Joel2: /* Volume Integrals */

2023-12-14T19:45:58Z

Volume Integrals

← Older revision		Revision as of 15:45, 14 December 2023
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	<font color="maroon"><b>Pressure-Truncated Polytropes</b></font>: But, a [[SSC/Virial/Polytropes#Nonrotating_Adiabatic_Configuration_Embedded_in_an_External_Medium\|configuration embedded in an external medium]] of pressure, <math>P_e</math>, will have a (pressure-truncated) surface whose radius, <math>R_\mathrm{limit}</math>, corresponds to the radial location at which the configuration's internal pressure drops to a value that equals <math>P_e</math>. In this case as well, one might choose to refer to <math>M_\mathrm{limit}</math> as the total mass; on the other hand, it might be more useful to distinguish <math>M_\mathrm{limit}</math> from <math>M_\mathrm{tot}</math>, continuing to rely on <math>M_\mathrm{tot}</math> to represent the mass of the corresponding ''isolated'' polytrope.		<font color="maroon"><b>Pressure-Truncated Polytropes</b></font>: But, a [[SSC/Virial/Polytropes#Nonrotating_Adiabatic_Configuration_Embedded_in_an_External_Medium\|configuration embedded in an external medium]] of pressure, <math>P_e</math>, will have a (pressure-truncated) surface whose radius, <math>R_\mathrm{limit}</math>, corresponds to the radial location at which the configuration's internal pressure drops to a value that equals <math>P_e</math>. In this case as well, one might choose to refer to <math>M_\mathrm{limit}</math> as the total mass; on the other hand, it might be more useful to distinguish <math>M_\mathrm{limit}</math> from <math>M_\mathrm{tot}</math>, continuing to rely on <math>M_\mathrm{tot}</math> to represent the mass of the corresponding ''isolated'' polytrope.

	<font color="maroon"><b>BiPolytropes</b></font>: When discussing [[SSC/~~BipolytropeGeneralization_Version2~~#Bipolytrope_Generalization\|bipolytropes]], the limit of integration, <math>R_\mathrm{limit}</math>, will naturally refer to the radial location that defines the outer edge of the configuration's "core" and, at the same time, identifies the radial "interface" between the bipolytrope's core and its envelope. In this case, <math>M_\mathrm{limit}</math> corresponds to the mass of the core rather than to the total mass of the bipolytropic configuration.		<font color="maroon"><b>BiPolytropes</b></font>: When discussing [[SSC/BipolytropeGeneralizationVersion2#Bipolytrope_Generalization\|bipolytropes]], the limit of integration, <math>R_\mathrm{limit}</math>, will naturally refer to the radial location that defines the outer edge of the configuration's "core" and, at the same time, identifies the radial "interface" between the bipolytrope's core and its envelope. In this case, <math>M_\mathrm{limit}</math> corresponds to the mass of the core rather than to the total mass of the bipolytropic configuration.
	</td></tr>		</td></tr>
	</table>		</table>

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2023-12-14T19:33:36Z

Created page with "__FORCETOC__  =Virial Equilibrium of Spherically Symmetric Configurations= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#9390DB;" | Free-Energy of Spherical Systems |} ==Free Energy Expression== ===Rev..."

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Joel2: /* Volume Integrals */