Multibaseline 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 SGWB, 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 [Class. Quant. Grav. 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 SGWB signal in (simulated) data. Although we use simulated noise and SGWB signals for making these comparisons, our method can be straightforwardly applied on real data.Comment: 17 pages and 19 figure

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 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 non-spherical. 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 $\epsilon$ as a function of the number of in-band Galactic neutron stars $N_\text{tot}$. For the plausible case of $N_\text{tot}\approx 53000$, and assuming one year of observation time with colocated initial LIGO detectors, we find it to be $\sigma_\epsilon=2.1\times10^{-7}$, which is comparable to current bounds on some nearby neutron stars. (The current best $95\%$ upper limits are $\epsilon\lesssim7\times10^{-8}.$) It is unclear if Advanced LIGO can significantly improve on this sensitivity using spatially separated detectors. For the proposed Einstein Telescope, we estimate that $\sigma\epsilon=5.6\times10^{-10}$. 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 ≳25  M_⊙ 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 (≳25  M_⊙) 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_⊙ and 100  M_⊙, 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 10  M_⊙ and 600  M_⊙, 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

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 $\mathord{\sim} 10^{13}$--$10^{15} \, \mathrm{gauss}$. These objects emit intermittent bursts of hard X-rays and soft gamma rays. Quasiperiodic oscillations in the X-ray tails of giant flares imply the existence of neutron star oscillation modes which could emit gravitational waves powered by the magnetar's magnetic energy reservoir. We describe a method to search for transient gravitational-wave signals associated with magnetar bursts with durations of 10s to 1000s of seconds. The sensitivity of this method is estimated by adding simulated waveforms to data from the sixth science run of Laser Interferometer Gravitational-wave Observatory (LIGO). We find a search sensitivity in terms of the root sum square strain amplitude of $h_{\mathrm{rss}} = 1.3 \times 10^{-21} \, \mathrm{Hz}^{-1/2}$ for a half sine-Gaussian waveform with a central frequency $f_0 = 150 \, \mathrm{Hz}$ and a characteristic time $\tau = 400 \, \mathrm{s}$. This corresponds to a gravitational wave energy of $E_{\mathrm{GW}} = 4.3 \times 10^{46} \, \mathrm{erg}$, the same order of magnitude as the 2004 giant flare which had an estimated electromagnetic energy of $E_{\mathrm{EM}} = \mathord{\sim} 1.7 \times 10^{46} (d/ 8.7 \, \mathrm{kpc})^2 \, \mathrm{erg}$, where $d$ is the distance to SGR 1806-20. We present an extrapolation of these results to Advanced LIGO, estimating a sensitivity to a gravitational wave energy of $E_{\mathrm{GW}} = 3.2 \times 10^{43} \, \mathrm{erg}$ for a magnetar at a distance of $1.6 \, \mathrm{kpc}$. These results suggest this search method can probe significantly below the energy budgets for magnetar burst emission mechanisms such as crust cracking and hydrodynamic deformation

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

MULTI-BASELINE SEARCHES FOR STOCHASTIC SOURCES AND BLACK HOLE RINGDOWN SIGNALS IN LIGO-VIRGO DATA

We present a framework for the detection of stochastic gravitational-wave (GW) backgrounds, from cosmological and astrophysical sources, using radiometry with a network of gravitational-wave interferometers. The search statistic itself is derived from the cross-correlations of the data across all possible baselines in a detector network, and reveals how much more sensitive a network is than any of its component baselines. We model the neutron star distribution in the Virgo cluster and apply the above framework to search for their stochastic GW signature in LIGO-VIRGO dataWe also present a template-based multi-detector coherent search for perturbed black hole ringdown signals. Like the past ``coincidence'' ringdown searches in LIGO data, our method incorporates knowledge of the ringdown waveform in constructing the search templates. Additionally, it checks for consistency of signal amplitudes and phases in the different detectors with their different orientations and signal arrival times. We demonstrate the advantages of implementing a coherent search in the ringdown search pipeline

Multi-baseline gravitational wave radiometry

We consider the maximum likelihood (ML) statistic for detecting an anisotropic astrophysical stochastic gravitational-wave background with multiple interferometric baselines. For any given baseline, we establish a formalism for constructing an orthonormal pixel basis in sky positions utilizing the knowledge of the point-spread function for that baseline. The ML statistic for a single baseline is then just the excess power in that orthonormal basis. An analogous formulation of the ML statistic is available for a spherical harmonic basis and lays the ground-work for a systematic comparison between the effectiveness of pixel-based and spherical-harmonic-based deconvolution techniques for a variety of stochastic source distributions. The sensitivities of three different baselines and their network for single- and multi-pixel sources are compared here. For detector noise that is Gaussian and uncorrelated across baselines, the network sensitivity-squared is the sum of the squares of the individual baseline sensitivities, analogous to what was found before for the network signal-to-noise ratio (SNR) of the "optimal filter" statistic for an isotropic stochastic gravitational wave background. Also, the accuracies with which a single-pixel source can be located with the separate baselines and their network are obtained and compared using the Fisher information matrix