Determination of Lens Mass Density Profile from Strongly-Lensed Gravitational-Wave Signals

As the interferometers tasked with the detection of gravitational waves are upgraded and their sensitivity is improved, the probability of observing strong lensing will also increase. Once such a detection is made, it will be critical to gain as much information as possible about the lensing object from the observations. To that end, in this work we present a methodology to rapidly perform model selection between differing mass density profiles for strongly lensed gravitational wave signals, using the results of the fast strong lensing analysis pipeline GOLUM. We determine the validity of this methodology by taking several simulated injections of lensed signals that have been analysed using GOLUM and seek to recover the model used to create the injection as well as the parameters used in that model. Using these injections, we also demonstrate our method's stability depending on the number of samples used with the inclusion of every hundredth sample being the approximate limit at which stability is reached. In addition to the analysis of simulations, we also apply our methodology to the gravitational wave event pair GW191230--LGW200104, two events with similar frequency evolutions and sky locations, as expected of lensed pairs, which was analysed in detail as a potential lensed candidate but ultimately discarded when considering the full population and the uncertain nature of the second event. We find a preference for the singular isothermal sphere model over the point mass one, though our posteriors are much wider than for lensed injections, in line with the non-lensed status of the event. The methodology developed in this work is made available as part of the Gravelamps package of lens mass profile model selection software.