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arXiv 2501.04495gr-qcastro-ph.HE
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偏心率对双黑洞并合中动力学量及其相关性建模的影响

Eccentricity Effects on Modeling Dynamic Quantities and Their Correlations in Binary Black Hole Mergers

Hao Wang, Yuan Chuan Zou, Qing Wen Wu

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18 pages, 11 figures, comments are very welcome, ready to submit to PRD
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AI总结：

本文研究BBH并合中偏心率对辐射量振荡及峰值光度、遗迹质量、自旋、反冲速度等动力学量的影响，通过包络分析和多项式建模揭示更宽取值域及相关性约束。

摘要：

在本研究中，我们首先重新考察了双黑洞（BBH）并合中与初始偏心率相关的辐射量——能量、角动量和线动量——的振荡行为。通过从后牛顿视角在参数范围[0,2π]内改变平近点角l_0，我们建立了一个包络，用以概括这些辐射量的振荡。分析表明，尽管振荡受到特定初始条件l_0的影响，但偏心率的作用促成了该包络的形成。随后，我们对圆轨道中的峰值光度L_peak、遗迹质量M_rem、自旋α_rem和反冲速度V_rem等动力学量进行建模。通过多项式建模，我们探究了它们与质量比的关系及相互间的相关性。结果证明，这些多项式能够有效捕捉圆轨道中这些量之间的复杂关系和相关性。此外，我们综合并分析了圆轨道和偏心轨道的动力学量，揭示了在对应不同质量比的特定范围内的连续变化。这些变化受到初始偏心率连续变化及相关包络的影响，并可外推至其他质量比。通过对这些动力学量的最大值和最小值进行插值，我们揭示了在轨道型和非轨道型BBH并合中，相对于圆轨道显著更宽的取值域。这些取值域为动力学量、质量比及其相关性之间的关系提供了稳健约束。最后，我们讨论了将这种偏心率效应扩展到BBH的自旋对齐和自旋进动构型。

英文摘要：

In this study, we begin by revisiting the oscillatory behavior of radiative quantities-energy, angular momentum, and linear momentum-linked with initial eccentricities in binary black hole (BBH) mergers. By varying the mean anomaly $l_0$ across the parameter range $[0,2π]$ from a post-Newtonian perspective, we establish an envelope that encapsulates the oscillations of these radiative quantities. Our analysis reveals that while the oscillations are influenced by the specific initial condition $l_0$, the effect of eccentricity contributes to the formation of this envelope. Subsequently, we model dynamical quantities such as peak luminosity $L_{\text{peak}}$, remnant mass $M_{\text{rem}}$, spin $α_{\text{rem}}$, and recoil velocity $V_{\text{rem}}$ in circular orbits. Through polynomial modeling, we explore their relationships with mass ratios and correlations. Our results demonstrate the effectiveness of these polynomials in capturing the intricate relationships and correlations among these quantities in circular orbits. Furthermore, we synthesize and analyze dynamical quantities for both circular and eccentric orbits, revealing continuous variations within specific ranges corresponding to distinct mass ratios. These variations are influenced by continuous changes in initial eccentricity and the associated envelope, which can be extrapolated to encompass other mass ratios. By interpolating the maximum and minimum values of these dynamical quantities, we unveil considerably broad domains relative to circular orbits in both orbital and non-orbital BBH mergers. These domains provide robust constraints on the relationships between dynamical quantities, mass ratios, and their correlations. Finally, we discuss the extension of this eccentricity effect to spin alignment and spin precession configurations of BBHs.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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