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1. Characterizing the Nanohertz Gravitational Wave Background Using a t-process Power Spectral Density

   https://doi.org/10.3847/1538-4357/ad8a60  

   Sardesai, Shashwat C; Simon, Joseph; Vigeland, Sarah J (November 2024, The Astrophysical Journal)

   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. 

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2. Detecting gravitational wave anisotropies from supermassive black hole binaries

   https://doi.org/10.1103/PhysRevD.111.063068  

   Lemke, Anna-Malin; Mitridate, Andrea; Gersbach, Kyle A (March 2025, Physical Review D)

   Several pulsar timing array (PTA) collaborations have recently found evidence for a gravitational wave background (GWB) permeating our Galaxy. The origin of this background is still unknown. Indeed, while the gravitational wave emission from inspiraling supermassive black hole binaries (SMBHB) is the primary candidate for its origin, several cosmological sources have also been proposed. One distinctive feature of SMBHB-generated backgrounds is the presence of GWB anisotropies stemming from the binaries distribution in the local Universe. However, none of the anisotropy searches performed to date reported a detection. In this work, we show that the lack of anisotropy detection is not currently in tension with a SMBHB origin of the background. We accomplish this by calculating the probability for present and future PTAs to observe deviations from an isotropic GWB. We find that a PTA with the noise characteristics of the NANOGrav 15-year data set had only a 2%–11% probability of detecting deviations from isotropy in an SMBHB-generated GWB, depending on the properties of the SMBHB population. However, we estimate that for the IPTA DR3 data set these probabilities will increase to 4%–28%, putting more pressure on the SMBHB interpretation in case of a null detection. We also identify SMBHB populations that are more likely to produce significant deviations from isotropy. This information could be used together with the spectral properties of the GWB to characterize the SMBHB population. 

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3. Gravitational-wave Statistics for Pulsar Timing Arrays: Examining Bias from Using a Finite Number of Pulsars

   https://doi.org/10.3847/1538-4357/ac6f5e  

   Johnson, Aaron D.; Vigeland, Sarah J.; Siemens, Xavier; Taylor, Stephen R. (June 2022, The Astrophysical Journal)

   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. 

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4. A sensitivity curve approach to tuning a pulsar timing array in the detection era

   https://doi.org/10.1088/1361-6382/adbbab  

   Baier, Jeremy G; Hazboun, Jeffrey S; Romano, Joseph D (March 2025, Classical and Quantum Gravity)

   As pulsar timing arrays (PTAs) transition into the detection era of the stochastic gravitational wave background (GWB), it is important for PTA collaborations to review and possibly revise their observing campaigns. The detection of a ‘single source’ would be a boon for gravitational astrophysics, as such a source would emit gravitational waves for millions of years in the PTA frequency band. Here we present generic methods for studying the effects of various observational strategies, taking advantage of detector sensitivity curves, i.e. noise-averaged, frequency-domain detection statistics. The statistical basis for these methods is presented along with myriad examples of how to tune a detector towards single, deterministic signals or a stochastic background. We demonstrate that trading observations of the worst pulsars for high cadence campaigns on the best pulsars increases sensitivity to single sources at high frequencies while hedging losses in GWB and single source sensitivity at low frequencies. We also find that sky-targeted observing campaigns yield minimal sensitivity improvements compared with other PTA tuning options. Lastly, we show the importance of the uncorrelated half of the GWB, i.e. the pulsar-term, as an increasingly prominent sources of noise and show the impact of this emerging noise source on various PTA configurations. 

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5. Regularizing the pulsar timing array likelihood: A path toward Fourier space

   https://doi.org/10.1103/s3gy-km61  

   Valtolina, Serena; van_Haasteren, Rutger (August 2025, Physical Review D)

   The recent announcement of evidence for a stochastic background of gravitational waves (GWB) in pulsar timing array (PTA) data has piqued interest across the scientific community. A combined analysis of all currently available data holds the promise of confirming the announced evidence as a solid detection of a GWB. However, the complexity of individual pulsar noise models and the variety of modeling tools used for different types of pulsars present significant challenges for a truly unified analysis. In this work we propose a novel approach to the analysis of PTA data: first a posterior distribution over Fourier modes is produced for each pulsar individually. Then, in a global analysis of all pulsars, these posterior distributions can be reused for a GWB search, which retains all information regarding the signals of interest without the added complexity of the underlying noise models or implementation differences. This approach facilitates combining radio and gamma-ray pulsar data, while reducing the complexity of the model and of its implementations when carrying out a GWB search with PTA data. 

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