P. Jaranowski

Data analysis of gravitational-wave signals from spinning neutron stars. I. The signal and its detection

We present a theoretical background for the data analysis of the gravitational-wave signals from spinning neutron stars for Earth-based laser interferometric detectors. We introduce a detailed model of the signal including both the frequency and the amplitude modulations. We include the effects of the intrinsic frequency changes and the modulation of the frequency at the detector due to Earths motion. We estimate the effects of the stars proper motion and of relativistic corrections. Moreover we consider a signal consisting of two components corresponding to a frequency

Dimensional regularization of the gravitational interaction of point masses

f

Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems

and twice that frequency. From the maximum likelihood principle we derive the detection statistics for the signal and we calculate the probability density function of the statistics. We obtain the data analysis procedure to detect the signal and to estimate its parameters. We show that for optimal detection of the amplitude modulated signal we need four linear filters instead of one linear filter needed for a constant amplitude signal. Searching for the doubled frequency signal increases further the number of linear filters by a factor of 2. We indicate how the fast Fourier transform algorithm and resampling methods commonly proposed in the analysis of periodic signals can be used to calculate the detection statistics for our signal. We find that the probability density function of the detection statistics is determined by one parameter: the optimal signal-to-noise ratio. We study the signal-to-noise ratio by means of the Monte Carlo method for all long-arm interferometers that are currently under construction. We show how our analysis can be extended to perform a joint search for periodic signals by a network of detectors and we perform a Monte Carlo study of the signal-to-noise ratio for a network of detectors.

The Binary black hole problem at the third postNewtonian approximation in the orbital motion: Static part

Abstract We show how to use dimensional regularization to determine, within the Arnowitt–Deser–Misner canonical formalism, the reduced Hamiltonian describing the dynamics of two gravitationally interacting point masses. Implementing, at the third post-Newtonian (3PN) accuracy, our procedure we find that dimensional continuation yields a finite, unambiguous (no pole part) 3PN Hamiltonian which uniquely determines the heretofore ambiguous “static” parameter: namely, ωs=0. Our work also provides a remarkable check of the perturbative consistency (compatibility with gauge symmetry) of dimensional continuation through a direct calculation of the “kinetic” parameter ωk, giving the unique answer compatible with global Poincare invariance (ωk=41/24) by summing ∼50 different dimensionally continued contributions.

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

We complete the analytical determination, at the 4th post-Newtonian (4PN) approximation, of the conservative dynamics of gravitationally interacting two-point-mass systems. This completion is obtained by resolving the infra-red ambiguity which had blocked a previous 4PN calculation [P.Jaranowski and G.Schafer, Phys. Rev. D 87, 081503(R) (2013)] by taking into account the 4PN breakdown of the usual near-zone expansion due to infinite-range tail-transported temporal correlations found long ago [L.Blanchet and T.Damour, Phys. Rev. D 37, 1410 (1988)]. This leads to a Poincare-invariant 4PN-accurate effective action for two masses, which mixes instantaneous interaction terms (described by a usual Hamiltonian) with a (time-symmetric) nonlocal-in-time interaction.

Data analysis of gravitational-wave signals from spinning neutron stars. III. Detection statistics and computational requirements

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.

Gravitational waves from black hole binary inspiral and merger: The span of third post-Newtonian effective-one-body templates

We develop a set of data analysis tools for a realistic all-sky search for continuous gravitational-wave signals and we test our tools against simulated data. The aim of the paper is to prepare for an analysis of the real data from the EXPLORER bar detector; however, the methods that we present apply both to data from the resonant bar detectors that are currently in operation and the laser interferometric detectors that are in the final stages of construction and commissioning. With our techniques we shall be able to perform an all-sky coherent search of 2 days of data from the EXPLORER detector for a frequency bandwidth of 0.76 Hz in one month with 250 Mflops computing power. This search will detect all the continuous gravitational-wave signals with the dimensionless amplitude larger than

Detectability of the gravitational wave signal from a close neutron star binary with mass transfer

2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}

Searching for gravitational waves from known pulsars using the {\cal F} and {\cal G} statistics

with 99% confidence, assuming that the noise in the detector is Gaussian.

On the four-loop static contribution to the gravitational interaction potential of two point masses

We develop the analytic and numerical tools for data analysis of the continuous gravitational-wave signals from spinning neutron stars for ground-based laser interferometric detectors. The statistical data analysis method that we investigate is maximum likelihood detection which for the case of Gaussian noise reduces to matched filtering. We study in detail the statistical properties of the optimum functional that needs to be calculated in order to detect the gravitational-wave signal and estimate its parameters. We find it particularly useful to divide the parameter space into elementary cells such that the values of the optimal functional are statistically independent in different cells. We derive formulas for false alarm and detection probabilities both for the optimal and the suboptimal filters. We assess the computational requirements needed to do the signal search. We compare a number of criteria to build sufficiently accurate templates for our data analysis scheme. We verify the validity of our concepts and formulas by means of the Monte Carlo simulations. We present algorithms by which one can estimate the parameters of the continuous signals accurately. We find, confirming earlier work of other authors, that given a 100 Gflops computational power an all-sky search for observation time of 7 days and directed search for observation time of 120 days are possible whereas an all-sky search for 120 days of observation time is computationally prohibitive.