小质量比极限下高偏心率束缚双星引力辐射的计算
Computing gravitational radiation from highly eccentric bound binaries in the small-mass-ratio limit
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中文总结 AI 辅助
本文提出频域方法修正，高效计算小质量比极限下高偏心率（至e=0.999）束缚双星的引力辐射，并揭示Peters-Mathews公式的系统性误差。
中文摘要 AI 辅助
描述束缚致密双星系统演化的精确强引力模型，为这类双星产生的引力辐射以及辐射反作用导致的演化提供了重要信息。极高偏心率极限（$e \to 1$）的建模具有挑战性：频域技术需要大量谐波才能准确描述该极限下的辐射，而时域技术由于系统的时间尺度较长，可能收敛缓慢。尽管如此，许多近期天体物理分析强调了理解该区域引力波发射的重要性，指出许多系统在成为可探测源的过程中可能经历$e \simeq 1$的阶段，并可能以显著偏心率进入探测器的灵敏频带。本文展示了如何调整频域方法，以在小质量比极限下有效处理高偏心率引力辐射的计算。该分析的关键部分是对频域Teukolsky方程源项的积分。我们研究了该积分在$e \to 1$时难以评估的特征，并探讨了规避这些困难的方法。我们发现了一个简单的修正，使得我们能够轻松计算引力波振幅以及相应的能量和角动量通量，直至偏心率$e = 0.99$；凭借耐心（和毅力），我们已推进到$e = 0.999$，尽管对于此类极端情况，数值精度似乎有所下降。有趣的是，我们发现广为人知且常用的Peters和Mathews经典公式存在系统性误差，该误差在相当宽的分离距离下依然存在。这对经历$e \simeq 1$演化的致密双星形成模型具有影响。
英文摘要
Precise strong-gravity models describing the evolution of bound compact binary systems provide important information about the gravitational radiation such binaries generate and how they evolve due to the radiation's backreaction. The limit of very high eccentricity, $e \to 1$, is challenging to model: frequency-domain techniques require many harmonics to accurately describe radiation in this limit, and time-domain techniques can be slow to converge due to the systems' long timescales. Many recent astrophysical analyses have nonetheless emphasized the importance of understanding gravitational-wave emission in this regime, highlighting the fact that many systems may evolve through $e \simeq 1$ en route to becoming detectable sources, and may enter the sensitive band of detectors with substantial eccentricity. In this paper, we show how to adapt frequency-domain methods for computing gravitational radiation in the small-mass-ratio limit to effectively handle high eccentricity. The key piece of this analysis is an integral over the source of the frequency-domain Teukolsky equation. We examine features of this integral that make it difficult to evaluate as $e \to 1$, and study methods to circumvent these difficulties. We find a simple fix which allows us to compute gravitational-wave amplitudes and the associated fluxes of energy and angular momentum with ease up to eccentricities $e = 0.99$; with patience (and stamina), we have pushed to $e = 0.999$, though numerical accuracy appears to degrade for such extreme cases. Interestingly, we find that the well-known and often used classic formulas of Peters and Mathews are subject to a systematic error which persists at quite wide separation. This has implications for models of compact binary formation which evolve through $e \simeq 1$.
发表机构
- Department of Physics, MIT（麻省理工学院物理系）
- MIT Kavli Institute, MIT（麻省理工学院卡弗里研究所）
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