The search for continuous gravitational waves: metric of the multi-detector F-statistic

We develop a general formalism for the parameter-space metric of the multi-detector F-statistic, which is a matched-filtering detection statistic for continuous gravitational waves. We find that there exists a whole family of F-statistic metrics, parametrized by the (unknown) amplitude parameters of the gravitational wave. The multi-detector metric is shown to be expressible in terms of noise-weighted averages of single-detector contributions, which implies that the number of templates required to cover the parameter space does not scale with the number of detectors. Contrary to using a longer observation time, combining detectors of similar sensitivity is therefore the computationally cheapest way to improve the sensitivity of coherent wide-parameter searches for continuous gravitational waves. We explicitly compute the F-statistic metric family for signals from isolated spinning neutron stars, and we numerically evaluate the quality of different metric approximations in a Monte-Carlo study. The metric predictions are tested against the measured mismatches and we identify regimes in which the local metric is no longer a good description of the parameter-space structure.Comment: 20 pages, 15 figures, revtex4; v2: some edits of style and notation, fixed minor typo

Parameter-space metric of semicoherent searches for continuous gravitational waves

Continuous gravitational-wave (CW) signals such as emitted by spinning neutron stars are an important target class for current detectors. However, the enormous computational demand prohibits fully coherent broadband all-sky searches for prior unknown CW sources over wide ranges of parameter space and for yearlong observation times. More efficient hierarchical "semicoherent" search strategies divide the data into segments much shorter than one year, which are analyzed coherently; then detection statistics from different segments are combined incoherently. To optimally perform the incoherent combination, understanding of the underlying parameter-space structure is requisite. This problem is addressed here by using new coordinates on the parameter space, which yield the first analytical parameter-space metric for the incoherent combination step. This semicoherent metric applies to broadband all-sky surveys (also embedding directed searches at fixed sky position) for isolated CW sources. Furthermore, the additional metric resolution attained through the combination of segments is studied. From the search parameters (sky position, frequency, and frequency derivatives), solely the metric resolution in the frequency derivatives is found to significantly increase with the number of segments.Comment: 14 pages, 5 figures (matching Phys.Rev.D version

A nonlinear detection algorithm for periodic signals in gravitational wave detectors

We present an algorithm for the detection of periodic sources of gravitational waves with interferometric detectors that is based on a special symmetry of the problem: the contributions to the phase modulation of the signal from the earth rotation are exactly equal and opposite at any two instants of time separated by half a sidereal day; the corresponding is true for the contributions from the earth orbital motion for half a sidereal year, assuming a circular orbit. The addition of phases through multiplications of the shifted time series gives a demodulated signal; specific attention is given to the reduction of noise mixing resulting from these multiplications. We discuss the statistics of this algorithm for all-sky searches (which include a parameterization of the source spin-down), in particular its optimal sensitivity as a function of required computational power. Two specific examples of all-sky searches (broad-band and narrow-band) are explored numerically, and their performances are compared with the stack-slide technique (P. R. Brady, T. Creighton, Phys. Rev. D, 61, 082001).Comment: 9 pages, 3 figures, to appear in Phys. Rev.

On the equation of motion of compact binaries in Post-Newtonian approximation

A third post-Newtonian (3 PN) equation of motion for two spherical compact stars in a harmonic coordinate has been derived based on the surface integral approach and the strong field point particle limit. The strong field point particle limit enables us to incorporate a notion of a self-gravitating regular star into general relativity. The resulting 3 PN equation of motion is Lorentz invariant, unambiguous, and conserves an energy of the binary orbital motion.Comment: 7 pages, no figure. Proceedings of the 5th Amaldi Conference on Gravitational Waves, Pisa, Italy, 6-11 July 200

A skeleton approximate solution of the Einstein field equations for multiple black-hole systems

An approximate analytical and non-linear solution of the Einstein field equations is derived for a system of multiple non-rotating black holes. The associated space-time has the same asymptotic structure as the Brill-Lindquist initial data solution for multiple black holes. The system admits an Arnowitt-Deser-Misner (ADM) Hamiltonian that can particularly evolve the Brill-Lindquist solution over finite time intervals. The gravitational field of this model may properly be referred to as a skeleton approximate solution of the Einstein field equations. The approximation is based on a conformally flat truncation, which excludes gravitational radiation, as well as a removal of some additional gravitational field energy. After these two simplifications, only source terms proportional to Dirac delta distributions remain in the constraint equations. The skeleton Hamiltonian is exact in the test-body limit, it leads to the Einsteinian dynamics up to the first post-Newtonian approximation, and in the time-symmetric limit it gives the energy of the Brill-Lindquist solution exactly. The skeleton model for binary systems may be regarded as a kind of analytical counterpart to the numerical treatment of orbiting Misner-Lindquist binary black holes proposed by Gourgoulhon, Grandclement, and Bonazzola, even if they actually treat the corotating case. Along circular orbits, the two-black-hole skeleton solution is quasi-stationary and it fulfills the important property of equality of Komar and ADM masses. Explicit calculations for the determination of the last stable circular orbit of the binary system are performed up to the tenth post-Newtonian order within the skeleton model.Comment: 15 pages, 1 figure, submitted to Phys. Rev. D, 3 references added, minor correction

Data analysis of gravitational-wave signals from spinning neutron stars. IV. An all-sky search

We develop a set of data analysis tools for a realistic all-sky search for continuous gravitational-wave signals. The methods that we present apply to data from both the resonant bar detectors that are currently in operation and the laser interferometric detectors that are in the final stages of construction and commissioning. We show that with our techniques we shall be able to perform an all-sky 2-day long coherent search of the narrow-band data from the resonant bar EXPLORER with no loss of signals with the dimensionless amplitude greater than $2.8\times10^{-23}$.Comment: REVTeX, 26 pages, 1 figure, submitted to Phys. Rev.

The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes the post-Newtonian expansions of the three metrics can be made to coincide up to the fifth post-Newtonian order resulting in identical static Hamiltonians up the third post-Newtonian approximation. The calculations shed light on previously performed binary point-mass calculations at the third post-Newtonian approximation.Comment: LaTeX, 9 pages, to be submitted to Physical Review

On bare masses in time-symmetric initial-value solutions for two black holes

The Brill-Lindquist time-symmetric initial-value solution for two uncharged black holes is rederived using the Hamiltonian constraint equation with Dirac delta distributions as a source for the binary black-hole field. The bare masses of the Brill-Lindquist black holes are introduced in a way which is applied, after straightforward modification, to the Misner-Linquist binary black-hole solution.Comment: LaTeX, 4 page