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Pulsar timing arrays are sensitive to low-frequency gravitational waves (GWs), such as those produced by supermassive binary black holes at subparsec separations. The incoherent superposition of GWs emitted by a cosmological population of these sources produces a gravitational wave background (GWB), while some individual sources may be resolvable as deterministic signals with slowly varying GW frequencies, which are often referred to as “continuous waves” (CWs). The ${\mathcal{F}}_p$-statistic is a frequentist method of detecting these CWs. In this paper, we study how the presence of pulsar red noise and a GWB affect the ${\mathcal{F}}_p$-statistic. We compare results when marginalizing over the red noise and using the maximum-likelihood values of the red noise, and find little difference between the two. We also present results of using the ${\mathcal{F}}_p$-statistic to analyze the NANOGrav 12.5-year dataset, where we find no evidence for CWs in agreement with the previously published Bayesian results. 

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 Pulsar timing arrays (PTAs) are sensitive to low-frequency gravitational waves (GWs), which induce correlated changes in millisecond pulsars’ timing residuals. PTA collaborations around the world have recently announced evidence of a nanohertz gravitational wave background (GWB), which may be produced by a population of supermassive black hole binaries (SMBHBs). The GWB is often modeled as following a power-law power spectral density (PSD); however, a GWB produced by a cosmological population of SMBHBs is expected to have a more complex power spectrum due to the discrete nature of the sources. In this paper, we investigate using at-process PSD to model the GWB, which allows us to fit for both the underlying power-law amplitude and spectral index as well as deviations from that power law, which may be produced by individual nearby binaries. We create simulated data sets based on the properties of the NANOGrav 15 yr data set, and we demonstrate that thet-process PSD can accurately recover the PSD when deviations from a power law are present. With longer timed data sets and more pulsars, we expect the sensitivity of our PTAs to improve, which will allow us to precisely measure the PSD of the GWB and study the sources producing it. 

Abstract 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. 

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. 

Abstract 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.