中子星在有效表面近似下作为平衡态致密液滴
Neutron stars as a dense liquid drop at equilibrium within the effective surface approximation
AI总结：
本文提出中子星作为平衡态致密液滴的宏观模型，在薄层近似下解析求解密度分布，并推导含表面修正的状态方程，其质量预测与观测相符。
摘要：
我们为处于平衡态的完美液滴状中子星（NS）建立了宏观模型。我们采用薄层近似 $a/R\ll 1$，其中 $a$ 是有效中子星表面（ES）的壳层厚度，$R$ 是 ES 曲率的平均半径。在广义相对论球对称系统的近似 Schwarzschild 度规解框架内，宏观引力通过总分离粒子能量和不可压缩性加以考虑。我们解析地得到了沿 ES 法线方向的密度分布 $\rho$，适用于一般形式的能量密度 $\mathcal{E}(\rho)$。对于典型的壳层厚度和有效半径，我们得到了密度 $\rho$ 的主导表达式。中子星质量被解析地计算为体积项和表面项之和，并考虑了度规空间的径向曲率，与近期测量的若干中子星质量合理吻合。我们推导了含表面修正的简单宏观状态方程（EoS）。Tolman-Oppenheimer-Volkoff 方程的压力解析解和数值解与我们的 EoS 的体积部分吻合良好。
英文摘要：
The macroscopic model is formulated for a neutron star (NS) as a perfect liquid drop at the equilibrium. We use the leptodermic approximation $a/R\ll 1$, where $a$ is the crust thickness of the effective NS surface (ES), and $R$ is the mean radius of the ES curvature. Within the approximate Schwarzschild metric solution to the general relativity theory equations for the spherically symmetric systems, the macroscopic gravitation is taken into account in terms of the total separation particle energy and incompressibility. Density distribution $ρ$ across the ES in the normal direction to the ES was obtained analytically for a general form of the energy density $\mathcal{E}(ρ)$. For the typical crust thickness, and effective radius, one finds the leading expression for the density $ρ$. NS masses are analytically calculated as a sum of the volume and surface terms, taking into account the radial curvature of the metric space, in reasonable agreement with the recently measured masses for several neutron stars. We derive the simple macroscopic equation of state (EoS) with the surface correction. The analytical and numerical solutions to Tolman-Oppenheimer-Volkoff equations for the pressure are in good agreement with the volume part of our EoS.
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