[Springer Theses] Development of a Numerical Simulation Method for Rocky Body Impacts and Theoretical Analysis of Asteroidal Shapes ||

This book describes numerical simulations of collisions between asteroids, based on a unique numerical code developed by the author. The code accurately solves the elastic dynamic equations and describes the effects of fracture and friction, which makes it possible to investigate the shapes of impact outcomes produced by asteroid collisions and subsequent gravitational accumulation of fragments. The author parallelizes the code with high parallelization efficiency; accordingly, it can be used to conduct high-resolution simulations with the aid of supercomputers and clarify the shapes of small remnants produced through the catastrophic destruction of asteroids. The author demonstrates that flat asteroids can only be produced by impacts involving objects with similar mass and low velocity, which suggests that the flat asteroids in our solar system were created in the planet formation era and have kept their shapes until today. The author also shows that asteroid collisions under certain conditions can produce the extremely elongated shape of an interstellar minor body, 1I/‘Oumuamua. In brief, the book offers a comprehensive investigation of asteroid impacts and shapes, making it a uniquely valuable resource. Supervisor’s Foreword 6 Parts of this thesis have been published in the following journal articles: 8 Acknowledgements 9 Contents 10 1 Introduction 13 1.1 Asteroids in the Solar System 13 1.2 Solar System Formation Scenario 17 1.3 Planetesimal or Asteroidal Collisions 20 1.3.1 Types of Collisional Outcomes 22 1.3.2 Collisions as the Origin of Asteroidal Shapes 24 References 26 2 Method 30 2.1 Elastic Dynamics 30 2.1.1 Basic Equations for Elastic Dynamics 30 2.1.2 Basic Concept of SPH Method 32 2.1.3 Equations for Standard SPH Method 34 2.1.4 Equations for Godunov SPH Method 38 2.1.5 Godunov SPH Method and Tensile Instability 48 2.1.6 Time Development Method 54 2.2 Tillotson Equation of State 55 2.3 Self Gravity 57 2.3.1 Self Gravity for SPH Method 57 2.3.2 Acceleration Scheme of Computation of Self Gravity 58 2.4 Fracture Model 58 2.4.1 Concept of Fracture Model 59 2.4.2 SPH Implementation of Fracture Model 60 2.5 Pressure Dependent Failure Model and Friction Model 61 2.5.1 Description of Models 62 2.5.2 Test Simulations for Friction Model 63 2.6 Parallelization of Simulation Code Using FDPS 64 2.7 Summary of Utilized Methods and Parameters 66 Appendix: Linear Stability Analysis for Godunov SPH Method 67 References 69 3 Results: Shapes of Impact Outcomes 72 3.1 Initial Conditions of Impacts 72 3.2 Analysis of Results 73 3.3 Equal-Mass and Non-destructive Impacts 75 3.3.1 Resolution Dependence on Resultant Shapes 75 3.3.2 Mass of the Largest Remnants 76 3.3.3 Characteristic Shapes Formed Through Collisions 78 3.3.4 Summary of Shapes Formed by Collisions 83 3.3.5 Discussion: Thresholds to Distinguish Impacts that Form Each Shape 87 3.4 Unequal-Mass and Non-destructive Impacts 88 3.4.1 Similar-Mass Impacts 88 3.4.2 Impacts with Large Mass Ratios 91 3.5 Destructive Impacts 92 References 97 4 Discussion: Collisional History of Asteroids 98 4.1 Connection Between Shapes of Asteroids and Collisional Environments 98 4.1.1 Summary of Shapes of Impact Outcomes 98 4.1.2 Impact Velocity and Collisional Environments 99 4.1.3 Shapes Formed in the Primordial and Present Environments 103 4.2 Comparison with Actual Asteroids 104 4.2.1 Databases Utilized in Our Analysis 104 4.2.2 Fraction of Family Asteroids 106 4.2.3 Shapes of Asteroids Larger Than 100 km 107 4.2.4 Shapes of Asteroids Larger Than 10 km 109 4.2.5 Direction of Rotation Axis 112 References 114 5 Application: Extremely Elongated Shape Of 1I/`Oumuamua 115 5.1 Introduction of 1I/`Oumuamua 115 5.2 Initial Conditions of Simulations for 1I/`Oumuamua 117 5.3 Results of Simulations for 1I/`Oumuamua 118 5.3.1 Equal-Mass Impacts with φd=40° 118 5.3.2 Dependence on the Friction Angle 120 5.3.3 Dependence on the Mass Ratio 123 5.4 Discussion: Environments for 1I/`Oumuamua Formation 125 5.4.1 Turbulence 125 5.4.2 Size of Larger Bodies 128 5.4.3 Survivability of Extremely Elongated Shapes Through Ejection Processes 129 References 130 6 Summary and Future Prospects 134 6.1 Summary 134 6.1.1 Development of the Numerical Simulation Method 134 6.1.2 Asteroidal Shapes Formed Through Collisions 135 6.1.3 Comparison with Actual Asteroids 137 6.1.4 Formation of Extremely Elongated Shape of 1I/`Oumuamua 138 6.2 Future Prospects 139 6.2.1 Application to Other Phenomena 139 6.2.2 Addition of Other Models 140 6.2.3 Comparison with Particle Based Codes 141 References 142