Effect of kick velocity on gravitational wave detection of binary black holes with space- and ground-based detectors

During the coalescence of binary black holes (BBHs), asymmetric gravitational wave (GW) emission imparts a kick velocity to the remnant black hole, affecting observed waveforms and parameter estimation. In this study, we investigate the impact of this effect on GW observations using space- and ground-based detectors. By applying Lorentz transformations, we analyze waveform modifications due to kick velocities. For space-based detectors, nearly 50% of detected signals require corrections, while for ground-based detectors, this fraction is below one-third. For Q3d population model, space-based detectors could observe kick effects in over 60% of massive BBH mergers, while in pop3 model, this fraction could drop to 3$\sim$4%. Third-generation ground-based detectors may detect kick effects in up to 16% of stellar-mass BBH mergers. Our findings highlight the importance of incorporating kick velocity effects into waveform modeling, enhancing GW signal interpretation and our understanding of BBH dynamics and astrophysical implications.