Lensing magnification: gravitational waves from coalescing stellar-mass binary black holes. (arXiv:2012.08381v3 [astro-ph.CO] UPDATED)

<a href="http://arxiv.org/find/astro-ph/1/au:+Shan_X/0/1/0/all/0/1">Xikai Shan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Wei_C/0/1/0/all/0/1">Chengliang Wei</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hu_B/0/1/0/all/0/1">Bin Hu</a>

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

$sigma(hat{d})/hat{d}simeq0.5%sim1%$. Beyond this observational horizon,

the estimation bias can not be ignored, and with the scatters

$sigma(hat{d})/hat{d} = 1%sim 15%$. 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 $sigma(hat{d})/hat{d} simeq 10%$ 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.

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

$sigma(hat{d})/hat{d}simeq0.5%sim1%$. Beyond this observational horizon,

the estimation bias can not be ignored, and with the scatters

$sigma(hat{d})/hat{d} = 1%sim 15%$. 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 $sigma(hat{d})/hat{d} simeq 10%$ 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.

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