The PROPERTIES AND STABILITY OF SELF-GRAVITATING, POLYTROPIC SPHERES WITH Γ = 1 TO 1.4 SPECIFIC HEAT RATIOS

Abstract

We study self-gravitating, hydrostatic spheres with a polytropic equation of state P ∝ ρ^γ (where γ is the specific heat ratio of the gas), considering structures with γ ≈ 1 as a model for molecular cloud cores with small departures from isother- mality. We derive the properties (i.e., mass, radius and center to edge density ratio) as a function of γ for the maximal stable sphere through an application of “Bonnor’s stability criterion”. We find that in the γ = 1 → 4/3 range the mass of the maximal sphere (for a given central temperature) is almost constant, and that its radius and center to edge density ratio are growing functions of γ. We therefore have maximal stable, self-gravitating spheres with similar masses, but with increasing center to edge density contrasts for increasing departures from isothermality.

Stability Analysis of Relativistic Polytropes

“…Earlier methods used to examine the stability of polytropic stars are listed in Bardeen et al (1966). More recently, the stability of polytropes with different polytropic indices was described by Horedt (2013) and Raga et al (2020).…”