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arXiv · 2208.06736

Linear Stability of liquid Lane-Emden stars

King Ming Lam
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Abstract

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

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King Ming Lam. 2023-05-09. Linear Stability of liquid Lane-Emden stars. https://arxiv.org/abs/2208.06736

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