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

As the interferometers detecting gravitational waves are upgraded, improving their sensitivity, the probability of observing strong lensing increases. Once a detection is made, it will be critical to gain as much information as possible about the lensing object from these observations. 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 demonstrate the validity of this methodology using some illustrative examples adopting the idealized singular isothermal sphere and point-mass lens models. We take several simulated lensed signals, analyze them with GOLUM, and subject them to our methodology to recover both the model and its parameters. To demonstrate the methodology's stability, we show how the result varies with the number of samples used for a subset of these injections. 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, which was analyzed in detail as a potential lensing 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, though our posteriors are much wider than for the lensed injections, in line with the expectations for a nonlensed event. The methodology developed in this work is made available as part of the Gravelamps software package.