Linear Stability of liquid Lane-Emden stars

TL;DR

This paper investigates the stability of liquid Lane-Emden stars, establishing bounds on their density and radius, and determining conditions under which they are linearly stable or unstable based on the adiabatic index and central density.

Contribution

It provides the first detailed analysis of linear stability for liquid Lane-Emden stars, highlighting the role of central density and the adiabatic index, contrasting with gaseous models.

Findings

Stars are linearly stable for b3 a7 2(d-1)/d when b3 a7 2(d-1)/d with small central density

Stars are linearly unstable for b3 a7 2(d-1)/d with large central density

Bounds for density profile b1 and radius R are established

Abstract

We establish various qualitative properties of liquid Lane-Emden stars in $\mathbb{R}^d$, including bounds for its density profile $\rho$ and radius $R$. Using them we prove that against radial perturbations, the liquid Lane-Emden stars are linearly stable when $\gamma\geq 2(d-1)/d$; linearly stable when $\gamma<2(d-1)/d$ for stars with small relative central density $\rho(0)-\rho(R)$; and linearly unstable when $\gamma<2(d-1)/d$ for stars with large central density. Such dependence on central density is not seen in the gaseous Lane-Emden stars.