Gravitational Wave Parameter Estimation through Post-Newtonian Templating and Markov Chain Monte Carlo

Abstract

In this thesis, we consider the problem of efficient parameter estimation for gravitational wave detectors such as LIGO (Laser Interferometer Gravitational-wave Observatory), both for electromagnetic follow-up of the signal and for learning about the set of gravitational wave generating systems around us. Specifically, we focus on signals from compact binary coalescences (CBCs), namely neutron star - neutron star (NSNS), and neutron star - black hole systems (NSBH). Given a gravitational wave candidate from one of these systems, we can consider possible vectors of parameters ~ 2 , the space of parameters, and attempt to find regions of high posterior probability, that of being the true vector of parameters given the data, in a technique known as template matching. However, a brute-force implementation requires searching over a 15 or 9 (in the absence of spin) dimensional , and using templates which are computationally expensive to generate using full numerical relativity. In this thesis, we consider a solution to this computational problem through focusing on the inspiral phase of the CBC, which can be templated by faster-generated Post-Newtonian (PN) expansions, and through the use of Markov chain Monte Carlo (MCMC) methods for efficiently traversing . We consider the effect of PN expansion order and source luminosity distance dL, on the posterior distributions of m1 and m2, the individual masses of the system, dL, the luminosity distance, and !0, the orbital frequency at the start of the data. We find that while the accuracy and precision of the dL and w0 posteriors are dependent on the luminosity distance of the source, the individual masses, m1 and m2, do not see the same effect on precision. We find that the total mass m is more accurately extracted than the individual masses for both NSNS and NSBH systems, and that the accuracy of the total mass depends on dL in the NSBH case. Most importantly, we find that both the accuracy and the precision of our MSMS results have little dependance on PN expansion order (especially when compared to the effect generated by dL), and thus we can further greatly increase the computational efficiency of this PN MCMC system by templating waveforms to lowest order during parameter searches while sacrificing comparatively little.