The Relevance of Black-Hole Kicks in Gravitational-Wave Astronomy

Gravitational-wave observations provide a unique opportunity to study black holes. With a growing catalog of binary black hole mergers, one of the main challenges is to extract as much information as possible from each detection to better understand the underlying black hole population. Spin measurements, in particular, are crucial for probing the origin of these systems. However, such measurements require accurate waveform models and are limited by the finite signal-to-noise ratio of the detections. In addition, accurate predictions of black hole properties across different formation scenarios are essential for a robust interpretation of the origin of these sources. In this thesis, we demonstrate that one particular feature of binary black hole mergers, the recoil or "kick" velocity of the remnant, can provide valuable insight into this challenge. When two black holes merge, the anisotropic emission of gravitational waves carries away linear momentum, imparting a kick to the final black hole. This kick is imprinted in the gravitational-wave signal, particularly during the highly relativistic merger phase, where waveform models are least accurate. Because the kick is sensitive to subtle features in this regime, we show that it can be used to investigate waveform systematics across the parameter space. Furthermore, we demonstrate that the imprint of the kick gives more structure to the signal, enabling more informative parameter measurements. In particular, our study shows that kicks lead to more precise spin measurements in binary configurations that previously were thought to be uninformative. Additionally, we explore the astrophysical role of kicks by investigating their impact on hierarchical mergers in dense star clusters. We demonstrate that black holes formed through hierarchical mergers may not necessarily have a spin of 0.7 as previously predicted. Instead, when accounting for kick velocities, the spin distribution is skewed towards higher values. We show that higher-generation black holes can have spins that span a broad range of values, a ∈ (0.4, 1). By improving parameter measurements and refining the spin distribution of hierarchical mergers, we show that the kick velocity can help us gain deeper insight into the population of black holes.