动态时空中具有不同较差自转程度的旋转中子星的基模
Fundamental modes of rotating neutron stars with various degrees of differential rotation in dynamical spacetimes
AI总结：
本研究首次结合不同较差自转程度与动态时空，通过二维轴对称模拟构建了可通过动能结合能比量化旋转中子星两类基模频率的线性关系，修正了既往考林近似方法的偏差。
摘要：
包括核心坍缩超新星和双中子星并合在内的剧烈天体物理事件，会产生具有不同较差自转程度的旋转中子星。这类中子星的振荡模式可能被激发并辐射出强引力波，探测这些模式有望获取中子星的结构、动力学等相关信息。因此，既往研究采用动力学模拟构建了量化振荡模式频率的关系，具体而言，研究者通过考林近似（Cowling approximation）下的模拟，建立了l=0基阶准径向模式f_F与l=2基阶四极模式f_{²f}的频率线性关系。但这些关系对f_F的高估、对f_{²f}的低估最高可达约30%，且较差自转程度对f_F与f_{²f}的影响尚未得到充分研究。本研究首次同时考虑不同的较差自转程度Ã与动态时空，构建量化f_F与f_{²f}的线性关系。通过二维轴对称模拟，我们首先证明对于不同的Ã取值，f_F与f_{²f}均几乎与恒星致密度M/R呈线性标度关系；我们还观测到，在不同Ã取值下，f_F与f_{²f}均和动能与结合能之比T/|W|存在准线性关系。最终我们构建了可通过T/|W|量化f_F与f_{²f}的线性拟合式，更新了动态时空中较差自转旋转中子星基模的对应关系。
英文摘要：
Violent astrophysical events, including core-collapse supernovae and binary neutron star mergers, can result in rotating neutron stars with diverse degrees of differential rotation. Oscillation modes of these neutron stars could be excited and emit strong gravitational waves. Detecting these modes may provide information about neutron stars, including their structures and dynamics. Hence, dynamical simulations were employed to construct relations for quantifying the oscillation mode frequency in previous studies. Specifically, linear relations for the frequencies of fundamental $l=0$ quasi-radial mode $f_{F}$ and fundamental $l=2$ quadrupolar mode $f_{^2f}$ were constructed by simulations with the Cowling approximation. Nevertheless, these relations can overestimate $f_{F}$ and underestimate $f_{^2f}$ up to $\sim 30\%$. Furthermore, it has yet to be fully studied how the degree of differential rotation affects $f_{F}$ and $f_{^2f}$. Here, for the first time, we consider both various degrees of differential rotation $\Tilde{A}$ and dynamical spacetime to construct linear relations for quantifying $f_{F}$ and $f_{^2f}$. Through 2D axisymmetric simulations, we first show that both $f_{F}$ and $f_{^2f}$ scale almost linearly with the stellar compactness $M/R$ for different values of $\Tilde{A}$. We also observe the quasi-linear relations for both $f_{F}$ and $f_{^2f}$ with the kinetic-to-binding energy ratio $T/|W|$ for different $\Tilde{A}$ values. Finally, we constructed linear fits that can quantify $f_{F}$ and $f_{^2f}$ by $T/|W|$. Consequently, this work updated the relations for the fundamental modes of rotating neutron stars with differential rotations in dynamical spacetime.
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