Less accurate but more efficient family of search templates for detection of gravitational waves from inspiraling compact binaries

Abstract

The network of interferometric detectors that is under construction at various locations on Earth is expected to start searching for gravitational waves in a few years. The number of search templates that is needed to be cross correlated with the noisy output of the detectors is a major issue since computing power capabilities are restricted. By choosing higher and higher post-Newtonian order expansions for the family of search templates we make sure that our filters are more accurate copies of the real waves that hit our detectors. However, this is not the only criterion for choosing a family of search templates. To make the process of detection as efficient as possible, one needs a family of templates with a relatively small number of members that manages to pick up any detectable signal with only a tiny reduction in signal-to-noise ratio. Evidently, one family is better than another if it accomplishes its goal with a smaller number of templates. Following the geometric language of Owen, we have studied the performance of the ${\mathrm{post}}^{1.5}\ensuremath{-}\mathrm{N}\mathrm{e}\mathrm{w}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{n}$ family of templates on detecting ${\mathrm{post}}^{2}\ensuremath{-}\mathrm{N}\mathrm{e}\mathrm{w}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{n}$ signals for binaries. Several technical issues arise from the fact that the two types of waveforms cannot be made to coincide by a suitable choice of parameters. In general, the parameter space of the signals is not identical with the parameter space of the templates, although in our case they are of the same dimension, and one has to take into account all such peculiarities before drawing any conclusion. An interesting result we have obtained is that the ${\mathrm{post}}^{1.5}\ensuremath{-}\mathrm{N}\mathrm{e}\mathrm{w}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{n}$ family of templates happens to be more economical for detecting ${\mathrm{post}}^{2}\ensuremath{-}\mathrm{N}\mathrm{e}\mathrm{w}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{n}$ signals than the perfectly accurate ${\mathrm{post}}^{2}\ensuremath{-}\mathrm{N}\mathrm{e}\mathrm{w}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{n}$ family of templates itself. The number of templates is reduced by $20\ensuremath{-}30%,$ depending on the acceptable level of reduction in signal-to-noise ratio due to discretization of the family of templates. This makes the ${\mathrm{post}}^{1.5}\ensuremath{-}\mathrm{N}\mathrm{e}\mathrm{w}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{n}$ family of templates more favorable for detecting gravitational waves from inspiraling, compact, nonspinning, binaries. Apart from this useful quantitative result, this study constitutes an application of the template-numbering technique, introduced by Owen, for families of templates that are not described by the same mathematical expression as the assumed signals. For example, this analysis will be very useful when constructing sufficiently simple templates for detecting precessing spinning binaries.