Extended hierarchical search (EHS) algorithm for detection of gravitational waves from inspiraling compact binaries

TL;DR

The paper introduces an extended hierarchical search algorithm for gravitational wave detection that significantly reduces computational costs by incorporating an additional parameter hierarchy, enabling faster and more efficient data analysis.

Contribution

It extends the hierarchical search method by including the signal's time of arrival, further decreasing computational costs for gravitational wave detection.

Findings

Achieves approximately 100-fold reduction in computational cost.

Validates the method using 2PN order templates with LIGO I noise.

Demonstrates efficiency for single detector searches.

Abstract

Pattern matching techniques like matched filtering will be used for online extraction of gravitational wave signals buried inside detector noise. This involves cross correlating the detector output with hundreds of thousands of templates spanning a multi-dimensional parameter space, which is very expensive computationally. A faster implementation algorithm was devised by Mohanty and Dhurandhar [1996] using a hierarchy of templates over the mass parameters, which speeded up the procedure by about 25 to 30 times. We show that a further reduction in computational cost is possible if we extend the hierarchy paradigm to an extra parameter, namely, the time of arrival of the signal. In the first stage, the chirp waveform is cut-off at a relatively low frequency allowing the data to be coarsely sampled leading to cost saving in performing the FFTs. This is possible because most of the signal power is at low frequencies, and therefore the advantage due to hierarchy over masses is not compromised. Results are obtained for spin-less templates up to the second post-Newtonian (2PN) order for a single detector with LIGO I noise power spectral density. We estimate that the gain in computational cost over a flat search is about 100.