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Register a new userSearching for Gravitational Wave Bursts via Bayesian Nonparametric Data Analysis with Pulsar Timing Arrays
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Xihao Deng
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Gravitational wave burst is a catch-all category for signals whose durations are shorter than the observation period. We apply a method new to gravitational wave data analysis --- Bayesian non-parameterics --- to the problem of gravitational wave detection, with an emphasis on pulsar timing array observations. In Bayesian non-parametrics, constraints are set on the function space that may be reasonably thought to characterize the range of gravitational-wave signals. This differs from the approaches currently employed or proposed, which focus on introducing parametric signal models or looking for excess power as evidence of the presence of a gravitational wave signal. Our Bayesian nonparametrics analysis method addresses two issues: (1) investigate if a gravitational wave burst is present in the data; (2) infer the sky location of the source and the duration of the burst. Compared with the popular method proposed by Finn & Lommen, our method improves in two aspects: (1) we can estimate the burst duration by adding the prior that the gravitational wave signals are smooth, while Finn & Lommen ignored this important point; (2) we perform a full Bayesian analysis by marginalizing over all possible parameters and provide robust inference on the presence of gravitational waves, while Finn & Lommen chose to optimize over parameters, which would increase false alarm risk and also underestimate the parameter uncertainties.
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We study how to probe bispectra of stochastic gravitational waves with pulsar timing arrays. The bispectrum is a key to probe the origin of stochastic gravitational waves. In particular, the shape of the bispectrum carries valuable information of inflation models. We show that an appropriate filter function for three point correlations enables us to extract a specific configuration of momentum triangles in bispectra. We also calculate the overlap reduction functions and discuss strategy for detecting the bispectrum with multiple pulsars.
Cosmic strings are potential gravitational wave (GW) sources that can be probed by pulsar timing arrays (PTAs). In this work we develop a detection algorithm for a GW burst from a cusp on a cosmic string, and apply it to Parkes PTA data. We find four events with a false alarm probability less than 1%. However further investigation shows that all of these are likely to be spurious. As there are no convincing detections we place upper limits on the GW amplitude for different event durations. From these bounds we place limits on the cosmic string tension of G mu ~ 10^{-5}, and highlight that this bound is independent from those obtained using other techniques. We discuss the physical implications of our results and the prospect of probing cosmic strings in the era of Square Kilometre Array (SKA).
In our previous paper cite{PTA1} we derived a generic expression for the pulse redshift the main observable for the Pulsar Timing Array (PTA) experiment for detection of gravitational waves for all possible polarizations induced by modifications of general relativity (GR). In this work we provide a generic expression of the overlap reduction function for PTA without using the short wavelength approximation for tensorial polarization. We are convinced, that the short wavelength approximation is not applicable to the overlap reduction function for PTAs, since the removal of the exponential terms in the integrand would lead to poles for $x, y$ and $l$ polarizations and discontinuities for $+$ and $times$. In this work we provide a series expansion to calculate the integral exactly and investigate the behaviour of the series for short wavelength values via numerical evaluation of the analytical series. We find a disagreement for the limit of co-located pulsars with the Hellings & Downs curve.
Recent years have seen a burgeoning interest in using pulsar timing arrays (PTAs) as gravitational-wave (GW) detectors. To date, that interest has focused mainly on three particularly promising source types: supermassive--black-hole binaries, cosmic strings, and the stochastic background from early-Universe phase transitions. In this paper, by contrast, our aim is to investigate the PTA potential for discovering unanticipated sources. We derive significant constraints on the available discovery space based solely on energetic and statistical considerations: we show that a PTA detection of GWs at frequencies above ~3.e-5 Hz would either be an extraordinary coincidence or violate cherished beliefs; we show that for PTAs GW memory can be more detectable than direct GWs, and that, as we consider events at ever higher redshift, the memory effect increasingly dominates an events total signal-to-noise ratio. The paper includes also a simple analysis of the effects of pulsar red noise in PTA searches, and a demonstration that the effects of periodic GWs in the 10^-8 -- 10^-4.5 Hz band would not be degenerate with small errors in standard pulsar parameters (except in a few narrow bands).
Anisotropic bursts of gravitational radiation produced by events such as super-massive black hole mergers leave permanent imprints on space. Such gravitational wave memory (GWM) signals are, in principle, detectable through pulsar timing as sudden changes in the apparent pulse frequency of a pulsar. If an array of pulsars is monitored as a GWM signal passes over the Earth, the pulsars would simultaneously appear to change pulse frequency by an amount that varies with their sky position in a quadrupolar fashion. Here we describe a search algorithm for such events and apply the algorithm to approximately six years of data from the Parkes Pulsar Timing Array. We find no GWM events and set an upper bound on the rate for events which could have been detected. We show, using simple models of black hole coalescence rates, that this non-detection is not unexpected.
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