标题： 暗物质和$σ$-截断势对中子星径向和非径向振荡模式的影响 显示英文标题

标题： Effect of Dark matter and $σ$-cut potential on radial and non-radial oscillation modes in neutron stars

摘要： 我们研究了介子非线性（NL）相互作用状态方程（EoS），采用相对论平均场模型，并探讨了$\sigma$-截断势（NL-$\sigma$截断）和暗物质（NL DM）对中子星非径向和径向振荡模式的影响。 对于NL-$\sigma$截断，我们包括$\sigma$-截断势$U_{cut} (\sigma)$来研究其影响。 对于暗物质，我们使用中子衰变异常模型。 对于每个模型，我们研究两种极端的EoS，刚性和柔软，覆盖给定模型的整个允许参数范围，与当前天体物理约束一致。 EoS和恒星特性，如质量和半径，被计算出来，并讨论了$\sigma$-截断和DM的影响。 非径向和径向振荡模式都在广义相对论框架下进行计算。 我们研究了非径向$f$和$p_1$模式频率、阻尼时间和一些准通用关系，这些关系将$f$模式的频率与平均密度和致密性联系起来。 分析表明，在 1.4~$M_{\odot}$和最大质量配置下，NL DM 模型中的$f$和$p_1$模式频率高于 NL 和 NL-$\sigma$模型。 我们之前的参数化与当前计算之间的一致性对准通用关系的存在提供了强有力的支持，这些关系无论涉及的具体物质成分如何都成立。 对于径向振荡，我们计算了10个最低阶模态（$f$，$p$），研究了径向扰动以及NL-$\sigma$截断和NL DM 方程态下的大频率间隔，表明NS方程态中涉及的微观物理在不同节点之间的频率间隔上留下了印记。 显示英文摘要

摘要： We study the mesonic nonlinear (NL) interaction equation of state (EoS) employing the relativistic mean-field model and investigate the effect of $\sigma$-cut potential (NL-$\sigma$ cut) and dark matter (NL DM) on the non-radial and radial oscillation modes of neutron stars. For NL-$\sigma$ cut, we include the $\sigma$-cut potential $U_{cut} (\sigma)$ to study its effect. For the dark matter, we use the neutron decay anomaly model. For each model, we investigate two extreme EoSs, stiff and soft, that cover the entire allowed parameter range from the given model, consistent with the current astrophysical constraints. The EoS and the stellar properties, such as mass and radius, are calculated, and the effect of $\sigma$-cut and DM is discussed. Both non-radial and radial oscillation modes are computed in the general relativistic framework. We study the non-radial $f$ and $p_1$ mode frequency, damping time, and some qusi-universal relations connecting the frequencies of the $f$-mode to the average density and compactness. The analysis showed that the $f$ and $p_1$ mode frequencies at both 1.4~$M_{\odot}$ and the maximum mass configuration are higher in the NL DM model compared to the NL and NL-$\sigma$ models. The consistent alignment between our prior parameterizations and current calculations strongly supports the existence of quasi-universal relations that hold true irrespective of the particular matter components involved. For the radial oscillations, we compute 10 lowest-order modes ($f$, $p$), study the radial perturbations as well as the large frequency separation with NL-$\sigma$ cut and NL DM EoS, showing that the microphysics involved in the NS EoS is imprinted on the frequency separation between different nodes.