SSC/Structure/BiPolytropes/51RenormaizePart3

BiPolytrope with n_c = 5 and n_e = 1

Eggleton, Faulkner & Cannon (1998) Analytic (nc, ne) = (5, 1)

Comment by J. E. Tohline on 30 March 2013: As far as I have been able to determine, this analytic structural model has not previously been published in a refereed, archival journal. Subsequent comment by J. E. Tohline on 23 June 2013: Last night I stumbled upon an article by Eagleton, Faulkner, and Cannon (1998) in which this identical analytically definable bipolytrope has been presented. Insight drawn from this article is presented in an additional subsection, below.

Here we construct a bipolytrope in which the core has an $n_c=5$ polytropic index and the envelope has an $n_e=1$ polytropic index. This system is particularly interesting because the entire structure can be described by closed-form, analytic expressions. In deriving the properties of this model, we will follow the general solution steps for constructing a bipolytrope that we have outlined elsewhere.  
 
 
 

See Also

• M. Gabriel & M. L. Roth (1974, A&A, Vol. 32, p. 309) … On the Secular Stability of Models with an Isothermal Core
• M. Gabriel & P. Ledoux (1967, Annales d'Astrophysique, Vol. 30, p. 975) … Sur la Stabilité Séculaire des Modeéles a Noyaux Isothermes
  

  In § 1 (p. 442) of 📚 Yabushita (1975) we find the following reference:   "A somewhat similar problem has been investigated by Gabriel & Ledoux (1967). Gaseous configurations with an isothermal core and polytropic envelope of index 3 were studied by 📚 Henrich & Chandrasekhar (1941) and by 📚 Schönberg & Chandrasekhar (1942). As is well known there is an upper limit (Schönberg-Chandrasekhar limit) to the mass of the core for the configurations to be in hydrostatic equilibria. Gabriel & Ledoux have investigated the stability of these configurations and have shown that secular stability is lost at the configuration that corresponds to the Schönberg-Chandrasekhar limit."