Effect of gravitational lensing on the population inference of binary black holes using gravitational-wave observations

Abstract

Gravitational lensing due to intervening matter distributions such as galaxies or clusters can (de)–magnify a gravitational-wave (GW) event, which can introduce a bias in the measurement of the astrophysical source’s properties. Hierarchical Bayesian inference on the catalog of detected GW events is performed to study the population properties of compact binaries, such as their mass and redshift distributions. Currently, the lensing probability is low and it is assumed that the events are not significantly (de)–magnified. A higher lensing probability (as expected for the next-generation detectors), can lead to biases in our estimation of the population hyper–parameters. In this work, we investigate the biases in population inference due to lensing, and develop a Bayesian hierarchical inference formalism for correct estimation of both the GW source population hyper–parameters, and the lenses.