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	<title>SSC/Stability/BiPolytropes/Index - Revision history</title>
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		<title>Joel2: Created page with &quot;__FORCETOC__  &lt;!-- __NOTOC__ will force TOC off --&gt;  =Organizational Index= This index helps organize and summarize the insight that we have gained from our broad investigation into the relative stability of spherically symmetric bipolytropic configurations.  The most relevant summary chapter is named, SSC/Stability/BiPolytropes.  ==Motivation== Sch&amp;ouml;nberg-Chandrasekhar mass limit: &lt;ul&gt;   &lt;li&gt; SSC/Structure/LimitingMasses#Schönberg-C...&quot;</title>
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		<updated>2024-01-09T15:47:20Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;__FORCETOC__  &amp;lt;!-- __NOTOC__ will force TOC off --&amp;gt;  =Organizational Index= This index helps organize and summarize the insight that we have gained from our broad investigation into the relative stability of spherically symmetric bipolytropic configurations.  The most relevant summary chapter is named, &lt;a href=&quot;/JETohline/index.php/SSC/Stability/BiPolytropes&quot; title=&quot;SSC/Stability/BiPolytropes&quot;&gt;SSC/Stability/BiPolytropes&lt;/a&gt;.  ==Motivation== Schönberg-Chandrasekhar mass limit: &amp;lt;ul&amp;gt;   &amp;lt;li&amp;gt; SSC/Structure/LimitingMasses#Schönberg-C...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;__FORCETOC__ &lt;br /&gt;
&amp;lt;!-- __NOTOC__ will force TOC off --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=Organizational Index=&lt;br /&gt;
This index helps organize and summarize the insight that we have gained from our broad investigation into the relative stability of spherically symmetric bipolytropic configurations.  The most relevant summary chapter is named, [[SSC/Stability/BiPolytropes|SSC/Stability/BiPolytropes]].&lt;br /&gt;
&lt;br /&gt;
==Motivation==&lt;br /&gt;
Sch&amp;amp;ouml;nberg-Chandrasekhar mass limit:&lt;br /&gt;
&amp;lt;ul&amp;gt;&lt;br /&gt;
  &amp;lt;li&amp;gt;&lt;br /&gt;
[[SSC/Structure/LimitingMasses#Schönberg-Chandrasekhar_Mass|Sch&amp;amp;ouml;nberg-Chandrasekhar mass limit]].&lt;br /&gt;
  &amp;lt;/li&amp;gt;&lt;br /&gt;
  &amp;lt;li&amp;gt;&lt;br /&gt;
Potential connection with [[SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|Bonnor-Ebert mass limit]]; another pointer is [[SSC/Structure/LimitingMasses#Bounded_Isothermal_Sphere_&amp;amp;_Bonnor-Ebert_Mass|contained here]].&lt;br /&gt;
  &amp;lt;/li&amp;gt;&lt;br /&gt;
  &amp;lt;li&amp;gt;&lt;br /&gt;
[[Appendix/Ramblings/OriginOfPlanetaryNebulae|Origin of Planetary Nebulae]]&lt;br /&gt;
  &amp;lt;/li&amp;gt;&lt;br /&gt;
&amp;lt;/ul&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Simpler Systems==&lt;br /&gt;
===Equilibrium Structures===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Stability===&lt;br /&gt;
====Normal Fluids====&lt;br /&gt;
&amp;lt;ul&amp;gt;&lt;br /&gt;
  &amp;lt;li&amp;gt;Buoyancy:  For stability, need gas density to decrease outward.  In bipolytropes, this reduces to the requirement that &amp;lt;math&amp;gt;\mu_e/\mu_c \le 1&amp;lt;/math&amp;gt;.&amp;lt;/li&amp;gt;&lt;br /&gt;
  &amp;lt;li&amp;gt;Convection:  For stability, need specific entropy to increase outward; uniform specific entropy is marginally stable.&amp;lt;/li&amp;gt;&lt;br /&gt;
&amp;lt;/ul&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==LAWE Solutions==&lt;br /&gt;
&lt;br /&gt;
{{ LAWEsolutions }}&lt;br /&gt;
&lt;br /&gt;
=See Also=&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{ SGFfooter }}&lt;/div&gt;</summary>
		<author><name>Joel2</name></author>
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