论文标题
镜头放大倍率：从融合恒星质量二进制黑洞的引力波
Lensing magnification: gravitational waves from coalescing stellar-mass binary black holes
论文作者
论文摘要
由于镜头，重力波（GWS）可能会放大或脱落。这种现象将基于匹配的滤波技术偏向距离估计。通过多球射线追踪技术，我们研究了GW放大效果和选择效果，并特别注意恒星质量的二元黑洞（BBHS）。 We find that, for the observed luminosity distance $\lesssim 3~\mathrm{Gpc}$, which is the aLIGO/Virgo observational horizon limit, the average magnification keeps as unity, namely unbiased estimation, with the relative distance uncertainty $σ(\hat{d})/\hat{d}\simeq0.5\%\sim1\%$.除了这个观察范围之外，估计偏差无法忽略，并且随着散布$σ（\ hat {d}）/\ hat {d} = 1 \％\ sim 15 \％$。此外，我们预测了爱因斯坦望远镜的这些数字。我们发现，对于观察到的光度距离$ \ Lessim 90〜 \ Mathrm {gpc} $，平均放大倍数与统一相近。爱因斯坦望远镜镜头造成的光度距离估计误差约为$σ（\ hat {d}）/\ hat {d} \ simeq 10 \％$，用于发光度距离$ \ gtrsim 25〜〜 \ mathrm {gpc} $。与Aligo/处女座案例不同，此相当大的误差不是由于选择效果。它纯粹来自不可避免地积累的镜头放大倍率。此外，我们研究了方向角度和BH质量分布模型的影响。我们发现结果很大程度上取决于这两个组成部分。
Gravitational waves (GWs) may be magnified or de-magnified due to lensing. This phenomenon will bias the distance estimation based on the matched filtering technique. Via the multi-sphere ray-tracing technique, we study the GW magnification effect and selection effect with particular attention to the stellar-mass binary black holes (BBHs). We find that, for the observed luminosity distance $\lesssim 3~\mathrm{Gpc}$, which is the aLIGO/Virgo observational horizon limit, the average magnification keeps as unity, namely unbiased estimation, with the relative distance uncertainty $σ(\hat{d})/\hat{d}\simeq0.5\%\sim1\%$. Beyond this observational horizon, the estimation bias can not be ignored, and with the scatters $σ(\hat{d})/\hat{d} = 1\%\sim 15\%$. Furthermore, we forecast these numbers for Einstein Telescope. We find that the average magnification keeps closely as unity for the observed luminosity distance $\lesssim 90~\mathrm{Gpc}$. The luminosity distance estimation error due to lensing for Einstein Telescope is about $σ(\hat{d})/\hat{d} \simeq 10\%$ for the luminosity distance $\gtrsim 25~\mathrm{Gpc}$. Unlike the aLIGO/Virgo case, this sizable error is not due to the selection effect. It purely comes from the unavoidably accumulated lensing magnification. Moreover, we investigated the effects of the orientation angle and the BH mass distribution models. We found that the results are strongly dependent on these two components.
