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Abstract Arrays of precisely-timed millisecond pulsars are used to search for gravitational waves with periods of months to decades. Gravitational waves affect the path of radio pulses propagating from a pulsar to Earth, causing the arrival times of those pulses to deviate from expectations based on the physical characteristics of the pulsar system. By correlating these timing residuals in a pulsar timing array (PTA), one can search for a statistically isotropic background of gravitational waves by revealing evidence for a distinctive pattern predicted by General Relativity, known as the Hellings & Downs curve. On June 29 2023, five regional PTA collaborations announced the first evidence for GWs at light-year wavelengths, predicated on support for this correlation pattern with statistical significances ranging from$$\sim \!2-4\sigma $$ $\sim 2-4\sigma$. The amplitude and shape of the recovered GW spectrum has also allowed many investigations of the expected source characteristics, ranging from a cosmic population of supermassive binary black holes to numerous processes in the early Universe. In the future, we expect to resolve signals from individual binary systems of supermassive black holes, and probe fundamental assumptions about the background, including its polarization, anisotropy, Gaussianity, and stationarity, all of which will aid efforts to discriminate its origin. In tandem with new facilities like DSA-2000 and the SKA, fueling further observations by regional PTAs and the International Pulsar Timing Array, PTAs have extraordinary potential to be engines of nanohertz GW discovery. 

Abstract Pulsar timing arrays (PTAs) are approaching the sensitivity required to resolve gravitational waves (GWs) from individual supermassive black hole (SMBH) binaries. However, the large uncertainty in source localization will make the identification of its host environment challenging. We show how to convert the posterior probability function of binary parameters inferred by GW analyses into distributions of apparent magnitudes of the host galaxy. We do so for a scenario in which the host environment is a regular early-type galaxy, and one in which it is an active galactic nucleus. We estimate the reach of PTAs in the near and intermediate future, and estimate whether the binary hosts will be detectable in all-sky electromagnetic (EM) surveys. A PTA with a baseline of 20 yr and 116 pulsars, resembling the upcoming data release of the International Pulsar Timing Array, can detect binaries out to a luminosity distance of 2 Gpc (corresponding to a redshift ofz ∼ 0.36), while a PTA with a baseline of 30 yr and 200 pulsars can reach out to distances slightly greater than 3 Gpc (z ∼ 0.53). We find that the host galaxies of all binaries detectable with a baseline of 20 yr are expected to be present in the Wide-field Infrared Survey Explorer and SuperCOSMOS surveys, if they lie outside the plane of the Milky Way. The Two Micron All Sky Survey becomes incomplete for hosts of binaries more massive than 10^9.8M_⊙at a luminosity distance greater than 1 Gpc. The EM surveys become slightly more incomplete when PTAs with longer baselines and therefore improved sensitivities are considered. 

Abstract The recent discovery of the stochastic gravitational-wave background via pulsar timing arrays will likely be followed by the detection of individual black hole binaries that stand out above the background. However, to confidently claim the detection of an individual binary, we need not only more and better data, but also more sophisticated analysis techniques. In this paper, we develop two new approaches that can help us more robustly ascertain if a candidate found by a search algorithm is indeed an individual supermassive black hole binary. One of these is a coherence test that directly compares the full signal model to an incoherent version of that. The other is a model scrambling approach that builds null distributions of our detection statistic and compares that with the measured value to quantify our confidence in signal coherence. Both of these rely on finding the coherence between pulsars characteristic to gravitational waves (GWs) from a binary system. We test these methods on simple simulated datasets and find that they work well in correctly identifying both true GWs and false positives. However, as expected for such a flexible and simple signal model, confidently identifying signal coherence is significantly harder than simply finding a candidate in most scenarios. Our analyses also indicate that the confidence with which we can identify a true signal depends not only on the signal-to-noise ratio, but also on the number of contributing pulsars and the amount of frequency evolution shown by the signal. 

Abstract Massive black hole binaries (MBHBs) produce gravitational waves (GWs) that are detectable with pulsar timing arrays. We determine the properties of the host galaxies of simulated MBHBs at the time they are producing detectable GW signals. The population of MBHB systems we evaluate is from theIllustriscosmological simulations taken in tandem with post processing semi-analytic models of environmental factors in the evolution of binaries. Upon evolving to the GW frequency regime accessible by pulsar timing arrays, we calculate the detection probability of each system using a variety of different values for pulsar noise characteristics in a plausible near-future International Pulsar Timing Array dataset. We find that detectable systems have host galaxies that are clearly distinct from the overall binary population and from most galaxies in general. With conservative noise factors, we find that host stellar metallicity, for example, peaks at $\sim 2Z_{\odot }$as opposed to the total population of galaxies which peaks at $\sim 0.6Z_{\odot }$. Additionally, the most detectable systems are much brighter in magnitude and more red in color than the overall population, indicating their likely identity as large ellipticals with diminished star formation. These results can be used to develop effective search strategies for identifying host galaxies and electromagnetic counterparts following GW detection by pulsar timing arrays. 

Abstract Supermassive black hole binaries (SMBHBs) are thought to form in galaxy mergers, possessing the potential to produce electromagnetic (EM) radiation as well as gravitational waves (GWs) detectable with pulsar timing arrays (PTAs). Once GWs from individually resolved SMBHBs are detected, the identification of the host galaxy will be a major challenge due to the ambiguity in possible EM signatures and the poor localization capability of PTAs. To aid EM observations in choosing follow-up sources, we use NANOGrav’s galaxy catalog to quantify the number of plausible hosts in both realistic and idealistic scenarios. We outline a host identification pipeline that injects a single-source GW signal into a simulated PTA data set, recovers the signal using production-level techniques, quantifies the localization region and number of galaxies contained therein, and finally imposes cuts on the galaxies using parameter estimates from the GW search. In an ideal case, the 90% credible areas span 29–241 deg², containing about 14–341 galaxies. After cuts, the number of galaxies remaining ranges from 22 at worst to one true host at best. In a realistic case, these areas range from 287 to 530 deg²and enclose about 285–1238 galaxies. After cuts, the number of galaxies is 397 at worst and 27 at best. While the signal-to-noise ratio is the primary determinant of the localization area of a given source, we find that the area is also influenced by the proximity to nearby pulsars on the sky and the binary chirp mass. 

Abstract A population of compact object binaries emitting gravitational waves that are not individually resolvable will form a stochastic gravitational-wave signal. While the expected spectrum over population realizations is well known from Phinney, its higher-order moments have not been fully studied before or computed in the case of arbitrary binary evolution. We calculate analytic scaling relationships as a function of gravitational-wave frequency for the statistical variance, skewness, and kurtosis of a stochastic gravitational-wave signal over population realizations due to finite source effects. If the time derivative of the binary orbital frequency can be expressed as a power law in frequency, we find that these moment quantities also take the form of power-law relationships. We also develop a numerical population synthesis framework against which we compare our analytic results, finding excellent agreement. These new scaling relationships provide physical context to understanding spectral fluctuations in a gravitational-wave background signal and may provide additional information that can aid in explaining the origin of the nanohertz-frequency signal observed by pulsar timing array campaigns. 

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.