The effect of dark matter (DM) on $f$-mode oscillations in DM admixed neutron stars (NSs) is investigated in a comprehensive analysis with particular attention to the role of the nuclear equation of state. Hadronic matter is modeled by the relativistic mean-field model and the DM model is based on the neutron decay anomaly. The nonradial $f$-mode oscillations for such DM admixed NSs are studied in a full general relativistic framework. We investigate the impact of DM, DM self-interaction, and DM fraction on the $f$-mode characteristics. We derive relations encoding the effect of DM on $f$-mode parameters. We then perform a systematic study by varying all the model parameters within their known uncertainty range and obtain a universal relation for the DM fraction based on the total mass of the star and DM self-interaction strength. We also perform a correlation study among model parameters, NS observables, and in particular, $f$-mode parameters. Finally, we check the $f$-mode universal relations for the case of DM admixed NSs and demonstrate the existence of a degeneracy between purely hadronic NSs and DM admixed NSs.

中文翻译：

---

暗物质对中子星f模振荡的影响


电子 $f$ $f$ 等等 $f$ 暗物质（DM）开启 $f$ 通过综合分析研究了 DM 混合中子星 (NS) 中的模式振荡，特别关注 DM 混合中子星 (NS) 的作用 $f$ 核方程 o $f$ 状态。强子物质通过相对论平均场模型进行建模，DM 模型基于中子衰变异常。在完整的广义相对论框架中研究了此类 DM 混合 NS 的非径向 f 模式振荡。我们研究了 DM、DM 自相互作用和 DM 分数对 f 模式特性的影响。我们推导了编码 DM 对 f 模式参数影响的关系。然后，我们通过在已知的不确定性范围内改变所有模型参数来进行系统研究，并根据恒星的总质量和 DM 自相互作用强度获得 DM 分数的普遍关系。我们还在模型参数、NS 可观测量，特别是 f 模式参数之间进行相关性研究。最后，我们检查了 DM 混合 NS 情况下的 f 模普遍关系，并证明了纯强子 NS 和 DM 混合 NS 之间存在简并性。