Noisy Spherical Resonant Detector of Gravitational Waves: Veto on the Longitudinal Part of the Signal

TL;DR

This paper develops a theoretical and numerical framework for a spherical gravitational wave detector with transducers, enabling vetoing of false signals by measuring the longitudinal component, and accounts for thermal noise effects.

Contribution

It introduces equations for a resonant sphere with multiple transducers using Lagrangian formalism and demonstrates a method to veto spurious signals by analyzing the longitudinal component.

Findings

Theoretical equations for a resonant sphere with transducers are derived.

Numerical simulations show the veto method can distinguish true signals from noise.

Thermal noise effects are incorporated into the simulation results.

Abstract

The equations of a resonant sphere in interaction with $N$ secondary radial oscillators (transducers) on its surface have been found in the context of Lagrangian formalism. It has been shown the possibility to exert a veto against spurious events measuring the longitudinal component of a signal. Numerical simulations has been performed, which take into account thermal noise between resonators and the sphere surface, for a particular configuration of the transducers.