Formalism for power spectral density estimation for non-identical and correlated noise using the null channel in Einstein Telescope

TL;DR

This paper develops a formalism to estimate the power spectral density of non-identical and correlated noise sources in the null channel of the Einstein Telescope, enhancing noise characterization in gravitational wave detectors.

Contribution

It introduces a novel formalism for noise spectral density estimation using the null channel in triangular gravitational wave detectors, accounting for correlated and non-identical noise sources.

Findings

Formalism is mathematically correct and consistent.

Validated with examples using known noise mixtures.

Highlights future integration into Bayesian estimation.

Abstract

Several proposed gravitational wave interferometers have a triangular configuration, such as the Einstein Telescope and the Laser Interferometer Space Antenna. For such a configuration one can construct a unique null channel insensitive to gravitational waves from all directions. We expand on earlier work and describe how to use the null channel formalism to estimate the power spectral density for the Einstein Telescope interferometers with non-identical as well as correlated noise sources. The formalism is illustrated with two examples in the context of the Einstein Telescope, with increasing degrees of complexity and realism. By using known mixtures of noises we show the formalism is mathematically correct and internally consistent. Finally we highlight future research needed to use this formalism as an ingredient for a Bayesian estimation framework.