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Pulsar timing arrays (PTAs) are Galactic-scale gravitational wave (GW) detectors consisting of precisely timed pulsars distributed across the sky. Within the decade, PTAs are expected to detect nanohertz GWs emitted by close-separation supermassive black hole binaries (SMBHBs), thereby opening up the low-frequency end of the GW spectrum for science. Individual SMBHBs which power active galactic nuclei are also promising multi-messenger sources; they may be identified via theoretically predicted electromagnetic (EM) signatures and be followed up by PTAs for GW observations. In this work, we study the detection and parameter estimation prospects of a PTA which targets EM-selected SMBHBs. Adopting a simulated Galactic millisecond pulsar population, we envisage three different pulsar timing campaigns which observe three mock sources at different sky locations. We find that an all-sky PTA which times the best pulsars is an optimal and feasible approach to observe EM-selected SMBHBs and measure their source parameters to high precision (i.e., comparable to or better than conventional EM measurements). We discuss the implications of our findings in the context of future PTA experiments with the planned Deep Synoptic Array-2000 and the multi-messenger studies of SMBHBs such as the well-known binary candidate OJ 287.

 

Recently, many different pulsar timing array (PTA) collaborations have reported strong evidence for a common stochastic process in their data sets. The reported amplitudes are in tension with previously computed upper limits. In this paper, we investigate how using a subset of a set of pulsars biases Bayesian upper limit recovery. We generate 500 simulated PTA data sets, based on the NANOGrav 11 yr data set with an injected stochastic gravitational-wave background (GWB). We then compute the upper limits by sampling the individual pulsar likelihoods, and combine them through a factorized version of the PTA likelihood to obtain upper limits on the GWB amplitude, using different numbers of pulsars. We find that it is possible to recover an upper limit (95% credible interval) below the injected value, and that it is significantly more likely for this to occur when using a subset of pulsars to compute the upper limit. When picking pulsars to induce the maximum possible bias, we find that the 95% Bayesian upper limit recovered is below the injected value in 10.6% of the realizations (53 of 500). Further, we find that if we choose a subset of pulsars in order to obtain a lower upper limit than when using the full set of pulsars, the distribution of the upper limits obtained from these 500 realizations is shifted to lower-amplitude values.

 

The millisecond pulsar J1713+0747 underwent a sudden and significant pulse shape change between 2021 April 16 and 17 (MJDs 59320 and 59321). Subsequently, the pulse shape gradually recovered over the course of several months. We report the results of continued multifrequency radio observations of the pulsar made using the Canadian Hydrogen Intensity Mapping Experiment and the 100 m Green Bank Telescope in a 3 yr period encompassing the shape change event, between 2020 February and 2023 February. As of 2023 February, the pulse shape had returned to a state similar to that seen before the event, but with measurable changes remaining. The amplitude of the shape change and the accompanying time-of-arrival residuals display a strong nonmonotonic dependence on radio frequency, demonstrating that the event is neither a glitch (the effects of which should be independent of radio frequency,ν) nor a change in dispersion measure alone (which would produce a delay proportional toν⁻²). However, it does bear some resemblance to the two previous “chromatic timing events” observed in J1713+0747, as well as to a similar event observed in PSR J1643−1224 in 2015.

 

Abstract Pulsar timing array (PTA) experiments are becoming increasingly sensitive to gravitational waves (GWs) in the nanohertz frequency range, where the main astrophysical sources are supermassive black hole binaries (SMBHBs), which are expected to form following galaxy mergers. Some of these individual SMBHBs may power active galactic nuclei, and thus their binary parameters could be obtained electromagnetically, which makes it possible to apply electromagnetic (EM) information to aid the search for a GW signal in PTA data. In this work, we investigate the effects of such an EM-informed search on binary detection and parameter estimation by performing mock data analyses on simulated PTA data sets. We find that by applying EM priors, the Bayes factor of some injected signals with originally marginal or sub-threshold detectability (i.e., Bayes factor ∼1) can increase by a factor of a few to an order of magnitude, and thus an EM-informed targeted search is able to find hints of a signal when an uninformed search fails to find any. Additionally, by combining EM and GW data, one can achieve an overall improvement in parameter estimation, regardless of the source’s sky location or GW frequency. We discuss the implications for the multi-messenger studies of SMBHBs with PTAs. 

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.

 

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.

 

Analyses of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nanohertz frequency band. The most plausible source of this background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for this background and assess its significance make several simplifying assumptions, namely (i) Gaussianity, (ii) isotropy, and most often, (iii) a power-law spectrum. However, a stochastic background from a finite collection of binaries does not exactly satisfy any of these assumptions. To understand the effect of these assumptions, we test standard analysis techniques on a large collection of realistic simulated data sets. The data-set length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15 yr data set. Simulated signals from millions of binaries drawn from models based on the Illustris cosmological hydrodynamical simulation were added to the data. We find that the standard statistical methods perform remarkably well on these simulated data sets, even though their fundamental assumptions are not strictly met. They are able to achieve a confident detection of the background. However, even for a fixed set of astrophysical parameters, different realizations of the universe result in a large variance in the significance and recovered parameters of the background. We also find that the presence of loud individual binaries can bias the spectral recovery of the background if we do not account for them.