We provide a comprehensive theoretical framework and a quantitative test of the method we recently proposed for processing data from a spherical detector with five or six transducers. Our algorithm is a trigger event generator performing a coherent analysis of the sphere channels. In order to test our pipeline we first built a detailed numerical model of the detector, including deviations from the ideal case such as quadrupole modes splitting, and non-identical transducer readout chains. This model, coupled with a Gaussian noise generator, has then been used to produce six time series, corresponding to the outputs of the six transducers attached to the sphere. We finally injected gravitational wave burst signals into the data stream, as well as bursts of non-gravitational origin in order to mimic the presence of non-Gaussian noise, and then processed the mock data. We report quantitative results for the detection efficiency versus false alarm rate and for the affordability of the reconstruction of the direction of arrival. In particular, the combination of the two direction reconstruction methods can reduce by a factor of 10 the number false alarms due to the non-Gaussian noise.
The principles and detection of gravitational waves by resonant antennas are briefly discussed. But the main purpose of this short note is to compare the two geometries of resonant antennas, the well-known cylindrical to the spherical type. Some features of a two sphere observatory are also discussed.
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.
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 …
We have calculated signal-to-noise ratios for eight spherical resonant-mass antennas interacting with gravitational radiation from inspiralling and coalescing binary neutron stars and from the dynamical and secular bar-mode instability of a rapidly rotating star. We find that by using technology that could be available in the next several years, spherical antennas can detect neutron star inspiral and coalescence at a distance of 15 Mpc and the dynamical bar-mode instability at a distance of 2 Mpc.
A spherical gravitational wave antenna is distinct from other types of gravitational wave antennas in that only a single detector is necessary to determine the direction and polarization of a gravitational wave. Zhou and Michelson showed that the inverse problem can be solved using the maximum likelihood method if the detector outputs are independent and have normally distributed noise with the same variance. This paper presents an analytic solution using only linear algebra that is found to produce identical results as the maximum likelihood method but with less computational burden. Applicat…
This paper analyses in quantitative detail the effect caused by a moving mass on a spherical gravitational wave detector. This applies to situations where heavy traffic or similar disturbances happen near the GW antenna. Such disturbances result in quadrupole tidal stresses in the antenna mass, and they therefore precisely fake a real gravitational signal. The study shows that there always are characteristic frequencies, depending on the motion of the external masses, at which the fake signals are most intense. It however appears that, even at those frequencies, fake signals should be orders o…
Internal friction effects are responsible for line widening of the resonance frequencies in spherical gravitational wave detectors, and result in exponentially damped oscillations of its eigenmodes with a decay time which is proportional to the quality factor of the mode and to its inverse frequency. We study the solutions to the equations of motion for a viscoelastic spherical GW detector based on various different assumptions about the material's constituent equations. Quality factor dependence on mode frequency is determined in each case, and a discussion of its applicability to actual dete…
Experimental projects using spherical antennas to detect gravitational waves are nowdays a concrete reality. The main purpose of this paper is to give a possible way of interpreting output data from such a system. Responses of the five fundamental quadrupole modes and of the six resonators in TIGA collocations are shown as a function of the incoming direction of the incident wave. Then, for a source lying in the galactic plane, sidereal time and galactic longitude dependence is given. Thus, once a candidate source of gravitational waves is considered, we can exactly predict the resonators' res…
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…
A general formalism is set up to analyse the response of an arbitrary solid elastic body to an arbitrary metric Gravitational Wave perturbation, which fully displays the details of the interaction antenna-wave. The formalism is applied to the spherical detector, whose sensitivity parameters are thereby scrutinised. A multimode transfer function is defined to study the amplitude sensitivity, and absorption cross sections are calculated for a general metric theory of GW physics. Their scaling properties are shown to be independent of the underlying theory, with interesting consequences for futur…
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 …
The detection of gravitational waves is a very active research field at the moment. In Brazil the gravitational wave detector is called Mario SCHENBERG. Due to its high sensitivity it is necessary to model mathematically all known noise sources so that digital filters can be developed that maximize the signal-to-noise ratio. One of the noise sources that must be considered are the disturbances caused by electromagnetic pulses due to lightning close to the experiment. Such disturbances may influence the vibrations of the antenna's normal modes and mask possible gravitational wave signals. In th…
We study the performance of a multidimensional matched filter as a follow-up module of the coherent method recently developed by two of us for the detection of gravitational wave bursts by spherical resonant detectors. We have tested this strategy on the same set of injections used for the coherent method and found that the matched filter sensibly improves the determination of relevant parameters as the arrival time, amplitude, central frequency and arrival direction of the signal. The matched filter also improves the false alarm rate, reducing it roughly by a factor of 3. The hierarchical str…
We investigate the gravitational collapse of a spherically symmetric, inhomogeneous star, which is described by a perfect fluid with heat flow and satisfies the equation of state $p=ρ/3$ at its center. In the process of the gravitational collapsing, the energy of the whole star is emitted into space. And the remaining spacetime is a Minkowski one without a remnant at the end of the process. For a star with a solar mass and solar radius, the total energy emitted is at the order of $10^{54}$ {\rm erg}, and the time-scale of the process is about $8s$. These are in the typical values for a gamma-r…
We study the response and cross sections for the absorption of GW energy in a Jordan-Brans-Dicke theory by a resonant mass detector shaped as a hollow sphere.
The construction of a massive (~ 40 ton) spherical antennas for gravitational wave astronomy has been proposed by a number of groups worldwide. Summed over all five quadrupole modes, the sphere has a direction-independent cross section, permitting full-sky coverage. Combined with its enhanced sensitivity due to its multi-nature and increased mass, sphereical detectors make ideal instruments for observational astronomy. Numerical calculations have shown that gravitational-wave signals from coalescing neutron star binaries and dynamic instabilities of rapidly rotating stars in the Virgo cluster …
We have developed a full model to simulate spherical detectors where all main sources of noise are considered. We have built a computer code for determining the source direction and the wave polarization (solution of the inverse problem) in real time acquisition. The digital filter used is a simple bandpass filter. The ``data'' used for testing our code was simulated, which considers both the source signal and detector noise. The detector noise includes the antenna thermal, back action, phase noise, series noise and thermal from transducer coupled masses. The simulated noise takes into account…
Motion sensing in a spherical GW detector requires a multiple set of transducers attached to its surface at suitable locations. If transducers are of the resonant type then their motion couples to that of the sphere and the joint dynamics of the system has to be properly understood before reliable conclusions can be drawn from its readout. In this paper we address the problem of the coupled motion of a sphere and a set of resonators attached to it at arbitrary points. A remarkably elegant and powerful scheme emerges from the general equations which shows how coupling takes place as a power ser…
The Brazilian spherical antenna (Schenberg) is planned to detect high frequency gravitational waves (GWs) ranging from 3.0 kHz to 3.4 kHz. There is a host of astrophysical sources capable of being detected by the Brazilian antenna, namely: core collapse in supernova events; (proto)neutron stars undergoing hydrodynamical instability; f-mode unstable neutron stars, caused by quakes and oscillations; excitation of the first quadrupole normal mode of 4-9 solar mass black holes; coalescence of neutron stars and/or black holes; exotic sources such as bosonic or strange matter stars rotating at 1.6 k…
We consider the case of highly noisy data coming from two different antennas, each data set containing a damped signal with the same frequency and decay factor but different amplitude, phase, starting point and noise. Formally, we treat the first data set as real numbers and the second one as purely imaginary and we add them together. This complex set of data is analyzed using Padé Approximations applied to its Z-transform. Complex conjugate poles are representative of the signal; other poles represent the noise and this property allows to identify the signal even in strong noise. The product …
Different studies show that dark matter of non-baryonic origin might exist. There have been experimental evidences that at least one form of dark matter has been detected through microlensing effects. This form of dark matter is named MACHOs (Massive Astrophysical Compact Halo Objects). The MACHO collaboration estimated that the masses of these objects are to be in the range 0.15-0.95 solar masses, where the most probable mass is of 0.5 solar masses. Some authors argue that MACHOs could be black holes, and that they could form binary systems, BHMACHO binaries. As is well known binary systems a…
We present the results of the first joint search for gravitational-wave bursts by the LIGO and GEO600 detectors. We search for bursts with characteristic central frequencies in the band 768 to 2048 Hz in the data acquired between the 22nd of February and the 23rd of March, 2005 (fourth LSC Science Run - S4). We discuss the inclusion of the GEO600 data in the Waveburst-CorrPower pipeline that first searches for coincident excess power events without taking into account differences in the antenna responses or strain sensitivities of the various detectors. We compare the performance of this pipel…
Recently Fuller & Shi proposed that the gravitational collapse of supermassive objects ($M \gtrsim 10^4M_\odot$) could be a cosmological source of $γ$-ray bursts (GRBs). The major advantage of their model is that supermassive object collapses are far more energetic than solar mass-scale compact mergers. Also, in their proposal the seeds of supermassive black holes (SMBHs) thus formed could give rise to the SMBHs observed at the center of many galaxies. We argue here that, besides the generation of GRBs, there could well occur a strong generation of gravitational waves (GWs) during the formatio…
Detecting gravitational wave bursts (characterised by short durations and poorly modelled waveforms) requires to have coincidences between several interferometric detectors in order to reject non-stationary noise events. As the wave amplitude seen in a detector depends on its location with respect to the source direction and as the signal to noise ratio of these bursts are expected to be low, coincidences between antennas may not be so likely. This paper investigates this question from a statistical point of view by using a simple model of a network of detectors; it also estimates the timing p…
The analysis of how a stochastic background of gravitational radiation interacts with a spherical detector is given in detail, which leads to explicit expressions for the system response functions, as well as for the cross-correlation matrix of different readout channels. It is shown that distinctive features of GW induced random detector excitations, relative to locally generated noise, are in practice insufficient to separate the signal from the noise by means of a single sphere, if prior knowledge on the GW spectral density is nil. The situation significantly improves when such previous kno…
We compare two advanced designs for gravitational-wave antennas in terms of their ability to detect two possible gravitational wave sources. Spherical, resonant mass antennas and interferometers incorporating resonant sideband extraction (RSE) were modeled using experimentally measurable parameters. The signal-to-noise ratio of each detector for a binary neutron star system and a rapidly rotating stellar core were calculated. For a range of plausible parameters we found that the advanced LIGO interferometer incorporating RSE gave higher signal-to-noise ratios than a spherical detector resonant…
We present the results of numerical simulations of the spherically symmetric gravitational collapse of supermassive stars (SMS). The collapse is studied using a general relativistic hydrodynamics code. The coupled system of Einstein and fluid equations is solved employing observer time coordinates, by foliating the spacetime by means of outgoing null hypersurfaces. The code contains an equation of state which includes effects due to radiation, electrons and baryons, and detailed microphysics to account for electron-positron pairs. In addition energy losses by thermal neutrino emission are incl…
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 t…
Following our result that for the final state of continued spherical gravitational collapse, the gravitational mass of the fluid, $M_f\to 0$, we show that for a physical fluid the eventual value of $2GM_f/R_f\to 1$ rather than $2GM_f/R_f <1$, indicating approach to a zero-mass black hole. We also indicate that as the final state would be approached, the curvature components tend to blow up, and the proper radial distance $l$ and the proper time $τ\to \infty$. This indicates that actually the singularity is never attained for the collapse of an isolated body. We also identify that, the final st…
We speculate that the universe is filled with stars composed of electromagnetic and dilaton fields which are the sources of the powerful gamma-ray bursts impinging upon us from all directions of the universe. We calculate soliton-like solutions of these fields and show that their energy can be converted into a relativistic plasma in an explosive way. As in classical detonation theory the conversion proceeds by a relativistic self-similar solution for a spherical detonation wave which extracts the energy from the scalar field via a plasma in the wave front.
We analyze two kinds of matched filters for data output of a spherical resonant GW detector. In order to filter the data of a real sphere, a strategy is proposed, firstly using an omnidirectional in-line filter, which is supposed to select periodograms with excitations, secondly by performing a directional filter on such selected periodograms, finding the wave arrival time, direction and polarization. We point out that, as the analytical simplifications occurring in the ideal 6 transducers TIGA sphere do not hold for a real sphere, using a 5 transducers configuration could be a more convenient…
We invoke the global properties of the actual GTR field equations for spherical collapse to directly show that the condition for formation of trapped surfaces, 2GM/R >1 is not allowed by GTR. And therefore all singularity theorems based on the assumption of formation of trapped surfaces are invalidated! Our conclusion is in perfect agreement with Einstein's intuitive idea that a Sch. like surface can not occur in reality. Further as singularity is approached R ->0, in order that 2GM/R <= 1, we must have M ->0! Harrison, et al. had also pointed out that collapse should come to a decisive end wi…
Stellar mass compact objects in short period orbits about a $10^{4.5}$--$10^{7.5}$ solar mass massive black hole (MBH) are thought to be a significant continuous-wave source of gravitational radiation for the ESA/NASA Laser Interferometer Space Antenna (LISA) gravitational wave detector. However, these extreme mass-ratio inspiral sources began in long-period, nearly parabolic orbits that have multiple close encounters with the MBH. The gravitational radiation emitted during these close encounters may be detectable by LISA as a gravitational wave burst if the characteristic passage timescale is…
We consider the problem of characterisation of burst sources detected with the Laser Interferometer Space Antenna (LISA) using the multi-modal nested sampling algorithm, MultiNest. We use MultiNest as a tool to search for modelled bursts from cosmic string cusps, and compute the Bayesian evidence associated with the cosmic string model. As an alternative burst model, we consider sine-Gaussian burst signals, and show how the evidence ratio can be used to choose between these two alternatives. We present results from an application of MultiNest to the last round of the Mock LISA Data Challenge, …
Extreme-mass-ratio bursts (EMRBs) are a class of potentially interesting gravitational wave signals. They are produced when a compact object passes through periapsis on a highly eccentric orbit about a much more massive object; we consider stellar mass objects orbiting the massive black holes (MBHs) found in galactic centres. Such a system may emit many EMRBs before eventually completing the inspiral. There are several nearby galaxies that could yield detectable bursts. For a space-borne interferometer like the Laser Interferometer Space Antenna, sensitivity is greatest for EMRBs from MBHs of …
