Optimal Strategies for Sinusoidal Signal Detection

We derive and study optimal and nearly-optimal strategies for the detection of sinusoidal signals hidden in additive (Gaussian and non-Gaussian) noise. Such strategies are an essential part of algorithms for the detection of the gravitational Continuous Wave (CW) signals produced by pulsars. Optimal strategies are derived for the case where the signal phase is not known and the product of the signal frequency and the observation time is non-integral.Comment: 18 pages, REVTEX4, 7 figures, 2 table

Data analysis strategies for the detection of gravitational waves in non-Gaussian noise

In order to analyze data produced by the kilometer-scale gravitational wave detectors that will begin operation early next century, one needs to develop robust statistical tools capable of extracting weak signals from the detector noise. This noise will likely have non-stationary and non-Gaussian components. To facilitate the construction of robust detection techniques, I present a simple two-component noise model that consists of a background of Gaussian noise as well as stochastic noise bursts. The optimal detection statistic obtained for such a noise model incorporates a natural veto which suppresses spurious events that would be caused by the noise bursts. When two detectors are present, I show that the optimal statistic for the non-Gaussian noise model can be approximated by a simple coincidence detection strategy. For simulated detector noise containing noise bursts, I compare the operating characteristics of (i) a locally optimal detection statistic (which has nearly-optimal behavior for small signal amplitudes) for the non-Gaussian noise model, (ii) a standard coincidence-style detection strategy, and (iii) the optimal statistic for Gaussian noise.Comment: 5 pages RevTeX, 4 figure

Estimation of parameters of gravitational waves from coalescing binaries

In this paper we deal with the measurement of the parameters of the gravitational wave signal emitted by a coalescing binary signal. We present the results of Monte Carlo simulations carried out for the case of the initial LIGO, incorporating the first post-Newtonian corrections into the waveform. Using the parameters so determined, we estimate the direction to the source. We stress the use of the time-of-coalescence rather than the time-of-arrival of the signal to determine the direction of the source. We show that this can considerably reduce the errors in the determination of the direction of the source.Comment: 5 pages, REVTEX, 2 figures (bundled via uufiles command along with this paper) submitted to Praman

Angular momentum effects in Michelson-Morley type experiments

The effect of the angular momentum density of a gravitational source on the times of flight of light rays in an interferometer is analyzed. The calculation is made imagining that the interferometer is at the equator of the gravity source and, as long as possible, the metric, provided it is stationary and axisymmetric, is not approximated. Finally, in order to evaluate the size of the effect in the case of the Earth a weak field approximation is introduced. For laboratory scales and non-geodesic paths the correction turns out to be comparable with the sensitivity expected in gravitational waves interferometric detectors, whereas it drops under the threshold of detectability when using free (geodesic) light rays.Comment: 12 pages, LaTeX; more about the detection technique, references added; accepted for publication in GR

The Kepler equation for inspiralling compact binaries

Compact binaries consisting of neutron stars / black holes on eccentric orbit undergo a perturbed Keplerian motion. The perturbations are either of relativistic origin or are related to the spin, mass quadrupole and magnetic dipole moments of the binary components. The post-Newtonian motion of such systems decouples into radial and angular parts. We present here for the first time the radial motion of such a binary encoded in a generalized Kepler equation, with the inclusion of all above-mentioned contributions, up to linear order in the perturbations. Together with suitably introduced parametrizations, the radial motion is solved completely

Data analysis of gravitational-wave signals from spinning neutron stars. II. Accuracy of estimation of parameters

We examine the accuracy of estimation of parameters of the gravitational-wave signals from spinning neutron stars that can be achieved from observations by Earth-based laser interferometers. We consider a model of the signal consisting of two narrowband components and including both phase and amplitude modulation. We calculate approximate values of the rms errors of the parameter estimators using the Fisher information matrix. We carry out extensive Monte Carlo simulations and obtain cumulative distribution functions of rms errors of astrophysically interesting parameters: amplitude of the signal, wobble angle, position of the source in the sky, frequency, and spindown coefficients. We consider both all-sky searches and directed searches. We also examine the possibility of determination of neutron star proper motion. We perform simulations for all laser-interferometric detectors that are currently under construction and for several possible lengths of the observation time and sizes of the parameter space. We find that observations of continuous gravitational-wave signals from neutron stars by laser-interferometric detectors will provide a very accurate information about their astrophysical properties. We derive several simplified models of the signal that can be used in the theoretical investigations of the data analysis schemes independently of the physical mechanisms generating the gravitational-wave signal.Comment: LaTeX, 34 pages, 15 figures, submitted to Phys. Rev.

Speed Meter As a Quantum Nondemolition Measuring Device for Force

Quantum noise is an important issue for advanced LIGO. Although it is in principle possible to beat the Standard Quantum Limit (SQL), no practical recipe has been found yet. This paper dicusses quantum noise in the context of speedmeter-a devise monitoring the speed of the testmass. The scheme proposed to overcome SQL in this case might be more practical than the methods based on monitoring position of the testmass.Comment: 7 pages of RevTex, 1 postscript figur

Approximate Analytical Solutions to the Initial Data Problem of Black Hole Binary Systems

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data solutions makes them easier to implement in numerical evolutions than the traditional numerical approach of solving the elliptic equations derived from the Einstein constraints. Although in general the problem of setting up initial conditions for black hole binary simulations is complicated by the presence of singularities, we show that the methods presented in this work provide initial data with $l_1$ and $l_\infty$ norms of violation of the constraint equations falling below those of the truncation error (residual error due to discretization) present in finite difference codes for the range of grid resolutions currently used. Thus, these data sets are suitable for use in evolution codes. Detailed results are presented for the case of a head-on collision of two equal-mass M black holes with specific angular momentum 0.5M at an initial separation of 10M. A straightforward superposition method yields data adequate for resolutions of $h=M/4$, and an "attenuated" superposition yields data usable to resolutions at least as fine as $h=M/8$. In addition, the attenuated approximate data may be more tractable in a full (computational) exact solution to the initial value problem.Comment: 6 pages, 5 postscript figures. Minor changes and some points clarified. Accepted for publication in Phys. Rev.

Sensitivity curves for spaceborne gravitational wave interferometers

To determine whether particular sources of gravitational radiation will be detectable by a specific gravitational wave detector, it is necessary to know the sensitivity limits of the instrument. These instrumental sensitivities are often depicted (after averaging over source position and polarization) by graphing the minimal values of the gravitational wave amplitude detectable by the instrument versus the frequency of the gravitational wave. This paper describes in detail how to compute such a sensitivity curve given a set of specifications for a spaceborne laser interferometer gravitational wave observatory. Minor errors in the prior literature are corrected, and the first (mostly) analytic calculation of the gravitational wave transfer function is presented. Example sensitivity curve calculations are presented for the proposed LISA interferometer. We find that previous treatments of LISA have underestimated its sensitivity by a factor of $\sqrt{3}$.Comment: 27 pages + 5 figures, REVTeX, accepted for publication in Phys Rev D; Update reflects referees comments, figure 3 clarified, figure 5 corrected for LISA baselin

Past and future gauge in numerical relativity

Numerical relativity describes a discrete initial value problem for general relativity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of present time. Here, we propose solving the discretized Einstein equations with a choice of gauge in the future and a dynamical gauge in the past. The method is illustrated on a polarized Gowdy wave.Comment: To appear in Class Quantum Grav, Let