SSC/Stability/BiPolytropes/RedGiantToPN/TryAgain: Difference between revisions

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Created page with "__FORCETOC__ =BiPolytrope with n<sub>c</sub> = 5 and n<sub>e</sub> = 1 (Pt 1)= =Related Discussions= * Polytropes emdeded in an external medium * Constructing BiPolytropes * Bonnor-Ebert spheres ** [http://en.wikipedia.org/wiki/Bonnor-Ebert_mass Bonnor-Ebert Mass] according to Wikipedia ** <font c..."
 
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__FORCETOC__
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=BiPolytrope with n<sub>c</sub> = 5 and n<sub>e</sub> = 1 (Pt 1)=
=BiPolytropes with n<sub>c</sub> = 5 and n<sub>e</sub> = 1=


==Review==


(October 30, 2026):  A significant portion of the information that we have gathered regarding the stability of (n<sub>c</sub>, n<sub>e</sub>) = (5, 1) bipolytropes is [[SSC/Stability/BiPolytropes/51Models|presented on the following page]] ...
The most important result is associated with the case of <math>\mu_e/\mu_c = 1</math>.  With our first numerical integration of the LAWE, we found that the interface location for which <math>\sigma_c^2 = 0</math> is <math>\xi = 1.6686460157</math>; a separate numerical integration gave the result: <font color="darkgreen"><math>\xi_i = 1.6639103365</math></font>.
Separately, we asked where along the equilibrium sequence we will find that <math>d M_\mathrm{tot}/d\xi = 0</math>. For the case of unity molecular-weight ratio, we found analytically that <math>\xi_i = 1.6684629814</math>.  These are virtually identical coordinate positions; it seems likely that they should be identically the same.
=See Also=


=Related Discussions=
* [[SSC/Structure/PolytropesEmbedded#Embedded_Polytropic_Spheres|Polytropes emdeded in an external medium]]
* [[SSC/Structure/BiPolytropes#BiPolytropes|Constructing BiPolytropes]]
* [[SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|Bonnor-Ebert spheres]]
** [http://en.wikipedia.org/wiki/Bonnor-Ebert_mass Bonnor-Ebert Mass] according to Wikipedia
** <font color="red">Link has disappeared:</font>  [http://www.astro.umd.edu/~cychen/MATLAB/ASTR320/matlabFrom320spring2011/Bonnor-EbertSphere/html/BonnorEbert.html A MATLAB script to determine the Bonnor-Ebert Mass coefficient] developed by [http://www.astro.umd.edu/people/cychen.html Che-Yu Chen] as a graduate student in the University of Maryland Department of Astronomy
* [[SSC/Structure/LimitingMasses#Sch.C3.B6nberg-Chandrasekhar_Mass|Sch&ouml;nberg-Chandrasekhar limiting mass]]
* [[SSC/Structure/LimitingMasses#Relationship_Between_the_Bonnor-Ebert_and_Sch.C3.B6nberg-Chandrasekhar_Critical_Masses|Relationship between Bonnor-Ebert and Sch&ouml;nberg-Chandrasekhar limiting masses]]


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Latest revision as of 19:33, 30 October 2026

BiPolytropes with nc = 5 and ne = 1[edit]

Review[edit]

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

The most important result is associated with the case of μe/μc=1. With our first numerical integration of the LAWE, we found that the interface location for which σc2=0 is ξ=1.6686460157; a separate numerical integration gave the result: ξi=1.6639103365.

Separately, we asked where along the equilibrium sequence we will find that dMtot/dξ=0. For the case of unity molecular-weight ratio, we found analytically that ξi=1.6684629814. These are virtually identical coordinate positions; it seems likely that they should be identically the same.

See Also[edit]

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