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__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =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><font size="+1">⓪</font> [[SSCpt1/Virial#Virial_Equilibrium_of_Spherically_Symmetric_Configurations|SphericallySymmetricConfigurations Virial]] (Introduction)</li> <li><font size="+1">①</font> & <font size="+1">②</font> [[SSC/VirialEquilibrium/UniformDensity#Uniform-Density_Sphere|SSC VirialEquilibrium UniformDensity]] (Isolated and Embedded)</li> <li><font size="+1">③</font> [[SSC/Virial/Polytropes#Isolated_Nonrotating_Adiabatic_Configuration|SSC Virial Polytropes]] (Isolated)</li> <li><font size="+1">④</font> [[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><font size="+1">⑤</font> & <font size="+1">⑥</font> [[SSC/Virial/Isothermal|SSC Virial Isothermal]] (Isolated and Bounded)</li> <li><font size="+1">⑦</font> [[SSC/BipolytropeGeneralizationVersion2#Bipolytrope_Generalization|SSC BipolytropeGeneralization_Version2]] (Overview)</li> <li><font size="+1">⑧</font> [[SSC/Structure/BiPolytropes/FreeEnergy00#Free_Energy_of_BiPolytrope_with|SSC Structure BiPolytropes FreeEnergy0_0]] <math>~(n_c,n_e) = (0,0)</math></li> <li><font size="+1">⑨</font> [[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%"> <font color="black">Detailed Force-Balance</font><br>([[SSCpt2/SolutionStrategies#Spherically_Symmetric_Configurations_.28Part_II.29|Introduction]]) </th> <th align="center"> <font color="black">Virial Equilibrium</font><br>([[SSCpt1/Virial#Virial_Equilibrium_of_Spherically_Symmetric_Configurations|Introduction]])<font size="+1">⓪</font> </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|<font size="+2">♠</font>]]</td><td align="center" width="25%">[[SSC/VirialEquilibrium/UniformDensity#Uniform-Density_Sphere|<font size="+1">①</font>]]</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|<font size="+2">♠</font>]]</td><td align="center" width="25%">[[SSC/VirialEquilibrium/UniformDensity#Adiabatic_Evolution_of_Pressure-truncated_Sphere|<font size="+1">②</font>]]</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|<font size="+2">♠</font>]]</td><td align="center" width="25%">[[SSC/Virial/Polytropes#Isolated_Nonrotating_Adiabatic_Configuration|<font size="+1">③</font>]]</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|<font size="+2">♠</font>]]</td><td align="center" width="25%">[[SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|<font size="+1">④</font>]] [[SSC/Virial/PolytropesEmbeddedOutline#3DIsothermalSurface|<font size="+2">🎦</font>]]</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|<font size="+2">♠</font>]]</td><td align="center" width="25%">[[SSC/Virial/Isothermal#Isothermal_Evolutions|<font size="+1">⑤</font>]]</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|<font size="+2">♠</font>]]<td align="center" width="25%">[[SSC/Virial/Isothermal#Bounded_Isothermal|<font size="+1">⑥</font>]]</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|<font size="+2">♠</font>]]</td> <td align="center" width="25%">[[SSC/Structure/OtherAnalyticRamblings|<font size="+2">♣</font>]] [[SSC/Stability/MoreGeneralApproach|<font size="+2">♣</font>]]</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]] <font size="+1">⑦</font></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|<font size="+2">♠</font>]]</td> <td align="center" width="25%">[[SSC/Structure/BiPolytropes/FreeEnergy00#Free_Energy_of_BiPolytrope_with|<font size="+1">⑧</font>]]</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|<font size="+2">♠</font>]]</td> <td align="center" width="25%">[[SSC/Structure/BiPolytropes/FreeEnergy51#Free_Energy_of_BiPolytrope_with|<font size="+1">⑨</font>]]</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|<font size="+2">♠</font>]]</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|<font size="+2">♠</font>]]</td> <td align="center" width="25%"> … </td> </tr> <!-- COMMENT OUT <tr> <td align="left"> </td><td align="left">Also to be studied: [http://adsabs.harvard.edu/abs/2012MNRAS.421.2713B Ball, Tout, & Żytkow] (2012, MNRAS, 421, 2713)</td> <td align="center" width="25%"> </td> <td align="center" width="25%"> </td> </tr> FINISH COMMENT OUT --> <tr> <td align="left" colspan="4"> * Limiting Masses — [[SSC/Structure/LimitingMasses#Mass_Upper_Limits|Summary]] </td> </tr> </table> </td> </tr> </table> =See Also= {{ SGFfooter }}
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