[论文解读] Back to post-Newtonian: parametrized-4.5PN TaylorF2 approximant(s) and tail effects to quartic nonlinear order from the effective one body formalism

Francesco Messina, Alessandro Nagar|arXiv (Cornell University)|Mar 23, 2017

High-pressure geophysics and materials被引用 1

一句话总结

本文从有效单体（EOB）形式出发，推导出一个参数化的4.5PN TaylorF2近似，包含高达5.5PN阶的高阶尾效应。结果表明，一个单一的4PN有效振幅参数即可准确复现IMRPhenomD的相位演化，直至最后稳定轨道，提示基于EOB的高阶近似可作为小质量双星搜寻中标准3.5PN TaylorF2的可行替代方案。

ABSTRACT

By post-Newtonian (PN) expanding the well-known, factorized and resummed, effective-one-body energy flux for circularized binaries we show that: (i) because of the presence of the resummed tail factor, the 4.5PN-accurate tails-of-tails-of-tails contribution to the energy flux recently computed by Marchand et al. [Class. Q. Grav. 33 (2016) 244003] is actually contained in the resummed expression; this is also the case of the the next-to-leading-order tail-induced spin-orbit term of Marsat et al. [Class. Q. Grav. 31 (2014) 025023]; (ii) in performing this expansion, we also obtain, for the first time, the explicit 3.5PN leading-order tail-induced spin-spin flux term; (iii) pushing the PN expansion of the (nonspinning) EOB flux up to 5.5PN order, we compute 4PN, 5PN and 5.5PN contributions to the energy flux, though in a form that explicitly depends on, currently unknown, 4PN and 5PN non-test-mass corrections to the factorized waveform amplitudes. Within this (parametrized) 4.5PN accuracy, we calculate the TaylorF2 approximant. Focusing for simplicity on the nonspinning case and using the numerical-relativity calibrated IMRPhenomD waveform model as benchmark, we demonstrate that it is possible to reproduce the derivative of the IMRPhenomD phase (say up to the frequency of the Schwarzschild last-stable-orbit) by flexing only a 4PN effective waveform amplitude parameter. A preliminary analysis also illustrates that similar results can be obtained for the spin-aligned case provided only the leading-order spin-orbit and spin-spin terms are kept. Our findings suggest that this kind of, EOB-derived, (parametrized), higher-order, PN approximants may serve as promising tools to construct Inspiral-Merger-Ringdown phenomenological models or even to replace the standardly used 3.5PN-accurate TaylorF2 approximant in searches of small-mass binaries.

研究动机与目标

• 将有效单体（EOB）能量通量的后牛顿（PN）展开扩展至5.5PN阶，包含重求和的尾效应。
• 从EOB形式中识别并提取此前未知的高阶尾诱导自旋-自旋和自旋-轨道通量贡献。
• 构建一个参数化的4.5PN TaylorF2近似，以准确模拟致密双星并合的相位演化。
• 检验单一4PN有效振幅参数是否可复现数值相对论校准的IMRPhenomD模型的相位。
• 探索基于EOB的高阶近似是否可作为引力波搜寻中标准3.5PN TaylorF2的可行替代方案。

提出的方法

• 对因子化、重求和的EOB能量通量进行后牛顿展开，包含重求和的尾因子以捕捉高阶尾效应。
• 首次从EOB框架中显式推导出3.5PN阶主导尾诱导自旋-自旋通量项。
• 将PN展开扩展至5.5PN阶，得到能量通量中4PN、5PN和5.5PN阶的贡献，但这些贡献依赖于目前未知的4PN和5PN非测试质量修正项。
• 利用扩展的EOB通量构建参数化的4.5PN TaylorF2近似，其中4PN阶的振幅参数可调。
• 在非自旋情况下，将参数化近似与IMRPhenomD波形模型进行基准对比，重点评估直至最后稳定轨道频率的相位精度。
• 初步将方法扩展至自旋对齐情形，仅使用主导阶自旋-轨道和自旋-自旋项以评估其通用性。

实验结果

研究问题

• RQ1 EOB形式能否复现Marchand等人近期计算的4.5PN阶尾尾尾通量贡献？
• RQ2 EOB框架中3.5PN阶主导尾诱导自旋-自旋通量项的显式形式为何？
• RQ3 在参数化4.5PN TaylorF2近似中，单一4PN有效振幅参数在多大程度上可复现IMRPhenomD模型的相位演化？
• RQ4 在自旋对齐情形下，仅使用主导阶自旋项是否也能实现类似的相位精度？
• RQ5 基于EOB的高阶PN近似是否可作为引力波搜寻中标准3.5PN TaylorF2的可行替代？

主要发现

• 重求和的EOB形式自然包含了能量通量中的4.5PN阶尾尾尾贡献，与近期独立计算结果一致。
• 首次从EOB框架中显式推导出3.5PN阶主导尾诱导自旋-自旋通量项。
• 5.5PN阶精度的EOB通量展开产生了4PN、5PN和5.5PN阶贡献，但这些贡献依赖于目前未知的4PN和5PN非测试质量修正项。
• 在参数化4.5PN TaylorF2近似中，单一4PN有效振幅参数足以复现IMRPhenomD的相位，直至施瓦茨希尔德最后稳定轨道的频率。
• 初步结果表明，当仅包含主导阶自旋-轨道和自旋-自旋项时，自旋对齐情形下也可实现类似的相位精度。
• 本研究表明，基于EOB的参数化高阶PN近似可能成为构建现象学旋进-并合- ringing-down模型的有效工具，或可替代标准3.5PN TaylorF2用于小质量双星的搜寻。