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Register a new userTesting the normality of the gravitational wave data with a low cost recursive estimate of the kurtosis
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Added by
Eric Chassande-Mottin
Publication date
2002
fields
Physics
and research's language is
English
Authors
E. Chassande-Mottin
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We propose a monitoring indicator of the normality of the output of a gravitational wave detector. This indicator is based on the estimation of the kurtosis (i.e., the 4th order statistical moment normalized by the variance squared) of the data selected in a time sliding window. We show how a low cost (because recursive) implementation of such estimation is possible and we illustrate the validity of the presented approach with a few examples using simulated random noises.
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The standard noise model in gravitational wave (GW) data analysis assumes detector noise is stationary and Gaussian distributed, with a known power spectral density (PSD) that is usually estimated using clean off-source data. Real GW data often depart from these assumptions, and misspecified parametric models of the PSD could result in misleading inferences. We propose a Bayesian semiparametric approach to improve this. We use a nonparametric Bernstein polynomial prior on the PSD, with weights attained via a Dirichlet process distribution, and update this using the Whittle likelihood. Posterior samples are obtained using a blocked Metropolis-within-Gibbs sampler. We simultaneously estimate the reconstruction parameters of a rotating core collapse supernova GW burst that has been embedded in simulated Advanced LIGO noise. We also discuss an approach to deal with non-stationary data by breaking longer data streams into smaller and locally stationary components.
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Observations of gravitational waves from compact binary mergers have enabled unique tests of general relativity in the dynamical and non-linear regimes. One of the most important such tests are constraints on the post-Newtonian (PN) corrections to the phase of the gravitational wave signal. The values of these PN coefficients can be calculated within standard general relativity, and these values are different in many alternate theories of gravity. It is clearly of great interest to constrain these deviations based on gravitational wave observations. In the majority of such tests which have been carried out, and which yield by far the most stringent constraints, it is common to vary these PN coefficients individually. While this might in principle be useful for detecting certain deviations from standard general relativity, it is a serious limitation. For example, we would expect alternate theories of gravity to generically have additional parameters. The corrections to the PN coefficients would be expected to depend on these additional non-GR parameters whence, we expect that the various PN coefficients to be highly correlated. We present an alternate analysis here using data from the binary neutron star coalescence GW170817. Our analysis uses an appropriate linear combination of non-GR parameters that represent absolute deviations from the corresponding post-Newtonian inspiral coefficients in the TaylorF2 approximant phase. These combinations represent uncorrelated non-GR parameters which correspond to principal directions of their covariance matrix in the parameter subspace. Our results illustrate good agreement with GR. In particular, the integral non-GR phase is $Psi_{mbox{non-GR}} = (0.447pm253)times10^{-1}$ and the deviation from GR percentile is $p^{mbox{Dev-GR}}_{n}=25.85%$.
The recent LIGO detection of gravitational waves from black-hole binaries offers the exciting possibility of testing gravitational theories in the previously inaccessible strong-field, highly relativistic regime. While the LIGO detections are so far consistent with the predictions of General Relativity, future gravitational-wave observations will allow us to explore this regime to unprecedented accuracy. One of the generic predictions of theories of gravity that extend General Relativity is the violation of the strong equivalence principle, i.e. strongly gravitating bodies such as neutron stars and black holes follow trajectories that depend on their nature and composition. This has deep consequences for gravitational-wave emission, which takes place with additional degrees of freedom besides the tensor polarizations of General Relativity. I will briefly review the formalism needed to describe these extra emission channels, and show that binary black-hole observations probe a set of gravitational theories that are largely disjoint from those that are testable with binary pulsars or neutron stars.
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