The radii and tidal deformabilities of neutron stars are investigated in the framework of relativistic mean-field (RMF) model with different density-dependent behaviors of symmetry energy. To study the effects of symmetry energy on the properties of neutron stars, an $\omega$ meson and $\rho$ meson coupling term is included in a popular RMF Lagrangian, i.e. the TM1 parameter set, which is used for the widely used supernova equation of state (EoS) table. The coupling constants relevant to the vector-isovector meson, $\rho$, are refitted by a fixed symmetry energy at subsaturation density and its slope at saturation density, while other coupling constants remain the same as the original ones in TM1 so as to update the supernova EoS table. The radius and mass of maximum neutron stars are not so sensitive to the symmetry energy in these family TM1 parameterizations. However, the radii at intermediate mass region are strongly correlated with the slope of symmetry energy. Furthermore, the dimensionless tidal deformabilities of neutron stars are also calculated within the associated Love number. We find that its value at $1.4 M_\odot$ has a linear correlation to the slope of symmetry energy being different from the previous studied. With the latest constraints of tidal deformabilities from GW170817 event, the slope of symmetry energy at nuclear saturation density should be smaller than $60$ MeV in the family TM1 parameterizations. This fact supports the usage of lower symmetry energy slope for the update supernova EoS, which is applicable to simulations of neutron star merger. Furthermore, the analogous analysis are also done within the family IUFSU parameter sets. It is found that the correlations between the symmetry energy slope with the radius and tidal deformability at $1.4 M_\odot$ have very similar linear relations in these RMF models.

中文翻译：

---

相对论平均场模型中对称能对中子星半径和潮汐变形能力的影响

在相对论平均场（RMF）模型的框架内研究了中子星的半径和潮汐变形能力，具有不同的对称能密度相关行为。为了研究对称能量对中子星性质的影响，流行的 RMF 拉格朗日函数中包含了 $\omega$ 介子和 $\rho$ 介子耦合项，即 TM1 参数集，用于广泛使用的超新星状态方程 (EoS) 表。与向量-等向量介子相关的耦合常数 $\rho$ 由饱和密度下的固定对称能及其在饱和密度下的斜率重新拟合，而其他耦合常数与 TM1 中的原始耦合常数相同，以便更新超新星 EoS 表。最大中子星的半径和质量对这些 TM1 族参数化中的对称能量不太敏感。然而，中等质量区域的半径与对称能量的斜率密切相关。此外，中子星的无量纲潮汐变形能力也在相关的洛夫数内计算。我们发现它在 $1.4 M_\odot$ 处的价值与对称能量的斜率呈线性相关，这与之前研究的不同。由于 GW170817 事件对潮汐变形能力的最新限制，在 TM1 族参数化中，核饱和密度下的对称能斜率应小于 60 美元 MeV。这一事实支持更新超新星 EoS 使用较低的对称能量斜率，这适用于中子星合并的模拟。此外，类似的分析也在 IUFSU 家族参数集中进行。发现在这些 RMF 模型中，对称能量斜率与半径和潮汐变形能力之间的相关性在 $1.4 M_\odot$ 中具有非常相似的线性关系。