Hierarchical search strategy for the detection of gravitational waves from coalescing binaries.

Abstract

The detection of gravitational waves from coalescing compact binaries would be a computationally intensive process if a single bank of template wave forms (i.e., a one-step search) is used. We present, in this paper, a method which leads to a large reduction in the computational power required as compared to a one-step search. This method is a hierarchical search strategy involving two template banks. We show that the computational power required by such a two-step search, for an on-line detection of the one-parameter family of Newtonian signals, is $\frac{1}{8}$ of that required when an on-line one-step search is used. This reduction is achieved when signals having a strength of \ensuremath{\sim}8.8 are required to be detected with a probability of \ensuremath{\sim}0.95 and an average of one false event per year. We present approximate formulas for the detection probability of a signal and the false alarm probability. We investigate the effect of statistical correlations on these probabilities and incorporate these effects whereever possible. Our numerical results are specific to the noise power spectral density expected for the initial LIGO.