Deconvolving the information from an imperfect spherical gravitational wave antenna

We have studied the effects of imperfections in spherical gravitational wave antenna on our ability to properly interpret the data it will produce. The results of a numerical simulation are reported that quantitatively describe the systematic errors resulting from imperfections in various components of the antenna. In addition, the results of measurements on a room-temperature prototype are presented that verify it is possible to accurately deconvolve the data in practice.Comment: 5 pages, 2 figures, to be published in Europhysics Letter

Observing mergers of non-spinning black-hole binaries

Advances in the field of numerical relativity now make it possible to calculate the final, most powerful merger phase of binary black-hole coalescence for generic binaries. The state of the art has advanced well beyond the equal-mass case into the unequal-mass and spinning regions of parameter space. We present a study of the nonspinning portion of parameter space, primarily using an analytic waveform model tuned to available numerical data, with an emphasis on observational implications. We investigate the impact of varied mass ratio on merger signal-to-noise ratios (SNRs) for several detectors, and compare our results with expectations from the test-mass limit. We note a striking similarity of the waveform phasing of the merger waveform across the available mass ratios. Motivated by this, we calculate the match between our 1:1 (equal mass) and 4:1 mass-ratio waveforms during the merger as a function of location on the source sky, using a new formalism for the match that accounts for higher harmonics. This is an indicator of the amount of degeneracy in mass ratio for mergers of moderate-mass-ratio systems.Comment: 13 pages, 11 figures, submitted to Phys. Rev.

The mathematical theory of resonant transducers in a spherical gravity wave antenna

The rigoruos mathematical theory of the coupling and response of a spherical gravitational wave detector endowed with a set of resonant transducers is presented and developed. A perturbative series in ascending powers of the square root of the ratio of the resonator to the sphere mass is seen to be the key to the solution of the problem. General layouts of arbitrary numbers of transducers can be assessed, and a specific proposal (PHC), alternative to the highly symmetric TIGA of Merkowitz and Johnson, is described in detail. Frequency spectra of the coupled system are seen to be theoretically recovered in full agreement with experimental determinations.Comment: 31 pages, 7 figures, LaTeX2e, \usepackage{graphicx,deleq

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

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.Comment: 13 pages, 4 figures, LaTeX2e, IOP style, submitted to CQ

Detection strategies for scalar gravitational waves with interferometers and resonant spheres

We compute the response and the angular pattern function of an interferometer for a scalar component of gravitational radiation in Brans-Dicke theory. We examine the problem of detecting a stochastic background of scalar GWs and compute the scalar overlap reduction function in the correlation between an interferometer and the monopole mode of a resonant sphere. While the correlation between two interferometers is maximized taking them as close as possible, the interferometer-sphere correlation is maximized at a finite value of f*d, where `f' is the resonance frequency of the sphere and `d' the distance between the detectors. This defines an optimal resonance frequency of the sphere as a function of the distance. For the correlation between the Virgo interferometer located near Pisa and a sphere located in Frascati, near Rome, we find an optimal resonance frequency f=590 Hz. We also briefly discuss the difficulties in applying this analysis to the dilaton and moduli fields predicted by string theory.Comment: 26 pages, Latex, 4 Postscript figures. Various minor improvements, misprint in eqs. 42, 127, 138 corrected, references adde

The TIGA technique for detecting gravitational waves with a spherical antenna

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.Comment: 15 pages, 14 figures, submitted to Physical Review

Astrophysics from data analysis of spherical gravitational wave detectors

The direct detection of gravitational waves will provide valuable astrophysical information about many celestial objects. Also, it will be an important test to general relativity and other theories of gravitation. The gravitational wave detector SCHENBERG has recently undergone its first test run. It is expected to have its first scientific run soon. In this work the data analysis system of this spherical, resonant mass detector is tested through the simulation of the detection of gravitational waves generated during the inspiralling phase of a binary system. It is shown from the simulated data that it is not necessary to have all six transducers operational in order to determine the source's direction and the wave's amplitudes.Comment: 8 pages and 3 figure

Extracting galactic binary signals from the first round of Mock LISA Data Challenges

We report on the performance of an end-to-end Bayesian analysis pipeline for detecting and characterizing galactic binary signals in simulated LISA data. Our principal analysis tool is the Blocked-Annealed Metropolis Hasting (BAM) algorithm, which has been optimized to search for tens of thousands of overlapping signals across the LISA band. The BAM algorithm employs Bayesian model selection to determine the number of resolvable sources, and provides posterior distribution functions for all the model parameters. The BAM algorithm performed almost flawlessly on all the Round 1 Mock LISA Data Challenge data sets, including those with many highly overlapping sources. The only misses were later traced to a coding error that affected high frequency sources. In addition to the BAM algorithm we also successfully tested a Genetic Algorithm (GA), but only on data sets with isolated signals as the GA has yet to be optimized to handle large numbers of overlapping signals.Comment: 13 pages, 4 figures, submitted to Proceedings of GWDAW-11 (Berlin, Dec. '06

Charge Management for Gravitational Wave Observatories using UV LEDs

Accumulation of electrical charge on the end mirrors of gravitational wave observatories, such as the space-based LISA mission and ground-based LIGO detectors, can become a source of noise limiting the sensitivity of such detectors through electronic couplings to nearby surfaces. Torsion balances provide an ideal means for testing gravitational wave technologies due to their high sensitivity to small forces. Our torsion pendulum apparatus consists of a movable Au-coated Cu plate brought near a Au-coated Si plate pendulum suspended from a non-conducting quartz fiber. A UV LED located near the pendulum photoejects electrons from the surface, and a UV LED driven electron gun directs photoelectrons towards the pendulum surface. We have demonstrated both charging and discharging of the pendulum with equivalent charging rates of $\sim$$10^5 e/\mathrm{s}$, as well as spectral measurements of the pendulum charge resulting in a white noise level equivalent to $3\times10^5 e/\sqrt{Hz}$.Comment: 5 pages, submitted to PR