Errors on the inverse problem solution for a noisy spherical gravitational wave antenna

TL;DR

This paper analyzes the errors in determining the direction and polarization of gravitational waves using a noisy spherical antenna, highlighting the error characteristics and potential for isotropic sensitivity.

Contribution

It derives the error estimates for direction and polarization measurements, demonstrating their independence from source direction and exploring polarization determination capabilities.

Findings

Solid angle error is direction independent.

Uncertainty on wave amplitude is direction independent.

Potential for isotropic polarization sensitivity.

Abstract

A single spherical antenna is capable of measuring the direction and polarization of a gravitational wave. It is possible to solve the inverse problem using only linear algebra even in the presence of noise. The simplicity of this solution enables one to explore the error on the solution using standard techniques. In this paper we derive the error on the direction and polarization measurements of a gravitational wave. We show that the solid angle error and the uncertainty on the wave amplitude are direction independent. We also discuss the possibility of determining the polarization amplitudes with isotropic sensitivity for any given gravitational wave source.