Towards a precision description of precessing black-hole-binaries

Abstract

There have been a number of gravitational wave events detected by the LIGO and Virgo detectors in recent years. Aside from simply detecting these signals we want to be able to make confident statements about the properties of the systems that emit them-- such as the masses and spins of the compact objects that make up the binaries that produce gravitational waves. Inferring these properties enables us to draw conclusions about the population of compact binaries in the universe and their formation mechanisms. To do this we compare the detected signals with theoretical predictions of the signals from sources with known properties. The aim of this thesis has been to provide a precision description of precessing black-hole-binary systems and the gravitational wave signals they produce. Due to the non-linearity of the Einstein equation, we can only obtain analytical solutions for the gravitational waves emitted by a source while the two black holes are inspiralling towards each other. Obtaining the waveforms during merger and ringdown requires numerical relativity. In order to explore the phenomenology of precessing signals we produced a catalogue of single spin numerical relativity simulations spanning the precessing parameter space up to mass ratio 8 and spin magnitude 0.8. The waveforms from these simulations can be used for direct comparisons with detected signals or for the development of waveform models. The catalogue presented here provides the basis of the tuned precessing model that forms the bulk of this thesis. We also further developed a method to reliably specify the orientation of a precessing binary at a given point in the waveform. For waveforms extracted from numerical relativity simulations this method also gives us a way of estimating the time shift between the waveform and dynamics data, thus giving us a way to specify the spins at the same point in the waveform. This is useful both for performing a direct comparison between a numerical waveform and a detected signal and for developing a tuned model of precessing systems based on numerical waveforms. It is too computationally expensive to perform the number of numerical simulations required to densely sample the parameter space of precessing binaries. We therefore produced a phenomenological model of the signal from precessing binaries. This model is based on the idea that it is possible to ``twist up'' a non-precessing waveform in order to get a precessing waveform. The model presented here focusses on modelling the precession effects rather than the non-precessing waveform. We used a model from post-Newtonian theory for the precession effects during inspiral and produced a phenomenological model for the effects during merger and ringdown. This phenomenological model has been tuned to the catalogue of numerical simulations described above