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arXiv 1409.6933gr-qc
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两体潮汐相互作用的引力自作用力修正和有效的单体形式

Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism

Donato Bini, Thibault Damour

备注：
38 pages, 5 figures, revtex style
发表信息：
Phys. Rev. D 90, 124037 (2014)
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摘要：

潮汐相互作用对致密双星系统的后期动力学有重大影响，而致密双星系统是即将到来的引力波探测器网络的主要目标。我们完善的潮汐相互作用的理论描述（迄今为止只知道第二后牛顿水平），我们最近开发的分析自作用力形式主义，极端质量比二元系统，几个潮汐不变量的计算。具体来说，我们计算，线性顺序的质量比和7.5 $^{\rm th}$后牛顿秩序，以下潮汐不变量：平方和立方的重力电四极潮汐张量，平方的重力磁四极潮汐张量，平方的重力电八极潮汐张量。我们的高精度分析结果相比，最近的数值自力潮汐数据Dolan等人。\cite{Dolan:2014pja}，值得注意的是，提供了一个分析理解的光环渐近行为，他们发现。我们转录我们的运动学潮汐不变的结果在更动态的显着有效的一个身体描述的潮汐相互作用能。通过结合，在一个协同的方式，分析和数值计算的结果，我们提供了简单，准确的分析表示的全球性，强场行为的重力电四极潮汐因子。一个惊人的发现是，后一个潮汐因子中的质量比线性部分在强场域中改变了符号，变成了负值（而它先前已知的第二个后牛顿近似总是正值）。然而，我们认为，这将超过补偿可能的快速增长，在强场域中，非线性的质量比贡献的潮汐因子。

英文摘要：

Tidal interactions have a significant influence on the late dynamics of compact binary systems, which constitute the prime targets of the upcoming network of gravitational-wave detectors. We refine the theoretical description of tidal interactions (hitherto known only to the second post-Newtonian level) by extending our recently developed analytic self-force formalism, for extreme mass-ratio binary systems, to the computation of several tidal invariants. Specifically, we compute, to linear order in the mass ratio and to the 7.5$^{\rm th}$ post-Newtonian order, the following tidal invariants: the square and the cube of the gravitoelectric quadrupolar tidal tensor, the square of the gravitomagnetic quadrupolar tidal tensor, and the square of the gravitoelectric octupolar tidal tensor. Our high-accuracy analytic results are compared to recent numerical self-force tidal data by Dolan et al. \cite{Dolan:2014pja}, and, notably, provide an analytic understanding of the light ring asymptotic behavior found by them. We transcribe our kinematical tidal-invariant results in the more dynamically significant effective one-body description of the tidal interaction energy. By combining, in a synergetic manner, analytical and numerical results, we provide simple, accurate analytic representations of the global, strong-field behavior of the gravitoelectric quadrupolar tidal factor. A striking finding is that the linear-in-mass-ratio piece in the latter tidal factor changes sign in the strong-field domain, to become negative (while its previously known second post-Newtonian approximant was always positive). We, however, argue that this will be more than compensated by a probable fast growth, in the strong-field domain, of the nonlinear-in-mass-ratio contributions in the tidal factor.

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