Contents

Primary (Tiled Menu) Chapters

NOTE:   ♣ means templates and references to other chapters have been checked for completeness.

Context

1. ♣ Principal Governing Equations (PGEs)
   1. ♣ Equations Cast in Cylindrical Coordinates
2. ♣ Continuity
3. ♣ Euler
   1. Axisymmetric Configurations (Solution Strategies); Double check vector identities   ⇐   also includes "Simple Rotation Profiles"
   2. ♣ Rotating Reference Frame; Euler equation viewed from a rotating frame of reference
      1. Compressible Analogs of Riemann S-Type Ellipsoids; Nonlinear velocity cross-product
      2. ♣ Korycansky and Papaloizou (1996); Nonlinear velocity cross-product   ⇐   bottom displays Andalib velocity maps
   3. ♣ Euler Equation (Conserving Momentum); Earlier draft of "Euler" presentation
4. ♣ 1^st Law of Thermodynamics
   1. Radiation-Hydrodynamcis; Nonadiabatic (optically thick) environments
5. ♣ Poisson
6. ♣ Global Energy Considerations
7. ♣ Equation of State (EOS)
   1. Axisymmetric Instabilities to Avoid; Poincaré-Wavre theorem
   2. BiPolytrope with $(n_c,n_e)=(\frac{3}{2},3)$; The parameter, β
8. ♣ Ideal Gas
9. ♣ Total Pressure
   1. ♣ Determining Temperature from Density & Pressure; A solution to quartic equation
10. ♣ Bond, Arnett, & Carr (1984)
    1. Spherically Symmetric Configurations (Stability — Part II); Brief summary of Ledoux and Pekeris (1941)

Spherically Symmetric Configurations

1. ♣ One-Dimensional PGEs
2. SSC Index
3. Index to Free-Energy and Virial Analyses
4. Virial Equilibrium of Embedded Polytropic Spheres   ⇐   Image of free-energy surface
5. Structural Form Factors
6. Free-Energy of Spherical Systems

Equilibrium Structures

1. Hydrostatic Balance Equation
2. ♣ Solution Strategies
3. Spherical Structures Synopsis   ⇐   Image of 1^st page of synopsis
4. ♣ Scalar Virial Theorem; subsection of Context - §VI (Global Energy Considerations)
5. ♣ Uniform-Density Sphere
6. Isothermal Sphere
7. Via Direct Numerical Integration; subsection of Equilibrium Structures - §VI (Isothermal Sphere)
8. Polytropic Spheres
   1. Isolated Polytropes
   2. Lane (1870)
   3. Known Analytic Solutions
   4. Via Direct Numerical Integration
   5. Via Self-Consistent Field (SCF) Technique