Relative calibration of the LIGO and Virgo detectors using astrophysical events from their third observing run

We explore a method to assess the relative scale of the strain measured in the different detectors of the gravitational-wave network, using binary black hole (BBH) events detected during the third observing run (O3). The number of such signals is becoming sufficiently large to adopt a statistical approach based on the ratio of the signal-to-noise ratio (SNR) of the events between the detectors and the number of observed events in each detector. We demonstrate the principle of the method on simulations of BBH signals and we present its application to published O3 events reported by the Multi-Band Template Analysis (MBTA) pipeline. Constraints on the relative calibration of the gravitational-wave network for O3 are obtained at the level of ~3.5% between the two LIGO detectors and at the level of ~10% between the LIGO Livingston detector and the Virgo detector.