Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation

Abstract

Inspiraling compact binaries are promising sources of gravitational waves for ground and spacebased laser interferometric detectors. The time-dependent signature of these sources in the detectors is a well-characterized function of a relatively small number of parameters; thus, the favored analysis technique makes use of matched filtering and maximum likelihood methods. As the parameters that characterize the source model are varied so do the templates against which the detector data are compared in the matched filter. For small variations in the parameters, the output of the matched filter for the different templates are closely correlated. Current analysis methodology samples the matched filter output at parameter values chosen so that the correlation between successive samples is 97%. Correspondingly, with the additional information available with each successive template evaluation is, in a real sense, only 3% of that already provided by the nearby templates. The reason for such a dense coverage of parameter space is to minimize the chance that a real signal, near the detection threshold, will be missed by the parameter space sampling. Here we describe a straightforward and practical way of using interpolation to take advantage of the correlation between the matched filter output associated with nearby points in the parameter space to significantly reduce the number of matched filter evaluations without sacrificing the efficiency with which real signals are recognized. Because the computational cost of the analysis is driven almost exclusively the matched filter evaluations, a reduction in the number of templates evaluations translates directly into an increase in computational efficiency. Because the computational cost of the analysis is large, the increased efficiency translates also into an increase in the size of the parameter space that can be analyzed and, thus, the science that can be accomplished with the data. As a demonstration we compare the present “dense sampling” analysis methodology with our proposed “interpolation” methodology, restricted to one dimension of the multi-dimensional analysis problem. We find that the interpolated search reduces by 25% the number of filter evaluations required by the dense search with 97% correlation to achieve the same efficiency of detection for an expected false alarm probability. Generalized to the two dimensional space used in the computationally-limited current analyses this suggests a factor of two increase in computational efficiency; generalized to the full seven dimensional parameter space that characterizes the signal associated with an eccentric binary system of spinning neutron stars or black holes it suggests an order of magnitude increase in computational efficiency.