Signal Space in the Triangular Network of Einstein Telescope

TL;DR

This paper analyzes the signal and null spaces in the Einstein Telescope's triangular configuration, showing that gravitational-wave information can be extracted efficiently from a reduced data set, simplifying analysis and noise estimation.

Contribution

It establishes the decomposition of the observation space into signal and null spaces and demonstrates the equivalence of Bayesian inference using the reduced signal space data.

Findings

Bayesian inference results are identical using signal space data and full data

Using the signal space reduces memory usage and speeds up likelihood evaluations

Null space allows unbiased noise property estimation

Abstract

The proposed third-generation gravitational-wave detectors Einstein Telescope will have a triangular design that consists of three colocated interferometers. Summing the strain outputs from the three interferometers will cancel any gravitational-wave signal and the resultant signal-free stream is known as null stream. The null stream is in a fixed subspace of the observation space of Einstein telescope where no gravitational-wave signal can exist. In this paper, we establish the decomposition of the observation space of Einstein Telescope into the signal space that contains all possible gravitational-wave signals and the null space that contains the null stream. We show that the results of Bayesian parameter estimation and model selection using the strain data in the signal space are identical to that using the full set of strain data. This implies that one could use a fraction of the strain data to extract all information of the source which reduces the memory usage and speeds up the likelihood evaluation. We also discuss the existence of a fixed null space in Einstein Telescope allows the unbiased estimation of the noise properties in the signal-free subspace.