Ordering the confusion: a study of the impact of lens models on gravitational-wave strong lensing detection capabilities

When travelling from their source to the observer, gravitational waves can get deflected by massive objects along their travel path. For a massive lens and a good source-lens alignment, the wave undergoes strong lensing, leading to several images with the same frequency evolution. These images are separated in time, magnified, and can undergo an overall phase shift. Searches for strongly lensed gravitational waves look for events with similar masses, spins, and sky location and linked through so-called lensing parameters. However, the agreement between these quantities can also happen by chance. To reduce the overlap between background and foreground, one can include lensing models. When doing realistic searches, one does not know which model is the correct one to be used. Using an incorrect model could lead to the non-detection of genuinely lensed events. In this work, we investigate how one can reduce the false alarm probability when searching for strongly lensed events. We focus on the impact of the addition of a model for the lens density profile and investigate the effect of potential errors in the modelling. We show that the risks of false alarm are high without the addition of a lens model. We also show that slight variations in the profile of the lens model are tolerable, but a model with an incorrect assumption about the underlying lens population causes significant errors in the identification process. We also suggest some strategies to improve confidence in the detection of strongly lensed gravitational waves.