标题： 从$w$-准正则模谱系重建中子星状态方程：采用分段多项式网格划分与细化方法 显示英文标题

标题： Reconstruction of the neutron star equation of state from $w$-quasinormal modes spectra with a piecewise polytropic meshing and refinement method

摘要： 本文提出了一种求解相对论恒星逆问题的新方法，使用了准正则模式和状态方程的分段多项式参数化。 该算法是一种分段多项式网格划分与细化方法，能够从质量及$wI$准正则模式的实验数据重建中子星的状态方程。 我们提出了一种能够高效数值计算中子星轴向准正则模式的算法。 我们使用初始网格中的$27440$个状态方程，在包含大多数现今常用候选状态方程的$4$参数分段多项式体积内进行操作。 细化过程引导我们以一定精度重建状态方程。 利用重建后的状态方程，我们计算了潮汐变形性和慢旋转参数（例如转动惯量和四极矩）的预测值。 为了用明确的例子验证该方法，我们将几个（五个）给定状态方程的配置作为输入数据。 我们以相当好的近似程度重建了状态方程，并比较了原始状态方程和重建后状态方程的物理参数曲线。 对于所有参数，我们得到的相对误差均小于$2.5\%$，除了潮汐变形性，其相对误差小于$6.5\%$。 我们还研究了来自 GW170817 事件对重建状态方程的约束。 显示英文摘要

摘要： In this paper we present a new approach to the inverse problem for relativistic stars using quasinormal modes and the piecewise polytropic parametrization of the equation of state. The algorithm is a piecewise polytropic meshing and refinement method that reconstructs the neutron star equation of state from experimental data of the mass and the $wI$-quasinormal modes. We present an algorithm able to numerically calculate axial quasinormal modes of neutron stars in an efficient way. We use an initial mesh of $27440$ equations of state in a $4$-volume of piecewise polytropic parameters that contains most of the candidate equations of state used today. The refinement process drives us to the reconstruction of the equation of state with a certain precision. Using the reconstructed equation of state, we calculate predictions for tidal deformability and slow rotation parameters (moment of inertia and quadrupole moment, for example). In order to check the method with an explicit example, we use as input data a few (five) configurations of a given equation of state. We reconstruct the equation of state in a quite good approximation, and then we compare the curves of physical parameters from the original equation of state and the reconstructed one. We obtain a relative difference for all of the parameters smaller than $2.5\%$ except for the tidal deformability, for which we obtain a relative difference smaller than $6.5\%$. We also study constraints from GW170817 event for the reconstructed equation of state.