D. Talukder

Probing the anisotropies of a stochastic gravitational-wave background using a network of ground-based laser interferometers

We present a maximum-likelihood analysis for estimating the angular distribution of power in an anisotropic stochastic gravitational-wave background using ground-based laser interferometers. The standard isotropic and gravitational-wave radiometer searches (optimal for point sources) are recovered as special limiting cases. The angular distribution can be decomposed with respect to any set of basis functions on the sky, and the single-baseline, cross-correlation analysis is easily extended to a network of three or more detectors--that is, to multiple baselines. A spherical-harmonic decomposition, which provides maximum-likelihood estimates of the multipole moments of the gravitational-wave sky, is described in detail. We also discuss (i) the covariance matrix of the estimators and its relationship to the detector response of a network of interferometers, (ii) a singular-value decomposition method for regularizing the deconvolution of the detector response from the measured sky map, (iii) the expected increase in sensitivity obtained by including multiple baselines, and (iv) the numerical results of this method when applied to simulated data consisting of both pointlike and diffuse sources. Comparisons between this general method and the standard isotropic and radiometer searches are given throughout, to make contact with the existing literature on stochastic background searches.

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 signals from non-spinning compact binary coalescences (CBCs) in the data of multiple earth-based detectors. This search 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. More importantly, it allows for the computation of a suite of alternative multi-detector coherent search statistics and signal-based discriminators that can improve the performance of CBC searches in real data, which can be both non-stationary and non-Gaussian. Also, unlike the coincident multi-detector search statistics that have been 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. Since the computation of coherent statistics entails searching in the sky, it is more expensive than that of the coincident statistics that do not require it. To reduce computational costs, 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. Here, we compare the performances of this hierarchical pipeline with and without the second (or coherent) stage in Gaussian noise. Although introducing hierarchy can be expected to cause some degradation in the detection efficiency compared to that of a single-stage coherent pipeline, nevertheless it improves the computational speed of the search considerably. The two main results of this work are as follows: (1) the performance of the hierarchical coherent pipeline on Gaussian data is shown to be better than the pipeline with just the coincident stage; (2) the three-site network of LIGO detectors, in Hanford and Livingston (USA), and Virgo detector in Cascina (Italy) cannot resolve the polarization of waves arriving from certain parts of the sky. This can cause the three-site coherent statistic at those sky positions to become singular. Regularized versions of the statistic can avoid that problem, but can be expected to be sub-optimal. The aforementioned improvement in the pipelines performance due to the coherent stage is in spite of this handicap.

Measuring neutron-star ellipticity with measurements of the stochastic gravitational-wave background

Galactic neutron stars are a promising source of gravitational waves in the analysis band of detectors such as Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo. Previous searches for gravitational waves from neutron stars have focused on the detection of individual neutron stars, which are either nearby or highly nonspherical. Here, we consider the stochastic gravitational-wave signal arising from the ensemble of Galactic neutron stars. Using a population synthesis model, we estimate the single-sigma sensitivity of current and planned gravitational-wave observatories to average neutron star ellipticity e as a function of the number of in-band Galactic neutron stars N_(tot). For the plausible case of N_(tot)≈53000, and assuming one year of observation time with colocated initial LIGO detectors, we find it to be σ_(e)=2.1×10^(−7), which is comparable to current bounds on some nearby neutron stars. (The current best 95% upper limits are e≲7×10^(−8).) It is unclear if Advanced LIGO can significantly improve on this sensitivity using spatially separated detectors. For the proposed Einstein Telescope, we estimate that σe=5.6×10^(−10). Finally, we show that stochastic measurements can be combined with measurements of individual neutron stars in order to estimate the number of in-band Galactic neutron stars. In this way, measurements of stochastic gravitational waves provide a complementary tool for studying Galactic neutron stars.

Multivariate Classification with Random Forests for Gravitational Wave Searches of Black Hole Binary Coalescence

Searches for gravitational waves produced by coalescing black hole binaries with total masses ≳25u2009u2009M_⊙ 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 (≳25u2009u2009M_⊙) 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 25u2009u2009M_⊙ and 100u2009u2009M_⊙, we find sensitive volume improvements as high as 70_(±13)%–109_(±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 10u2009u2009M_⊙ and 600u2009u2009M_⊙, we find sensitive volume improvements as high as 61_(±4)%–241_(±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.

Improved Coincident and Coherent Detection Statistics for Searches for Gravitational Wave Ringdown Signals

We study an improved method for detecting gravitational wave (GW) signals from perturbed black holes by earth-based detectors in the quest for searching for intermediate-mass black holes (IMBHs). Such signals, called ringdowns, are damped sinusoids whose frequency and damping constant can be used to measure a black hole’s mass and spin. Utilizing the output from a matched lter analysis pipeline, we present an improved statistic for the detection of a ringdown signal that is found to be coincident in multiple detectors. The statistic addresses the non-Gaussianity of the data without the use of an additional signal-based waveform consistency test. We also develop coherent network statistics to check for consistency of signal amplitudes and phases in the dierent detectors with their dierent orientations and signal arrival times. We nd that the detection eciency can be improved at least by a few tens of percent by applying these multi-detector statistics primarily because of the ineectiveness of single-detector based discriminators of non-stationary noise, such as the chi-square test, in the case of ringdown signals studied here.

Multi-baseline gravitational wave radiometry

We present a statistic for the detection of stochastic gravitational wave backgrounds (SGWBs) using radiometry with a network of multiple baselines. We also quantitatively compare the sensitivities of existing baselines and their network to SGWBs. We assess how the measurement accuracy of signal parameters, e.g., the sky position of a localized source, can improve when using a network of baselines, as compared to any of the single participating baselines. The search statistic itself is derived from the likelihood ratio of the cross correlation of the data across all possible baselines in a detector network and is optimal in Gaussian noise. Specifically, it is the likelihood ratio maximized over the strength of the nSGWB and is called the maximized-likelihood ratio (MLR). One of the main advantages of using the MLR over past search strategies for inferring the presence or absence of a signal is that the former does not require the deconvolution of the cross correlation statistic. Therefore, it does not suffer from errors inherent to the deconvolution procedure and is especially useful for detecting weak sources. In the limit of a single baseline, it reduces to the detection statistic studied by Ballmer [Classical Quantum Gravity 23, S179 (2006).] and Mitra et al. [Phys. Rev. D 77, 042002 (2008).]. Unlike past studies, here the MLR statistic enables us to compare quantitatively the performances of a variety of baselines searching for a nSGWB signal in (simulated) data. Although we use simulated noise and SGWB signals for making these comparisons, our method can be straight forwardly applied on real data.

Exploring a search for long-duration transient gravitational waves associated with magnetar bursts

Soft gamma repeaters and anomalous X-ray pulsars are thought to be magnetars, neutron stars with strong magnetic fields of order

Advanced LIGO searches for gravitational waves associated with gamma-ray bursts

mathord{sim} 10^{13}

Coherently searching for perturbed black-hole ringdown signals with a network of gravitational-wave detectors

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Searching for perturbed black-hole ringdown signals with a network of gravitational-wave detectors

10^{15} , mathrm{gauss}