Techniques for detecting gravitational waves with a spherical antenna

Abstract

We report the results of a theoretical and experimental study of a spherical gravitational wave antenna. We show that it is possible to understand the data from a spherical antenna with 6 radial resonant transducers attached to the surface in the truncated icosahedral arrangement. We find that the errors associated with small deviations from the ideal case are small compared to other sources of error, such as a finite signal-to-noise ratio. An in situ measurement technique is developed along with a general algorithm that describes a procedure for determining the direction of an external force acting on the antenna, including the force from a gravitational wave, using a combination of the transducer responses. The practicality of these techniques was verified on a room-temperature prototype antenna.

The coherent detection method of gravitational wave bursts for spherical antennas

“…Another method to reconstruct the direction of arrival GW by exploiting the (redundancy of the) five quadrupolar modes is based on linear algebra considerations [18]. A general metric perturbation in the transverce-traceless gauge is necessarily parametrized by a symmetric, traceless 3×3 matrix with zero determinant.…”

“…As the relevant equations have been already discussed in detail by several authors (see for instance [18,22,23]), we jump to the mathematical core of the problem, skipping introductory material and definitions that can be found in the literature. These equations hold for any number of sphere modes and transducers, although in the following subsections we will specify our choices for such numbers.…”

“…(13), the I k 's are easily found. This particular case is nothing but a rephrasing of the idea of mode channels of an ideal TIGA configuration, see [18][34].…”

“…This distinguishing feature not only determines its isotropic sensitivity and its capability to reconstruct the GW direction, but also opens the way to new opportunities, and issues, from the data analysis point of view. After the seminal work of Wagoner and Paik [12], where the basic features of the detector have been pointed out, more and more detailed sphere models and configurations have been studied by several authors [13,14,15,16,18,19,20,21,22]. In particular, various solutions have been proposed to the problems of the ideal transducers configuration [20], parameter reconstruction [13,19], and multidimensional data analysis [16].…”

The Confrontation between General Relativity and Experiment: A 1995 Update

“…Actually, the analysis assumes that the resonators are all identical, any deviations from this being eventually assessed by suitable methods [47,48]. The fundamental result links the spring deformations to the the GW amplitudes g (l,m) (t) by the following formula, expressed in terms of Laplace transforms -noted with a caret (ˆ):…”