二元黑洞反冲的解剖：多极分析
Anatomy of the binary black hole recoil: A multipolar analysis
摘要：
我们提出了一个多极分析的引力反冲计算在最近的数值模拟的二进制黑洞（BH）合并，为不相等的质量和非零，非旋进自旋。我们表明，多极矩，并包括l=4是足够的，以准确地再现最终的反冲速度（在~2%），只有少数占主导地位的模式显着的贡献（在~5%）。我们描述了如何相对振幅，更重要的是，相对相位，这几种模式控制的方式，反冲建立在整个螺旋，合并，和振铃阶段。我们还发现，数值结果可以重现的“有效牛顿”的多极矩公式，通过取代牛顿公式中的径向分离的有效半径计算的数值数据。除了合并，数值结果再现的三个克尔准正常模式（QNM）的叠加。通过用克尔BH的基本QNM表示多极矩得到的解析公式能够解释每个模拟的“反踢”的发生和数量。最后，我们应用多极分析，以帮助解释显着的差异，平面和非平面踢等质量旋转黑洞的振幅。
英文摘要：
We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole (BH) coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within ~2%) and that only a few dominant modes contribute significantly to it (within ~5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical results can be reproduced by an ``effective Newtonian'' formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulae with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes (QNMs). Analytic formulae, obtained by expressing the multipole moments in terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and amount of ``anti-kick'' for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and non-planar kicks for equal-mass spinning black holes.
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