63 research outputs found

### 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 $\chi^2$ 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 LIGOâ€™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

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