论文标题
中子星数正常模式中一维近似的精度
Accuracy of one-dimensional approximation in neutron star quasi-normal modes
论文作者
论文摘要
由于来自冷中子星的重力波的特征频变成了一个复杂的数字，其中真实和虚构的部分分别对应于振荡频率和阻尼率，因此必须以某种方式解决特征值问题，使特征值在二维参数中相关。为了避免这种困扰，有时会采用近似值，其中特征值位于一维参数空间中。在这项研究中，首先，我们显示了零阻尼近似的准确性，这是基本压力模式和第一压力模式的一维近似值之一。但是，此近似值不适用于时空模式，因为时空模式的阻尼率通常与振荡频率相当。然而，我们发现假想部分与本征频率的实际部分的比率的经验关系几乎完全独立于中子恒星物质的状态方程式而表达为Steller紧凑型的函数。通过这种经验关系，就可以从实际的部分来表达特征频率，即解决的问题成为一维征值的特征值问题。然后，我们发现即使在第1个时空模式下，即使在这种近似值的情况下，频率也可以很好地估计。
Since the eigenfrequency of gravitational waves from cold neutron stars becomes a complex number, where the real and imaginary parts respectively correspond to an oscillation frequency and damping rate, one has to somehow solve the eigenvalue problem concerning the eigenvalue in two-dimensional parameter space. To avoid this bother, one sometimes adopts an approximation, where the eigenvalue is in one-dimensional parameter space. In this study, first, we show the accuracy of the zero-damping approximation, which is one of the one-dimensional approximations, for the fundamental and 1st pressure modes. But, this approximation is not applicable to the spacetime mode, because the damping rate of the spacetime mode is generally comparable to the oscillation frequency. Nevertheless, we find the empirical relation for the ratio of the imaginary part to the real part of the eigenfrequency, which is expressed as a function of the steller compactness almost independently of the adopted equations of state for neutron star matter. Adopting this empirical relation, one can express the eigenfrequency in terms of just the real part, i.e., the problem to solve becomes an eigenvalue problem with a one-dimensional eigenvalue. Then, we find that the frequencies are estimated with good accuracy even with such approximations even for the 1st spacetime mode.
