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.
|Number of pages||21|
|Journal||Japan Journal of Industrial and Applied Mathematics|
|State||Published - 1 Jan 1996|
- Isentropic gas
- Lane-Emden equation
- Solid core