Correlation of Gravitational Wave Background Noises and Statistical Loss for Angular Averaged Sensitivity Curves

TL;DR

This paper analyzes how correlated gravitational wave background noises affect the sensitivity of detector networks, deriving formulas to quantify statistical losses and suggesting optimal configurations for future interferometers.

Contribution

It provides simple expressions for statistical losses due to correlated noises in angular averaged sensitivity curves, considering network geometries and background noise strength.

Findings

Derived formulas for statistical loss depending on overlap reduction functions

Identified network geometries that minimize statistical losses for future detectors

Quantified the impact of background noise strength on detector sensitivity

Abstract

Gravitational wave backgrounds generate correlated noises to separated detectors. This correlation can induce statistical losses to actual detector networks, compared with idealized noise-independent networks. Assuming that the backgrounds are isotropic, we examine the statistical losses specifically for the angular averaged sensitivity curves, and derive simple expressions that depend on the overlap reduction functions and the strength of the background noises relative to the instrumental noises. For future triangular interferometers such as ET and LISA, we also discuss preferred network geometries to suppress the potential statistical losses.