Effectual template bank for the detection of gravitational waves from inspiralling compact binaries with generic spins

We report the construction of a three-dimensional template bank for the search for gravitational waves from inspiralling binaries consisting of spinning compact objects. The parameter space consists of two dimensions describing the mass parameters and one ``reduced-spin'' parameter, which describes the secular (nonprecessing) spin effects in the waveform. The template placement is based on an efficient stochastic algorithm and makes use of the semianalytical computation of a metric in the parameter space. We demonstrate that for ``low-mass'' (${m}_{1}+{m}_{2}\ensuremath{\lesssim}12{M}_{\ensuremath{\bigodot}}$) binaries, this template bank achieves effective fitting factors $\ensuremath{\sim}0.92--\text{ }0.99$ towards signals from generic spinning binaries in the advanced detector era over the entire parameter space of interest (including binary neutron stars, binary black holes, and black-hole neutron-star binaries). This provides a powerful and viable method for searching for gravitational waves from generic spinning low-mass compact binaries. Under the assumption that spin magnitudes of black holes (neutron stars) are uniformly distributed between 0--0.98 [0--0.4] and spin angles are isotropically distributed, the expected improvement in the average detection volume (at a fixed signal-to-noise-ratio threshold) of a search using this reduced-spin bank is $\ensuremath{\sim}20%--52%$, as compared to a search using a nonspinning bank.