UR: Searching for Sub-threshold Gravitationally-Lensed Gravitational Waves

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Storm Colloms

University of Edinburgh

This guest post was written by Storm Colloms. Storm is a final year integrated master’s student at the University of Edinburgh, studying astrophysics. They were part of the 2021 LIGO SURF program at Caltech, working with Alvin Li and Professor Alan Weinstein.
(twitter: @chirpmass)

Over 90 gravitational wave events have been detected with LIGOVirgo from the merging of compact objects since their first detection in 2015. It is predicted that some of these gravitational waves could be lensed by lens masses such as galaxy clusters, curving the intervening spacetime between us and the gravitational wave source. While this is yet to have been observed, there are different pipelines which work in different ways to search for gravitational lensing in LIGO-Virgo data.

In this work I implemented a constraint on the one of the search pipelines for lensed images of gravitational waves, specifically searching for those whose amplitudes are reduced via lensing, making them sub-threshold images hidden amongst noise in the detectors (Figure 1). This constraint exploits a feature of lensed images: while the lensed images will appear to come from slightly different locations on the sky due to distortion by the lens, these separations between images are much much smaller than the current error on sky localisations of gravitational waves. Therefore, lensed images of gravitational waves can be approximated to come from the same place on the sky.

Figure 1: The time-domain strain (bottom) and corresponding signal-to-noise ratio (SNR) (top) of a lensed pair of gravitational waves. The first wave is amplified by the lensing, and surpasses the SNR threshold, causing it to be a ‘trigger’ in the search. However the second wave is de-amplified and does not reach the SNR threshold to make it a trigger, and is hence called ‘sub-threshold’.

The improvements I made to the pipeline aim to highlight in the results of the search sub-threshold lensed images which come from a similar area on the sky to a previously detected gravitational wave event. We can measure the sky location of an incoming gravitational wave from two values for each pair of operating detectors: the difference in arrival time of the gravitational wave at each detector and the difference in phase (Figure 2). I tested the updated pipeline on real data and observed changes in the ordering of the lensed image candidates in the results of the search, where the likelihood of a signal being a true lensed image is determined and listed in order of most to least likely.

With more testing on simulated lensed images, this work has a large potential to increase the detectability of sub-threshold lensed gravitational waves. Hopefully, it won’t be too long before we can dig these shrunken waves out of the data!

Figure 2: The sky localisation of a gravitational wave can be constrained by considering the difference in arrival time and arrival phase between a pair of detectors. For example, a wave arriving parallel to the line connecting 2 detectors (red) will be observed to take the maximum time (given by the distance between the detectors divided by the speed of light) to travel between the two locations with some phase difference, while a gravitational wave arriving perpendicular to the detectors (cyan) will arrive at both detectors in phase and at the same time. Illustration by Storm Colloms.

Featured image credit: Riccardo Buscicchio (University of Birmingham) via ligo.org

Astrobite edited by: Sumeet Kulkarni

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