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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-Emdenstars 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 withlarge central density. Such dependence on central density is not seen in thegaseous Lane-Emden stars.

Linear Stability of liquid Lane-Emden stars