Geometrical Expression for the Angular Resolution of a Network of Gravitational-Wave Detectors

TL;DR

This paper derives general geometrical formulas for the angular resolution of any gravitational-wave detector network, highlighting how detector placement and sensitivities influence localization accuracy and proposing improvements with additional detectors.

Contribution

It introduces new geometrical expressions for GW network localization, accounting for unknown arrival times and detector sensitivities, and evaluates potential improvements with future detectors.

Findings

Angular resolution depends on areas formed by detector projections.

Adding new detectors significantly improves localization accuracy.

Current LIGO-Virgo network has poor resolution along certain planes.

Abstract

We report for the first time general geometrical expressions for the angular resolution of an arbitrary network of interferometric gravitational-wave (GW) detectors when the arrival-time of a GW is unknown. We show explicitly elements that decide the angular resolution of a GW detector network. In particular, we show the dependence of the angular resolution on areas formed by projections of pairs of detectors and how they are weighted by sensitivities of individual detectors. Numerical simulations are used to demonstrate the capabilities of the current GW detector network. We confirm that the angular resolution is poor along the plane formed by current LIGO-Virgo detectors. A factor of a few to more than ten fold improvement of the angular resolution can be achieved if the proposed new GW detectors LCGT or AIGO are added to the network. We also discuss the implications of our results for the design of a GW detector network, optimal localization methods for a given network, and electromagnetic follow-up observations.