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21:40, 12 December 2023 Joel2 talk contribs created page Template:TT1867figure (Created page with "[https://books.google.com/books?id=wwO9X3RPt5kC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false W. Thomson & P. G. Tait (1867)]<br />''Treatise on Natural Philosophy''<br />Oxford at the Clarendon Press (London: MacMillan and Co.)")
21:39, 12 December 2023 Joel2 talk contribs created page Template:TT1867 (Created page with "📚 [https://books.google.com/books?id=wwO9X3RPt5kC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Thomson & Tait (1867)]")
21:36, 12 December 2023 Joel2 talk contribs created page Appendix/References (Created page with "__FORCETOC__  =Journal Articles= ==Explanation== Three or four templates are available for each individual journal-article reference. For example, for the Dyson (1893) publication or for BAC84: <ol type="1"> <li>Dyson1893</li> <li>Dyson1893full</li> <li>Dyson1893figure <math>\Leftarrow</math> This template is highlighted below.</li> <li>BAC84hereafter</li> </ol> If you want to see which of our M...")
21:28, 12 December 2023 Joel2 talk contribs created page Apps/Korycansky Papaloizou 1996 (Created page with "__FORCETOC__  =Korycansky and Papaloizou (1996)= {| class="NonaxisymmetricDisks" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:lightgreen;" |<b>Constructing<br />Infinitesimally Thin<br />Nonaxisymmetric<br />Disks</b> |} [http://adsabs.harvard.edu/abs/1996ApJS..105..181K K...")
20:59, 12 December 2023 Joel2 talk contribs created page File:RmodeImage8.png
20:59, 12 December 2023 Joel2 talk contribs uploaded File:RmodeImage8.png
20:11, 12 December 2023 Joel2 talk contribs created page SSC/Structure/Polytropes (Created page with "__FORCETOC__  =Polytropic Spheres= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;" | <font size="-1"><b>Isolated<br />Polytropes</b></font> |}  Here we will supplement the SSCpt1/PGE|simplified set of...")
20:06, 12 December 2023 Joel2 talk contribs created page File:Work-in-progress.png
20:06, 12 December 2023 Joel2 talk contribs uploaded File:Work-in-progress.png
20:02, 12 December 2023 Joel2 talk contribs created page Template:SGFworkInProgress (Created page with "---- <div align="center"> 100px|center Material that appears after this point in our presentation is under development and therefore <br />may contain incorrect mathematical equations and/or physical misinterpretations. <br /><font size="-1">| Go Home | </font> </div> ----")
19:58, 12 December 2023 Joel2 talk contribs created page SSC/Structure/BiPolytropes (Created page with "__FORCETOC__ =BiPolytropes= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;" | <font size="-1"><b>Composite<br />Polytropes</b><br />(Bipolytropes)</font> |} ==Background== While polytropic spheres can give us useful ''general'' insight into the internal s...")
19:54, 12 December 2023 Joel2 talk contribs created page SSC/Perturbations (Created page with "__FORCETOC__   =Spherically Symmetric Configurations (Stability — Part II)=  {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:white;" | <font size="-1">H_BookTiledMenu#Stability_Analysis|<b...")
19:47, 12 December 2023 Joel2 talk contribs created page SSC/Structure/BiPolytropes/Analytic1.53 (Created page with "__FORCETOC__ =BiPolytrope with (n<sub>c</sub>, n<sub>e</sub>) = (3/2, 3)= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:white;" | <font size="-1"><b>Milne</b><br /> (1930)</font> |} Here we lay out the procedure for constructing a bipolytrope in which the core has an...")
19:41, 12 December 2023 Joel2 talk contribs created page 2DStructure/AxisymmetricInstabilities (Created page with "__FORCETOC__  =Axisymmetric Instabilities to Avoid= {| class="AxisymmetricConfigurations" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:white;" |<b>Axisymmetric<br />Instabilities<br />to Avoid</b> |} When constructing rotating equilibrium configurations...")
19:31, 12 December 2023 Joel2 talk contribs created page PGE/ConservingMomentum (Created page with "__FORCETOC__   =Euler Equation (Conserving Momentum)= ==Various Forms== ===Lagrangian Representation=== Among the principal governing equations we have included the <div align="center"> <span id="ConservingMomentum:Lagrangian"><font color="#770000">'''Lagrangian Representation'''</font></span><br /> of the Euler Equation, {{ Math/EQ_Euler01 }} </div> Multiplying thi...")
16:29, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ TRApproximation (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Other_Equations_with_Assigned_Templates </td> <td align="right"> <math>\Phi_\mathrm{TR}(\varpi,z)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math>-\biggl[ \frac{2GM}{\pi } \biggr]\frac{K(k)}{\sqrt{(\varpi+a)^2 + z^2}}</math> </td> </tr> <tr> <td align="center" colspan="4"> <math>\mathrm{where:}~~~k...")
16:27, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ Polytrope03 (Created page with "<math>\rho = \biggl[ \frac{H}{(n+1)K_\mathrm{n}} \biggr]^n </math>")
16:26, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ Polytrope02 (Created page with "<math>H = (n+1)K_\mathrm{n} \rho^{1/n}</math>")
16:25, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ Polytrope01 (Created page with "<math>P = K_\mathrm{n} \rho^{1+1/n}</math>")
16:24, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ EOSideal02 (Created page with "<math>P = (\gamma_\mathrm{g} - 1)\epsilon \rho </math>")
16:23, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ EOSideal00 (Created page with "<math>P = n_g k T</math>")
16:22, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ CT99Axisymmetric (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Other_Equations_with_Assigned_Templates </td> <td align="right"> <math>\Phi(\varpi,z)\biggr|_\mathrm{axisym}</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> - \frac{G}{\pi} \iint\limits_\mathrm{config} \biggl[ \frac{\mu}{(\varpi~ \varpi^')^{1 / 2}} \biggr] K(\mu) \rho(\varpi^', z^') 2\pi \varpi^'~ d\v...")
16:19, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ RadialPulsation04 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation </td> <td align="center"> <math>0 = \frac{d^2x}{dr_0^2} + \frac{1}{r_0}\biggl[4 + \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{dx}{dr_0} + \biggl[ \biggl(3 - \frac{4}{\gamma_g}\biggr) \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{x}{r_0^2} - \frac{1}{\Delta} \biggl[\frac{d\ln P_0}{d\ln r_0}\cdot \frac{\rho_c}{\rho_0} \biggl( \frac{\sigma_c...")
16:18, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ RadialPulsation01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation </td> <td align="center"> <math> \frac{d^2x}{dr_0^2} + \biggl[\frac{4}{r_0} - \biggl(\frac{g_0 \rho_0}{P_0}\biggr) \biggr] \frac{dx}{dr_0} + \biggl(\frac{\rho_0}{\gamma_\mathrm{g} P_0} \biggr)\biggl[\omega^2 + (4 - 3\gamma_\mathrm{g})\frac{g_0}{r_0} \biggr] x = 0 </math> </td> </tr> </table>")
15:48, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ SSradiationTransport01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{dT}{dr} = - \frac{ 3 }{ 4a_\mathrm{rad} c} \biggl(\frac{ \kappa \rho }{ T^3 }\biggr) \frac{ L_r }{ 4\pi r^2 }</math> </td> </tr> </table>")
15:47, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ SSmassConservation01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{dM_r}{dr} = 4\pi r^2 \rho</math> </td> </tr> </table>")
15:46, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ SSenergyConservation01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{dL_r}{dr} = 4\pi r^2 \rho \epsilon_\mathrm{nuc}</math> </td> </tr> </table>")
15:44, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ ZTFG01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right" width="35%"> 25px|link=Appendix/EquationTemplates#Equations_of_State </td> <td align="left"> <font><math>P_\mathrm{deg} = A_\mathrm{F} F(\chi) </math></font> </td> </tr> <tr> <td align="center" colspan="2"> where: <math>F(\chi) \equiv \chi(2\chi^2 - 3)(\chi^2 + 1)^{1/2} + 3\sinh^{-1}\chi</math> </td> </tr> <tr> <td align="right" colspan="1"> and: </td> <td align="left"...")
15:43, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ PressureTotal01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Equations_of_State </td> <td align="center"> <math>p_\mathrm{total} = \biggl(\frac{\mu_e m_p}{\bar{\mu} m_u} \biggr) 8 \chi^3 \frac{T}{T_e} + F(\chi) + \frac{8\pi^4}{15} \biggl( \frac{T}{T_e} \biggr)^4</math> </td> </tr> </table>")
15:43, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ EOSradiation01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Equations_of_State </td> <td align="center"> <math>P_\mathrm{rad} = \frac{1}{3} a_\mathrm{rad} T^4</math> </td> </tr> </table>")
15:42, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ EOSideal0A (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Equations_of_State </td> <td align="center"> <math>P_\mathrm{gas} = \frac{\Re}{\bar{\mu}} \rho T</math> </td> </tr> </table>")
15:39, 12 December 2023 Xxsrm talk contribs created page Appendix/EquationTemplates (Created page with "__FORCETOC__  =50px<font size="+2" color="black">Key Equations</font>= Each of the equations displayed in the Tables, below, encapsulates a physical concept that is fundamental to our understanding of — and, hence our discussion of — the '''structure, stability, and dynamics of self-gravitating fluids.''' The pervasiveness of these physical concepts throughout astrophysics is reflected in the fact t...")
15:35, 12 December 2023 Xxsrm talk contribs created page Template:Math/MP PolytropicIndex (Created page with "<span title="Polytropic index"><math>n</math></span>")
15:35, 12 December 2023 Xxsrm talk contribs created page Template:Math/MP PolytropicConstant (Created page with "<span title="Polytropic constant"><math>K_\mathrm{n}</math></span>")
15:34, 12 December 2023 Xxsrm talk contribs created page Template:Math/MP MeanMolecularWeight (Created page with "<span title="Mean molecular weight"><math>\bar{\mu}</math></span>")
15:33, 12 December 2023 Xxsrm talk contribs created page Template:Math/MP ElectronMolecularWeight (Created page with "<span title="Molecular weight of electrons"><math>\mu_e</math></span>")
15:32, 12 December 2023 Xxsrm talk contribs created page Template:Math/MP AdiabaticIndex (Created page with "<span title="Adiabatic index = Ratio of specific heats"><math>\gamma_\mathrm{g}</math></span>")
15:30, 12 December 2023 Xxsrm talk contribs created page Template:Math/VAR SpecificVolume01 (Created page with "<span title="Specific volume"><math>V</math></span>")
15:30, 12 December 2023 Xxsrm talk contribs created page Template:Math/VAR NumberDensity01 (Created page with "<span title="Number density of gas particles"><math>n_g</math></span>")
15:28, 12 December 2023 Xxsrm talk contribs created page Template:Math/VAR Enthalpy01 (Created page with "<span title="Enthalpy"><math>H</math></span>")
15:26, 12 December 2023 Xxsrm talk contribs created page Template:Math/C ThompsonCrossSection (Created page with "<span title="Thompson cross-section: 0.6652458E-24 square-centimeters"><math>\sigma_T</math></span>")
15:25, 12 December 2023 Xxsrm talk contribs created page Template:Math/C SpeedOfLight (Created page with "<span title="Speed of light:2.99792458E+10 cm/s"><math>c</math></span>")
15:25, 12 December 2023 Xxsrm talk contribs created page Template:Math/C RadiationConstant (Created page with "<span title="Radiation constant: 7.566E-15 cgs"><math>a_\mathrm{rad}</math></span>")
15:24, 12 December 2023 Xxsrm talk contribs created page Template:Math/C ProtonMass (Created page with "<span title="Mass of the proton: 1.6726216E-24 g"><math>m_p</math></span>")
15:23, 12 December 2023 Xxsrm talk contribs created page Template:Math/C PlanckConstant (Created page with "<span title="Planck constant:6.626069E-27 cgs"><math>h</math></span>")
15:22, 12 December 2023 Xxsrm talk contribs created page Template:Math/C GasConstant (Created page with "<span title="Gas constant: 8.3145E+07 erg/(K mole)"><math>\Re</math></span>")
15:21, 12 December 2023 Xxsrm talk contribs created page Template:Math/C FineStructureConstant (Created page with "<span title="Fine structure constant: 7.29735E-3 (dimensionless)"><math>\alpha_\mathrm{fs}</math></span>")
15:21, 12 December 2023 Xxsrm talk contribs created page Template:Math/C FermiPressure (Created page with "<span title="Characteristic Fermi pressure: 6.002E+22 cgs"><math>A_\mathrm{F}</math></span>")
15:20, 12 December 2023 Xxsrm talk contribs created page Template:Math/C FermiDensity (Created page with "<span title="Characteristic Fermi density: ~ 1E+06 cgs"><math>B_\mathrm{F}</math></span>")
15:19, 12 December 2023 Xxsrm talk contribs created page Template:Math/C ElectronTemperature (Created page with "<span title="Temperature associated with rest-mass energy of the electron: 5.9381E+09 K"><math>T_e</math></span>")

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