标题： 重新审视黑洞踢动与多极不对称性的关系 显示英文标题

标题： Revisiting the relationship of black-hole kicks and multipole asymmetries

摘要： 黑洞双星中的进动是由于总自旋和轨道角动量之间的不对齐引起的。 这类系统的引力波辐射具有各向异性，这导致在分解为球谐函数基时，$\pm m$多极矩出现不对称性。 这种不对称的辐射可能导致合并后的黑洞残骸获得一个冲量，这是动量守恒的结果。 尽管冲量在天体物理上非常重要，但多极矩的不对称性对整体信号强度的贡献非常小，因此目前大多数引力波模型并未包含这些因素。 最近已经有一些努力将不对称性纳入波形模型中。 然而，这些努力主要集中在捕捉进动波形的更精细特征，而没有明确考虑残骸冲量速度。 在这里，我们填补了这一空白，并提出了一个关于以多极矩不对称性表示的线性动量通量的全面分析。 如预期的那样，需要较大的不对称性才能实现最大的冲量速度。 有趣的是，如果反称和对称的波形部分在合并时相互垂直，那么同样的大不对称性可能会导致可忽略的冲量速度。 我们还提出了一种现象学工具，用于测试包含多极矩不对称性的波形模型的性能。 这个工具帮助我们解决了IMRPhenomXO4a波形模型相位定义中的不一致问题。 显示英文摘要

摘要： Precession in black-hole binaries is caused by a misalignment between the total spin and the orbital angular momentum. The gravitational-wave emission of such systems is anisotropic, which leads to an asymmetry in the $\pm m$ multipoles when decomposed into a spherical harmonic basis. This asymmetric emission can impart a kick to the merger remnant black hole as a consequence of linear momentum conservation. Despite the astrophysical importance of kicks, multipole asymmetries contribute very little to the overall signal strength and, therefore, the majority of current gravitational-wave models do not include them. Recent efforts have been made to include asymmetries in waveform models. However, those efforts focus on capturing finer features of precessing waveforms without making explicit considerations of remnant kick velocities. Here we close that gap and present a comprehensive analysis of the linear momentum flux expressed in terms of multipole asymmetries. As expected, large asymmetries are needed to achieve the largest kick velocities. Interestingly, the same large asymmetries may lead to negligible kick velocities if the antisymmetric and symmetric waveform parts are perpendicular to each other around merger. We also present a phenomenological tool for testing the performance of waveform models with multipole asymmetries. This tool helped us to fix an inconsistency in the phase definition of the IMRPhenomXO4a waveform model.