中子星外壳再审视：基于多项式状态方程方法的近似
The Crusts of Neutron Stars Revisited: Approximations within a Polytropic Equation of State Approach
AI总结：
本文通过比较不同理论框架下的状态方程，重新审视中子星外壳近似，并发现简单处理外壳足以满足结构需求。
摘要：
在本文中，我们重新审视了文献中提出的几种薄外壳近似，并将其与 Tolman--Oppenheimer--Volkoff (TOV) 方程的精确解进行比较。此外，我们使用了三种不同的状态方程 (EoSs)，包括一个包含 pasta 相的 EoS，每种基于不同的理论框架：变分法、相对论性 Brueckner--Hartree--Fock 理论和相对论平均场理论。我们强调，这些近似只需要 TOV 解的核心部分以及核心-外壳界面处的 EoS 性质；在我们的方法中，仅需能量密度。最后，相对论近似以及带有修正的牛顿近似与精确解显示出良好的一致性。这表明，对外壳的简单处理对于结构目的来说是足够的，无论子核状态方程的不确定性如何，这些不确定性并不非常大。统一的 EoS SINPA（相对论平均场理论），包括 pasta 相，被用来研究薄外壳近似，而通过：(i) 修改的 TOV 方程中的各向异性压力，(ii) f(R, L_m, T) 引力模型，以及 (iii) 暗物质混合物，展示了退化在 M--R 关系中的退化。正如所展示的，对引力描述的修改引入了在质量-半径关系中具有挑战性的退化，这些退化难以区分或精确量化。
英文摘要：
In this work, we revisit several thin-crust approximations presented in the literature and compare them with the exact solutions of the Tolman--Oppenheimer--Volkoff (TOV) equations. In addition, we employ three different equations of state (EoSs), including one with a pasta phase, each based on a distinct theoretical framework: the variational method, relativistic Brueckner--Hartree--Fock theory, and relativistic mean-field theory. We emphasize that these approximations require only the TOV solutions for the core and the EoS properties at the core--crust interface; in our approach, only the energy density is needed. Finally, the relativistic approximation, as well as the Newtonian approximation with corrections, shows good agreement with the exact solutions. This indicates that a simple treatment of the crust is sufficient for structural purposes, independently of the uncertainties in the sub-nuclear equation of state, which are not very large. The unified EoS SINPA (relativistic mean-field theory), including the pasta phase, was used to study the thin-crust approximation, while degeneracy in the $M$--$R$ relation is demonstrated through: (i) anisotropic pressure in the modified TOV equations, (ii) the $f(R, L_m, T)$ gravity model, and (iii) dark matter admixture. As demonstrated, modifications to the description of gravitation introduce degeneracies in the mass--radius relation that are challenging to disentangle or quantify precisely.
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