真实各向异性中子星的非径向振荡：极向模
Nonradial oscillations of realistic anisotropic neutron stars: Polar modes
- Universidad Mayor（乌马约尔大学）
- Universidad Antonio Nariño（安东尼奥·纳里尼奥大学）
- Universidad Industrial de Santander（桑坦德工业大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在广义相对论框架下研究各向异性中子星的极向扰动，计算f模频率与阻尼时间，发现频率随质量增大、阻尼时间减小，并建立了与致密度无关状态方程的准普适关系，可用于约束各向异性。
AI中文摘要：
在这项工作中，我们在完整广义相对论框架下研究了具有各向异性压力的静态、球对称中子星的极向扰动，包括度规和流体的线性阶扰动。我们利用对径向矢量$k^\alpha$扰动的一致处理方法计算了$f$模频率及相应的阻尼时间。特别地，其拉格朗日扰动$\Delta k^\alpha$由度规扰动和流体拉格朗日位移确定，并被约束在$(\tilde{u},\tilde{k})$平面上，其中$\tilde{u}^\alpha$是归一化的流体四速度。这一约束在扰动方程中引入了额外的动力学自由度。考虑三种状态方程以及Horvat和Bowers-Liang压力各向异性方案，我们发现$f$模频率随恒星质量增加而增大，范围从$1$到$3$~kHz，而阻尼时间则减小，范围从$0.5$到$1.25$~s。在切向压力超过径向压力的意义上增加各向异性，通常会降低振荡频率，而其对阻尼时间的影响取决于各向异性方案：对于Horvat模型，阻尼时间随各向异性增加而减小，但对于Bowers-Liang模型，阻尼时间随各向异性增加而增大。我们进一步发现$f$模频率的实部和虚部$M\omega_R$与$M\omega_I$与恒星致密度$\mathcal{C}=M/R$之间存在准普适关系，这些关系在很大程度上不依赖于状态方程。对这些关系的多项式拟合达到了优于$10\\%$的精度，为通过未来的星震学观测约束中子星压力各向异性提供了一个简单的唯象框架。
英文摘要：
In this work, we study the polar perturbations of static, spherically symmetric neutron stars with anisotropic pressure in full general relativity, including linear-order perturbations of both the metric and the fluid. We calculate the $f$-mode frequencies and the corresponding damping times using a consistent treatment of the perturbation of the radial vector $k^α$. In particular, its Lagrangian perturbation $Δk^α$ is determined by the metric perturbations and the fluid Lagrangian displacement and is constrained to the $(\tilde{u},\tilde{k})$ plane, where $\tilde{u}^α$ is the normalized fluid four-velocity. This constraint introduces an additional dynamical degree of freedom into the perturbation equations. Considering three equations of state and the Horvat and Bowers-Liang prescriptions for pressure anisotropy, we find that the $f$-mode frequency increases with stellar mass, ranging from $1$ to $3$~kHz, while the damping time decreases, ranging from $0.5$ to $1.25$~s. Increasing anisotropy, in the sense of tangential pressure exceeding radial pressure, generally lowers the oscillation frequency, while its effect on the damping time depends on the anisotropy prescription: the damping time decreases with increasing anisotropy for the Horvat model but increases with increasing anisotropy for the Bowers-Liang model. We further find quasi-universal relations between the real and imaginary parts of the $f$-mode frequency, $Mω_R$ and $Mω_I$, and the stellar compactness $\mathcal{C}=M/R$, which are largely insensitive to the equation of state. Polynomial fits to these relations achieve an accuracy better than $10\%$, providing a simple phenomenological framework for constraining neutron-star pressure anisotropy through future asteroseismology observations.
