Inertial modes of rigidly rotating neutron stars in Cowling approximation
Inertial modes of rigidly rotating neutron stars in Cowling approximation
复制标题
考林近似中刚性旋转中子星的惯性模态
DOI：
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发表时间：
2008
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通讯作者：
W. Kastaun
中科院分区：
文献类型：
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作者：
W. Kastaun
在这篇文章中，我们研究的惯性模式的刚性旋转中子星，即模式的科里奥利力是占主导地位的。这是使用固定时空的假设（考林近似）来完成的。我们目前的频率和本征函数的一系列恒星与多方状态方程，涵盖了广泛的旋转速率。模式得到了一个非线性广义相对论流体动力学演化代码。我们进一步表明，振动模式的本征方程可以写在一个特别简单的形式的情况下，任意快速，但刚性旋转。使用这些方程，我们调查的惯性模式，然后比较数值得到的本征函数的一些一般特性。特别是，我们推导出一个粗略的分析估计的频率作为本征函数的节点数的函数，并发现一个类似的经验关系匹配的数值结果与意想不到的精度。我们研究了本征方程的慢旋转极限，得到了两组不同的描述压力和惯性模式的方程。对于数值计算，我们只考虑轴对称模式，而分析部分也包括非轴对称模式。本征函数表明，分类的惯性模式的球谐分解的主导项的量子数是人为的，在这个意义上，最大的长期是不强烈占主导地位，即使在缓慢的旋转限制。压力模态和惯性模态的不同结构的原因在于，科里奥利力仅在惯性模态的慢旋转极限中保持重要。相应地，我们在该极限下得到的标量本征方程对于压力模态是球对称的，而对于惯性模态则不是。
In this article, we investigate inertial modes of rigidly rotating neutron stars, i.e. modes for which the Coriolis force is dominant. This is done using the assumption of a fixed spacetime (Cowling approximation). We present frequencies and eigenfunctions for a sequence of stars with a polytropic equation of state, covering a broad range of rotation rates. The modes were obtained with a nonlinear general relativistic hydrodynamic evolution code. We further show that the eigenequations for the oscillation modes can be written in a particularly simple form for the case of arbitrary fast but rigid rotation. Using these equations, we investigate some general characteristics of inertial modes, which are then compared to the numerically obtained eigenfunctions. In particular, we derive a rough analytical estimate for the frequency as a function of the number of nodes of the eigenfunction, and find that a similar empirical relation matches the numerical results with unexpected accuracy. We investigate the slow rotation limit of the eigenequations, obtaining two different sets of equations describing pressure and inertial modes. For the numerical computations we only considered axisymmetric modes, while the analytic part also covers nonaxisymmetric modes. The eigenfunctions suggest that the classification of inertial modes by the quantum numbers of the leading term of a spherical harmonic decomposition is artificial in the sense that the largest term is not strongly dominant, even in the slow rotation limit. The reason for the different structure of pressure and inertial modes is that the Coriolis force remains important in the slow rotation limit only for inertial modes. Accordingly, the scalar eigenequation we obtain in that limit is spherically symmetric for pressure modes, but not for inertial modes.