High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
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DOI：
10.1103/physrevd.76.124038
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发表时间：
2007-09
影响因子：
5
通讯作者：
M. Boyle;Duncan A. Brown;Lawrence E. Kidder;A. Mroué;H. Pfeiffer;M. Scheel;G. B. Cook;S. Teukolsky
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文献类型：
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作者：
M. Boyle;Duncan A. Brown;Lawrence E. Kidder;A. Mroué;H. Pfeiffer;M. Scheel;G. B. Cook;S. Teukolsky
对等质量双黑洞系统的15个轨道进行了数值模拟。从这些模拟的引力波形，涵盖了30多个周期，并在合并前结束约1.5个周期，从准圆零自旋后牛顿（PN）公式进行了比较。这些比较的累积相位不确定性约为0.05弧度，主要是由模拟中黑洞的小剩余自旋和小剩余轨道偏心率引起的影响。在运行早期将数值结果与PN波形匹配，在前15个周期内产生极好的一致性（在0.05弧度内），从而验证了数值模拟并建立了PN理论准确的状态。然而，在合并的最后15个周期中，通用时域泰勒近似建立了几个弧度的相位差。但是，显然是巧合，一个特定的后牛顿近似，泰勒T4在3.5PN阶，同意更好地与数值模拟，与累积相位差小于0.05弧度超过30个周期的波形。引力波振幅的数值模拟和后牛顿之间的比较也完成了，和协议依赖于后牛顿的振幅展开的顺序：振幅差约为6%-7%的零阶和变得更小的顺序。与先前已知的2.5PN振幅项相比，新推导的3.0PN振幅校正显著提高了一致性（在大部分运行中振幅差异<1%，在合并附近增加到4%）。
Numerical simulations of 15 orbits of an equal-mass binary black-hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasicircular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first ~15 cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, generic time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6%–7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly (<1% amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.