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       [Chapter has been segmented into 3 Parts]
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     ⇒     See also here; or original definition     ⇒     or Best     ⇐     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     ⇐     See also, Power-Law Density Distribution
   4. Via Direct Numerical Integration
   5. Via Self-Consistent Field (SCF) Technique
9. Chandrasekhar Limiting Mass (1935)
10. Pressure-Truncated Configurations
    1. Bonnor-Ebert (Isothermal) Spheres (1955 - 56)
    2. Embedded Polytropes
       1. General Properties
       2. Truncated Configurations with n = 1
       3. Truncated Configurations with n = 5
       4. Other
    3. Equilibrium Sequence Turning-Points
    4. Equilibrium Sequences of Pressure-Truncated Polytropes   ⇐   Image of sequences with turning points
    5. Turning-Points (Broader Context)
    6. Virial Equilibrium of Pressure-Truncated Polytropes (Summary)
       1. Free Energy
          1. Free Energy Synopsis
          2. Supporting Free-Energy PowerPoint Presentation    ⇐     Excellent Overview!
       2. Virial Equilibrium of Adiabatic Spheres
          1. SSC/Virial/Isothermal
          2. SSC/Virial/Polytropes
             1. Isolated Polytropes
             2. Polytropes Embedded in an External Medium
          3. SSC/Virial/PolytropesEmbedded/FirstEffortAgain
             1. Isolated Configurations
             2. Configurations Embedded in an External Medium
          4. SSC/Virial/PolytropesEmbedded/SecondEffortAgain
             1. Force Balance, Free Energy, & Virial
             2. Mass-Radius Relation
             3. Discussion & Other Model Sequences
11. Composite Polytropes (Bipolytropes)
    1. ♣ Milne (1930)
    2. Schönberg-Chandrasekhar Mass (1942)       ⇐     Includes broader discussion of Limiting Masses
    3. Murphy (1983) Analytic (n_c, n_e) = (1, 5)
    4. Eggleton, Faulkner & Cannon (1998) Analytic (n_c, n_e) = (5, 1)
    5. Search for Marginally Unstable (n_c, n_e) = (5, 1) Bipolytropes   ⇐   Image of sequences with turning points
    6. Free Energy of (n_c, n_e) = (5, 1) Bipolytropes