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Just like light, gravitational waves can undergo gravitational lensing by a galaxy on their path from source to observer, resulting in multiple images. Different types of images are possible, depending on how a wave passes through the potential of the “lens” galaxy. New work shows how, and under what circumstances, the individual image types can be identified. This opens up the possibility of unambiguously confirming that different observed gravitational wave signals are indeed the images of a lensed gravitational wave.

In a paper led by UU PhD candidate Justin Janquart which was recently published in The Astrophysical Journal Letters, researchers from the Institute for Gravitational and Subatomic Physics (GRASP), the Chinese ľ�ϸ���Ӱ�� of Hong Kong, and KU Leuven have demonstrated the possibility of identifying the individual image types of a lensed gravitational wave. When a wave gets lensed, the images receive different phase shifts depending on how they travel through the Fermat potential of the lensing galaxy: through a minimum, a saddle point, or a maximum. Until recently, it was only known how to measure relative phase shifts between images. As shown by the authors, if one takes into account “overtones” of the basic gravitational wave signal, then the absolute phase shifts can also be obtained, thus identifying the image types.

The images of a lensed gravitational wave would manifest themselves in observatories like LIGO, Virgo, and KAGRA as signals with the same basic shape but different magnifications, and  separated in time-of-arrival by seconds to months due to the different paths they take on their way to the detectors. Hence, a way to identify lensed images among the many gravitational wave signals that are being detected (currently there are 90 candidate detections, with hundreds more expected in the next few years) is to search for pairs of signals that “look alike”. However, signals can also resemble each other by coincidence, for example if they were emitted by the mergers of different binary black holes that happened to have similar masses and positions on the sky, which could then lead to a false positive. By contrast, the distinctive phase shifts that get added to the signal in the case of lensing would constitute smoking-gun evidence for the lensing scenario, as there is no other physical effect that could plausibly mimic this. 

Thus, the ability to identify individual image types by accessing gravitational-wave overtones would enable an unambiguous determination that lensing had indeed taken place. The authors also show that conversely, by combining information from the different images, the structure of the overtones can be probed in more detail than would be possible with single signals. This is expected to lead to novel tests of general relativity, as well as having an impact on black hole astrophysics, and on the use of gravitational waves in studying the evolution of the Universe as a whole.

Overtones of gravitational waves have already been by LIGO and Virgo, thanks to developed by Dr. Soumen Roy (then at IIT Gandhinagar, India), who recently joined GRASP as a postdoctoral researcher. Clear evidence for lensing of gravitational waves has not yet been found, but a led by former Bachelor student Renske Wierda has forecast that this is likely to happen in a few years’ time, after planned detector upgrades. 

The analysis of possible lensed gravitational-wave images is a computationally intensive effort. The simulations that led to the demonstration of image type identification were made feasible thanks to a that had previously been developed at GRASP, and whose significant computational speed-up compared to previous methods is likely to play a key role in the discovery of lensed gravitational waves in data from the LIGO, Virgo, and KAGRA detectors. 

Publication:
On the Identification of Individual Gravitational-wave Image Types of a Lensed System Using Higher-order Modes
Justin Janquart, Eungwang Seo, Otto A. Hannuksela, Tjonnie G.F. Li and Chris Van Den Broeck
December 2021, DOI: