通过Tolman IV解进行恒星建模：大质量脉冲星J0740+6620与HESS J1731-347致密天体的案例
Stellar modeling via the Tolman IV solution: The cases of the massive pulsar J0740+6620 and the HESS J1731-347 compact object
AI总结：
本文在Einstein引力下采用Tolman IV精确解析解，对已知质量和半径的致密天体进行各向同性建模，首次成功刻画大质量脉冲星PSR J0740+6620与异常轻的HESS致密天体，并指出引入多方状态方程薄壳层可解决表面绝热指数发散问题。
摘要：
我们在Einstein引力理论框架下，对由各向同性物质构成的、已知恒星质量和半径的致密天体进行建模。我们在整篇手稿中使用的描述流体静力学平衡的内部解，对应于早先获得的Tolman IV精确解析解。通过施加已知恒星质量和半径天体的匹配条件，确定了该解的三个自由参数。最后，利用公认的判据，我们表明与Kohler Chao解相反，Tolman IV解符合行为良好且符合现实的解的所有要求，除了相对论绝热指数在恒星表面发散。包含采用多方状态方程的薄壳层或许可以解决指数$Γ$的发散问题，而这正是中子星研究中出现的情况。据我们所知，我们在此首次通过Tolman IV解对最近发现的大质量脉冲星PSR J0740+6620和异常轻的HESS致密天体进行了建模。本研究可能对模型构建者具有参考价值，并可作为未来研究的有用参考。
英文摘要：
We model compact objects of known stellar mass and radius made of isotropic matter within Einstein's gravity. The interior solution describing hydrostatic equilibrium we are using throughout the manuscript corresponds to the Tolman IV exact analytic solution obtained long time ago. The three free parameters of the solutions are determined imposing the matching conditions for objects of known stellar mass and radius. Finally, using well established criteria it is shown that contrary to the Kohler Chao solution, the Tolman IV solution is compatible with all requirements for well behaved and realistic solutions. except for the relativistic adiabatic index that diverges at the surface of the stars. The divergence of the index $Γ$ may be resolved including a thin crust assuming a polytropic equation-of-state, which is precisely the case seen in studies of neutron stars. To the best of our knowledge, we model here for the first time the recently discovered massive pulsar PSR J0740+6620 and the strangely light HESS compact object via the Tolman IV solution. The present work may be of interest to model builders as well as a useful reference for future research.
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