We review detection methods that are currently in use or have been proposed to search for a stochastic background of gravitational radiation. We consider both Bayesian and frequentist searches using ...ground-based and space-based laser interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we allow for anisotropy, non-Gaussianity, and non-standard polarization states. Our focus is on relevant data analysis issues, and not on the particular astrophysical or early Universe sources that might give rise to such backgrounds. We provide a unified treatment of these searches at the level of detector response functions, detection sensitivity curves, and, more generally, at the level of the likelihood function, since the choice of signal and noise models and prior probability distributions are actually what define the search. Pedagogical examples are given whenever possible to compare and contrast different approaches. We have tried to make the article as self-contained and comprehensive as possible, targeting graduate students and new researchers looking to enter this field.
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The detection rate for compact binary mergers has grown as the sensitivity of the global network of ground based gravitational wave detectors has improved, now reaching the stage where robust ...automation of the analyses is essential. Automated low-latency algorithms have been developed that send out alerts when candidate signals are detected. The alerts include sky maps to facilitate electromagnetic follow-up observations, along with probabilities that the system might contain a neutron star, and hence be more likely to generate an electromagnetic counterpart. Data quality issues, such as loud noise transients (glitches), can adversely affect the low-latency algorithms, causing false alarms and throwing off parameter estimation. Here a new analysis method is presented that is robust against glitches, and capable of producing fully Bayesian parameter inference, including sky maps and mass estimates, in a matter of minutes. Key elements of the method are wavelet-based de-noising, penalized maximization of the likelihood during the initial search, rapid sky localization using precomputed inner products, and heterodyned likelihoods for full Bayesian inference.
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Data from gravitational wave detectors are recorded as time series that include contributions from myriad noise sources in addition to any gravitational wave signals. When regularly sampled data are ...available, such as for ground based and future space based interferometers, analyses are typically performed in the frequency domain, where stationary (time invariant) noise processes can be modeled very efficiently. In reality, detector noise is not stationary due to a combination of short duration noise transients and longer duration drifts in the power spectrum. This nonstationarity produces correlations across samples at different frequencies, obviating the main advantage of a frequency domain analysis. Here an alternative time-frequency approach to gravitational wave data analysis is proposed that uses discrete, orthogonal wavelet wave packets. The time domain data is mapped onto a uniform grid of time-frequency pixels. For locally stationary noise-that is, noise with an adiabatically varying spectrum-the time-frequency pixels are uncorrelated, which greatly simplifies the calculation of quantities such as the likelihood. Moreover, the gravitational wave signals from binary systems can be compactly represented as a collection of lines in time-frequency space, resulting in a computational cost for computing waveforms and likelihoods that scales as the square root of the number of time samples, as opposed to the linear scaling for time or frequency based analyses. Key to this approach is having fast methods for computing binary signals directly in the wavelet domain. Multiple fast transform methods are developed in detail.
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Galactic ultracompact binaries are expected to be the dominant source of gravitational waves in the milli-Hertz frequency band. Of the tens of millions of Galactic binaries with periods shorter than ...an hour, it is estimated that a few tens of thousand will be resolved by the future Laser Interferometer Space Antenna (LISA). The unresolved remainder will be the main source of "noise" between 1 and 3 mHz. Typical Galactic binaries are millions of years from merger, and consequently their signals will persist for the duration of the LISA mission. Extracting tens of thousands of overlapping Galactic signals and characterizing the unresolved component is a central challenge in LISA data analysis, and a key contribution to arriving at a global solution that simultaneously fits for all signals in the band. Here we present an end-to-end analysis pipeline for Galactic binaries that uses transdimensional Bayesian inference to develop a time-evolving catalog of sources as data arrive from the LISA constellation.
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A central challenge in gravitational wave astronomy is identifying weak signals in the presence of non-stationary and non-Gaussian noise. The separation of gravitational wave signals from noise ...requires good models for both. When accurate signal models are available, such as for binary Neutron star systems, it is possible to make robust detection statements even when the noise is poorly understood. In contrast, searches for 'un-modeled' transient signals are strongly impacted by the methods used to characterize the noise. Here we take a Bayesian approach and introduce a multi-component, variable dimension, parameterized noise model that explicitly accounts for non-stationarity and non-Gaussianity in data from interferometric gravitational wave detectors. Instrumental transients (glitches) and burst sources of gravitational waves are modeled using a Morlet-Gabor continuous wavelet frame. The number and placement of the wavelets is determined by a trans-dimensional reversible jump Markov chain Monte Carlo algorithm. The Gaussian component of the noise and sharp line features in the noise spectrum are modeled using the BayesLine algorithm, which operates in concert with the wavelet model.
Black hole hunting with LISA Cornish, Neil J.; Shuman, Kevin
Physical review. D,
06/2020, Volume:
101, Issue:
12
Journal Article
Peer reviewed
Open access
The Laser Interferometer Space Antenna (LISA) will be able to detect massive black hole mergers throughout the visible Universe. These observations will provide unique information about black hole ...formation and growth, and the role black holes play in galaxy evolution. Here we develop several key building blocks for detecting and characterizing black hole binary mergers with LISA, including fast heterodyned likelihood evaluations, and efficient stochastic search techniques.
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Abstract
Hundreds of millions of supermassive black hole binaries are expected to contribute to the gravitational-wave signal in the nanohertz frequency band. Their signal is often approximated ...either as an isotropic Gaussian stochastic background with a power-law spectrum or as an individual source corresponding to the brightest binary. In reality, the signal is best described as a combination of a stochastic background and a few of the brightest binaries modeled individually. We present a method that uses this approach to efficiently create realistic pulsar timing array data sets using synthetic catalogs of binaries based on the Illustris cosmological hydrodynamic simulation. We explore three different properties of such realistic backgrounds that could help distinguish them from those formed in the early universe: (i) their characteristic strain spectrum, (ii) their statistical isotropy, and (iii) the variance of their spatial correlations. We also investigate how the presence of confusion noise from a stochastic background affects detection prospects of individual binaries. We calculate signal-to-noise ratios of the brightest binaries in different realizations for a simulated pulsar timing array based on the NANOGrav 12.5 yr data set extended to a time span of 15 yr. We find that ∼6% of the realizations produce systems with signal-to-noise ratios larger than 5, suggesting that individual systems might soon be detected (the fraction increases to ∼41% at 20 yr). These can be taken as a pessimistic prediction for the upcoming NANOGrav 15 yr data set, since it does not include the effect of potentially improved timing solutions and newly added pulsars.
With the goal of observing a stochastic gravitational-wave background (SGWB) with LISA, the spectral separability of the cosmological and astrophysical backgrounds is important to estimate. We ...attempt to determine the level with which a cosmological background can be observed given the predicted astrophysical background level. We predict detectable limits for the future LISA measurement of the SGWB. Adaptive Markov chain Monte Carlo methods are used to produce estimates with the simulated data from the LISA Data Challenge. We also calculate the Cramer-Rao lower bound on the variance of the SGWB parameter estimates based on the inverse Fisher information using the Whittle likelihood. The estimation of the parameters is done with the three LISA channels A , E , and T . We simultaneously estimate the noise using a LISA noise model. Assuming the expected astrophysical background around ΩGW,astro ( 25 Hz ) = 0.355 → 35.5 × 10−9, a cosmological SGWB normalized energy density of around ΩGW, Cosmo ≈ 1 × 10−12 to 1 × 10-13 can be detected by LISA after 4 years of observation.
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The coalescence of compact objects is one of the most promising sources, as well as the source of the first detections, of gravitational waves for ground-based interferometric detectors, such as ...advanced LIGO and Virgo. Generically, compact objects in binaries are expected to be spinning with spin angular momenta misaligned with the orbital angular momentum, causing the orbital plane to precess. This precession adds rich structure to the gravitational waves, introducing such complexity that an analytic closed-form description has been unavailable until now. We here construct the first closed-form frequency-domain gravitational waveforms that are valid for generic spin-precessing quasicircular compact binary inspirals. We first construct time-domain gravitational waves by solving the post-Newtonian precession equations of motion with radiation reaction through multiple scale analysis. We then Fourier transform these time-domain waveforms with the method of shifted uniform asymptotics to obtain closed-form expressions for frequency-domain waveforms. We study the accuracy of these analytic, frequency-domain waveforms relative to waveforms obtained by numerically evolving the post-Newtonian equations of motion and find that they are suitable for unbiased parameter estimation for 99.2%(94.6%) of the binary configurations we studied at a signal-to-noise ratio of 10(25). These new frequency-domain waveforms could be used for detection and parameter estimation studies due to their accuracy and low computational cost.
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A significant fraction of stars are members of gravitationally bound hierarchies containing three or more components. Almost all low-mass stars in binaries with periods shorter than three days are ...part of a hierarchical system. We therefore anticipate that a large fraction of compact galactic binaries detected by the Laser Interferometer Space Antenna will be members of hierarchical triple or quadruple system. The acceleration imparted by the hierarchical companions can be detected in the gravitational wave signal for outer periods as large as 100 years. For systems with periods that are shorter than, or comparable to, the mission lifetime, it will be possible to measure the period and eccentricity of the outer orbit. Laser Interferometer Space Antenna observations of hierarchical stellar systems will provide insight into stellar evolution, including the role that Lidov-Kozai oscillations play in driving systems toward merger.
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