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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 Statistical anisotropy in the nanohertz-frequency gravitational wave background (GWB) is expected to be detected by pulsar timing arrays (PTAs) in the near future. By developing a frequentist statistical framework that intrinsically restricts the GWB power to be positive, we establish scaling relations for multipole-dependent anisotropy decision thresholds that are a function of the noise properties, timing baselines, and cadences of the pulsars in a PTA. We verify that (i) a larger number of pulsars, and (ii) factors that lead to lower uncertainty on spatial cross-correlation measurements between pulsars, lead to a higher overall GWB signal-to-noise ratio, and lower anisotropy decision thresholds with which to reject the null hypothesis of isotropy. Using conservative simulations of realistic NANOGrav data sets, we predict that an anisotropic GWB with angular power C l =1 > 0.3 C l =0 may be sufficient to produce tension with isotropy at the p = 3 × 10 −3 (∼3 σ ) level in near-future NANOGrav data with a 20 yr baseline. We present ready-to-use scaling relationships that can map these thresholds to any number of pulsars, configuration of pulsar noise properties, or sky coverage. We discuss how PTAs can improve the detection prospects for anisotropy, as well as how our methods can be adapted for more versatile searches. 

ABSTRACT Time-domain data sets of many varieties can be prone to statistical outliers that result from instrumental or astrophysical anomalies. These can impair searches for signals within the time series and lead to biased parameter estimation. Versatile outlier mitigation methods tuned toward multimessenger time-domain searches for supermassive binary black holes have yet to be fully explored. In an effort to perform robust outlier isolation with low computational costs, we propose a Gibbs sampling scheme. This provides structural simplicity to outlier modelling and isolation, as it requires minimal modifications to adapt to time-domain modelling scenarios with pulsar-timing array or photometric data. We robustly diagnose outliers present in simulated pulsar-timing data sets, and then further apply our methods to pulsar J1909−3744 from the NANOGrav 9-year Data set. We also explore the periodic binary-AGN candidate PG1302−102 using data sets from the Catalina Real-time Transient Survey, All-Sky Automated Survey for Supernovae, and the Lincoln Near-Earth Asteroid Research. We present our findings and outline future work that could improve outlier modelling and isolation for multimessenger time-domain searches. 

Abstract Supermassive black hole binaries (SMBHBs) are an inevitable consequence of galaxy mergers. At sub-parsec separations, they are practically impossible to resolve, and the most promising technique is to search for quasars with periodic variability. However, searches for quasar periodicity in time-domain data are challenging due to the stochastic variability of quasars. In this paper, we used Bayesian methods to disentangle periodic SMBHB signals from intrinsic damped random walk (DRW) variability in active galactic nuclei light curves. We simulated a wide variety of realistic DRW and DRW+sine light curves. Their observed properties are modeled after the Catalina Real-time Transient Survey (CRTS) and expected properties of the upcoming Legacy Survey of Space and Time (LSST) from the Vera C. Rubin Observatory. Through a careful analysis of parameter estimation and Bayesian model selection, we investigated the range of parameter space for which binary systems can be detected. We also examined which DRW signals can mimic periodicity and be falsely classified as binary candidates. We found that periodic signals are more easily detectable if the period is short or the amplitude of the signal is large compared to the contribution of the DRW noise. We saw similar detection rates both in the CRTS and LSST-like simulations, while the false-detection rate depends on the quality of the data and is minimal in LSST. Our idealized simulations provide an excellent way to uncover the intrinsic limitations in quasar periodicity searches and set the stage for future searches for SMBHBs. 

ABSTRACT The search for gravitational waves using Pulsar Timing Arrays (PTAs) is a computationally expensive complex analysis that involves source-specific noise studies. As more pulsars are added to the arrays, this stage of PTA analysis will become increasingly challenging. Therefore, optimizing the number of included pulsars is crucial to reduce the computational burden of data analysis. Here, we present a suite of methods to rank pulsars for use within the scope of PTA analysis. First, we use the maximization of the signal-to-noise ratio as a proxy to select pulsars. With this method, we target the detection of stochastic and continuous gravitational wave signals. Next, we present a ranking that minimizes the coupling between spatial correlation signatures, namely monopolar, dipolar, and Hellings & Downs correlations. Finally, we also explore how to combine these two methods. We test these approaches against mock data using frequentist and Bayesian hypothesis testing. For equal-noise pulsars, we find that an optimal selection leads to an increase in the log-Bayes factor two times steeper than a random selection for the hypothesis test of a gravitational wave background versus a common uncorrelated red noise process. For the same test but for a realistic European PTA (EPTA) data set, a subset of 25 pulsars selected out of 40 can provide a log-likelihood ratio that is 89 % of the total, implying that an optimally selected subset of pulsars can yield results comparable to those obtained from the whole array. We expect these selection methods to play a crucial role in future PTA data combinations.