论文标题

偏心二进制黑洞:比较数值相对论和小质量比率扰动理论

Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory

论文作者

Ramos-Buades, Antoni, van de Meent, Maarten, Pfeiffer, Harald P., Rüter, Hannes R., Scheel, Mark A., Boyle, Michael, Kidder, Lawrence E.

论文摘要

不等的质量二进制黑洞系统的建模对于从这些系统中检测和估计参数非常重要。数值相对论(NR)非常适合具有可比组件质量的研究系统,$ m_1 \ sim m_2 $,而小质量比(SMR)扰动理论适用于二进制文件,其中$ q = m_2/m_1 << 1 $。这项工作研究了NR和SMR的适用性,这是偏心非旋转二进制黑洞的质量比的函数。我们生产$ 52 $ NR模拟,质量比在$ 1:10 $和$ 1:1 $的质量比和最初的偏心率最高$ 0.7 $。从这些中,我们提取了重力波能和角动量通量和periastron的进步等数量,并评估其准确性。为了促进比较,我们开发了在NR和SMR Inspiral Evolation的怪异二进制黑洞之间绘制的工具。我们得出了牛顿后的精确关系,不同的偏心率定义。基于这些分析,我们基于重力辐射的(2,2)模板引入了一个新的偏心率定义,该定义降低了牛顿对牛顿极限的偏心率的定义。从NR模拟和SMR结果之间的比较,我们量化了未知的临近阶级SMR对重力能量和角动量通量的贡献,以及periastron的前进。我们表明,在可比的质量制度中,这些贡献是亚辅助的,高阶SMR贡献可以忽略不计。

The modelling of unequal mass binary black hole systems is of high importance to detect and estimate parameters from these systems. Numerical relativity (NR) is well suited to study systems with comparable component masses, $m_1\sim m_2$, whereas small mass ratio (SMR) perturbation theory applies to binaries where $q=m_2/m_1<< 1$. This work investigates the applicability for NR and SMR as a function of mass ratio for eccentric non-spinning binary black holes. We produce $52$ NR simulations with mass ratios between $1:10$ and $1:1$ and initial eccentricities up to $0.7$. From these we extract quantities like gravitational wave energy and angular momentum fluxes and periastron advance, and assess their accuracy. To facilitate comparison, we develop tools to map between NR and SMR inspiral evolutions of eccentric binary black holes. We derive post-Newtonian accurate relations between different definitions of eccentricity. Based on these analyses, we introduce a new definition of eccentricity based on the (2,2)-mode of the gravitational radiation, which reduces to the Newtonian definition of eccentricity in the Newtonian limit. From the comparison between NR simulations and SMR results, we quantify the unknown next-to-leading order SMR contributions to the gravitational energy and angular momentum fluxes, and periastron advance. We show that in the comparable mass regime these contributions are subdominant and higher order SMR contributions are negligible.

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