Numbers of equilibria for the equation of self-gravitating isentropic gas surrounding a solid ball

Wen Chi Kuan*, Song-Sun Lin

*Corresponding author for this work

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

For self-gravitating, spherically symmetric and isentropic gas surrounding a solid star, when the adiabatic index γ ∈ [4/3, 2) we prove that there is a unique equilibrium for given momentum and total mass. When γ ∈ (1, 4/3), we prove that there are multiple equilibria for a certain range of momentum and total mass and the number of equilibria may grow arbitrarily larger for certain γ. These results are consistent with the beliefs of astrophysicists; the stationary solutions are stable if γ > 4/3 and unstable if γ < 4/3. The problems were studied through the classical Lane-Emden equation.

Original languageEnglish
Pages (from-to)311-331
Number of pages21
JournalJapan Journal of Industrial and Applied Mathematics
Volume13
Issue number2
DOIs
StatePublished - 1 Jan 1996

Keywords

  • Equilibria
  • Isentropic gas
  • Lane-Emden equation
  • Self-gravitating
  • Solid core

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