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===Equilibrium Structures=== | ===Equilibrium Structures=== | ||
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! style="height: 75px; width: 800px; background-color:lightblue;"|<font color="white" size="+2">1D STRUCTURE</font> | |||
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Revision as of 16:20, 30 August 2018
Tiled Menu
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| Tiled Menu | Tables of Content | Banner Video | Tohline Home Page | |
Context
Global Energy Considerations |
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Principal Governing Equations (PGEs) |
Continuity | Euler | 1st Law of Thermodynamics |
Poisson |
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Equation of State (EOS) |
Total Pressure |
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Spherically Symmetric Configurations
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Structural Form Factors |
Free-Energy of Spherical Systems |
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One-Dimensional PGEs |
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Equilibrium Structures
1D STRUCTURE |
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Scalar Virial Theorem |
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Hydrostatic Balance Equation |
Solution Strategies |
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Isothermal Sphere |
via Direct Numerical Integration |
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Isolated Polytropes |
Known Analytic Solutions |
via Direct Numerical Integration |
via Self-Consistent Field (SCF) Technique |
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Zero-Temperature White Dwarf |
Chandrasekhar Limiting Mass (1935) |
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Pressure-Truncated Configurations |
Bonnor-Ebert (Isothermal) Spheres (1955 - 56) |
Polytropes | Equilibrium Sequence Turning-Points |
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Stability Analysis
Variational Principle |
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Radial Pulsation Equation |
Example Derivations & Statement of Eigenvalue Problem |
Relationship to Sound Waves |
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Uniform-Density Configurations |
Sterne's Analytic Sol'n of Eigenvalue Problem (1937) |
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Pressure-Truncated Isothermal Spheres |
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via Direct Numerical Integration |
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Yabushita's Analytic Sol'n for Marginally Unstable Configurations (1974) |
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Polytropes |
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Isolated n = 3 Polytrope |
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Pressure-Truncated Configurations |
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Exact Demonstration of B-KB74 Conjecture |
Exact Demonstration of Variational Principle |
Pressure-Truncated n = 5 Polytropes |
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Our Analytic Sol'n for Marginally Unstable Configurations (2017) |
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Nonlinear Dynamical Evolution
Free-Fall Collapse |
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Collapse of Isothermal Spheres |
via Direct Numerical Integration |
Similarity Solution |
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Collapse of an Isolated n = 3 Polytrope |
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Two-Dimensional Configurations (Axisymmetric)
PGEs for Axisymmetric Systems |
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Axisymmetric Equilibrium Structures
Constructing Axisymmetric Equilibrium Configurations |
Axisymmetric Instabilities to Avoid |
Simple Rotation Profiles |
Hachisu Self-Consistent-Field [HSCF] Technique |
Solving the Poisson Equation |
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Using Toroidal Coordinates to Determine the Gravitational Potential |
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Attempt at Simplification |
Wong's Analytic Potential (1973) |
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Spheroidal & Spheroidal-Like
Uniform-Density (Maclaurin) Spheroids |
Maclaurin's Original Text & Analysis (1742) |
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Rotationally Flattened Isothermal Configurations |
Hayashi, Narita & Miyama's Analytic Sol'n (1982) |
Review of Stahler's (1983) Technique |
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Toroidal & Toroidal-Like
Definition: anchor ring |
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Massless Polytropic Configurations |
Papaloizou-Pringle Tori (1984) |
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Self-Gravitating Incompressible Configurations |
Dyson (1893) |
Dyson-Wong Tori |
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Self-Gravitating Compressible Configurations |
Ostriker (1964) |
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Stability Analysis
Toroidal & Toroidal-Like
Defining the Eigenvalue Problem |
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(Massless) Papaloizou-Pringle Tori |
Analytic Analysis by Blaes (1985) |
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Two-Dimensional Configurations (Nonaxisymmetric Disks)
Constructing Infinitesimally Thin Nonaxisymmetric Disks |
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Three-Dimensional Configurations
Equilibrium Structures
Ellipsoidal & Ellipsoidal-Like
Constructing Ellipsoidal & Ellipsoidal-Like Configurations |
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Free-Energy Evolution from the Maclaurin to the Jacobi Sequence |
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Jacobi Ellipsoids |
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See Also
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© 2014 - 2021 by Joel E. Tohline |