Time and Frequency Domain Modelling of Gravitational Waves

Abstract

Detections of gravitational waves from astrophysical sources such as binary black holes by LIGO and Virgo has attracted widespread attention from the scientific community, the media and the general public. Among these sources, precessing systems with a misalignment of the black hole spin and the orbital angular momentum are of particular interest because of the rich dynamics they offer. For aligned-spin systems, the energy and momentum emitted above the orbital plane is symmetric to the emission below the plane. For mis-aligned systems, however, this is not the case and amplitude and phase modulations will appear in the waveform itself. Even when transformed to a coprecessing frame that follows the orbital angular momentum direction, such asymmetric features are clearly visible. When the signal is decomposed into modes of spin-weighted spherical harmonics, we can discuss the asymmetry between the negative and positive m-modes by defining an anti-symmetric waveform, which is neglected in most waveform models used in gravitational wave data analysis to date. Mode asymmetry is therefore a hot topic in the gravitational wave community, with many questions still to be answered. In this thesis, we analyse the phenomenology of the anti-symmetric waveform for several binary black hole configurations and relate it to the physics of remnant black hole recoil. We find strong correlations between the intrinsic system parameters and the amplitude and phase of the anti-symmetric waveform, and hence the magnitude of the out-of-plane recoil velocity.