Constructive summation of the (2,2) quasi normal mode from a population of black holes

Abstract

The quasi normal modes (QNMs) associated with gravitational-wave signals from binary black hole (BBH) mergers can provide deep insight into the remnant's properties. Once design sensitivity is achieved, present ground-based gravitational wave interferometers could detect potentially hundreds of BBH signals in the coming years. For most, the ringdown phase will have a very weak signal-to-noise ratio (SNR). Signal summation techniques allow information extraction from the weak SNR ringdowns. We propose a method to constructively sum the (2,2) QNM from different BBH signals by synchronizing and rescaling them. The parameter space adopted to test the method is presently limited to mass ratio $q\leq3$, initially non-spinning black holes with face-on orientation. Moreover, since the synchronisation procedure fails for the weakest signals, we select all ringdowns with SNR above 2.6. Under these conditions, we show that for different BBH populations, 40 to 70% of all the potential detections could be used for the summation while still ensuring a summed SNR of $\sim$80% of the maximal achievable SNR (i.e. for ideally synchronized signals).