SSC/Stability/Yabushita75

Stability of a BiPolytrope with an Isothermal Core

This analysis pulls largely from 📚 S. Yabushita (1975, MNRAS, Vol. 172, pp. 441 - 453); the focus is on bipolytropes having $(n_c,n_e)=(\mathrm{\infty },\frac{3}{2})$. In an accompanying discussion, we summarize the steps that Yabushita took — from 1968 and 1974, to 1975 — that led up to his discovery of an analytic description of the isothermal displacement function.

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."