论文标题
液路填充星的线性稳定性
Linear Stability of liquid Lane-Emden stars
论文作者
论文摘要
我们在$ \ mathbb {r}^d $中建立了液体车道填充星的各种定性特性，其中包括其密度概况$ρ$和半径$ r $的界限。使用它们，我们证明了针对径向扰动，当$γ\ geq 2（d-1）/d $ $γ\ geq 2（d-1）/d $时，液体车道损耗恒星是线性稳定的。 $γ<2（D-1）/d $的线性稳定，适用于具有小相对中央密度$ρ（0）-ρ（r）$的星星;当$γ<2（D-1）/d $的恒星中中央密度较大时，线性不稳定。在气态车道层恒星中没有看到这种对中央密度的依赖性。
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.
