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1. Comparing Recent Pulsar Timing Array Results on the Nanohertz Stochastic Gravitational-wave Background

   https://doi.org/10.3847/1538-4357/ad36be  

   Agazie, G; Antoniadis, J; Anumarlapudi, A; Archibald, A M; Arumugam, P; Arumugam, S; Arzoumanian, Z; Askew, J; Babak, S; Bagchi, M; et al (April 2024, The Astrophysical Journal)

   Abstract The Australian, Chinese, European, Indian, and North American pulsar timing array (PTA) collaborations recently reported, at varying levels, evidence for the presence of a nanohertz gravitational-wave background (GWB). Given that each PTA made different choices in modeling their data, we perform a comparison of the GWB and individual pulsar noise parameters across the results reported from the PTAs that constitute the International Pulsar Timing Array (IPTA). We show that despite making different modeling choices, there is no significant difference in the GWB parameters that are measured by the different PTAs, agreeing within 1σ. The pulsar noise parameters are also consistent between different PTAs for the majority of the pulsars included in these analyses. We bridge the differences in modeling choices by adopting a standardized noise model for all pulsars and PTAs, finding that under this model there is a reduction in the tension in the pulsar noise parameters. As part of this reanalysis, we “extended” each PTA’s data set by adding extra pulsars that were not timed by that PTA. Under these extensions, we find better constraints on the GWB amplitude and a higher signal-to-noise ratio for the Hellings–Downs correlations. These extensions serve as a prelude to the benefits offered by a full combination of data across all pulsars in the IPTA, i.e., the IPTA’s Data Release 3, which will involve not just adding in additional pulsars but also including data from all three PTAs where any given pulsar is timed by more than a single PTA. 

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2. 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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3. 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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4. The NANOGrav 15 yr Data Set: Chromatic Gaussian Process Noise Models for Six Pulsars

   https://doi.org/10.3847/1538-4357/ad5291  

   Larsen, Bjorn; Mingarelli, Chiara_M F; Hazboun, Jeffrey S; Chalumeau, Aurélien; Good, Deborah C; Simon, Joseph; Agazie, Gabriella; Anumarlapudi, Akash; Archibald, Anne M; Arzoumanian, Zaven; et al (August 2024, The Astrophysical Journal)

   Abstract Pulsar timing arrays (PTAs) are designed to detect low-frequency gravitational waves (GWs). GWs induce achromatic signals in PTA data, meaning that the timing delays do not depend on radio frequency. However, pulse arrival times are also affected by radio-frequency-dependent “chromatic” noise from sources such as dispersion measure (DM) and scattering delay variations. Furthermore, the characterization of GW signals may be influenced by the choice of chromatic noise model for each pulsar. To better understand this effect, we assess if and how different chromatic noise models affect the achromatic noise properties in each pulsar. The models we compare include existing DM models used by the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and noise models used for the European PTA Data Release 2 (EPTA DR2). We perform this comparison using a subsample of six pulsars from the NANOGrav 15 yr data set, selecting the same six pulsars as from the EPTA DR2 six-pulsar data set. We find that the choice of chromatic noise model noticeably affects the achromatic noise properties of several pulsars. This is most dramatic for PSR J1713+0747, where the amplitude of its achromatic red noise lowers from ${\log }_{10}{A}_{\mathrm{RN}}=-{14.1}_{-0.1}^{+0.1}$ to $-{14.7}_{-0.5}^{+0.3}$ , and the spectral index broadens from ${\gamma }_{\mathrm{RN}}={2.6}_{-0.4}^{+0.5}$ to ${\gamma }_{\mathrm{RN}}={3.5}_{-0.9}^{+1.2}$ . We also compare each pulsar's noise properties with those inferred from the EPTA DR2, using the same models. From the discrepancies, we identify potential areas where the noise models could be improved. These results highlight the potential for custom chromatic noise models to improve PTA sensitivity to GWs. 

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5. Forecasting Pulsar Timing Array Sensitivity to Anisotropy in the Stochastic Gravitational Wave Background

   https://doi.org/10.3847/1538-4357/ac9836  

   Pol, Nihan; Taylor, Stephen R.; Romano, Joseph D. (December 2022, The Astrophysical Journal)

   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. 

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