Hierarchical search strategy for the detection of gravitational waves from coalescing binaries: Extension to post-Newtonian wave forms

TL;DR

This paper extends a hierarchical two-step search method for gravitational wave detection from coalescing binaries to more realistic post-Newtonian wave forms, significantly reducing computational costs while maintaining detection performance.

Contribution

It introduces an extension of the two-step hierarchical search to 1.5 post-Newtonian wave forms and provides formulas accounting for statistical correlations in detection probabilities.

Findings

Two-step search reduces computational power to 1/21 of one-step for advanced LIGO.

For initial LIGO, the reduction is about 1/27 in computational requirements.

Detection probabilities and false alarm rates are maintained with the hierarchical approach.

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. In an earlier paper we had presented a detection strategy, called a two step search}, that utilizes a hierarchy of template banks. It was shown that in the simple case of a family of Newtonian signals, an on-line two step search was about 8 times faster than an on-line one step search (for initial LIGO). In this paper we extend the two step search to the more realistic case of zero spin 1.5 post-Newtonian wave forms. We also present formulas for detection and false alarm probabilities which take statistical correlations into account. We find that for the case of a 1.5 post-Newtonian family of templates and signals, an on-line two step search requires about 1/21 the computing power that would be required for the corresponding on-line one step search. This reduction is achieved when signals having strength S = 10.34 are required to be detected with a probability of 0.95, at an average of one false event per year, and the noise power spectral density used is that of advanced LIGO. For initial LIGO, the reduction achieved in computing power is about 1/27 for S = 9.98 and the same probabilities for detection and false alarm as above.