Software and theoretical methods for gravitational-wave data analysis

The direct detection of gravitational waves has opened the era of gravitational-wave astronomy. The LIGO and Virgo detectors observed dozens of gravitational-wave signals from the coalescence of binary black holes and one confirmed binary neutron star merger hitherto. Moreover, as the detector sensitivity increases, gravitational-wave observations will become an everyday reality. The analysis of such signals through parameter estimation software programs allowed the LIGO-Virgo Collaboration to shed light on the properties of the compact sources and to test general relativity in the strong-field regime for the first time. Therefore, the importance to develop robust software for parameter estimation of gravitational waves cannot be understated. However, currently, only few software packages are available for gravitational-wave data analysis. In this thesis we present GWModel, a software package that we developed for parameter estimation of gravitational waves from compact binaries. By analysing a set of simulated events as well as public LIGO-Virgo data, we demonstrate that GWModel can infer the parameters of the compact sources observed by LIGO and Virgo, thus being a valid tool for the analysis of current and future ground-based detector data. Moreover, we investigate a specific aspect of gravitational waves: gravitational lensing. Gravitational lensing of gravitational waves is predicted by general relativity and might be first observed by ground-based detectors in the coming years. Besides magnifying the signal amplitude, lensing distorts the gravitational waveform by inducing characteristic signatures that might allow us to study the lens properties. Moreover, if not accounted for, the lensing magnification will bias the inferred source characteristics: the binaries will appear to be more massive and closer than they actually are. Hence, it is fundamental to develop software and data analysis techniques for gravitational-wave gravitational lensing. However, only few lensing systems can be solved analytically and a limited number of lensing configurations has been worked out in the context of lensing of gravitational waves. In this thesis we also present LensingGW, a software package that we developed to model lensing of gravitational waves from arbitrary lensing configurations. We demonstrate that LensingGW is an efficient tool to predict lensed gravitational waves and show that it can be used to study prospects of detection and the properties of such signals. In this respect, we find that LIGO-Virgo might in principle be able to distinguish lensing signatures at design sensitivity. We further provide theoretical methods to determine lensing magnifications and asses or rule out lensing for binary neutron star mergers. We show their application to simulated highly magnified gravitational waves and to the more massive coalescence consistent with a binary neutron star merger observed by LIGO-Virgo hitherto. We find no evidence in support of lensing for this detection.