Variability of signal to noise ratio and the network analysis of gravitational wave burst signals

TL;DR

This paper addresses the challenge of detecting gravitational wave burst signals by proposing a network analysis method that penalizes waveforms with high signal-to-noise ratio variability, resolving the two detector paradox and improving detection performance.

Contribution

The authors introduce a physically motivated restriction based on SNR variability to improve network analysis of gravitational wave bursts, resolving the two detector paradox and enhancing detection statistics.

Findings

Penalizing high SNR variability waveforms resolves the two detector paradox.

The proposed method outperforms the global maximum likelihood statistic.

Applicable to any detector network regardless of configuration.

Abstract

The detection and estimation of gravitational wave burst signals, with {\em a priori} unknown polarization waveforms, requires the use of data from a network of detectors. For determining how the data from such a network should be combined, approaches based on the maximum likelihood principle have proven to be useful. The most straightforward among these uses the global maximum of the likelihood over the space of all waveforms as both the detection statistic and signal estimator. However, in the case of burst signals, a physically counterintuitive situation results: for two aligned detectors the statistic includes the cross-correlation of the detector outputs, as expected, but this term disappears even for an infinitesimal misalignment. This {\em two detector paradox} arises from the inclusion of improbable waveforms in the solution space of maximization. Such waveforms produce widely different responses in detectors that are closely aligned. We show that by penalizing waveforms that exhibit large signal-to-noise ratio (snr) variability, as the corresponding source is moved on the sky, a physically motivated restriction is obtained that (i) resolves the two detector paradox and (ii) leads to a better performing statistic than the global maximum of the likelihood. Waveforms with high snr variability turn out to be precisely the ones that are improbable in the sense mentioned above. The coherent network analysis method thus obtained can be applied to any network, irrespective of the number or the mutual alignment of detectors.