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arXiv 2202.06334gr-qcastro-ph.HE
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II型透镜化双黑洞信号的探测与参数估计挑战

Detection and parameter estimation challenges of Type-II lensed binary black hole signals

Aditya Vijaykumar, Ajit Kumar Mehta, Apratim Ganguly

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12 pages, 8 figures, Accepted version
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AI总结：

本文研究强透镜引力波II型像的π/2相移畸变，证明其可用于高倾角双黑洞信号的识别，并揭示忽略该效应会导致参数估计显著偏差，强调未来需使用考虑透镜变形的模板。

摘要：

引力波信号的强透镜效应可以产生三种类型的像，分别记为I型、II型和III型，对应于透镜化像的透镜势的极小值、鞍点和极大值。特别是II型像会获得一个非平凡的π/2相移。根据信号形态的不同，例如当信号包含高阶谐波、进动、偏心率等贡献时，这一相移会在双黑洞信号的II型像所产生的应变中引入额外的畸变。观测到II型像的概率与强透镜效应本身的概率几乎相同，因此这些信号很可能在不久的将来被观测到。在这项工作中，我们研究了这些畸变在帮助从单次探测中识别II型信号方面的潜在适用性，以及如果使用未考虑该畸变的引力波模板来恢复信号时，参数推断中可能产生的系统性偏差。我们表明，透镜畸变将使我们能够自信地识别高度倾斜双星的II型像：在网络信噪比（SNR）ρ=20(50)时，对于倾角ι>5π/12(π/3)，单个II型像应当能够以ln贝叶斯因子lnB>2被识别。此外，基于我们在这些结果中观察到的趋势，我们预测在高信噪比（≳100）下，即使倾角低得多（∼π/6），单个II型像也能被识别。随后我们表明，忽略这些可识别II型像所产生的物理效应会显著偏置源参数的估计。因此，在未来，使用考虑透镜变形的模板对于从II型透镜化信号中提取源参数将是必要的。

英文摘要：

Strong lensing of {gravitational-wave signals} can produce three types of images, denoted as Type-I, Type-II and Type-III, corresponding to the minima, saddle and maxima of the lensing potential of the lensed images. Type-II images, in particular, receive a non-trivial phase shift of $π/2$. This phase shift can introduce additional distortions in the strains produced by the Type-II image of the binary black hole signals depending on the morphology of the signals, e.g., when they have contributions from higher harmonics, precession, eccentricity, etc. {The probability of observing Type-II images is nearly the same as that of strong lensing itself, and thus these signals are likely to be observed in the near future.} In this work, we investigate the potential applicability of these distortions in helping identify Type-II signals from a single detection and the systematic biases that could arise in the inference of parameters if they are recovered with gravitational-wave templates that do not take the distortion into account. We show that the lensing distortions will allow us to confidently identify the Type-II images for highly inclined binaries: at network signal-to-noise ratio (SNR) $ρ=20(50)$, individual Type-II images should be identifiable with ln Bayes factor $\ln \mathcal{B} > 2$ for inclinations $ ι> 5 π/12 (π/3) $. Furthermore, based on the trends we observe in these results, we predict that, at high SNRs ($\gtrsim 100$), individual Type-II images would be identifiable even when the inclination angle is much lower ($\sim π/6$). We then show that neglecting physical effects arising from these identifiable Type-II images can significantly bias the estimates of source parameters. Thus, in the future, using templates that take into account the lensing deformation would be necessary to extract source parameters from Type-II lensed signals.

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