AI 中文总结
本研究系统探究冷中子星的$g$模频率，基于核子状态方程推导出一阶$g$模频率与恒星致密度、核饱和参数组合的经验关系，为探测中子星内部新自由度或新成分提供了观测判据。
AI 中文摘要
中子星中激发的振荡频率对于提取其内部性质至关重要。除了基模和压力模之外，由于成分梯度的存在，即便在零温度恒星模型中也能激发引力（$g$-）模。本研究聚焦于核子状态方程，系统研究了$g$模频率。随后，我们推导得出了一阶$g$模频率的经验关系，该关系是恒星致密度与核饱和参数组合$η_0 \equiv L/K_0$的函数，其中$K_0$和$L$分别表示对称核物质的不可压缩性与核对称能的密度依赖性。如果观测到的一阶$g$模频率与我们的经验关系存在显著偏差，则可能表明恒星内部出现了额外的自由度或新的成分。
英文摘要
Oscillation frequencies excited in neutron stars are crucial for extracting their interior properties. In addition to the fundamental and pressure modes, the gravity ($g$-) modes can be excited even in zero-temperature stellar models due to the composition gradient. In this study, we systematically study the $g$-mode frequencies, focusing on the nucleonic equation of state. Then, we can derive an empirical relation for the 1st $g$-mode frequencies as a function of the stellar compactness and the combination of the nuclear saturation parameters, $η_0 \equiv L/K_0$, where $K_0$ and $L$ denote the incompressibility of symmetric nuclear matter and the density dependence of the nuclear symmetry energy, respectively. If an observed 1st $g$-mode frequency significantly deviates from our empirical relation, it may indicate the emergence of additional degrees of freedom or new compositions inside the star.
