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• 22:46, 23 December 2023 Joel2 talk contribs created page Template:Miller29full (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1929MNRAS..90...59M/abstract J. C. P. Miller (1929, MNRAS, Vol. 90, pp. 59 - 64)]")
• 22:45, 23 December 2023 Joel2 talk contribs created page Template:Miller29figure (Created page with "[https://ui.adsabs.harvard.edu/abs/1929MNRAS..90...59M/abstract J. C. P. Miller (1929)]<br />''The Effect of Distribution of Density on the Period of Pulsation of a Star''<br />Monthly Notices of the Royal Astronomical Society, Vol. 90, pp. 59 - 64")
• 22:44, 23 December 2023 Joel2 talk contribs created page Template:Miller29 (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1929MNRAS..90...59M/abstract Miller (1929)]")
• 22:26, 23 December 2023 Joel2 talk contribs created page File:CaseMfreeEnergy50.gif
• 22:26, 23 December 2023 Joel2 talk contribs uploaded File:CaseMfreeEnergy50.gif
• 22:25, 23 December 2023 Joel2 talk contribs created page File:CaseMcompareTogether.png
• 22:25, 23 December 2023 Joel2 talk contribs uploaded File:CaseMcompareTogether.png
• 22:19, 23 December 2023 Joel2 talk contribs created page File:MimicStahlerPlot3.png
• 22:19, 23 December 2023 Joel2 talk contribs uploaded File:MimicStahlerPlot3.png
• 22:13, 23 December 2023 Joel2 talk contribs created page File:PvsR simplest.png
• 22:13, 23 December 2023 Joel2 talk contribs uploaded File:PvsR simplest.png
• 21:59, 23 December 2023 Joel2 talk contribs created page SSC/FreeEnergy/Powerpoint (Created page with "__FORCETOC__ =Supporting Derivations for Free-Energy PowerPoint Presentation= The derivations presented here are an extension of our accompanying free-energy synopsis. These additional details proved to be helpful while developing an overarching PowerPoint presentation. ==General Free-Energy Expression== We're considering a free-energy function of the following form: <div align="center"> <table border="0" ce...")
• 18:03, 23 December 2023 Joel2 talk contribs created page Template:Bonnor56hereafter (Created page with "Bonnor56")
• 18:02, 23 December 2023 Joel2 talk contribs created page Template:Bonnor56full (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1956MNRAS.116..351B/abstract W. B. Bonnor (1956, MNRAS, Vol. 116, pp. 351 - 359)]")
• 18:01, 23 December 2023 Joel2 talk contribs created page Template:Bonnor56figure (Created page with "[https://ui.adsabs.harvard.edu/abs/1956MNRAS.116..351B/abstract W. B. Bonnor (1956)]<br />''Boyle's Law and gravitational instability''<br />Monthly Notices of the Royal Astronomical Society<br />Vol. 116, pp. 351 - 359")
• 18:00, 23 December 2023 Joel2 talk contribs created page Template:Bonnor56 (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1956MNRAS.116..351B/abstract Bonnor (1956)]")
• 17:52, 23 December 2023 Joel2 talk contribs created page File:Bonnor1956Fig1.jpg
• 17:52, 23 December 2023 Joel2 talk contribs uploaded File:Bonnor1956Fig1.jpg
• 17:45, 23 December 2023 Joel2 talk contribs created page File:WhitworthLogFig1a norm.jpg
• 17:45, 23 December 2023 Joel2 talk contribs uploaded File:WhitworthLogFig1a norm.jpg
• 17:33, 23 December 2023 Joel2 talk contribs created page SSC/Virial/Isothermal (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Virial Equilibrium of Isothermal Spheres= ==Review== In an introductory discussion of the virial equilibrium structure of spherically symmetric configurations — see especially the section titled, ''Energy Extrema'' — we deduced that a system's equilibrium radius, <math>~R_\mathrm{eq}</math>, measured relative to a reference length scale...")
• 16:58, 23 December 2023 Joel2 talk contribs created page SSC/Virial/Polytropes/Pt1 (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Virial Equilibrium of Adiabatic Spheres= Highlights of the rather detailed discussion presented below have been summarized in an accompanying chapter of this H_Book. ==Review== ===Adopted Normalizations=== In an introductory discussion of the virial equilibrium structure of spherically symmetric configuration...")
• 16:56, 23 December 2023 Joel2 talk contribs created page SSC/Virial/Polytropes/Pt2 (Created page with " ==Nonrotating Adiabatic Configuration Embedded in an External Medium== For a nonrotating configuration <math>~(C=J=0)</math> that is embedded in, and is influenced by the pressure <math>~P_e</math> of, an external medium, the statement of virial equilibrium is, <div align="center"> <math> 3 B\chi_\mathrm{eq}^{3 -3\gamma_g} -~3A\chi_\mathrm{eq}^{-1} -~ 3D\chi_\mathrm{eq}^3 = 0 \, . </math> </div> ====Solution Expressed in Terms of K and M (Whitworth's 1981 Relation)==...")
• 23:39, 22 December 2023 Joel2 talk contribs created page SSC/Structure/LimitingMasses (Created page with "__FORCETOC__ =Mass Upper Limits= Spherically symmetric, self-gravitating, equilibrium configurations can be constructed from gases exhibiting a wide variety of degrees of compressibility. When examining how the internal structure of such configurations varies with compressibility, or when examining the relative stability of such structures, it can be instructive to construct models using a polytropic equation of state because the degree of compressibility can be adjust...")
• 23:09, 22 December 2023 Joel2 talk contribs created page SSC/Virial/PolytropesEmbedded/FirstEffortAgain/Pt2 (Created page with " ==Nonrotating Adiabatic Configuration Embedded in an External Medium== For a nonrotating configuration <math>~(C=J=0)</math> that is embedded in, and is influenced by the pressure <math>~P_e</math> of, an external medium, the statement of virial equilibrium is, <div align="center"> <math> 3 B\chi_\mathrm{eq}^{3 -3\gamma_g} -~3A\chi_\mathrm{eq}^{-1} -~ 3D\chi_\mathrm{eq}^3 = 0 \, . </math> </div> ====Solution Expressed in Terms of K and M (Whitworth's 1981 Relation)==...")
• 23:08, 22 December 2023 Joel2 talk contribs created page SSC/Virial/PolytropesEmbedded/FirstEffortAgain/Pt1 (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Virial Equilibrium of Adiabatic Spheres= Highlights of the rather detailed discussion presented below have been summarized in an accompanying chapter of this H_Book. ==Review== ===Adopted Normalizations=== In an introductory discussion o...")
• 22:43, 22 December 2023 Joel2 talk contribs created page SSC/Structure/PowerLawDensity (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Power-Law Density Distributions= Here we begin with the same second-order, one-dimensional ODE that governs the structure of polytropic spheres, namely, the <div align="center"> <span id="LaneEmdenEquation"><font color="#770000">'''Lane-Emden Equation'''</font></span> {{ Math/EQ_SSLaneEmden01 }} </div> and examine whether or not this governing relation can be satisfied...")
• 22:32, 22 December 2023 Joel2 talk contribs created page File:FreeEnergySurface.png
• 22:32, 22 December 2023 Joel2 talk contribs uploaded File:FreeEnergySurface.png
• 22:32, 22 December 2023 Joel2 talk contribs created page File:FreeEnergyFaceOn.png
• 22:32, 22 December 2023 Joel2 talk contribs uploaded File:FreeEnergyFaceOn.png
• 22:31, 22 December 2023 Joel2 talk contribs created page File:VirialEquilibria.png
• 22:31, 22 December 2023 Joel2 talk contribs uploaded File:VirialEquilibria.png
• 22:20, 22 December 2023 Joel2 talk contribs created page File:Xi9.8461.png
• 22:20, 22 December 2023 Joel2 talk contribs uploaded File:Xi9.8461.png
• 22:19, 22 December 2023 Joel2 talk contribs created page File:Xi3.850652.png
• 22:19, 22 December 2023 Joel2 talk contribs uploaded File:Xi3.850652.png
• 22:19, 22 December 2023 Joel2 talk contribs created page File:Xi3.5.png
• 22:19, 22 December 2023 Joel2 talk contribs uploaded File:Xi3.5.png
• 22:18, 22 December 2023 Joel2 talk contribs created page File:Xi3.0.png
• 22:18, 22 December 2023 Joel2 talk contribs uploaded File:Xi3.0.png
• 22:18, 22 December 2023 Joel2 talk contribs created page File:Xi2.0.png
• 22:18, 22 December 2023 Joel2 talk contribs uploaded File:Xi2.0.png
• 22:18, 22 December 2023 Joel2 talk contribs created page File:Xi1.26419.png
• 22:18, 22 December 2023 Joel2 talk contribs uploaded File:Xi1.26419.png
• 21:43, 22 December 2023 Joel2 talk contribs created page File:CorrectedStahlerN5.png
• 21:43, 22 December 2023 Joel2 talk contribs uploaded File:CorrectedStahlerN5.png
• 21:13, 22 December 2023 Joel2 talk contribs created page File:AdabaticBoundedSpheres Virial.jpg
• 21:13, 22 December 2023 Joel2 talk contribs uploaded File:AdabaticBoundedSpheres Virial.jpg
• 20:50, 22 December 2023 Joel2 talk contribs created page SSC/Virial/PolytropesEmbedded/SecondEffortAgain/Pt2 (Created page with " ==Mass-Radius Relation== Up to this point in our discussion, we have focused on an analysis of the pressure-radius relationship that defines the equilibrium configurations of pressure-truncated polytropes. In effect, we have viewed the problem through the same lens as did {{ Horedt70full }} and, separately, {{ Whitworth81full }}, defining variable normalizations in terms of the polytropic constant, <math>K</math>, and the configuration mass, <math>M_\mathrm{tot}</math>...")