Bayesian estimation of pulsar parameters from gravitational wave data

We present a method of searching for, and parameterizing, signals from known radio pulsars in data from interferometric gravitational wave detectors. This method has been applied to data from the LIGO and GEO 600 detectors to set upper limits on the gravitational wave emission from several radio pulsars. Here we discuss the nature of the signal and the performance of the technique on simulated data. We show how to perform a coherent multiple detector analysis and give some insight in the covariance between the signal parameters.Comment: 9 pages, 6 figures. Accepted to Phys. Rev. D. A few small changes from previous versio

Of `Cocktail Parties' and Exoplanets

The characterisation of ever smaller and fainter extrasolar planets requires an intricate understanding of one's data and the analysis techniques used. Correcting the raw data at the 10^-4 level of accuracy in flux is one of the central challenges. This can be difficult for instruments that do not feature a calibration plan for such high precision measurements. Here, it is not always obvious how to de-correlate the data using auxiliary information of the instrument and it becomes paramount to know how well one can disentangle instrument systematics from one's data, given nothing but the data itself. We propose a non-parametric machine learning algorithm, based on the concept of independent component analysis, to de-convolve the systematic noise and all non-Gaussian signals from the desired astrophysical signal. Such a `blind' signal de-mixing is commonly known as the `Cocktail Party problem' in signal-processing. Given multiple simultaneous observations of the same exoplanetary eclipse, as in the case of spectrophotometry, we show that we can often disentangle systematic noise from the original light curve signal without the use of any complementary information of the instrument. In this paper, we explore these signal extraction techniques using simulated data and two data sets observed with the Hubble-NICMOS instrument. Another important application is the de-correlation of the exoplanetary signal from time-correlated stellar variability. Using data obtained by the Kepler mission we show that the desired signal can be de-convolved from the stellar noise using a single time series spanning several eclipse events. Such non-parametric techniques can provide important confirmations of the existent parametric corrections reported in the literature, and their associated results. Additionally they can substantially improve the precision exoplanetary light curve analysis in the future.Comment: ApJ accepte

A blind hierarchical coherent search for gravitational-wave signals from coalescing compact binaries in a network of interferometric detectors

We describe a hierarchical data analysis pipeline for coherently searching for gravitational wave (GW) signals from non-spinning compact binary coalescences (CBCs) in the data of multiple earth-based detectors. It assumes no prior information on the sky position of the source or the time of occurrence of its transient signals and, hence, is termed "blind". The pipeline computes the coherent network search statistic that is optimal in stationary, Gaussian noise, and allows for the computation of a suite of alternative statistics and signal-based discriminators that can improve its performance in real data. Unlike the coincident multi-detector search statistics employed so far, the coherent statistics are different in the sense that they check for the consistency of the signal amplitudes and phases in the different detectors with their different orientations and with the signal arrival times in them. The first stage of the hierarchical pipeline constructs coincidences of triggers from the multiple interferometers, by requiring their proximity in time and component masses. The second stage follows up on these coincident triggers by computing the coherent statistics. The performance of the hierarchical coherent pipeline on Gaussian data is shown to be better than the pipeline with just the first (coincidence) stage.Comment: 12 pages, 3 figures, accepted for publication in Classical and Quantum Gravit

Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities

We analyze the signal processing required for the optimal detection of a stochastic background of gravitational radiation using laser interferometric detectors. Starting with basic assumptions about the statistical properties of a stochastic gravity-wave background, we derive expressions for the optimal filter function and signal-to-noise ratio for the cross-correlation of the outputs of two gravity-wave detectors. Sensitivity levels required for detection are then calculated. Issues related to: (i) calculating the signal-to-noise ratio for arbitrarily large stochastic backgrounds, (ii) performing the data analysis in the presence of nonstationary detector noise, (iii) combining data from multiple detector pairs to increase the sensitivity of a stochastic background search, (iv) correlating the outputs of 4 or more detectors, and (v) allowing for the possibility of correlated noise in the outputs of two detectors are discussed. We briefly describe a computer simulation which mimics the generation and detection of a simulated stochastic gravity-wave signal in the presence of simulated detector noise. Numerous graphs and tables of numerical data for the five major interferometers (LIGO-WA, LIGO-LA, VIRGO, GEO-600, and TAMA-300) are also given. The treatment given in this paper should be accessible to both theorists involved in data analysis and experimentalists involved in detector design and data acquisition.Comment: 81 pages, 30 postscript figures, REVTE

Optimal detection of burst events in gravitational wave interferometric observatories

We consider the problem of detecting a burst signal of unknown shape. We introduce a statistic which generalizes the excess power statistic proposed by Flanagan and Hughes and extended by Anderson et al. The statistic we propose is shown to be optimal for arbitrary noise spectral characteristic, under the two hypotheses that the noise is Gaussian, and that the prior for the signal is uniform. The statistic derivation is based on the assumption that a signal affects only affects N samples in the data stream, but that no other information is a priori available, and that the value of the signal at each sample can be arbitrary. We show that the proposed statistic can be implemented combining standard time-series analysis tools which can be efficiently implemented, and the resulting computational cost is still compatible with an on-line analysis of interferometric data. We generalize this version of an excess power statistic to the multiple detector case, also including the effect of correlated noise. We give full details about the implementation of the algorithm, both for the single and the multiple detector case, and we discuss exact and approximate forms, depending on the specific characteristics of the noise and on the assumed length of the burst event. As a example, we show what would be the sensitivity of the network of interferometers to a delta-function burst.Comment: 21 pages, 5 figures in 3 groups. Submitted for publication to Phys.Rev.D. A Mathematica notebook is available at http://www.ligo.caltech.edu/~avicere/nda/burst/Burst.nb which allows to reproduce the numerical results of the pape

Accurate measurement of the time delay in the response of the LIGO gravitational wave detectors

We present a method to precisely calibrate the time delay in a long baseline gravitational-wave interferometer. An accurate time stamp is crucial for data analysis of gravitational wave detectors, especially when performing coincidence and correlation analyses between multiple detectors. Our method uses an intensity-modulated radiation pressure force to actuate on the mirrors. The time delay is measured by comparing the phase of the signal at the actuation point with the phase of the recorded signal within the calibrated data stream used for gravitational wave searches. Because the signal-injection path is independent of the interferometer's control system, which is used for the standard calibration, this method can be an independent verification of the timing error in the system. A measurement performed with the 4 km interferometer at the LIGO Hanford Observatory shows a 1 µs relative accuracy when averaging over 50 min. Our understanding of the systematic time delay in the detector response has reached the level of 10 µs