Joel2: Created page with "FORCETOC =Index to Free-Energy and Virial Analyses= I have put this index together in an effort to help me, first find, then keep track of all chapters that discuss the use of a free-energy expression and/or virial equilibrium constructs to analyze the structure and stability of spherically symmetric configurations. First, let's explain what the topic is of each chapter t..."

2023-12-14T05:41:03Z

Created page with "__FORCETOC__   =Index to Free-Energy and Virial Analyses= I have put this index together in an effort to help me, first find, then keep track of all chapters that discuss the use of a free-energy expression and/or virial equilibrium constructs to analyze the structure and stability of spherically symmetric configurations. First, let's explain what the topic is of each chapter t..."

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__FORCETOC__ 

=Index to Free-Energy and Virial Analyses=

I have put this index together in an effort to help me, first find, then keep track of all chapters that discuss the use of a free-energy expression and/or virial equilibrium constructs to analyze the structure and stability of spherically symmetric configurations.

First, let's explain what the topic is of each chapter that is currently (up to July 2016) in the template titled, ''LSU_HBook_SSC_Structure''.

<ul>
<li>⓪  [[SSCpt1/Virial#Virial_Equilibrium_of_Spherically_Symmetric_Configurations|SphericallySymmetricConfigurations Virial]] (Introduction)</li>
<li>① & ②  [[SSC/VirialEquilibrium/UniformDensity#Uniform-Density_Sphere|SSC VirialEquilibrium UniformDensity]] (Isolated and Embedded)</li>
<li>③  [[SSC/Virial/Polytropes#Isolated_Nonrotating_Adiabatic_Configuration|SSC Virial Polytropes]] (Isolated)</li>
<li>④  [[SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|SSC Virial PolytropesEmbeddedOutline]] (w/ Movie)</li>
<li>[[SSC/FreeEnergy/PolytropesEmbedded|Free Energy of Truncated Polytropes]]     <math>~\Leftarrow</math>     This chapter contains key summary expressions used in the PowerPoint presentation (see especially the "Summary" subsection)</li>
<li>⑤ & ⑥  [[SSC/Virial/Isothermal|SSC Virial Isothermal]] (Isolated and Bounded)</li>
<li>⑦  [[SSC/BipolytropeGeneralizationVersion2#Bipolytrope_Generalization|SSC BipolytropeGeneralization_Version2]] (Overview)</li>
<li>⑧  [[SSC/Structure/BiPolytropes/FreeEnergy00#Free_Energy_of_BiPolytrope_with|SSC Structure BiPolytropes FreeEnergy0_0]] <math>~(n_c,n_e) = (0,0)</math></li>
<li>⑨  [[SSC/Structure/BiPolytropes/FreeEnergy51#Free_Energy_of_BiPolytrope_with|SSC Structure BiPolytropes FreeEnergy5_1]] <math>~(n_c,n_e) = (5,1)</math></li>
<li>Two key graphical summaries:<ul>
<li>[[SSC/Virial/PolytropesEmbedded/SecondEffortAgain#Plotting_Concise_Mass-Radius_Relation|For Pressure-truncated Polytropes]]</li>
<li>[[SSC/Structure/BiPolytropes/Analytic51#Stability_Condition|For Bipolytropes with]] <math>~(n_e,n_c) = (5,1)</math></li>
</ul>
</li>
</ul>

<table border="1" width="100%" cellspacing="2" cellpadding="8">
<tr>
<th align="right" width="50%">
Solution Strategies:    
</th>
<th align="center" width="25%">
Detailed Force-Balance ([[SSCpt2/SolutionStrategies#Spherically_Symmetric_Configurations_.28Part_II.29|Introduction]])
</th>
<th align="center">
Virial Equilibrium ([[SSCpt1/Virial#Virial_Equilibrium_of_Spherically_Symmetric_Configurations|Introduction]])⓪
</th>
</tr>
<tr>
<td align="left" colspan="3">
<table border="0" cellpadding="0" width="100%">
<tr>
<td align="left" colspan="4">Example Solutions: </td>
</tr>
<tr>
<td align="left" colspan="4">
* Uniform-density sphere
</td>
</tr>
<tr>
<td align="left">        </td><td align="left">Isolated …</td>
<td align="center" width="25%">[[SSC/Structure/UniformDensity#Isolated_Uniform-Density_Sphere|&spades;]]</td><td align="center" width="25%">[[SSC/VirialEquilibrium/UniformDensity#Uniform-Density_Sphere|①]]</td>
</tr>
<tr>
<td align="left">    </td><td align="left">Embedded in an External Medium …</td>
<td align="center" width="25%">[[SSC/Structure/UniformDensity#Uniform-Density_Sphere_Embedded_in_an_External_Medium|&spades;]]</td><td align="center" width="25%">[[SSC/VirialEquilibrium/UniformDensity#Adiabatic_Evolution_of_Pressure-truncated_Sphere|②]]</td>
</tr>
<tr>
<td align="left" colspan="4">
* Polytropes
</td>
</tr>
<tr>
<td align="left">    </td><td align="left">Isolated …</td>
<td align="center" width="25%">[[SSC/Structure/Polytropes#Polytropic_Spheres|&spades;]]</td><td align="center" width="25%">[[SSC/Virial/Polytropes#Isolated_Nonrotating_Adiabatic_Configuration|③]]</td>
</tr>
<tr>
<td align="left">    </td><td align="left">Embedded in an External Medium …</td>
<td align="center" width="25%">[[SSC/Structure/PolytropesEmbedded#Embedded_Polytropic_Spheres|&spades;]]</td><td align="center" width="25%">[[SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|④]]   [[SSC/Virial/PolytropesEmbeddedOutline#3DIsothermalSurface|🎦]]</td>
</tr>
<tr>
<td align="left" colspan="4">
* Isothermal sphere
</td>
</tr>
<tr>
<td align="left">    </td><td align="left">Isolated …</td>
<td align="center" width="25%">[[SSC/Structure/IsothermalSphere#Isothermal_Sphere|&spades;]]</td><td align="center" width="25%">[[SSC/Virial/Isothermal#Isothermal_Evolutions|⑤]]</td>
</tr>
<tr>
<td align="left">    </td><td align="left">Embedded in an External Medium (Bonnor-Ebert Sphere) …</td>
<td align="center" width="25%">[[SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|&spades;]]<td align="center" width="25%">[[SSC/Virial/Isothermal#Bounded_Isothermal|⑥]]</td>
</tr>
<tr>
<td align="left" colspan="4">
* Zero-temperature White Dwarf — [[SSC/Structure/WhiteDwarfs#White_Dwarfs|Overview]]
* Power-law density distribution — [[SSC/Structure/PowerLawDensity#Power-Law_Density_Distributions|Overview]]
</td>
</tr>
<tr>
<td align="left" colspan="2">
* Other Analytically Definable Models
</td>
<td align="center" width="25%">[[SSC/Structure/OtherAnalyticModels|&spades;]]</td>
<td align="center" width="25%">[[SSC/Structure/OtherAnalyticRamblings|&clubs;]]   [[SSC/Stability/MoreGeneralApproach|&clubs;]]</td>
</tr>
<tr>
<td align="left" colspan="2">
* BiPolytropes (also referred to as ''Composite Polytropes'')
</td>
<td align="center" width="25%">[[SSC/Structure/BiPolytropes#BiPolytropes|Overview]]</td>
<td align="center" width="25%">[[SSC/BipolytropeGeneralizationVersion2#Bipolytrope_Generalization|Overview]] ⑦</td>
</tr>
<tr>
<td align="left">        </td><td align="left">Core-Envelope Structure with <math>~(n_c,n_e) = (0,0)</math> …</td>
<td align="center" width="25%">[[SSC/Structure/BiPolytropes/Analytic00#BiPolytrope_with_nc_.3D_0_and_ne_.3D_0|&spades;]]</td>
<td align="center" width="25%">[[SSC/Structure/BiPolytropes/FreeEnergy00#Free_Energy_of_BiPolytrope_with|⑧]]</td>
</tr>
<tr>
<td align="left">        </td><td align="left">Core-Envelope Structure with <math>~(n_c,n_e) = (5,1)</math> …</td>
<td align="center" width="25%">[[SSC/Structure/BiPolytropes/Analytic51#BiPolytrope_with_nc_.3D_5_and_ne_.3D_1|&spades;]]</td>
<td align="center" width="25%">[[SSC/Structure/BiPolytropes/FreeEnergy51#Free_Energy_of_BiPolytrope_with|⑨]]</td>
</tr>
<tr>
<td align="left">        </td><td align="left">Core-Envelope Structure with <math>~(n_c,n_e) = (1,5)</math> …</td>
<td align="center" width="25%">[[SSC/Structure/BiPolytropes/Analytic15#BiPolytrope_with_nc_.3D_1_and_ne_.3D_5|&spades;]]</td>
<td align="center" width="25%">  …  </td>
</tr>
<tr>
<td align="left">        </td><td align="left">Core-Envelope Structure with <math>~(n_c,n_e) = (\tfrac{3}{2},3)</math> …</td>
<td align="center" width="25%">[[SSC/Structure/BiPolytropes/Analytic1.53|&spades;]]</td>
<td align="center" width="25%">  …  </td>
</tr>

<tr>
<td align="left" colspan="4">
* Limiting Masses — [[SSC/Structure/LimitingMasses#Mass_Upper_Limits|Summary]]
</td>
</tr>
</table>
</td>
</tr>
</table>

=See Also=
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