| dc.description.abstract | Gravitational wave (GW) observations made with the LIGO and Virgo interferometers are transforming our understanding of the astrophysics of stellar origin compact objects (CO). The planned Laser Interferometer Space Antennae (LISA) will extend these observations to lower frequencies, thus higher mass systems and will have similar transformative potential. However, this potential can only be realised through the development of new waveform models and data analysis tools. This is the focus of this thesis.
The primary GW source discussed in this work are Extreme mass-ratio inspirals (EMRIs), the inspiral of a small CO of mass $1M_{\odot} - 100M_{\odot}$ into a super-massive black hole (SMBH) with mass $10^{(4-7)}M_{\odot}$. Through analytical and numerical means, we develop tools that model circular and equatorial adiabatic inspiral-transition-plunge trajectories and resultant EMRI waveforms, regardless of the central SMBH spin. From a Fisher matrix (FM) approach we show analytically and verify numerically that constraints on the spin parameter from LISA observations of near-extremal EMRIs surpass those of moderately spinning EMRIs by $\sim$ 3 orders of magnitude. Using the Cutler-Vallisneri (CV) formalism that is based off the FM, we investigate accuracy requirements of low eccentricity Schwarzschild based EMRI waveforms. We determine what level of numerical precision the components of the gravitational-self-force must be computed in order to not significantly bias parameter estimates. The CV formalism is then extended to account for an arbitrary number of waveforms with modelling errors and an astrophysical foreground and detector noise. The formalism is illustrated with simplified, yet realistic, scenarios appropriate to third-generation ground-based and the space-based detectors. In the final piece of this work, we present the impact that data gaps have on parameter estimation in the context of LISA. Data gaps could potentially introduce correlations amongst noise components in the frequency domain. The likelihood, signal-to-noise ratio and FM are generalised to take these correlations into account. We conclude by presenting a case study, exemplifying the detrimental effect of mis-modelling the noise as a stationary process rather than the correct non-stationary process due to the presence of data gaps. | en |
