Detecting gravitational waves from inspiraling binaries with a network of detectors : coherent versus coincident strategies

TL;DR

This paper compares the effectiveness of coherent and coincident detection strategies for gravitational waves from inspiraling binaries, concluding that the coherent approach offers significantly better detection performance despite higher computational costs.

Contribution

The study provides a detailed comparison of coherent versus coincident detection strategies, including analytical and numerical results, demonstrating the superiority of the coherent method for gravitational wave detection.

Findings

Coherent strategy has lower false dismissal rates than coincidence.

Analytical and numerical methods confirm the superiority of the coherent approach.

Coherent detection is more effective despite higher computational demands.

Abstract

We compare two strategies of multi-detector detection of compact binary inspiral signals, namely, the coincidence and the coherent. For simplicity we consider here two identical detectors having the same power spectral density of noise, that of initial LIGO, located in the same place and having the same orientation. We consider the cases of independent noise as well as that of correlated noise. The coincident strategy involves separately making two candidate event lists, one for each detector, and from these choosing those pairs of events from the two lists which lie within a suitable parameter window, which then are called as coincidence detections. The coherent strategy on the other hand involves combining the data phase coherently, so as to obtain a single network statistic which is then compared with a single threshold. Here we attempt to shed light on the question as to which strategy is better. We compare the performances of the two methods by plotting the Receiver Operating Characteristics (ROC) for the two strategies. Several of the results are obtained analytically in order to gain insight. Further we perform numerical simulations in order to determine certain parameters in the analytic formulae and thus obtain the final complete results. We consider here several cases from the relatively simple to the astrophysically more relevant in order to establish our results. The bottom line is that the coherent strategy although more computationally expensive in general than the coincidence strategy, is superior to the coincidence strategy - considerably less false dismissal probability for the same false alarm probability in the viable false alarm regime.