Searching for continuous gravitational wave sources in binary systems

We consider the problem of searching for continuous gravitational wave sources orbiting a companion object. This issue is of particular interest because the LMXB's, and among them Sco X-1, might be marginally detectable with 2 years coherent observation time by the Earth-based laser interferometers expected to come on line by 2002, and clearly observable by the second generation of detectors. Moreover, several radio pulsars, which could be deemed to be CW sources, are found to orbit a companion star or planet, and the LIGO/VIRGO/GEO network plans to continuously monitor such systems. We estimate the computational costs for a search launched over the additional five parameters describing generic elliptical orbits using match filtering techniques. These techniques provide the optimal signal-to-noise ratio and also a very clear and transparent theoretical framework. We provide ready-to-use analytical expressions for the number of templates required to carry out the searches in the astrophysically relevant regions of the parameter space, and how the computational cost scales with the ranges of the parameters. We also determine the critical accuracy to which a particular parameter must be known, so that no search is needed for it. In order to disentangle the computational burden involved in the orbital motion of the CW source, from the other source parameters (position in the sky and spin-down), and reduce the complexity of the analysis, we assume that the source is monochromatic and its location in the sky is exactly known. The orbital elements, on the other hand, are either assumed to be completely unknown or only partly known. We apply our theoretical analysis to Sco X-1 and the neutron stars with binary companions which are listed in the radio pulsar catalogue.Comment: 31 pages, LaTeX, 6 eps figures, submitted to PR

A data-analysis strategy for detecting gravitational-wave signals from inspiraling compact binaries with a network of laser-interferometric detectors

A data-analysis strategy based on the maximum-likelihood method (MLM) is presented for the detection of gravitational waves from inspiraling compact binaries with a network of laser-interferometric detectors having arbitrary orientations and arbitrary locations around the globe. The MLM is based on the network likelihood ratio (LR), which is a function of eight signal-parameters that determine the Newtonian inspiral waveform. In the MLM-based strategy, the LR must be maximized over all of these parameters. Here, we show that it is possible to maximize it analytically over four of the eight parameters. Maximization over a fifth parameter, the time of arrival, is handled most efficiently by using the Fast-Fourier-Transform algorithm. This allows us to scan the parameter space continuously over these five parameters and also cuts down substantially on the computational costs. Maximization of the LR over the remaining three parameters is handled numerically. This includes the construction of a bank of templates on this reduced parameter space. After obtaining the network statistic, we first discuss `idealized' networks with all the detectors having a common noise curve for simplicity. Such an exercise nevertheless yields useful estimates about computational costs, and also tests the formalism developed here. We then consider realistic cases of networks comprising of the LIGO and VIRGO detectors: These include two-detector networks, which pair up the two LIGOs or VIRGO with one of the LIGOs, and the three-detector network that includes VIRGO and both the LIGOs. For these networks we present the computational speed requirements, network sensitivities, and source-direction resolutions.Comment: 40 pages, 2 figures, uses RevTex and psfig, submitted to Phys. Rev. D, A few minor changes adde

Marginalizing the likelihood function for modeled gravitational wave searches

Matched filtering is a commonly used technique in gravitational wave searches for signals from compact binary systems and from rapidly rotating neutron stars. A common issue in these searches is dealing with four extrinsic parameters which do not affect the phase evolution of the system: the overall amplitude, initial phase, and two angles determining the overall orientation of the system. The F-statistic maximizes the likelihood function analytically over these parameters, while the B-statistic marginalizes over them. The B-statistic, while potentially more powerful and capable of incorporating astrophysical priors, is not as widely used because of the computational difficulty of performing the marginalization. In this paper we address this difficulty and show how the marginalization can be done analytically by combining the four parameters into a set of complex amplitudes. The results of this paper are applicable to both transient non-precessing binary coalescence events, and to long lived signals from rapidly rotating neutron stars.Comment: 26 page

Detection of gravitational waves using a network of detectors

We formulate the data analysis problem for the detection of the Newtonian coalescing-binary signal by a network of laser interferometric gravitational wave detectors that have arbitrary orientations, but are located at the same site. We use the maximum likelihood method for optimizing the detection problem. We show that for networks comprising of up to three detectors, the optimal statistic is essentially the magnitude of the network correlation vector constructed from the matched network-filter. Alternatively, it is simply a linear combination of the signal-to-noise ratios of the individual detectors. This statistic, therefore, can be interpreted as the signal-to-noise ratio of the network. The overall sensitivity of the network is shown to increase roughly as the square-root of the number of detectors in the network. We further show that these results continue to hold even for the restricted post-Newtonian filters. Finally, our formalism is general enough to be extended to address the problem of detection of such waves from other sources by some other types of detectors, e.g., bars or spheres, or even by networks of spatially well-separated detectors.Comment: 14 pages, RevTex, 1 postscript figure. Based on talk given at Workshop on Cosmology: Observations confront theories, IIT-Kharagpur, India (January 1999

A unified approach to χ2\chi^2 discriminators for searches of gravitational waves from compact binary coalescences

We describe a general mathematical framework for $\chi^2$ discriminators in the context of the compact binary coalescence search. We show that with any $\chi^2$ is associated a vector bundle over the signal manifold, that is, the manifold traced out by the signal waveforms in the function space of data segments. The $\chi^2$ is then defined as the square of the $L_2$ norm of the data vector projected onto a finite dimensional subspace (the fibre) of the Hilbert space of data trains and orthogonal to the signal waveform - any such fibre leads to a $\chi^2$ discriminator and the full vector bundle comprising the subspaces and the base manifold constitute the $\chi^2$ discriminator. We show that the $\chi^2$ discriminators used so far in the CBC searches correspond to different fiber structures constituting different vector bundles on the same base manifold, namely, the parameter space. The general formulation indicates procedures to formulate new $\chi^2$s which could be more effective in discriminating against commonly occurring glitches in the data. It also shows that no $\chi^2$ with a reasonable degree of freedom is foolproof. It could also shed light on understanding why the traditional $\chi^2$ works so well. As an example, we propose a family of ambiguity $\chi^2$ discriminators that is an alternative to the traditional one. Any such ambiguity $\chi^2$ makes use of the filtered output of the template bank, thus adding negligible cost to the overall search. We test the performance of ambiguity $\chi^2$ on simulated data using spinless TaylorF2 waveforms. We show that the ambiguity $\chi^2$ essentially gives a clean separation between glitches and signals. Finally, we investigate the effects of mismatch between signal and templates on the $\chi^2$ and also further indicate how the ambiguity $\chi^2$ can be generalized to detector networks for coherent observations.Comment: 21 pages, 5 figure, abstract is shortened to comply with the arXiv's 1920 characters limitation, v2: accepted for publication in PR

Cosmic sirens: discovery of gravitational waves and their impact on astrophysics and fundamental physics

On 14 September 2015, the twin detectors belonging to the Laser Interferometer Gravitational Wave Observatory (LIGO) made a triple discovery: the first direct detection of gravitational waves (GWs), first observation of formation of a black hole and first observation of a binary black hole. Since then LIGO has reported two other events and a marginal candidate. These discoveries have heralded a new era in observational astronomy. They will help us in exploring extremes of astrophysics and gravity. GWs are our best chance of getting an idea of what went on a small fraction of a second after the big bang, even if that takes many more decades. With LIGO’s discoveries we hope to solve many puzzles in astronomy and fundamental physics, but GWs are guaranteed to show up objects and phenomena never imagined before

Detection of gravitational waves from inspiraling compact binaries using a network of interferometric detectors

We formulate the data analysis problem for the detection of the Newtonian waveform from an inspiraling compact-binary by a network of arbitrarily oriented and arbitrarily distributed laser interferometric gravitational wave detectors. We obtain for the first time the relation between the optimal statistic and the magnitude of the network correlation vector, which is constructed from the matched network-filter. This generalizes the calculation reported in an earlier work (gr-qc/9906064), where the detectors are taken to be coincident.Comment: 6 pages, RevTeX. Based on talk given at GWDAW-99, Rom

The cross-correlation search for a hot spot of gravitational waves : Numerical study for point spread function

The cross-correlation search for gravitational wave, which is known as 'radiometry', has been previously applied to map of the gravitational wave stochastic background in the sky and also to target on gravitational wave from rotating neutron stars/pulsars. We consider the Virgo cluster where may be appear as `hot spot' spanning few pixels in the sky in radiometry analysis. Our results show that sufficient signal to noise ratio can be accumulated with integration times of the order of a year. We also construct numerical simulation of radiometry analysis, assuming current constructing/upgrading ground-based detectors. Point spread function of the injected sources are confirmed by numerical test. Typical resolution of radiometry analysis is a few square degree which corresponds to several thousand pixels of sky mapping.Comment: 9 pages, 9 figures, Amaldi 9 & NRD