Influence of Black Hole kicks on Gravitational Wave Ringdown

Abstract

Asymmetric emission of gravitational waves (GWs) during a binary black hole (BBH) merger leads to a recoil of the remnant black hole, commonly known as a black hole (BH) kick. The final stage of a BBH merger where the final BH which is in the perturbed state settles down by emitting gravitational radiation is known as ringdown. Using the linear black hole perturbation theory, ringdown is modeled as a linear superposition of damped sinusoids. Neglecting the e!ect of BH kicks in ringdown waveform models can introduce systematic biases in the inferred parameters. The recoil motion induces relativistic e!ects in the waveform, primarily Doppler shift and aberration: Doppler shift modifies the Quasi-normal mode frequencies, while aberration leads to mode mixing and a!ects the mode amplitudes. In this thesis, we investigate the systematic biases that arise when these e!ects are not incorporated in the ringdown model. Previous studies have primarily considered only the frequency shifts due to Doppler e!ects. Because the Doppler shift is degenerate with the remnant mass, neglecting this e!ect leads to biases in the estimated final mass. Aberration, on the other hand, introduces biases in the mode amplitudes and final spin through mode mixing. After incorporating these e!ects in the waveform model, we further study the prospects for detecting BH kicks using ringdown measurements alone. Due to the degeneracy between Doppler shift and the final mass, including only the Doppler e!ect does not allow an independent measurement of the kick, using only ringdown. We find that incorporating aberration does not significantly break this degeneracy, as the kick also couples to the mode amplitudes. Consequently, detecting kicks from ringdown observations alone remains challenging. Nevertheless, these e!ects must be accounted for to avoid systematic biases, particularly for future GW detectors where higher signal-to-noise ratios will make such biases more significant.