Editing SSC/Virial/Polytropes (section)

===Central Pressure===
It is also worth pointing out that [[Appendix/References|Chandrasekhar [C67]]] &#8212; see his Equations (80) &amp; (81), p. 99 &#8212; introduces a dimensionless structural form factor, <math>~W_n</math>, for the central pressure via the expression,
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<math>~P_c</math>
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<math>~=</math>
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<math>~W_n \biggl( \frac{GM^2}{R^4} \biggr) \, ,</math>
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</table>
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and demonstrates that,
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<math>~\frac{1}{W_n}</math>
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<math>~\equiv</math>
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<math>~4\pi (n+1) \biggl[ \Theta^' \biggr]^2_{\xi_1} \, .</math>
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It is therefore clear that a spherical polytrope's central pressure is expressible in terms of our structural form factor, <math>~\mathfrak{f}_A</math>, as,
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<math>~P_c</math>
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<math>~=</math>
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<math>~\frac{3}{4\pi (5-n)} \biggl( \frac{GM_\mathrm{tot}^2}{R_\mathrm{eq}^4} \biggr) \frac{1}{\mathfrak{f}_A} \, .</math>
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Looking back at our [[SSCpt1/Virial#FormFactors|original definition of the structural form factors]], we note that,
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<math>\mathfrak{f}_A = \biggl( \frac{\bar{P}}{P_c} \biggr)_\mathrm{eq} \, .</math>
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Hence, this last equilibrium relation can be rewritten as,
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<math> \frac{\bar{P} R_\mathrm{eq}^4}{GM_\mathrm{tot}^2} = \frac{3}{4\pi (5-n)} \, .</math>
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