhler, Patrick Fischer, Chris Spalding, Ian Wong, Elizabeth Bailey, and Nancy Thomas. I am very thankful to our administrative staff for helping me in many ways, including Irma Black, Margaret Carlos, Bronagh Glaser and Ulrika Terrones. I am very thankful to Tobias Bischoff, Belinda Pang, Rebecca Schwantes, John vi Chris Rollins, and Bryan Riel for working at home and having fun with me. You are my extended family in Pasadena. Last but certainly not least, I would like to thank my family, Tsuneo Nakajima, Kazuyo Nakajima, Emi Matsubara, and Nobuko Nakajima. Without any of you, I would not have been here (literally). I am so thankful that you supported me in pursuing my passion even though my career is quite unusual as a Japanese woman. It has been a wonderful journey with you all and I am excited for our upcoming years. I would like to thank my American family Steven Yoda, who is related to me through my great great grand parents, for welcoming me as a part of your family. vii Abstract According to the giant impact hypothesis, the Moon formed from a disk created by an impact between the proto-Earth and an impactor. Three major models for this hypothesis are (a) standard model: a Mars-sized impactor hit the Earth; (b) fast-spinning Earth model: a small impactor hit a rapidly spinning Earth; and (c) sub-Earths model: two half-Earth sized planets collided. These models have been supported because they can explain several observed features of the Earth-Moon system, such as the Moon's mass, angular momentum, and potentially geochemical measurements that suggest that the Earth and Moon have nearly identical isotopic ratios. However, it is uncertain if these models are consistent with other geochemical constraints. For example, isotopic measurements of Earth's rocks indicate that the early Earth's mantle was chemically heterogeneous and this signature was preserved for billions of years. However, it is not clear if the giant impact hypothesis is consistent with this geochemical constraint because the giant impact could have been so energetic that the Earth's mantle could have completely mixed and homogenized. Furthermore, the fraction of the Earth's mantle that became molten by the impact is not well known, even though it is known to have significantly affected the subsequent evolutions of viii the Earth's interior and atmosphere. Additionally, the water and volatile content of the Moon may have an important implication for the lunar origin. Since the Moon- forming disk formed through a giant impact process, it must have been hot and partially vaporized. From this disk, a significant amount of water and volatiles may have escaped to space. However, this idea may contradict recent geochemical studies that indicate that Moon may not be as dry as previously thought. Furthermore, moons of other planets may provide comprehensive pictures of the origin and evolution of the moons. For example, the Pluto-Charon system could have formed via a giant impact. Recent studies also suggest that Mars' satellites Phobos and Deimos could have formed in the same way. In contrast, satellites around the gas giants could have formed in situ from their proto-satellite disks and by gravitational capture. One of the Saturnian satellites, Enceladus has very unique geological and dynamical features. Cassini spacecraft observed that water plumes are emanating from cracks on the surface (so-called \tiger stripes"). These plumes may originate from a few kilometer deep subsurface liquid ocean. Along the cracks, strong ther- mal emissions have been observed and these are thought to be related to the plume activities, but the connection has been still unclear. In my Ph.D. thesis, I aim to understand the origin and evolution of the Earth, Moon, and the Saturnian moon Enceladus. In order to understand the initial state of the Earth's mantle and the Moon-forming disk, I perform giant impact simula- tions with a method called smoothed particle hydrodynamics (SPH). I show that the Earth's mantle becomes mostly molten by the impact and that the mantle re- ix mains unmixed in (a), but it may be at least partly mixed in (b) and (c). Therefore, (a) is most consistent with the preservation of the mantle heterogeneity. As for the Moon-forming disk, my calculations show that the disk of the standard model has a relatively low temperature (up to 4500 K) and low vapor mass fraction (∼ 20 − 30%) while the disk formed by other models could be much hotter (6000-7000 K) and has a higher vapor mass fraction (80 − 90%). Furthermore, I investigate the structure of the Moon-forming disk and estimated the extent of water escape. I show that escape is in the diffusion-limited regime and water escape from the disk to space is minor. This result could explain recent measurements on lunar water abundance. Furthermore, I develop a dynamical model that includes flow dynamics and flow-ice wall interaction that explains the Enceladus plume mass flux, heat flux, and several observed signatures. These studies will deepen comprehensive understanding of the origin of the moons in the solar system. x Contents Acknowledgements iv Abstract vii List of Figures xv List of Tables xvii 1 Introduction 1 2 Initial state of the Earth's mantle after the Moon-forming impact 7 2.1 Introduction . 8 2.2 Model . 15 2.2.1 Smoothed particle hydrodynamics (SPH) . 15 2.2.2 Equation of state . 16 2.2.3 Melting criterion . 17 2.2.4 Mixing criterion . 17 2.2.5 Initial conditions . 20 2.3 Results . 21 2.3.1 Comparison of equations of state . 21 xi 2.3.2 Mantle structure . 22 2.3.3 Mantle melting and mixing . 24 2.4 Discussion . 25 2.4.1 A discrepancy between SPH and the Rankine-Hugoniot equations 25 2.4.2 Mixing analysis . 27 2.4.3 Mixing during subsequent cooling . 29 2.4.4 Impactor's isotopic signature . 31 2.5 Conclusions . 32 2.6 Supplementary Materials . 40 2.6.1 Equation of state . 40 2.6.2 Mixing criterion . 42 2.6.3 MgSiO3 bridgmanite EOS . 43 2.6.4 Correction of the outer boundary . 44 2.6.5 The Rankine-Hugoniot equations . 45 2.6.6 Pressure vs. entropy increase . 46 2.6.7 Further discussions on the mixing analysis . 48 3 Initial state of the Moon-forming disk 50 3.1 Introduction . 51 3.2 Model . 54 3.2.1 SPH integrated with GRAPE . 54 3.2.2 Entropy of the disk .
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