Search for: All records

Pulsar timing arrays (PTAs) detect gravitational waves (GWs) via the correlations they create in the arrival times of pulses from different pulsars. The mean correlation, a function of the angle between the directions to two pulsars, was predicted in 1983 by Hellings and Downs (HD). Observation of this angular pattern is crucial evidence that GWs are present, so PTAs “reconstruct the HD curve” by estimating the correlation using pulsar pairs separated by similar angles. Several studies have examined the amount by which this curve is expected to differ from the HD mean. The variance arises because (a) a finite set of pulsars at specific sky locations is used, (b) the GW sources interfere, and (c) the data are contaminated by noise. Here, for a Gaussian ensemble of sources, we predict that variance by constructing an optimal estimator of the HD correlation, taking into account the pulsar sky locations and the frequency distribution of the GWs and the pulsar noise. The variance is a ratio: the numerator depends upon the pulsar sky locations, and the denominator is the (effective) number of frequency bins for which the GW signal dominates the noise. In effect, after suitable combination, each such frequency bin gives an independent estimate of the HD correlation. Published by the American Physical Society2025 

Pulsar timing arrays (PTAs) hunt for gravitational waves (GWs) by searching for the correlations that GWs induce in the time-of-arrival residuals from different pulsars. If the GW sources are of astrophysical origin, then they are located at discrete points on the sky. However, PTA data are often modeled, and subsequently analyzed, via a “standard Gaussian ensemble.” That ensemble is obtained in the limit of an infinite density of vanishingly weak, Poisson-distributed sources. In this paper, we move away from that ensemble, to study the effects of two types of “source anisotropy.” The first (a), which is often called “shot noise,” arises because there are $N$discrete GW sources at specific sky locations. The second (b) arises because the GW source positions are not a Poisson process, for example, because galaxy locations are clustered. Here, we quantify the impact of (a) and (b) on the mean and variance of the pulsar-averaged Hellings and Downs correlation. For conventional PTA sources, we show that the effects of shot noise (a) are much larger than the effects of clustering (b). Published by the American Physical Society2024 

Abstract Statistical anisotropy in the nanohertz-frequency gravitational wave background (GWB) is expected to be detected by pulsar timing arrays (PTAs) in the near future. By developing a frequentist statistical framework that intrinsically restricts the GWB power to be positive, we establish scaling relations for multipole-dependent anisotropy decision thresholds that are a function of the noise properties, timing baselines, and cadences of the pulsars in a PTA. We verify that (i) a larger number of pulsars, and (ii) factors that lead to lower uncertainty on spatial cross-correlation measurements between pulsars, lead to a higher overall GWB signal-to-noise ratio, and lower anisotropy decision thresholds with which to reject the null hypothesis of isotropy. Using conservative simulations of realistic NANOGrav data sets, we predict that an anisotropic GWB with angular power C l =1 > 0.3 C l =0 may be sufficient to produce tension with isotropy at the p = 3 × 10 −3 (∼3 σ ) level in near-future NANOGrav data with a 20 yr baseline. We present ready-to-use scaling relationships that can map these thresholds to any number of pulsars, configuration of pulsar noise properties, or sky coverage. We discuss how PTAs can improve the detection prospects for anisotropy, as well as how our methods can be adapted for more versatile searches. 

Abstract The collection of gravitational waves (GWs) that are either too weak or too numerous to be individually resolved is commonly referred to as the gravitational-wave background (GWB). A confident detection and model-driven characterization of such a signal will provide invaluable information about the evolution of the universe and the population of GW sources within it. We present a new, user-friendly, Python-based package for GW data analysis to search for an isotropic GWB in ground-based interferometer data. We employ cross-correlation spectra of GW detector pairs to construct an optimal estimator of the Gaussian and isotropic GWB, and Bayesian parameter estimation to constrain GWB models. The modularity and clarity of the code allow for both a shallow learning curve and flexibility in adjusting the analysis to one’s own needs. We describe the individual modules that make up pygwb , following the traditional steps of stochastic analyses carried out within the LIGO, Virgo, and KAGRA Collaboration. We then describe the built-in pipeline that combines the different modules and validate it with both mock data and real GW data from the O3 Advanced LIGO and Virgo observing run. We successfully recover all mock data injections and reproduce published results. 

Abstract Evidence has emerged for a stochastic signal correlated among 67 pulsars within the 15 yr pulsar-timing data set compiled by the NANOGrav collaboration. Similar signals have been found in data from the European, Indian, Parkes, and Chinese pulsar timing arrays. This signal has been interpreted as indicative of the presence of a nanohertz stochastic gravitational-wave background (GWB). To explore the internal consistency of this result, we investigate how the recovered signal strength changes as we remove the pulsars one by one from the data set. We calculate the signal strength using the (noise-marginalized) optimal statistic, a frequentist metric designed to measure the correlated excess power in the residuals of the arrival times of the radio pulses. We identify several features emerging from this analysis that were initially unexpected. The significance of these features, however, can only be assessed by comparing the real data to synthetic data sets. After conducting identical analyses on simulated data sets, we do not find anything inconsistent with the presence of a stochastic GWB in the NANOGrav 15 yr data. The methodologies developed here can offer additional tools for application to future, more sensitive data sets. While this analysis provides an internal consistency check of the NANOGrav results, it does not eliminate the necessity for additional investigations that could identify potential systematics or uncover unmodeled physical phenomena in the data. 

Abstract Recently we found compelling evidence for a gravitational-wave background with Hellings and Downs (HD) correlations in our 15 yr data set. These correlations describe gravitational waves as predicted by general relativity, which has two transverse polarization modes. However, more general metric theories of gravity can have additional polarization modes, which produce different interpulsar correlations. In this work, we search the NANOGrav 15 yr data set for evidence of a gravitational-wave background with quadrupolar HD and scalar-transverse (ST) correlations. We find that HD correlations are the best fit to the data and no significant evidence in favor of ST correlations. While Bayes factors show strong evidence for a correlated signal, the data does not strongly prefer either correlation signature, with Bayes factors ∼2 when comparing HD to ST correlations, and ∼1 for HD plus ST correlations to HD correlations alone. However, when modeled alongside HD correlations, the amplitude and spectral index posteriors for ST correlations are uninformative, with the HD process accounting for the vast majority of the total signal. Using the optimal statistic, a frequentist technique that focuses on the pulsar-pair cross-correlations, we find median signal-to-noise ratios of 5.0 for HD and 4.6 for ST correlations when fit for separately, and median signal-to-noise ratios of 3.5 for HD and 3.0 for ST correlations when fit for simultaneously. While the signal-to-noise ratios for each of the correlations are comparable, the estimated amplitude and spectral index for HD are a significantly better fit to the total signal, in agreement with our Bayesian analysis.