Modelling the Capture Theory for the Origin of Planetary Systems

by



Stephen Oxley

Submitted for the Degree of
Doctor of Philosophy



University of York
Department of Physics
December 1999

• 
  Abstract
• .
• Contents
• List of Figures
• List of Tables
• Acknowledgements
• Declaration
• Introduction
  • Thesis Outline
  • Introduction to Cosmogony
  • The Laplace Nebula Theory: Monistic
    • Revival of the Laplace Model
    • The Roche Limit
  • Jeans' Tidal Theory: Dualistic
    • The Jeans Mass
    • Objections to Jeans' Tidal Theory
    • Further Comments on Jeans' Tidal Theory
  • The Capture Theory
    • The Solar Nebula Theory
    • The Capture Process
  • Towards a Complete Theory of Planetary Formation
    • The Interstellar Medium and Star Formation
    • Star-Star Interactions
    • Planetary Formation
    • Satellite Formation
    • Orbital Evolution
    • The Terrestrial Planets
    • Explained Features of the Solar System
      • Gross features
      • Secondary features
      • Finer details of the Solar System
• Smoothed Particle Hydrodynamics
  • Motivation
  • The Kernel and the Smoothing Length
  • Variable Smoothing Lengths
    • Constant Number of Neighbours
    • Neighbour Search Algorithm
  • Forces
  • Hydrodynamical Forces
  • General SPH Equations and Derivatives
  • Artificial Viscosity
  • Gravitational Forces
    • Gravitational Softening
    • Consistent Representation of Matter
    • Sphere-Sphere Gravitational Softening
    • Point-Sphere Gravitational Softening
  • The Equation of State
  • Energy Equations
  • Time Integration
    • Choice of Integrator
    • Embedded Improved Euler Scheme
    • Time-Step Control
• Additional Computational Techniques
  • Tree Gravity
    • Principles and Methods
    • Tree implementation
    • Tree Construction
    • Tree Storage in Memory
    • Centre of Mass Calculation
    • Force Calculation
    • TreeSPH
  • Tree Radiation
    • Motivation
    • Radiative Principles and Assumptions
    • Opacity
    • A First Idea
      • Radiators
      • Receivers
      • Interparticle Absorption Grid
      • Discussion
      • Conclusion
    • Tree Radiation Method
    • Defining the Tree
      • Tree Construction
      • Tree Pruning
    • Interpolating the Particle Properties to the Tree
    • Tree Absorption Properties
    • Radiative Energy Transfer Process
      • Leaf same size in the same square, Figure 3.20(a)
      • Leaf same size different square, Figure 3.20(b)
      • Larger leaf, Figure 3.20(c)
      • Subdivided square, Figure 3.20(d)
    • Additional Tree Walking Considerations
      • Neighbour Search
      • Absorption Softening
    • Time integration
      • Implementation
    • Rate of Transfer Considerations
    • Interpolating the Tree Energy to the Particles
• Testing the Code
  • Gravity
    • Initial Configuration
    • Uniform Grid - Point Mass Force
    • Uniform Grid - Softened Force
    • Displaced Grid - Softened Force
    • Free-Fall curves
  • Hydrodynamics
    • The Structure of Polytropes
    • The Oscillation of Polytropes
  • Radiation Transport
    • Luminosity of an Isolated Sphere
    • Radiation Received from a Point Source
    • Equilibrium Temperatures of Illuminated Bodies
    • Radiation Transport in the Opaque Regime
• Simulating the Capture Theory
  • Quasi-Static Collapse of Spherical Bodies
    • Low Mass Bodies
    • Results
      • Comparison of Resolution
      • Dynamic Equilibrium Profiles
      • 1067 Particle Experiment
    • Larger Mass Bodies
  • The Capture Mechanism
    • Initial Orbital Components
    • Quasi-Static Collapsing Protostar Interactions
    • Near Free-Fall Protostar Interactions: Tidal Induced Fragmentation Followed by Capture
    • Results
    • An Example Encounter: Without Solar Radiation
    • An Example Encounter: With Solar Radiation
    • Evolution of Protoplanets
• Conclusion
  • Introduction
  • Smoothed Particle Hydrodynamics
  • Additional Computational Techniques
  • Testing the Code
  • Simulating the Capture Theory
  • Future Work
  • Conclusion
• Pseudo-Code
  • Particle Insertion Routine During Tree Construction
  • Mass and Centre of Mass Calculation via Tree Traversal
  • Smoothing Length Calculation Routine for Particle
  • Density Calculation for Particle
  • Force Calculation Routine for Particle
  • Tree Pruning via 1 Tree Traversal
  • Compact Tree Creation
  • Tree Walk for 1 Power Packet
• Derivations
  • Free-Fall Derivation
  • Point Source Absorption Derivation
• References
• About this document ...

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