A 3PN Fourier domain waveform for non-spinning binaries with moderate eccentricity
A 3PN Fourier domain waveform for non-spinning binaries with moderate eccentricity
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DOI：
10.1088/1361-6382/ab3778
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发表时间：
2019-03
影响因子：
3.5
通讯作者：
B. Moore;N. Yunes
中科院分区：
文献类型：
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作者：
B. Moore;N. Yunes
虽然目前使用地面探测器观测到的引力波与准圆形轨道上的紧凑双星是一致的，但在不久的将来，偏心双星可能会被地面和空间仪器探测到。偏心率显著地使引力波信号复杂化，并且我们目前缺乏在中等到大偏心率范围内有效的快速和准确的模型。在以前的论文中，我们建立了一个傅立叶域，偏心波形模型在领先的顺序在后牛顿近似，即作为一个扩展在小速度和弱场。在这里，我们将这个模型扩展到第三后牛顿秩序，将近星点进动和更高的后牛顿秩序的影响，定性地改变波形的行为。我们的3PN模型结合了固定相位近似，截断的两个轨道频率（方位角和径向的）的组合的谐波和，以及在轨道分离和偏心率的双变量扩展。我们通过与完全数值的时域后牛顿模型的比较来验证该模型，并在大部分参数空间中找到了良好的一致性（匹配）。我们通过探索偏心校正的信噪比来估计偏心效应在参数空间的哪些区域是重要的。我们还研究了更高的后牛顿阶项的波形振幅的影响，以及不同的PN一致的，数值的，时域模型之间的协议。为了指导模型的未来改进，我们评估了3PN模型中用于构建它的不同解析近似所产生的误差。该模型对于初步数据分析调查很有用，并且可以允许将偏心率纳入的现象学混合到激励中合并振铃模型。
While current gravitational wave observations with ground based detectors have been consistent with compact binaries in quasi-circular orbits, eccentric binaries may be detectable by ground-based and space-based instruments in the near future. Eccentricity significantly complicates the gravitational wave signal, and we currently lack fast and accurate models that are valid in the moderate to large eccentricity range. In a previous paper, we built a Fourier domain, eccentric waveform model at leading order in the post-Newtonian approximation, i.e. as an expansion in small velocities and weak fields. Here we extend this model to 3rd post-Newtonian order, incorporating the effects of periastron precession and higher post-Newtonian order effects that qualitatively change the waveform behavior. Our 3PN model combines the stationary phase approximation, a truncated sum of harmonics of combinations of two orbital frequencies (an azimuthal one and a radial one), and a bivariate expansion in the orbital separation and the eccentricity. We validate the model through comparisons with a fully-numerical, time domain post-Newtonian model, and find good agreement (matches between ) in much of the parameter space. We estimate in what regions of parameter space eccentric effects are important by exploring the signal to noise ratio of eccentric corrections. We also examine the effects of higher post-Newtonian order terms in the waveform amplitude, and the agreement between different PN-consistent, numerical, time-domain models. In an effort to guide future improvements to the model, we gauge the error in our 3PN model incurred by the different analytic approximations used to construct it. This model is useful for preliminary data analysis investigations and it could allow for a phenomenological hybrid that incorporates eccentricity into an inspiral-merger-ringdown model.