Editing SSC/Structure/BiPolytropes (section)

===The Tohline Generalization===
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[Introduced '''<font color="red">10 June 2013</font>'''] It should be pointed out that, while the interface conditions shown in Table 2 and the solution steps that follow do ensure that the gas pressure is continuous across the interface and allow for a discontinuity in the mass-density across the interface, they do not actually force the temperature to be continuous across the interface.  More generally, pressure continuity is ensured if,
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\frac{\rho(r_i)}{\mu/T(r_i)}\biggr|_c = \frac{\rho(r_i)}{\mu/T(r_i)}\biggr|_e \, .
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So a discontinuity across the interface will arise if the ratio of the molecular weights, <math>\mu_c/\mu_e</math>, is not unity, or if there is a discontinuity in the temperature across the interface &#8212; that is, if <math>T(r_i)|_e \ne T(r_i)|_c</math>, or both.  Because they were using bipolytropes to model optically thick stellar interiors, {{ SC42 }} argued that the temperature should also be continuous across the interface and, hence, that a discontinuity in the density would be introduced at the interface from a discontinuity in the molecular weight.  [[SSC/Structure/LimitingMasses#Relationship_Between_the_Bonnor-Ebert_and_Sch.C3.B6nberg-Chandrasekhar_Critical_Masses|In a separate chapter where we discuss the relationship between the Sch&ouml;nberg-Chandrasekhar critical mass and the Bonnor-Ebert critical mass]], we will argue that a discontinuous drop in the density is introduced by a substantial jump in the gas temperature at the interface.  In making this alternate assumption, the structural equations describing the bipolytropic model will remain unchanged; we will only need to replace the ratio <math>\mu_c/\mu_e</math> by the ratio <math>T(r_i)|_e/T(r_i)|_c</math>.