Harmonic decomposition versus metric-based template banks in precessing gravitational-wave searches

Recent techniques have emerged to enable gravitational-wave searches for precessing compact binary systems, previously too computationally prohibitive. These techniques include generalized matched-filter statistic methods over restricted parameter regions and harmonic decomposition methods. We present a study of the relative template bank sizes and sensitivities of these two methods. We restrict ourselves to l = 2 and m = ± 2 mode, and use the fact that a signal from a precessing binary can be decomposed into five harmonics that form a power series. We construct a large fully precessing template bank with the metric approximation code \texttt{mbank} and five harmonic template banks using a stochastic placement method. We demonstrate that harmonic banks can be constructed with approximately 60,000 templates and still obtain fitting factors ≥ 0.9. We further discuss interpretation considerations when performing matched-filter calculation across a single fully precessing bank versus five harmonic banks.