title: Probing the general dynamics of compact binary systems with multi-band gravitational-wave observations
Creators: name: Linley, Jethro
Publisher: name: University of Glasgow
Year: 2022

description: There are two main goals of this thesis. The first is developing our so-called ‘downsampling’ procedure: an approximation technique for reproducing the likelihood function (in simulation) in relatively short time, of the sort of signals we expect to observe with the LISA Gravitational Wave (GW) detector, such as the inspiral part of binary black-hole mergers. The procedure is tested on a variety of signals and shown to provide highly accurate reproductions of the likelihood function up to a few thousand times faster than our estimates of convergence time considering the fastest type of analysis one could perform (frequency domain, stationary noise) using all the data points. The second goal is to understand the features and effectiveness of using multi-band GW data in data analysis, in particular on expansion of the signal model to include anticipated physical effects that modify the low-frequency part of the waveform, such as acceleration and relativistic time-delays. In addition, we extend the model to cover two well-known modified gravity theories, to test the assertion that multi-band GW data analysis will provide strong theory constraints. Since the degree to which the various time delays (which have their own parameter space) modify the waveform ranges from being negligible to significant and essential to model, we devise a formalism for splitting the time-delay parameter space into distinct regions that either fully model, ‘dimensionally reduce’, or neglect the time-delays from the model. The advantages of doing this are that one acquires posteriors that are considerably more informative, since the waveform is not being ‘over-modelled’. The posteriors we obtain confirm what one would expect to see (particularly in terms of parameter degeneracies) after considering and comparing the effects on the GW phase that arise from varying different combinations of parameters. In the fully modelled region, it is possible to recover well constrained time-delay parameters (i.e., the Keplerian orbital parameters, including supermassive black hole mass), but it is very difficult to derive general results about the expected behaviours of posteriors since the time-delay functions are complicated functions of time. The behaviour of posteriors of the ‘parameter reduced’ models are far easier to predict and understand, but the new parameters are relegated to nuisance parameters. The modified gravity theories we analyse are not well-constrained simply by multi-band observations alone; very high SNR appears to be the more important factor, but even then, different aspects of the nature of the waveform modifications (depending on the theory) can lead to significant bias, or render the effects too weak for GW astronomy to provide any useful constraints. By inspecting one-parameter families of posterior distributions (treating the posteriors as functions of some model parameter or signal property) and observing their structural evolution as that parameter is varied, we uncover and discuss some interesting features and behaviours of the distributions. Topics for future study are highlighted and include extensions and refinements of the waveform, population, and detector models, further studies of the Kepler parameter space division scheme, and posterior sampling issues to be addressed.