Editing Contents (section)

=Primary (Tiled Menu) Chapters=
NOTE: &nbsp; <font color="pink">&clubs;</font> means templates and references to other chapters have been checked for completeness.

==Context==
<ol type="I">
  <li><font color="pink">&clubs;</font> [[PGE|Principal Governing Equations]] (PGEs)
  <ol type="A">
    <li><font color="pink">&clubs;</font> [[Cylindrical3D|Equations Cast in Cylindrical Coordinates]]</li>
  </ol>
  </li>
  <li><font color="pink">&clubs;</font> [[PGE/ConservingMass|Continuity]]</li>
  <li><font color="pink">&clubs;</font> [[PGE/Euler|Euler]]
  <ol type="A">
    <li>[[AxisymmetricConfigurations/SolutionStrategies|Axisymmetric Configurations (Solution Strategies)]]; Double check vector identities &nbsp; &lArr; &nbsp; also includes "Simple Rotation Profiles"</li>
   <li>
<font color="pink">&clubs;</font> [[PGE/RotatingFrame|Rotating Reference Frame]]; Euler equation viewed from a rotating frame of reference
  <ol type="1">
    <li>[[Apps/RiemannEllipsoidsCompressible|Compressible Analogs of Riemann S-Type Ellipsoids]]; Nonlinear velocity cross-product </li>
    <li><font color="pink">&clubs;</font> [[Apps/Korycansky_Papaloizou_1996|Korycansky and Papaloizou (1996)]]; Nonlinear velocity cross-product &nbsp; &lArr; &nbsp; bottom displays [https://digitalcommons.lsu.edu/gradschool_disstheses/6650/ Andalib] velocity maps</li>
  </ol>
   </li>
   <li><font color="pink">&clubs;</font> [[PGE/ConservingMomentum|Euler Equation (Conserving Momentum)]]; Earlier draft of "Euler" presentation</li>
  </ol>
  </li>
  <li><font color="pink">&clubs;</font> [[PGE/FirstLawOfThermodynamics|1<sup>st</sup> Law of Thermodynamics]]
  <ol type="A">
    <li><font color="pink">&clubs;</font> [[Appendix/Ramblings/Radiation/RadHydro|Radiation-Hydrodynamcis]]; Nonadiabatic (optically thick) environments 
    </li>
  </ol>
  </li>
  <li><font color="pink">&clubs;</font> [[PGE/PoissonOrigin|Poisson]]</li>

  <li><font color="pink">&clubs;</font> [[VE|Global Energy Considerations]]</li>

  <li><font color="pink">&clubs;</font> [[SR|Equation of State]] (EOS)
  <ol type="A">
    <li>[[2DStructure/AxisymmetricInstabilities|Axisymmetric Instabilities to Avoid]]; Poincar&eacute;-Wavre theorem</li>
    <li>[[SSC/Structure/BiPolytropes/Analytic1.53#BetaDefinition|BiPolytrope with <math>(n_c, n_e) = (\tfrac{3}{2}, 3)</math>]]; The parameter, &beta; &nbsp; &nbsp; &nbsp; <font color="orange">[Chapter has been segmented into 3 Parts]</font></li>
  </ol>
  </li>

  <li><font color="pink">&clubs;</font> [[SR/IdealGas|Ideal Gas]]</li>
  <li><font color="pink">&clubs;</font> [[SR/PressureCombinations|Total Pressure]]
  <ol type="A">
    <li><font color="pink">&clubs;</font> [[SR/Ptot_QuarticSolution|Determining Temperature from Density &amp; Pressure]]; A solution to quartic equation
    </li>
  </ol>
  </li>

  <li><font color="pink">&clubs;</font> [[Apps/SMS|Bond, Arnett, &amp; Carr (1984)]]
  <ol type="A">
    <li>[[SSC/Perturbations|Spherically Symmetric Configurations (Stability &#8212; Part II)]]; Brief summary of Ledoux and Pekeris (1941) &nbsp; &nbsp; &nbsp; <font color="orange">[Chapter needs to be segmented &hellip;]</font>
    </li>
  </ol>
  </li>
</ol>

==Spherically Symmetric Configurations==
<ol type="I">
  <li><font color="pink">&clubs;</font> [[SSCpt1/PGE|One-Dimensional PGEs]]
  </li>
  <li>[[SSC/Index|SSC Index]]</li>
  <li>[[SphericallySymmetricConfigurations/IndexFreeEnergy|Index to Free-Energy and Virial Analyses]]</li>

<li>SSCpt1/Virial/&hellip;
  <ol type="A">
  <li>[[SSCpt1/Virial/PolytropesEmbeddedOutline|Virial Equilibrium of Embedded Polytropic Spheres]] &nbsp; &lArr; &nbsp; Tiled menu contains image of free-energy surface</li>
  <li>[[SSCpt1/Virial/FormFactors#Structural_Form_Factors|Structural Form Factors]] &nbsp; &nbsp; &nbsp; <font color="orange">[Chapter has been segmented into 3 Parts]</font> &nbsp; &nbsp; &rArr; &nbsp; &nbsp; See also [[SSC/FreeEnergy/PolytropesEmbedded/Pt2#PTtable|here]]; or [[SSCpt1/Virial#Structural_Form_Factors|original definition]] &nbsp; &nbsp; &rArr; &nbsp; &nbsp; or [[SSC/FreeEnergy/Powerpoint#Structural_Form_Factors|Best]] &nbsp; &nbsp; <b><font color="red">&lArr; &nbsp; &nbsp; Structural Form Factors</font></b></li>
  <li>[[SSCpt1/Virial|Free-Energy of Spherical Systems]]</li>
  </ol>
</li>

</ol>

===Equilibrium Structures===
<ol type="I">
  <li>SSCpt2 &hellip;
  <ol type="A">
    <li>[[SSCpt2/IntroductorySummary|Hydrostatic Balance Equation]]</li>
  <li><font color="pink">&clubs;</font> [[SSCpt2/SolutionStrategies|Solution Strategies]]</li>
  </ol>

  <li>[[SSC/SynopsisStyleSheet|Spherical Structures Synopsis]] &nbsp; &lArr; &nbsp; Image of 1<sup>st</sup> page of synopsis</li>
  <li><font color="pink">&clubs;</font> <b>Scalar Virial Theorem</b>; subsection of ''Context'' - &sect;VI [[VE#Scalar_Virial_Theorem|(Global Energy Considerations)]]</li>
  <li><font color="pink">&clubs;</font> [[SSC/Structure/UniformDensity|Uniform-Density Sphere]]</li>
  <li>[[SSC/Structure/IsothermalSphere|Isothermal Sphere]]</li>
  <li><b>Via Direct Numerical Integration</b>; subsection of ''Equilibrium Structures'' - &sect;VI [[SSC/Structure/IsothermalSphere#Our_Numerical_Integration|(Isothermal Sphere)]]</li>
  <li>Polytropic Spheres
  <ol type="A">
    <li>[[SSC/Structure/Polytropes|Isolated Polytropes]]</li>
    <li>[[SSC/Structure/Lane1870|Lane (1870)]]</li>
    <li>[[SSC/Structure/Polytropes/Analytic|Known Analytic Solutions]] &nbsp; &nbsp; &lArr; &nbsp; &nbsp; See also, [[SSC/Structure/PowerLawDensity|Power-Law Density Distribution]]</li>
    <li>[[SSC/Structure/Polytropes/Numerical#Straight_Numerical_Integration|Via Direct Numerical Integration]]</li>
    <li>[[SSC/Structure/Polytropes/Numerical#HSCF_Technique|Via Self-Consistent Field (SCF) Technique]]</li>
  </ol>
  </li>
  <li>[[SSC/Structure/WhiteDwarfs|Chandrasekhar Limiting Mass (1935)]]</li>
  <li>Pressure-Truncated Configurations
  <ol type="A">
    <li>[[SSC/Structure/BonnorEbert|Bonnor-Ebert (Isothermal) Spheres (1955 - 56)]]</li>
    <li>Embedded Polytropes
      <ol type="1">
        <li>[[SSC/Structure/PolytropesEmbedded|General Properties]]</li>
        <li>[[SSC/Structure/PolytropesEmbedded/n1|Truncated Configurations with n = 1]]</li>
        <li>[[SSC/Structure/PolytropesEmbedded/n5|Truncated Configurations with n = 5]]</li>
        <li>[[SSC/Structure/PolytropesEmbedded/Other|Other]]</li>
      </ol>
    </li>
    <li>[[SSC/Stability/InstabilityOnsetOverview|Equilibrium Sequence Turning-Points]]</li>
    <li>[[SSC/Stability/InstabilityOnsetOverview#Turning_Points_along_Sequences_of_Pressure-Truncated_Polytropes|Equilibrium Sequences of Pressure-Truncated Polytropes]] &nbsp; &lArr; &nbsp; Image of sequences with turning points</li>
    <li>[[Appendix/Ramblings/TurningPoints#Turning_Points|Turning-Points (Broader Context)]]</li>
    <li>[[SSC/Structure/Polytropes/VirialSummary|Virial Equilibrium of Pressure-Truncated Polytropes]] (Summary)
      <ol type="1">
        <li>Free Energy
          <ol type="a">
            <li>[[SSC/FreeEnergy/PolytropesEmbedded|Free Energy Synopsis]]</li>
            <li>[[SSC/FreeEnergy/Powerpoint|Supporting Free-Energy PowerPoint Presentation]]&nbsp; &nbsp; <b><font color="red">&lArr; &nbsp; &nbsp; Excellent Overview!</font></b></li>
          </ol>
        </li>
        <li>Virial Equilibrium of Adiabatic Spheres
          <ol type="a">
            <li>[[SSC/Virial/Isothermal|SSC/Virial/Isothermal]]</li>
            <li>SSC/Virial/Polytropes
              <ol type="i">
<li>[[SSC/Virial/Polytropes/Pt1|Isolated Polytropes]]</li>
<li>[[SSC/Virial/Polytropes/Pt2|Polytropes Embedded in an External Medium]]</li>
              </ol>
            </li>
            <li>SSC/Virial/PolytropesEmbedded/FirstEffortAgain
              <ol type="i">
<li>[[SSC/Virial/PolytropesEmbedded/FirstEffortAgain/Pt1|Isolated Configurations]]</li>
<li>[[SSC/Virial/PolytropesEmbedded/FirstEffortAgain/Pt2|Configurations Embedded in an External Medium]]</li>
              </ol>
            </li>
            <li>SSC/Virial/PolytropesEmbedded/SecondEffortAgain
              <ol type="i">
<li>[[SSC/Virial/PolytropesEmbedded/SecondEffortAgain/Pt1|Force Balance, Free Energy, &amp; Virial]]</li>
<li>[[SSC/Virial/PolytropesEmbedded/SecondEffortAgain/Pt2|Mass-Radius Relation]]</li>
<li>[[SSC/Virial/PolytropesEmbedded/SecondEffortAgain/Pt3|Discussion &amp; Other Model Sequences]]</li>
              </ol>
            </li>
          </ol>
          </li>
      </ol>
    </li>
  </ol>
  </li>
  <li>[[SSC/Structure/BiPolytropes|Composite Polytropes]] (Bipolytropes)
    <ol type="A">
      <li><font color="pink">&clubs;</font> [[SSC/Structure/BiPolytropes/Analytic1.53#BiPolytrope_with_(nc,_ne)_=_(3/2,_3)|Milne (1930)]]</li>
      <li>[[SSC/Structure/LimitingMasses#Sch.C3.B6nberg-Chandrasekhar_Mass|Sch&ouml;nberg-Chandrasekhar Mass (1942)]] &nbsp; &nbsp; &nbsp; &lArr; &nbsp; &nbsp; Includes broader discussion of ''Limiting Masses''</li>
      <li>[[SSC/Structure/BiPolytropes/Analytic15#BiPolytrope_with_nc_.3D_1_and_ne_.3D_5|Murphy (1983) Analytic (n<sub>c</sub>, n<sub>e</sub>) = (1, 5)]]</li>
      <li>[[SSC/Structure/BiPolytropes/Analytic51#BiPolytrope_with_nc_=_5_and_ne_=_1_(Pt_1)|Eggleton, Faulkner &amp; Cannon (1998) Analytic (n<sub>c</sub>, n<sub>e</sub>) = (5, 1)]]</li>
      <li>[[SSC/Stability/BiPolytropes#Organizational_Index|Search for Marginally Unstable (n<sub>c</sub>, n<sub>e</sub>) = (5, 1) Bipolytropes]] &nbsp; &lArr; &nbsp; Image of sequences with turning points</li>
       <li>[[SSC/Structure/BiiPolytropes/FreeEnergy51|Free Energy of (n<sub>c</sub>, n<sub>e</sub>) = (5, 1) Bipolytropes]] &nbsp; &nbsp; &nbsp; <font color="orange">[Chapter has been segmented into 3 Parts]</font> </li>
  </ol>
  </li>
</ol>