SSC/Stability/BiPolytropes/RedGiantToPN/TryAgain

BiPolytropes with n_c = 5 and n_e = 1

Review

(October 30, 2026): A significant portion of the information that we have gathered regarding the stability of (n_c, n_e) = (5, 1) bipolytropes is presented on the following page ...

The most important result is associated with the case of ${\mu }_e/{\mu }_c=1$. With our first numerical integration of the LAWE, we found that the interface location for which ${\sigma }_c^2=0$ is $\xi =1.6686460157$; a separate numerical integration gave the result: ${\xi }_i=1.6639103365$.

Separately, we asked where along the equilibrium sequence we will find that $d{M}_{\mathrm{t}\mathrm{o}\mathrm{t}}/d\xi =0$. For the case of unity molecular-weight ratio, we found analytically that ${\xi }_i=1.6684629814$. These are virtually identical coordinate positions; it seems likely that they should be identically the same.

See Also