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

Building upon the statistical formulation for parameter estimation (PE) 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 in Europe and compare the expectation of PE of gravitational wave (GW) 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 correlation. In this specific detector setup, our observations indicate an enhancement in the precision of intrinsic parameter measurements as the correlation increases. This trend suggests that noise correlation may beneficially influence the accuracy of PE. 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 in the US, the uncertainty of extrinsic parameters is significantly reduced. This reduction is further amplified as the noise correlation increases. When the noise correlation exceeds a certain level, the collocated configuration outperforms the noncollocated configuration. For instance, when the 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 GW detectors.