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Abstract Finding and characterizing gravitational waves from individual supermassive black hole binaries is a central goal of pulsar timing array experiments, which will require analysis methods that can be efficient on our rapidly growing datasets. Here we present a novel approach built on three key elements: (i) precalculating and interpolating expensive matrix operations; (ii) semi-analytically marginalizing over the gravitational-wave phase at the pulsars; (iii) numerically marginalizing over the pulsar distance uncertainties. With these improvements the recent NANOGrav 15 yr dataset can be analyzed in minutes after an $O\left(1\mathrm{h}\right)$setup phase, instead of an analysis taking days–weeks with previous methods. The same setup can be used to efficiently analyze the dataset under any sinusoidal deterministic model. In particular, this will aid testing the binary hypothesis by allowing for efficient analysis of competing models (e.g. incoherent, monopolar, or dipolar sine wave model) and scrambled datasets for false alarm studies. The same setup can be updated in minutes for new realizations of the data, which enables large simulation studies. 

Abstract While supermassive black hole (SMBH) binaries are not the only viable source for the low-frequency gravitational wave background (GWB) signal evidenced by the most recent pulsar timing array (PTA) data sets, they are expected to be the most likely. Thus, connecting the measured PTA GWB spectrum and the underlying physics governing the demographics and dynamics of SMBH binaries is extremely important. Previously, Gaussian processes (GPs) and dense neural networks have been used to make such a connection by being built as conditional emulators; their input is some selected evolution or environmental SMBH binary parameters and their output is the emulated mean and standard deviation of the GWB strain ensemble distribution over many Universes. In this paper, we use a normalizing flow (NF) emulator that is trained on the entirety of the GWB strain ensemble distribution, rather than only mean and standard deviation. As a result, we can predict strain distributions that mirror underlying simulations very closely while also capturing frequency covariances in the strain distributions as well as statistical complexities such as tails, non-Gaussianities, and multimodalities that are otherwise not learnable by existing techniques. In particular, we feature various comparisons between the NF-based emulator and the GP approach used extensively in past efforts. Our analyses conclude that the NF-based emulator not only outperforms GPs in the ease and computational cost of training but also outperforms in the fidelity of the emulated GWB strain ensemble distributions. 

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. 

Abstract The nanohertz frequency band explored by pulsar timing arrays provides a unique discovery space for gravitational wave (GW) signals. In addition to signals from anticipated sources, such as those from supermassive black hole binaries, some previously unimagined sources may emit transient GWs (a.k.a. bursts) with unknown morphology. Unmodeled transients are not currently searched for in this frequency band, and they require different techniques from those currently employed. Possible sources of such GW bursts in the nanohertz regime are parabolic encounters of supermassive black holes, cosmic string cusps and kinks, or other, as-yet-unknown phenomena. In this paper we present BayesHopperBurst , a Bayesian search algorithm capable of identifying generic GW bursts by modeling both coherent and incoherent transients as a sum of Morlet–Gabor wavelets. A trans-dimensional reversible jump Markov chain Monte Carlo sampler is used to select the number of wavelets best describing the data. We test BayesHopperBurst on various simulated datasets including different combinations of signals and noise transients. Its capability to run on real data is demonstrated by analyzing data of the pulsar B1855 + 09 from the NANOGrav 9 year dataset. Based on a simulated dataset resembling the NANOGrav 12.5 year data release, we predict that at our most sensitive time–frequency location we will be able to probe GW bursts with a root-sum-squared amplitude higher than ∼5 × 10 −11  Hz −1/2 , which corresponds to ∼40 M ⊙ c 2 emitted in GWs at a fiducial distance of 100 Mpc. 

Abstract Pulsar timing array observations have found evidence for an isotropic gravitational-wave background with the Hellings–Downs angular correlations between pulsar pairs. This interpretation hinges on the measured shape of the angular correlations, which is predominantly quadrupolar under general relativity. Here we explore a more flexible parameterization: we expand the angular correlations into a sum of Legendre polynomials and use a Bayesian analysis to constrain their coefficients with the 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). When including Legendre polynomials with multipolesℓ≥ 2, we only find a significant signal in the quadrupole with an amplitude consistent with general relativity and nonzero at the ∼95% confidence level and a Bayes factor of 200. When we include multipolesℓ≤ 1, the Bayes factor evidence for quadrupole correlations decreases by more than an order of magnitude due to evidence for a monopolar signal at approximately 4 nHz, which has also been noted in previous analyses of the NANOGrav 15 yr data. Further work needs to be done in order to better characterize the properties of this monopolar signal and its effect on the evidence for quadrupolar angular correlations. 

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.