A binary tree approach to template placement for searches for gravitational waves from compact binary mergers

Abstract

We demonstrate a new geometric method for fast template placement for searches for gravitational waves from the inspiral, merger and ringdown of compact binaries. The method is based on a binary tree decomposition of the template bank parameter space into non-overlapping hypercubes. We use a numerical approximation of the signal overlap metric at the center of each hypercube to estimate the number of templates required to cover the hypercube and determine whether to further split the hypercube. As long as the expected number of templates in a given cube is greater than a given threshold, we split the cube along its longest edge according to the metric. When the expected number of templates in a given hypercube drops below this threshold, the splitting stops and a template is placed at the center of the hypercube. Using this method, we generate aligned-spin template banks covering the mass range suitable for a search of Advanced LIGO data. The aligned-spin bank required ~24 CPU-hours and produced 2 million templates. In general, we find that other methods, namely stochastic placement, produces a more strictly bounded loss in match between waveforms, with the same minimal match between waveforms requiring about twice as many templates with our proposed algorithm. Though we note that the average match is higher, which would lead to a higher detection efficiency. Our primary motivation is not to strictly minimize the number of templates with this algorithm, but rather to produce a bank with useful geometric properties in the physical parameter space coordinates. Such properties are useful for population modeling and parameter estimation.