Optimal template placement for searches of gravitational waves from precessing compact binary coalescences

A new field of astronomy was opened up on Monday September 14th 2015, when the first detection of a Gravitational Wave was observed, GW150914. So far there have been no observations of gravitational waves produced from neutron-star--black-hole mergers. The observation of a neutron-star--black-hole merger would be significant because it would provide another way to study how compact binary coalescence gravitational wave signals relate to companion electromagnetic and neutrino emission signals. The difficulty in detecting precessing neutron-star--black-hole binaries (systems that allow for the full range of physical spin configurations) is that template banks for these precessing compact binary coalescence systems require many more templates than compact binary coalescence template banks that have been implemented previously. The purpose of the work presented in this thesis is to both improve the construction and efficiency of compact binary coalescence template banks. Template bank construction in the high dimensional precessing compact binary coalescence parameter spaces is complicated by the absence of a known analytic expression of mismatch inspiral-merger-ringdown metric. Previously, these restraints only permitted the use of the inefficient and slow to converge stochastic template placement algorithms. In this thesis, I constructed a template bank, the face-on-precessing template bank, over a subspace of this precessing neutron-star--black-hole template bank parameter space. I accomplished this by implementing a new algorithm for speeding up the convergence of the stochastic placement of these templates. I found that this subspace required 53 times more templates than the aligned-spin bank. Additionally, I developed an alternative template placement algorithm, the template nudging algorithm, to reposition compact binary coalescence templates into more effectual configurations in order to eliminate the effect of gridlines, artificially dense regions of the bank, that are characteristic of the hybrid template bank construction methods previously implemented in LIGO-Virgo compact binary coalescence searches. Finally, I developed a technique for constructing flat coordinates for compact binary coalescence template placements in high dimensional parameter spaces to ease in the construction of a fully precessing compact binary coalescence template bank