Performance of Newtonian filters in detecting gravitational waves from coalescing binaries

Abstract

As coalescing binary systems are one of the most promising sources of gravitational waves, it becomes necessary to devise efficient detection strategies. The detection strategy should be efficient enough so as not to miss any detectable signal and at the same time minimize the false alarm probability. The technique of matched filtering used in the detection of gravitational waves from coalescing binaries relies on the construction of accurate templates. Until recently filters modeled on the quadrupole or the Newtonian approximation were deemed sufficient. Such filters or templates have, in addition to the amplitude, three parameters which are the chirp mass, the time of arrival, and the initial phase. Recently it was shown that post-Newtonian effects contribute to a secular growth in the phase difference between the actual signal and its corresponding Newtonian template. This affects the very foundation of the technique of matched filtering, which relies on the correlation of the signal with the filter and hence is extremely sensitive to errors in phase. In this paper we investigate the possibility of compensating for the phase difference caused by the post-Newtonian terms by allowing for a shift in the Newtonian filter parameters. The analysis is carried out for cases where one of the components is a black hole and the other a neutron star or a small black hole. The alternative strategy would be to increase the number of parameters of the lattice of filters which might prove to be prohibitive in terms of computing power. We find that Newtonian filters perform reasonably for the purpose of detecting the presence of the signal for both the initial and the advanced LIGO detectors. As such a strategy may be used for a preliminary analysis a lower threshold can be used.