AI 中文总结
研究被孤立点质量透镜微透镜化的致密双星并合引力波，提出构建乘积模板库方法，利用几何光学近似和放大因子相位计算度量元素，增加时间延迟和相对放大率参数，构建约4000个模板库，有效减少失配，与最小匹配标准一致。
AI 中文摘要
来自恒星质量致密双星并合（CBCs）的引力波，若遇到史瓦西半径与引力波波长相当的透镜，将会被微透镜化，导致观测信号出现频率相关调制。在标准的CBCs模板搜索中忽略此类波动光学效应，可能导致信噪比损失高达30%。本文提出一种构建针对微透镜化引力波的模板库的方法。考虑被孤立点质量透镜微透镜化的CBCs，其频率相关放大因子有解析表达式。构建模板库时，使用几何光学近似，将微透镜化信号有效建模为重叠信号。鉴于匹配滤波对引力波信号相位敏感，利用放大因子的相位计算度量元素。通常的CBC参数空间增加两个额外参数：图像间的时间延迟（$t_d$）和相对放大率（$\mu_r$）。通过确定因波动光学效应拟合因子（FF）降至97%以下的透镜参数空间区域，构建包含约4000个模板的模板库，覆盖选定的透镜区域，与未透镜化CBCs参数值无关。结果表明，针对微透镜化CBCs的模板库近似为未透镜化CBC模板库与跨越透镜参数的模板库的笛卡尔积。通过使用未透镜化CBC模板库和乘积模板库评估拟合因子，证明了该方法的有效性，失配减少高达约10倍，且与构建模板库时规定的最小匹配标准0.97一致。
英文摘要
Gravitational waves (GW) from stellar mass compact binary coalescences (CBCs) that encounter a lens whose Schwarzschild radius is comparable to the GW wavelength, will be microlensed, leading to frequency-dependent modulations in the observed signal. Neglecting such wave-optics effects in standard templated searches for CBCs can result in signal-to-noise ratio (SNR) losses as large as 30%. Here, we present a prescription for constructing a template bank targeted at microlensed GWs. We consider CBCs microlensed by isolated point mass lenses, whose frequency-dependent amplification factor is known to have a closed-form analytical expression. However, to construct the template bank, it suffices to use the geometric optics approximation, effectively modeling the microlensed signal as overlapping signals. Moreover, given that matched filtering is mostly sensitive to the phase of the GW signal, we use the phase of the amplification factor to compute the metric elements. The usual CBC parameter space is appended by two extra parameters: (i) the time-delay ($t_d$) between images and (ii) the relative-magnification ($μ_r$). By identifying the region of the lensing parameter space where the fitting factor (FF) falls below 97% due to wave-optics effects, we construct a template bank consisting of ~4000 templates covering the selected lensing region, independent of the values of the unlensed CBCs' parameters. We show that the bank targeting microlensed CBCs is, to a very good approximation, a Cartesian product of the unlensed CBC bank and the bank spanning the lensing parameters. We demonstrate the effectiveness of our method by evaluating fitting factors using both the unlensed CBC bank and the product template bank, finding a reduction of up to a factor of ~10 in the mismatch, as well as consistency with the prescribed minimal match criterion of 0.97 used in the construction of the banks.
Comments17 pages, 9 figures
