Identifying type II strongly lensed gravitational-wave images in third-generation gravitational-wave detectors

Abstract

Strong gravitational lensing is a gravitational wave (GW) propagation effect that influences the inferred GW source parameters and the cosmological environment. Identifying strongly lensed GW images is challenging as waveform amplitude magnification is degenerate with a shift in the source intrinsic mass and redshift. However, even in the geometric-optics limit, type II strongly lensed images cannot be fully matched by type I (or unlensed) waveform templates, especially with large binary mass ratios and orbital inclination angles. We propose to use this mismatch to distinguish individual type II images. Using planned noise spectra of Cosmic Explorer, Einstein Telescope and LIGO Voyager, we show that a significant fraction of type II images can be distinguished from unlensed sources, given sufficient SNR (∼30). Incorporating models on GW source population and lens population, we predict that the yearly detection rate of lensed GW sources with detectable type II images is 172.2, 118.2 and 27.4 for CE, ET and LIGO Voyager, respectively. Among these detectable events, 33.1%, 7.3% and 0.22% will be distinguishable via their type II images with a log Bayes factor larger than 10. We conclude that such distinguishable events are likely to appear in the third-generation detector catalog; our strategy will significantly supplement existing strong lensing search strategies.

Inferring the Intermediate Mass Black Hole Number Density from Gravitational Wave Lensing Statistics

“…One has to build up detection statistics, e.g. the Bayes factor statistics from a large scale injection campaign [44] or the mismatch from the waveform [45], for identifying the events that belong to the lensed population. Besides being inflexible, this approach depends on a number of artificial choices, such as the choice of prior and the threshold of detection statistics for a lensed signal.…”

Characteristic features of gravitational wave lensing as probe of lens mass model

“…To understand how well a template matches a real signal, it is necessary to calculate uncertainties. We follow a similar approach to that of [42]. In particular, the likelihood of a given GW event can be determined assuming that after the subtraction of the waveform from the signal, the noise is Gaussian [39], i.e.…”

Microlensing of type II gravitational-wave macroimages

“…We have many examples of EM lensing observations (Ohanian 1974;Thorne 1982;Deguchi & Watson 1986;Wang et al 1996;Nakamura 1998;Takahashi & Nakamura 2003). Recently, searches for GW lensing using LIGO and Virgo data have also started (Hannuksela et al 2019;Li et al 2019a;McIsaac et al 2020;Pang et al 2020;Dai et al 2020;Liu et al 2020;Collaboration & Collaboration 2021), and many of the detection methodologies have been outlined in recent years (Cao et al 2014;Lai et al 2018;Christian et al 2018;Hannuksela et al 2019;Li et al 2019a;McIsaac et al 2020;Pang et al 2020;Hannuksela et al 2020;Dai et al 2020;Liu et al 2020;Wang et al 2021b;Lo & Magana Hernandez 2021;Janquart et al 2021a,b). If observed, lensed GWs could enable studies spanning the domains of fundamental physics, astrophysics, and cosmology Sereno et al (2011); Baker & Trodden (2017); Fan et al (2017); Liao et al (2017); Lai et al (2018); Liao (2019); Cao et al (2019); Li et al (2019b); Hou et al (2020); Mukherjee et al (2020a,b); Goyal et al (2020); Diego (2020); Hannuksela et al (2020);…”

“…The GW images would differ in arrival times, amplitudes and overall phases (Wang et al 1996;Haris et al 2018;Ezquiaga et al 2020;Dai et al 2020;Liu et al 2020;Wang et al 2021a;Lo & Magana Hernandez 2021;Janquart et al 2021b,a). The frequency evolution of the GW is still the same for these macroimages.…”