Construction of a template family for the detection of gravitational waves from coalescing binaries

A discrete set of theoretical waveforms should be ready to use when searches for gravitational waves at the noisy output of the laser interferometric detectors that are presently under construction begin. In this paper we extend the method introduced by Sathyaprakash and Dhurandhar to construct such a family of templates, that was based on simple Newtonian signals, to ${\mathrm{post}}^2$-Newtonian signals that may be modulated due to spin-induced precession. More specifically, we show that if post-Newtonian terms of the phase are taken into account then the Newtonian templates turn out to be a rather inadequate type of search templates and other templates of higher post-Newtonian order should be used instead. This expands the number of parameters that the templates depend on, and, therefore, it leads to a required number of templates that is 2 orders of magnitude larger than it was previously thought, when precessionally modulation effects are ignored and a formidable number of templates when precessionally modulated signals are considered. From our analysis it becomes clear that a ${\mathrm{post}}^{1.5}$-Newtonian family of templates, with vanishing spin term, is a very promising family of search templates for signals coming from nonprecessing binaries. Furthermore, adding an extra oscillatory term in the phase of these ${\mathrm{post}}^{1.5}$-Newtonian templates would extend their detecting ability to signals coming from moderately precessing binaries; but, unfortunately, the number of templates then needed leaves no hope for an on-line search. This extended family of templates could be used more effectively in a hierarchical off-line search.