Data analysis of continuous gravitational wave: Fourier transform – I

We present the Fourier Transform of a continuous gravitational wave. We have analysed the data set for a 1-d observation time and our analysis is applicable for an arbitrary location of detector and source. We have taken into account the effects arising due to the rotational as well as orbital motions of the Earth.     

Data analysis of continuous gravitational wave: Fourier transform – II

In this paper we obtain the Fourier Transform of a continuous gravitational wave. We have analysed the data set for (i) a 1-yr observation time and (ii) an arbitrary observation time, for an arbitrary location of detector and source, taking into account the effects arising due to the rotational as well as orbital motion of the Earth. As an application of the transform we considered spin-down and N -component signal analysis.     

Investigating ultra-long gravitational waves with measurements of pulsar rotational parameters

A method is suggested with which to explore the gravitational wave background (GWB) in the frequency range 10⁻¹²–10⁻⁸ Hz. This method is based on the precise measurements of pulsar rotational parameters: the influence of gravitational waves (GWs) in this frequency range will affect these parameters and therefore some conclusions about the energy density of the GWB can be made using analysis of the derivatives of pulsar rotational frequency. The calculated values of the second derivative from a number of pulsars limit the density of the GWB, Ω_gw, as follows:  Ω_gw < 2 × 10⁻⁶  . Also, the time series of the frequency ν of different pulsars in a pulsar array can be cross-correlated pairwise in the same manner as in anomalous residuals analysis, thus providing the possibility of GWB detection in the ultra-low-frequency range.     

tempo2: a new pulsar timing package – III. Gravitational wave simulation

Analysis of pulsar timing data sets may provide the first direct detection of gravitational waves. This paper, the third in a series describing the mathematical framework implemented into the tempo2 pulsar timing package, reports on using tempo2 to simulate the timing residuals induced by gravitational waves. The tempo2 simulations can be used to provide upper bounds on the amplitude of an isotropic, stochastic, gravitational wave background in our Galaxy and to determine the sensitivity of a given pulsar timing experiment to individual, supermassive, binary black hole systems.     

On measuring the gravitational-wave background using Pulsar Timing Arrays

The long-term precise timing of Galactic millisecond pulsars holds great promise for measuring the long-period (months to years) astrophysical gravitational waves. Several gravitational-wave observational programs, called Pulsar Timing Arrays (PTA), are being pursued around the world.
Here, we develop a Bayesian algorithm for measuring the stochastic gravitational-wave background (GWB) from the PTA data. Our algorithm has several strengths: (i) it analyses the data without any loss of information; (ii) it trivially removes systematic errors of known functional form, including quadratic pulsar spin-down, annual modulations and jumps due to a change of equipment; (iii) it measures simultaneously both the amplitude and the slope of the GWB spectrum and (iv) it can deal with unevenly sampled data and coloured pulsar noise spectra. We sample the likelihood function using Markov Chain Monte Carlo simulations. We extensively test our approach on mock PTA data sets and find that the algorithm has significant benefits over currently proposed counterparts. We show the importance of characterizing all red noise components in pulsar timing noise by demonstrating that the presence of a red component would significantly hinder the detection of the GWB.
Lastly, we explore the dependence of the signal-to-noise ratio on the duration of the experiment, number of monitored pulsars and the magnitude of the pulsar timing noise. These parameter studies will help formulate observing strategies for the PTA experiments.     

Pulsar timing residuals due to individual non-evolving gravitational wave sources

The pulsar timing residuals induced by gravitational waves from non- evolving single binary sources are affected by many parameters related to the relative positions of the pulsar and the gravitational wave sources. We will analyze the various effects due to different parameters. The standard deviations of the timing residuals will be calculated with a variable parameter fixing a set of other parameters. The or- bits of the binary sources will be generally assumed to be elliptical. The influences of different eccentricities on the pulsar timing residuals will also be studied in detail. We find that the effects of the related parameters are quite different, and some of them display certain regularities.     

Fast and accurate computational tools for gravitational waveforms from binary stars with any orbital eccentricity

The relevance of orbital eccentricity in the detection of gravitational radiation from (steady state) binary stars is emphasized. Computationally effective (fast and accurate) tools for constructing gravitational wave templates from binary stars with any orbital eccentricity are introduced including tight estimation criteria of the pertinent truncation and approximation errors.     

A data analysis approach for detecting gravitational waves from PSR 0437–4715

A search for gravitational waves from the millisecond pulsar PSR 0437-4715 has been initiated using the bar detector NIOBE which is located at the University of Western Australia. We present a detailed report on the data analysis algorithm, called phase plane rotation , which will be used in this search. A discussion of the actual implementation of the algorithm is presented. The data analysis algorithm mentioned above has the advantage that it requires minimal changes to the already-existing data acquisition facility of NIOBE but, at the same time, it is as efficient as optimal filtering in detecting a signal. This search involves a very long coherent integration of the bar output which may stretch over a few years. With some planned improvements in the detector, a three-year integration should be able to put an upper limit of h  ∼ 10⁻²⁶ on the signal amplitude.     

All-sky search algorithms for monochromatic signals in resonant bar gravitational wave detector data

In this paper we design and develop several filtering strategies for the analysis of data generated by a resonant bar gravitational wave (GW) antenna, with the goal of assessing the presence (or absence) therein of long-duration monochromatic GW signals, as well as the eventual amplitude and frequency of the signals, within the sensitivity band of the detector. Such signals are most likely generated in the fast rotation of slightly asymmetric spinning stars. We develop practical procedures, together with a study of their statistical properties, which will provide us with useful information on the performance of each technique. The selection of candidate events will then be established according to threshold-crossing probabilities, based on the Neyman–Pearson criterion. In particular, it will be shown that our approach, based on phase estimation, presents a better signal-to-noise ratio than does pure spectral analysis, the most common approach.     

Non-parametric inversion of gravitational lensing systems with few images using a multi-objective genetic algorithm

Galaxies acting as gravitational lenses are surrounded by, at most, a handful of images. This apparent paucity of information forces one to make the best possible use of what information is available to invert the lens system. In this paper, we explore the use of a genetic algorithm to invert in a non-parametric way strong lensing systems containing only a small number of images. Perhaps the most important conclusion of this paper is that it is possible to infer the mass distribution of such gravitational lens systems using a non-parametric technique. We show that including information about the null space (i.e. the region where no images are found) is prerequisite to avoid the prediction of a large number of spurious images, and to reliably reconstruct the lens mass density. While the total mass of the lens is usually constrained within a few per cent, the fidelity of the reconstruction of the lens mass distribution depends on the number and position of the images. The technique employed to include null space information can be extended in a straightforward way to add additional constraints, such as weak-lensing data or time-delay information.     

Weak gravitational shear and flexion with polar shapelets

We derive expressions, in terms of 'polar shapelets', for the image distortion operations associated with weak gravitational lensing. Shear causes galaxy shapes to become elongated, and is sensitive to the second derivative of the projected gravitational potential along their line of sight; flexion bends galaxy shapes into arcs, and is sensitive to the third derivative. Polar shapelets provide a natural representation, in which both shear and flexion transformations are compact. Through this tool, we understand progress in several weak lensing methods. We then exploit various symmetries of shapelets to construct a range of shear estimators with useful properties. Through an analogous investigation, we also explore several flexion estimators. In particular, some of the estimators can be measured simultaneously and independently for every galaxy, and will provide unique checks for systematics in future weak lensing analyses. Using simulated images from the Shear TEsting Programme, we show that we can recover input shears with no significant bias. A complete software package to parametrize astronomical images in terms of polar shapelets, and to perform a full weak lensing analysis, is available on the Internet.