Geometrical Expression of the Angular Resolution of a Network of Gravitational-Wave Detectors and Improved Localization Methods

TL;DR

This paper introduces a new geometrical framework for understanding the angular resolution of gravitational-wave detector networks, offering insights to enhance localization accuracy and proposing an improved null-stream localization method.

Contribution

It provides the first method-independent geometrical expression for the angular resolution of any GW detector network with unknown arrival times, advancing localization techniques.

Findings

Derived a geometrical expression for angular resolution.

Showed how to improve GW localization methods.

Demonstrated an enhancement to the null-stream localization technique.

Abstract

We report for the first time a method-independent geometrical expression for the angular resolution of an arbitrary network of interferometric gravitational wave (GW) detectors when the arrival-time of a GW is unknown. We discuss the implications of our results on how to improve angular resolutions of a GW network and on improvements of localization methods. An example of an improvement to the null-stream localization method for GWs of unknown waveforms is demonstrated.