Abstract
ABSTRACT Gravitational waves, like light, can be gravitationally lensed by massive astrophysical objects such as galaxies and galaxy clusters. Strong gravitational-wave lensing, forecasted at a reasonable rate in ground-based gravitational-wave detectors such as Advanced LIGO, Advanced Virgo, and KAGRA, produces multiple images separated in time by minutes to months. These images appear as repeated events in the detectors: gravitational-wave pairs, triplets, or quadruplets with identical frequency evolution originating from the same sky location. To search for these images, we need to, in principle, analyse all viable combinations of individual events present in the gravitational-wave catalogues. An increasingly pressing problem is that the number of candidate pairs that we need to analyse grows rapidly with the increasing number of single-event detections. At design sensitivity, one may have as many as $\mathcal {O}(10^5)$ event pairs to consider. To meet the ever-increasing computational requirements, we develop a fast and precise Bayesian methodology to analyse strongly lensed event pairs, enabling future searches. The methodology works by replacing the prior used in the analysis of one strongly lensed gravitational-wave image by the posterior of another image; the computation is then further sped up by a pre-computed lookup table. We demonstrate how the methodology can be applied to any number of lensed images, enabling fast studies of strongly lensed quadruplets.
Highlights
Gravitational waves (GWs) result from cataclysmic events that distort the fabric of space and time
The Advanced LIGO (Aasi et al 2015) and Advanced Virgo (Acernese et al 2015) detectors have found dozens of GW signals emitted by the mergers of binary neutron stars or black holes (Abbott et al 2019, 2021)
The combination of speed and precision allowed by our method will likely become crucial in the future when we expect the number of detected individual events, each of which could, in principle, be a lensed image, to rise rapidly
Summary
Gravitational waves (GWs) result from cataclysmic events that distort the fabric of space and time. Strongly lensed events allow us to detect the same event multiple times at different detector orientations, effectively multiplying the number of detectors by the number of images to arrive at an enlarged (synthetic) detector network; this could be exploited to probe the full GW polarisation content, including alternative polarizations (Goyal et al 2021) Another prospective avenue is detecting intermediate-mass and primordial black holes through microlensing observations (Lai et al 2018; Jung & Shin 2019; Diego 2020; Oguri & Takahashi 2020). The first one is the posterior-overlap methodology, which performs a Gaussian kernel density estimation (KDE)-based fit on the single-event posterior density functions It tests if any given event pair is consistent with lensing by assessing the consistency of the posteriors (Haris et al 2018).
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