Complete model of a spherical gravitational wave detector with capacitive transducers. Calibration and sensitivity optimization

TL;DR

This paper presents a comprehensive numerical model of a spherical gravitational wave detector with capacitive transducers, analyzing noise sources, sensitivity, and antenna patterns to optimize design and operation for future gravitational wave detection.

Contribution

It introduces a detailed electro-mechanical model including all noise sources and asymmetries, providing new insights for optimizing large spherical detectors and their calibration procedures.

Findings

Sensitivity analysis for a 30-ton spherical detector

Impact of transducer asymmetries on signal-to-noise ratio

Optimized antenna patterns for multiple transducer configurations

Abstract

We report the results of a detailed numerical analysis of a real resonant spherical gravitational wave antenna operating with six resonant two-mode capacitive transducers read out by superconducting quantum interference devices (SQUID) amplifiers. We derive a set of equations to describe the electro-mechanical dynamics of the detector. The model takes into account the effect of all the noise sources present in each transducer chain: the thermal noise associated with the mechanical resonators, the thermal noise from the superconducting impedance matching transformer, the back-action noise and the additive current noise of the SQUID amplifier. Asymmetries in the detector signal-to-noise ratio and bandwidth, coming from considering the transducers not as point-like objects but as sensor with physically defined geometry and dimension, are also investigated. We calculate the sensitivity for an ultracryogenic, 30 ton, 2 meter in diameter, spherical detector with optimal and non-optimal impedance matching of the electrical read-out scheme to the mechanical modes. The results of the analysis is useful not only to optimize existing smaller mass spherical detector like MiniGrail, in Leiden, but also as a technological guideline for future massive detectors. Furthermore we calculate the antenna patterns when the sphere operates with one, three and six resonators. The sky coverage for two detectors based in The Netherlands and Brasil and operating in coincidence is also estimated. Finally, we describe and numerically verify a calibration and filtering procedure useful for diagnostic and detection purposes in analogy with existing resonant bar detectors.