Authors: James S. Graber
Date: Tue, 15 Mar 2005
Abstract: First, for each case to be tested, a specific target inspiral signal is selected for parameter extraction. In a future real analysis, the target signal would be a real signal actually observed by a gravitational wave detector such as LISA. In this study, however, the target signals are themselves simulations. Some cases were selected to resemble sources likely to be detected by LISA when it flies; others were selected to facilitate comparison with previous work using Fisher matrix techniques. Then, for each target inspiral signal, a grid search of the input parameter space is conducted to determine the set of input parameters that produce a simulated inspiral output signal compatible with the target. In this study, we consider four parameters: the two masses, the spin of the larger black hole, and the eccentricity of the orbit. Searching through this four dimensional parameter space requires that hundreds of possible input source parameter combinations be simulated for each target signal analyzed. For each input parameter combination, the detailed time history of the phase of the resulting inspiral is simulated and compared with the phase history of the target signal. The simulation, comparison, and grid search technique used in this study requires more work than the Fisher matrix technique used in most previous studies of this topic. However, this method yields a detailed map of the acceptable region of input parameter space, in contrast to the multidimensional ellipsoids of the Fisher matrix method. Nevertheless, the final results are in general agreement with those obtained previously by the Fisher matrix method, providing a partly independent confirmation of both results.
Authors: Carlos F. Sopuerta (1), Pengtao Sun (1 and 2), Pablo Laguna (1), Jinchao Xu (1) ((1) Penn State University, (2) Simon Fraser University)
Date: Tue, 26 Jul 2005 17:04:14 GMT (2475
Abstract: Extreme mass ratio binary systems, binaries involving stellar mass objects orbiting massive black holes, are considered to be a primary source of gravitational radiation to be detected by the space-based interferometer LISA. The numerical modelling of these binary systems is extremely challenging because the scales involved expand over several orders of magnitude. One needs to handle large wavelength scales comparable to the size of the massive black hole and, at the same time, to resolve the scales in the vicinity of the small companion where radiation reaction effects play a crucial role. Adaptive finite element methods, in which quantitative control of errors is achieved automatically by finite element mesh adaptivity based on posteriori error estimation, are a natural choice that has great potential for achieving the high level of adaptivity required in these simulations. To demonstrate this, we present the results of simulations of a toy model, consisting of a point-like source orbiting a black hole under the action of a scalar gravitational field.
Authors: K. Rajesh Nayak, S. Koshti, S. V. Dhurandhar, J-Y. Vinet
Date: Mon, 25 Jul 2005
Abstract: The joint NASA-ESA mission LISA relies crucially on the stability of the three spacecraft constellation. All three spacecraft are on heliocentric and weakly eccentric orbits forming a stable triangle. It has been shown that for certain spacecraft orbits, the arms keep constant distances to the first order in the eccentricities. However, exact orbitography shows the so-called ‘breathing modes’ of the arms where the arms slowly change their lengths over the time-scale of a year. In this paper we analyse the breathing modes (the flexing of the arms) with the help of the geodesic deviation equations to octupole order which are shown to be equivalent to higher order Clohessy-Wiltshire equations. We show that the flexing of the arms of LISA as given by the ‘exact’ solution of Keplerian orbits, which gives constant armlengths to the first order in eccentricity and whose maximum flexing amplitude is $\sim 115,000$ km, can be improved, by tilting the plane of the LISA triangle slightly from the proposed orientation of $60ˆ\circ$ with the ecliptic to obtain a maximum flexing amplitude of $\sim 48,000$ km, reducing it by a factor of $\sim 2.4$. The reduction factor is even larger if we consider the corresponding Doppler shifts, for which the reduction factor reaches almost a factor of 6. We solve the second order equations and obtain the general solution. We then use the general solution to establish the optimality of the solutions that we have found.
Authors: Frans Pretorius
Date: Mon, 4 Jul 2005
Abstract: We describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary systems for enough time to extract information about the orbit, merger and gravitational waves emitted during the event. As an example we show results from the evolution of a binary composed of two equal mass, non-spinning black holes, through a single plunge-orbit, merger and ring down. The resultant black hole is estimated to be a Kerr black hole with angular momentum parameter a~0.70. At present, lack of resolution far from the binary prevents an accurate estimate of the energy emitted, though a rough calculation suggests on the order of 5% of the initial rest mass of the system is radiated as gravitational waves during the final orbit and ringdown.
Authors: S. Mitra, S. V. Dhurandhar, L. S. Finn
Date: Mon, 4 Jul 2005
Abstract: Inspiraling compact binaries are promising sources of gravitational waves for ground and space-based laser interferometric detectors. The time-dependent signature of these sources in the detectors is a well-characterized function of a relatively small number of parameters; thus, the favored analysis technique makes use of matched filtering and maximum likelihood methods. Current analysis methodology samples the matched filter output at parameter values chosen so that the correlation between successive samples is 97% for which the filtered output is closely correlated. Here we describe a straightforward and practical way of using interpolation to take advantage of the correlation between the matched filter output associated with nearby points in the parameter space to significantly reduce the number of matched filter evaluations without sacrificing the efficiency with which real signals are recognized. Because the computational cost of the analysis is driven almost exclusively by the matched filter evaluations, this translates directly into an increase in computational efficiency, which in turn, translates into an increase in the size of the parameter space that can be analyzed and, thus, the science that can be accomplished with the data. As a demonstration we compare the present "dense sampling" analysis methodology with our proposed "interpolation" methodology, restricted to one dimension of the multi-dimensional analysis problem. We find that the interpolated search reduces by 25% the number of filter evaluations required by the dense search with 97% correlation to achieve the same efficiency of detection for an expected false alarm probability. Generalized to higher dimensional space of a generic binary including spins suggests an order of magnitude increase in computational efficiency.
© M. Vallisneri 2012 — last modified on 2010/01/29
Tantum in modicis, quantum in maximis