Universal description of the Neutron Star's surface and its key global properties: A Machine Learning Approach for nonrotating and rapidly rotating stellar models
当核物质密度超过原子核内部密度时，中子星为探索基础物理提供了理想的理论框架。尽管其至关重要，但状态方程中的不确定性掩盖了其内部结构。对于旋转中子星，其表面形状取决于 EoS 和旋转动力学。本研究采用机器学习回归技术，提出了关于恒星表面的新普适关系。具体而言，我们为中子星的偏心率、极半径与赤道半径之比，以及极点和赤道处的有效引力加速度开发了高精度的普适关系。此外，我们提出了 $(d\log R(μ)/dθ)_{\max}$ 的精确理论公式。本研究利用这些全局参数作为神经网络训练阶段的特征，解决了关键天文学问题。同时，我们为每颗恒星的全局表面特性引入了新的有效参数化方法。我们的回归方法能够精确估计恒星表面 $R(μ)$、对应的对数导数 $d\log R(μ)/dθ$ 及有效引力加速度 $g(μ)$，精度优于 $1\\%$。该分析针对扩展的旋转构型样本进行，这些样本使用包含 70 种表格化强子、超子和混合 EoS 模型的大型集合构建，这些模型遵守当前多信使约束并涵盖广泛的刚度范围。最重要的是，所提出的关系可为利用 NICER X 射线望远镜或未来任务获取的数据进行恒星表面估计提供精确框架，并在相关可观测量测量数据可用时约束核物质的 EoS。
英文摘要：
Neutron stars provide an ideal theoretical framework for exploring fundamental physics when nuclear matter surpasses densities encountered within atomic nuclei. Despite their paramount importance, uncertainties in the equation of state (EoS) have shrouded their internal structure. For rotating neutron stars, the shape of their surface is contingent upon the EoS and the rotational dynamics. This work proposes new universal relations regarding the star's surface, employing machine-learning techniques for regression. More specifically, we developed highly accurate universal relations for a neutron star's eccentricity, the star's ratio of the polar to the equatorial radius, and the effective gravitational acceleration at both the pole and the equator. Furthermore, we propose an accurate theoretical formula for $(d\log R(μ)/dθ)_{\max}$. This research addresses key astronomical aspects by utilizing these global parameters as features for the training phase of a neural network. Along the way, we introduce new effective parameterizations for each star's global surface characteristics. Our regression methodology enables accurate estimations of the star's surface $R(μ)$, its corresponding logarithmic derivative $d\log R(μ)/dθ$, and its effective acceleration due to gravity $g(μ)$ with accuracy better than $1 \%$. The analysis is performed for an extended sample of rotating configurations constructed using a large ensemble of 70 tabulated hadronic, hyperonic, and hybrid EoS models that obey the current multimessenger constraints and cover a wide range of stiffnesses. Above all, the suggested relations could provide an accurate framework for the star's surface estimation using data acquired from the NICER X-ray telescope or future missions, and constrain the EoS of nuclear matter when measurements of the relevant observables become available.
A versatile numerical method for obtaining structures of rapidly rotating baroclinic stars: self-consistent and systematic solutions with shellular-type rotation
