SSC/Virial/PolytropesEmbedded/FirstEffortAgain/Pt2 - Revision history

Joel2: /* n = 5 Polytropic */

2023-12-23T04:25:21Z

n = 5 Polytropic

← Older revision		Revision as of 00:25, 23 December 2023
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	</div>		</div>
	This result can be compared to [[SSC/Structure/LimitingMasses#Bounded_Isothermal_Sphere_.26_Bonnor-Ebert_Mass\|other determinations of the Bonnor-Ebert mass limit]].		This result can be compared to [[SSC/Structure/LimitingMasses#Bounded_Isothermal_Sphere_.26_Bonnor-Ebert_Mass\|other determinations of the Bonnor-Ebert mass limit]].

			=See Also=


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Joel2: /* n=5 Polytropic */

2023-12-23T04:22:36Z

n=5 Polytropic

← Older revision		Revision as of 00:22, 23 December 2023
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	====Maximum Mass====		====Maximum Mass====

	=====~~<math>~~n=5~~</math>~~ Polytropic=====		=====n = 5 Polytropic=====
	When <math>~\gamma_a = 6/5</math> — which corresponds to an <math>~n=5</math> polytropic configuration — we obtain,		When <math>~\gamma_a = 6/5</math> — which corresponds to an <math>~n=5</math> polytropic configuration — we obtain,
	<div align="center">		<div align="center">
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	= \biggl(\frac{3^{19}}{2^{12}\cdot 5^{7}\pi} \biggr)^{1/2} \biggl( \frac{\bar{c_s}^8}{G^3 P_e} \biggr)^{1/2} \, .</math>		= \biggl(\frac{3^{19}}{2^{12}\cdot 5^{7}\pi} \biggr)^{1/2} \biggl( \frac{\bar{c_s}^8}{G^3 P_e} \biggr)^{1/2} \, .</math>
	</div>		</div>
	This result can be compared to [[~~User:Tohline/~~SSC/Structure/LimitingMasses#Bounded_Isothermal_Sphere_.26_Bonnor-Ebert_Mass\|other determinations of the Bonnor-Ebert mass limit]].		This result can be compared to [[SSC/Structure/LimitingMasses#Bounded_Isothermal_Sphere_.26_Bonnor-Ebert_Mass\|other determinations of the Bonnor-Ebert mass limit]].

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Joel2 at 04:19, 23 December 2023

2023-12-23T04:19:14Z

← Older revision		Revision as of 00:19, 23 December 2023
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			=Virial Equilibrium of Adiabatic Spheres (1<sup>st</sup> Effort)=

			<table border="1" align="center" width="100%" colspan="8">
			<tr>
			<td align="center" rowspan="1" bgcolor="lightblue" width="50%"><br />[[SSC/Virial/PolytropesEmbedded/FirstEffortAgain/Pt1\|Part I:   Isolated Configurations]]<br /> </td>
			<td align="center" rowspan="1" bgcolor="lightblue" width="50%"><br />[[SSC/Virial/PolytropesEmbedded/FirstEffortAgain/Pt2\|Part II:  Configurations Embedded in an External Medium]]<br /> </td>
			</tr>
			</table>

	==Nonrotating Adiabatic Configuration Embedded in an External Medium==		==Nonrotating Adiabatic Configuration Embedded in an External Medium==

Joel2: Created page with " ==Nonrotating Adiabatic Configuration Embedded in an External Medium== For a nonrotating configuration $~(C=J=0)$ that is embedded in, and is influenced by the pressure $~P_e$ of, an external medium, the statement of virial equilibrium is,
$3 B\chi_\mathrm{eq}^{3 -3\gamma_g} -~3A\chi_\mathrm{eq}^{-1} -~ 3D\chi_\mathrm{eq}^3 = 0 \, .$
====Solution Expressed in Terms of K and M (Whitworth's 1981 Relation)==..."

2023-12-23T04:09:33Z

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)==..."

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