Editing SSC/Perturbations (section)

=====Set the Surface Pressure Fluctuation to Zero=====
Using the [[#PGE:AdiabaticFirstLaw|above "Linearized Adiabatic Form of the First Law of Thermodynamics"]] to replace the fractional density variation, <math>~d</math>, in favor of the fractional pressure variation, <math>~p</math> in the [[#Continuity|above "Linearized Equation of Continuity"]], gives,

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<math>~p</math>
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<math>~=</math>
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<math>~-\gamma_g \biggl( 3 x +  r_0 \frac{dx}{dr_0} \biggr) \, .</math>
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[http://adsabs.harvard.edu/abs/1941ApJ....94..124L Ledoux &amp; Pekeris (1941]; see [[#Ledoux_and_Pekeris_.281941.29|additional discussion below]]) suggest that an adequate outer boundary condition is provided by setting the fractional pressure fluctuation, <math>~p</math>, to zero at the surface.  Leaning on this just-derived relation, therefore, they recommend (see their equation 4) imposing the following surface boundary constraint on the fractional radial variation, <math>~x</math>:
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<math>~-\gamma_g \biggl( 3 x +  r_0 \frac{dx}{dr_0} \biggr)</math>
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<math>~=</math>
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<math>~0</math>&nbsp; &nbsp; &nbsp; &nbsp; at &nbsp; &nbsp; &nbsp; &nbsp; <math>~r_0 = R \, .</math>
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