Potential impact of noise correlation in next-generation gravitational wave detectors

Building upon the statistical formulation for parameter estimation in the presence of correlated noise proposed by Cireddu et al., we present the initial study to incorporate the effects of correlated noise into the analyses of various detector designs' performance. We consider a two-L-shaped-detector configuration located in Europe and compare the expectation of parameter estimation of gravitational wave transients between noncollocated and hypothetical collocated configurations. In our study, we posit the existence of low-frequency correlated noise within the 5--10 Hz range for the collocated detector configuration, with a varying degree of correlation. In this specific detector setup, our observations indicate an enhancement in the precision of intrinsic parameter measurements as the degree of correlation increases. This trend suggests that higher degrees of noise correlation may beneficially influence the accuracy of parameter estimation. In particular, when the noise is highly correlated, the uncertainty on chirp mass decreases by up to 30%. The absence of an inter-European baseline does hinder the estimation of the extrinsic parameters. However, given a realistic global network with the additional detector located in the United States, the uncertainty of extrinsic parameters is significantly reduced. This reduction is further amplified as the degree of noise correlation increases. When the degree of noise correlation exceeds a certain level, the collocated configuration outperforms the noncollocated configuration. For instance, when the degree of correlation is high, the collocated configuration decreases the 90% credible area of sky location by up to 10% compared to the noncollocated configuration. We conclude that the impact of noise correlation is not trivial and can potentially alter both the quantitative and qualitative outcomes in detector performance. We therefore recommend the inclusion of noise correlation for a comprehensive assessment of the design of third-generation gravitational wave detectors.