Eccentric-orbit extreme-mass-ratio-inspiral radiation. II. 1PN correction to leading-logarithm and subleading-logarithm flux sequences and the entire perturbative 4PN flux
Eccentric-orbit extreme-mass-ratio-inspiral radiation. II. 1PN correction to leading-logarithm and subleading-logarithm flux sequences and the entire perturbative 4PN flux
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DOI：
10.1103/physrevd.102.104006
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发表时间：
2020-09
期刊：
影响因子：
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通讯作者：
Christopher Munna;C. Evans
中科院分区：
文献类型：
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作者：
Christopher Munna;C. Evans
在最近的一篇论文中，我们证明了对于偏心轨道极值质量比吸气，前导对数能量和角动量的解析形式后牛顿（PN）通量项（辐射到无穷远）可以在任意PN阶上由牛顿四极矩的傅立叶谱的和来确定。我们进一步表明，在对称质量比$\nu$中最低阶的相关次导对数PN序列的偏心依赖性的重要部分也源于牛顿四极矩。一旦这一部分被排除在外，剩下的偏心率依赖就更容易由黑洞摄动理论来确定了。在本文中，我们展示了整个前导对数级数的1PN修正序列，即出现在PN阶$x^{3k+1} \log^k(x)$和$x^{3k+5/2} \log^k(x)$（对于PN紧性参数$x$和整数$k\ge 0$）的项，在$\nu$中最低阶，如何由牛顿质量八极、牛顿电流四极和质量四极矩的1PN部分的傅立叶谱决定。我们还开发了一种推测的（但似是而非的）形式，用于对$\nu$中的二阶领先日志进行1PN校正。此外，与第一篇论文类似，我们表明，这些相同的源多极矩也产生了次导对数序列的1PN改正的非平凡部分，并且剩余的偏心依赖（在$\nu$中处于最低阶）可以更容易地使用黑洞摄动理论确定。我们使用这种方法分别确定能量和角动量的微扰（即$\nu$中的最低阶）4PN非对数项$\mathcal{R}_4(e_t)$和$\mathcal{Z}_4(e_t)$的整个解析偏心依赖。
In a recent paper we showed that for eccentric-orbit extreme-mass-ratio inspirals the analytic forms of the leading-logarithm energy and angular momentum post-Newtonian (PN) flux terms (radiated to infinity) can, to arbitrary PN order, be determined by sums over the Fourier spectrum of the Newtonian quadrupole moment. We further showed that an essential part of the eccentricity dependence of the related subleading-logarithm PN sequences, at lowest order in the symmetric mass ratio $\nu$, stems as well from the Newtonian quadrupole moment. Once that part is factored out, the remaining eccentricity dependence is more easily determined by black hole perturbation theory. In this paper we show how the sequences that are the 1PN corrections to the entire leading-logarithm series, namely terms that appear at PN orders $x^{3k+1} \log^k(x)$ and $x^{3k+5/2} \log^k(x)$ (for PN compactness parameter $x$ and integers $k\ge 0$), at lowest order in $\nu$, are determined by the Fourier spectra of the Newtonian mass octupole, Newtonian current quadrupole, and 1PN part of the mass quadrupole moments. We also develop a conjectured (but plausible) form for 1PN correction to the leading logs at second order in $\nu$. Further, in analogy to the first paper, we show that these same source multipole moments also yield nontrivial parts of the 1PN correction to the subleading-logarithm series, and that the remaining eccentricity dependence (at lowest order in $\nu$) can then more easily be determined using black hole perturbation theory. We use this method to determine the entire analytic eccentricity dependence of the perturbative (i.e., lowest order in $\nu$) 4PN non-log terms, $\mathcal{R}_4(e_t)$ and $\mathcal{Z}_4(e_t)$, for energy and angular momentum respectively.