An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole
An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole
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DOI：
10.1143/ptp.121.843
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发表时间：
2009-04
影响因子：
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通讯作者：
R. Fujita;W. Hikida;H. Tagoshi
中科院分区：
文献类型：
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作者：
R. Fujita;W. Hikida;H. Tagoshi
我们开发了一个数值程序来计算粒子在克尔黑洞的偏心倾斜轨道上运动所引起的引力波。对于这样的系统，黑洞微扰方法是适用的。引力波可以通过求解具有点状源项的Teukolsky方程来计算，该点状源项由在一般束缚测地线轨道上运动的测试粒子的应力-能量张量计算。在我们以前的论文中，我们使用Mano，Suzuki和Takasugi开发的形式计算了Teukolsky方程的齐次解，并表明我们可以在赤道平面上的圆形轨道的情况下有效且非常准确地计算引力波。在这里，我们将这种方法应用于偏心倾斜轨道。克尔黑洞周围的测地线有三个运动常数：能量、角动量和卡特常数。我们计算卡特常数以及能量和角动量的变化率。这是第一次卡特常数的变化率已被准确评估。我们还处理的情况下，高偏心轨道$e=0.9$。为了确认我们的代码的准确性，进行了几次测试。我们发现，精确度只受$\ell$-，$k$-和$n$-模截断的限制，其中$\ell$是自旋加权球谐函数的指数，$n$和$k$分别是径向和极向运动的谐函数.当我们将$\ell$的最大值设置为20时，即使在高度偏心的情况下，$e=0.9$，我们也可以获得10 ^{-5}$的相对精度。偏心距越小，精度越高。我们的数值代码预计将是有用的计算模板的极端质量比的inspirals，这是一个主要目标的激光干涉仪空间天线（丽莎）。
We develop a numerical code to compute gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole. For such systems, the black hole perturbation method is applicable. The gravitational waves can be evaluated by solving the Teukolsky equation with a point like source term, which is computed from the stress-energy tensor of a test particle moving on generic bound geodesic orbits. In our previous papers, we computed the homogeneous solutions of the Teukolsky equation using a formalism developed by Mano, Suzuki and Takasugi and showed that we could compute gravitational waves efficiently and very accurately in the case of circular orbits on the equatorial plane. Here, we apply this method to eccentric inclined orbits. The geodesics around a Kerr black hole have three constants of motion: energy, angular momentum and the Carter constant. We compute the rates of change of the Carter constant as well as those of energy and angular momentum. This is the first time that the rate of change of the Carter constant has been evaluated accurately. We also treat the case of highly eccentric orbits with $e=0.9$. To confirm the accuracy of our codes, several tests are performed. We find that the accuracy is only limited by the truncation of $\ell$-, $k$- and $n$-modes, where $\ell$ is the index of the spin-weighted spheroidal harmonics, and $n$ and $k$ are the harmonics of the radial and polar motion, respectively. When we set the maximum of $\ell$ to 20, we obtain a relative accuracy of $10^{-5}$ even in the highly eccentric case of $e=0.9$. The accuracy is better for lower eccentricity. Our numerical code is expected to be useful for computing templates of the extreme mass ratio inspirals, which is one of the main targets of the Laser Interferometer Space Antenna (LISA).