Addressing the spin question in gravitational-wave searches: Waveform templates for inspiralling compact binaries with nonprecessing spins

Abstract

This paper presents a post-Newtonian (PN) template family of gravitational waveforms from inspiralling compact binaries with nonprecessing spins, where the spin effects are described by a single ``reduced-spin'' parameter. This template family, which reparametrizes all the spin-dependent PN terms in terms of the leading-order (1.5PN) spin-orbit coupling term in an approximate way, has very high overlaps (fitting factor $>0.99$) with nonprecessing binaries with arbitrary mass ratios and spins. We also show that this template family is ``effectual'' for the detection of a significant fraction of generic spinning binaries in the comparable-mass regime (${m}_{2}/{m}_{1}\ensuremath{\lesssim}10$), providing an attractive and feasible way of searching for gravitational waves from spinning low-mass binaries. We also show that the secular (nonoscillatory) spin-dependent effects in the phase evolution (which are taken into account by the nonprecessing templates) are more important than the oscillatory effects of precession in the comparable-mass (${m}_{1}\ensuremath{\simeq}{m}_{2}$) regime. Hence the effectualness of nonspinning templates is particularly poor in this case, as compared to non-precessing-spin templates. For the case of binary neutron stars observable by Advanced LIGO, even moderate spins (${\stackrel{^}{\mathbf{L}}}_{N}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}/{m}^{2}\ensuremath{\simeq}0.015--0.1$) will cause considerable mismatches ($\ensuremath{\sim}3%--25%$) with nonspinning templates. This is contrary to the expectation that neutron-star spins may not be relevant for gravitational wave detection.