We extend the formalisms developed in Gair et al. 1 and Cornish and van Haasteren 2 to create maps of gravitational-wave backgrounds using a network of ground-based laser interferometers. We show ...that in contrast to pulsar timing arrays, which are insensitive to the curl modes of the background, a network of ground-based interferometers is sensitive to both the gradient and curl components. The spatial separation of a network of interferometers, or of a single interferometer at different times during its rotational and orbital motion around the Sun, allows for recovery of both components. We derive expressions for the response functions of a laser interferometer in the small-antenna limit and use these expressions to calculate the overlap reduction function for a pair of interferometers. We also construct maximum-likelihood estimates of the +- and x-polarization modes of the gravitational-wave sky in terms of the response matrix for a network of ground-based interferometers, evaluated at discrete times during Earth's rotational and orbital motion around the Sun. We demonstrate the feasibility of this approach for some simple simulated backgrounds (a single point source and two spatially extended distributions having only gradient or curl components), calculating maximum-likelihood sky maps and uncertainty maps based on the (pseudo)inverse of the response matrix. The distinction between this approach and standard methods for mapping gravitational-wave power is also discussed.
Gravitational wave astronomy: needle in a haystack Cornish, Neil J
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
02/2013, Letnik:
371, Številka:
1984
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A worldwide array of highly sensitive ground-based interferometers stands poised to usher in a new era in astronomy with the first direct detection of gravitational waves. The data from these ...instruments will provide a unique perspective on extreme astrophysical objects, such as neutron stars and black holes, and will allow us to test Einstein's theory of gravity in the strong field, dynamical regime. To fully realize these goals, we need to solve some challenging problems in signal processing and inference, such as finding rare and weak signals that are buried in non-stationary and non-Gaussian instrument noise, dealing with high-dimensional model spaces, and locating what are often extremely tight concentrations of posterior mass within the prior volume. Gravitational wave detection using space-based detectors and pulsar timing arrays bring with them the additional challenge of having to isolate individual signals that overlap one another in both time and frequency. Promising solutions to these problems will be discussed, along with some of the challenges that remain.
Searches for gravitational waves produced by coalescing black hole binaries with total masses gap 25 M sub(odot) use matched filtering with templates of short duration. Non-Gaussian noise bursts in ...gravitational wave detector data can mimic short signals and limit the sensitivity of these searches. Previous searches have relied on empirically designed statistics incorporating signal-to-noise ratio and signal-based vetoes to separate gravitational wave candidates from noise candidates. We report on sensitivity improvements achieved using a multivariate candidate ranking statistic derived from a supervised machine learning algorithm. We apply the random forest of bagged decision trees technique to two separate searches in the high mass (gap 25 M sub(odot)) parameter space. For a search which is sensitive to gravitational waves from the inspiral, merger, and ringdown of binary black holes with total mass between 25 M sub(odot) and 100 M sub(odot), we find sensitive volume improvements as high as 70 sub(+ or -13)%- 109 sub(+ or -11)% when compared to the previously used ranking statistic. For a ringdown-only search which is sensitive to gravitational waves from the resultant perturbed intermediate mass black hole with mass roughly between 10 M sub(odot) and 600 M sub(odot), we find sensitive volume improvements as high as 61 sub(+ or-4)%-241 sub(+ or -12)% when compared to the previously used ranking statistic. We also report how sensitivity improvements can differ depending on mass regime, mass ratio, and available data quality information. Finally, we describe the techniques used to tune and train the random forest classifier that can be generalized to its use in other searches for gravitational waves.
In this work we focus on the search and detection of massive black hole binary (MBHB) systems, including systems at high redshift. As well as expanding on previous works where we used a variant of ...Markov chain Monte Carlo (MCMC), called Metropolis Hastings Monte Carlo, with simulated annealing, we introduce a new search method based on frequency annealing which leads to a more rapid and robust detection. We compare the two search methods on systems where we do and do not see the merger of the black holes. In the non-merger case, we also examine the posterior distribution exploration using a 7D MCMC algorithm. We demonstrate that this method is effective in dealing with the high correlations between parameters, has a higher acceptance rate than previously proposed methods and produces posterior distribution functions that are close to the prediction from the Fisher information matrix. Finally, after carrying out searches where there is only one binary in the data stream, we examine the case where two black hole binaries are present in the same data stream. We demonstrate that our search algorithm can accurately recover both binaries, and more importantly showing that we can safely extract the MBHB sources without contaminating the rest of the data stream.
Gravitational wave data from ground-based detectors is dominated by instrument noise. Signals will be comparatively weak, and our understanding of the noise will influence detection confidence and ...signal characterization. Mismodeled noise can produce large systematic biases in both model selection and parameter estimation. Here we introduce a multicomponent, variable dimension, parametrized model to describe the Gaussian-noise power spectrum for data from ground-based gravitational wave interferometers. Called BayesLine, the algorithm models the noise power spectral density using cubic splines for smoothly varying broadband noise and Lorentzians for narrow-band line features in the spectrum. We describe the algorithm and demonstrate its performance on data from the fifth and sixth LIGO science runs. Once fully integrated into LIGO/Virgo data analysis software, BayesLine will produce accurate spectral estimation and provide a means for marginalizing inferences drawn from the data over all plausible noise spectra.
Supermassive black hole binaries are the most promising source of gravitational-waves in the frequency band accessible to pulsar timing arrays. Most of these binaries will be too distant to detect ...individually, but together they will form an approximately stochastic background that can be detected by measuring the correlation pattern induced between pairs of pulsars. A small number of nearby and especially massive systems may stand out from this background and be detected individually. Analyses have previously been developed to search for stochastic signals and isolated signals separately. Here we present BayesHopper, an algorithm capable of jointly searching for both signal components simultaneously using trans-dimensional Bayesian inference. Our implementation uses the reversible jump Markov chain Monte Carlo method for sampling the relevant parameter space with changing dimensionality. We have tested BayesHopper on various simulated datasets. We find that it gives results consistent with fixed-dimensional methods when tested on data with a stochastic background or data with a single binary. For the full problem of analyzing a dataset with both a background and multiple black hole binaries, we find two kinds of interactions between the binary and background components. First, the background effectively increases the noise level, thus making individual binary signals less significant. Second, weak binary signals can be absorbed by the background model due to the natural parsimony of Bayesian inference. Because of its flexible model structure, we anticipate that BayesHopper will outperform existing approaches when applied to realistic data sets produced from population synthesis models.
Constraining the topology of the universe Cornish, Neil J; Spergel, David N; Starkman, Glenn D ...
Physical review letters,
05/2004, Letnik:
92, Številka:
20
Journal Article
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The first year data from the Wilkinson Microwave Anisotropy Probe are used to place stringent constraints on the topology of the Universe. We search for pairs of circles on the sky with similar ...temperature patterns along each circle. We restrict the search to back-to-back circle pairs, and to nearly back-to-back circle pairs, as this covers the majority of the topologies that one might hope to detect in a nearly flat universe. We do not find any matched circles with radius greater than 25 degrees. For a wide class of models, the nondetection rules out the possibility that we live in a universe with topology scale smaller than 24 Gpc.
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