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Pulsar timing arrays (PTAs) are ensembles of millisecond pulsars observed for years to decades. The primary goal of PTAs is to study gravitational-wave astronomy at nanohertz frequencies, with secondary goals of undertaking other fundamental tests of physics and astronomy. Recently, compelling evidence has emerged in established PTA experiments for the presence of a gravitational-wave background. To accelerate a confident detection of such a signal and then study gravitational-wave emitting sources, it is necessary to observe a larger number of millisecond pulsars to greater timing precision. The SKA telescopes, which will be a factor of three to four greater in sensitivity compared to any other southern hemisphere facility, is poised to make such an impact. In this chapter, we motivate an SKAO pulsar timing array (SKAO PTA) experiment. We discuss the classes of gravitational waves present in PTA observations and how an SKAO PTA can detect and study them. We then describe the sources that can produce these signals. We discuss the astrophysical noise sources that must be mitigated to undertake the most sensitive searches. We then describe a realistic PTA experiment implemented with the SKA and place it in context alongside other PTA experiments likely ongoing in the 2030s. We describe the techniques necessary to search for gravitational waves in the SKAO PTA and motivate how very long baseline interferometry can improve the sensitivity of an SKAO PTA. The SKAO PTA will provide a view of the Universe complementary to those of the other large facilities of the 2030s. 

Abstract Based on the rate of change of its orbital period, PSR J2043+1711 has a substantial peculiar acceleration of 3.5 ± 0.8 mm s^–1yr^–1, which deviates from the acceleration predicted by equilibrium Milky Way (MW) models at a 4σlevel. The magnitude of the peculiar acceleration is too large to be explained by disequilibrium effects of the MW interacting with orbiting dwarf galaxies (∼1 mm s^–1yr^–1), and too small to be caused by period variations due to the pulsar being a redback. We identify and examine two plausible causes for the anomalous acceleration: a stellar flyby, and a long-period orbital companion. We identify a main-sequence star in Gaia DR3 and Pan-STARRS DR2 with the correct mass, distance, and on-sky position to potentially explain the observed peculiar acceleration. However, the star and the pulsar system have substantially different proper motions, indicating that they are not gravitationally bound. However, it is possible that this is an unrelated star that just happens to be located near J2043+1711 along our line of sight (chance probability of 1.6%). Therefore, we also constrain possible orbital parameters for a circumbinary companion in a hierarchical triple system with J2043+1711; the changes in the spindown rate of the pulsar are consistent with an outer object that has an orbital period of 60 kyr, a companion mass of 0.3M_⊙(indicative of a white dwarf or low-mass star), and a semimajor axis of 1900 au. Continued timing and/or future faint optical observations of J2043+1711 may eventually allow us to differentiate between these scenarios. 

Abstract With strong evidence of a common-spectrum stochastic process in the most recent data sets from the NANOGrav Collaboration, the European Pulsar Timing Array (PTA), Parkes PTA, and the International PTA, it is crucial to assess the effects of the several astrophysical and cosmological sources that could contribute to the stochastic gravitational wave background (GWB). Using the same data set creation and injection techniques as in Pol et al., we assess the separability of multiple GWBs by creating single and multiple GWB source data sets. We search for these injected sources using Bayesian PTA analysis techniques to assess recovery and separability of multiple astrophysical and cosmological backgrounds. For a GWB due to supermassive black hole binaries and an underlying weaker background due to primordial gravitational waves with a GW energy-density ratio of Ω_PGW/Ω_SMBHB= 0.5, the Bayes’ factor for a second process exceeds unity at 17 yr, and increases with additional data. At 20 yr of data, we are able to constrain the spectral index and amplitude of the weaker GWB at this density ratio to a fractional uncertainty of 64% and 110%, respectively, using current PTA methods and techniques. Using these methods and findings, we outline a basic protocol to search for multiple backgrounds in future PTA data sets. 

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. 

Abstract We present the results of a search for nonlinear gravitational-wave (GW) memory in the NANOGrav 15 yr data set. We find no significant evidence for memory signals in the data set, with a maximum Bayes factor of 3.1 in favor of a model including memory. We therefore place upper limits on the strain of potential GW memory events as a function of sky location and observing epoch. We find upper limits that are not always more constraining than previous NANOGrav results. We show that it is likely due to the increase in common red noise between the 12.5 and 15 yr NANOGrav data sets. 

Abstract We have used X-ray data from the Neutron Star Interior Composition Explorer (NICER) to search for long-timescale temporal correlations (“red noise”) in the pulse times of arrival (TOAs) from the millisecond pulsars PSR J1824−2452A and PSR B1937+21. These data more closely track intrinsic noise because X-rays are unaffected by the radio-frequency-dependent propagation effects of the interstellar medium. Our search yields strong evidence (natural log Bayes factor of 9.634 ± 0.016) for red noise in PSR J1824−2452A, but the search is inconclusive for PSR B1937+21. In the interest of future X-ray missions, we devise and implement a method to simulate longer and higher-precision X-ray data sets to determine the timing baseline necessary to detect red noise. We find that the red noise in PSR B1937+21 can be reliably detected in a 5 yr mission with a TOA error of 2μs and an observing cadence of 20 observations per month compared to the 5μs TOA error and 11 observations per month that NICER currently achieves in PSR B1937+21. We investigate detecting red noise in PSR B1937+21 with other combinations of observing cadences and TOA errors. We also find that time-correlated red noise commensurate with an injected stochastic gravitational-wave background having an amplitude ofA_GWB= 2 × 10⁻¹⁵and spectral index of timing residuals ofγ_GWB= 13/3 can be detected in a pulsar with similar TOA precision to PSR B1937+21. This is with no additional red noise in a 10 yr mission that observes the pulsar 15 times per month and has an average TOA error of 1μs. 

Abstract Using Bayesian analyses we study the solar electron density with the NANOGrav 11 yr pulsar timing array (PTA) data set. Our model of the solar wind is incorporated into a global fit starting from pulse times of arrival. We introduce new tools developed for this global fit, including analytic expressions for solar electron column densities and open source models for the solar wind that port into existing PTA software. We perform an ab initio recovery of various solar wind model parameters. We then demonstrate the richness of information about the solar electron density, n E , that can be gleaned from PTA data, including higher order corrections to the simple 1/ r 2 model associated with a free-streaming wind (which are informative probes of coronal acceleration physics), quarterly binned measurements of n E and a continuous time-varying model for n E spanning approximately one solar cycle period. Finally, we discuss the importance of our model for chromatic noise mitigation in gravitational-wave analyses of pulsar timing data and the potential of developing synergies between sophisticated PTA solar electron density models and those developed by the solar physics community.