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1. The NANOGrav 12.5-year Data Set: Search for Non-Einsteinian Polarization Modes in the Gravitational-wave Background

   https://doi.org/10.3847/2041-8213/ac401c  

   Arzoumanian, Zaven; Baker, Paul T.; Blumer, Harsha; Bécsy, Bence; Brazier, Adam; Brook, Paul R.; Burke-Spolaor, Sarah; Charisi, Maria; Chatterjee, Shami; Chen, Siyuan; et al (December 2021, The Astrophysical Journal Letters)

   Abstract We search NANOGrav’s 12.5 yr data set for evidence of a gravitational-wave background (GWB) with all the spatial correlations allowed by general metric theories of gravity. We find no substantial evidence in favor of the existence of such correlations in our data. We find that scalar-transverse (ST) correlations yield signal-to-noise ratios and Bayes factors that are higher than quadrupolar (tensor-transverse, TT) correlations. Specifically, we find ST correlations with a signal-to-noise ratio of 2.8 that are preferred over TT correlations (Hellings and Downs correlations) with Bayesian odds of about 20:1. However, the significance of ST correlations is reduced dramatically when we include modeling of the solar system ephemeris systematics and/or remove pulsar J0030+0451 entirely from consideration. Even taking the nominal signal-to-noise ratios at face value, analyses of simulated data sets show that such values are not extremely unlikely to be observed in cases where only the usual TT modes are present in the GWB. In the absence of a detection of any polarization mode of gravity, we place upper limits on their amplitudes for a spectral index ofγ= 5 and a reference frequency off_yr= 1 yr⁻¹. Among the upper limits for eight general families of metric theories of gravity, we find the values of $A_{\mathrm{TT}}^{95\%}=(9.7\pm 0.4)\times {10}^{-16}$and $A_{\mathrm{ST}}^{95\%}=(1.4\pm 0.03)\times {10}^{-15}$for the family of metric spacetime theories that contain both TT and ST modes. 

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2. The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background

   https://doi.org/10.3847/2041-8213/acdac6  

   Agazie, Gabriella; Anumarlapudi, Akash; Archibald, Anne M.; Arzoumanian, Zaven; Baker, Paul T.; Bécsy, Bence; Blecha, Laura; Brazier, Adam; Brook, Paul R.; Burke-Spolaor, Sarah; et al (June 2023, The Astrophysical Journal Letters)

   Abstract We report multiple lines of evidence for a stochastic signal that is correlated among 67 pulsars from the 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. The correlations follow the Hellings–Downs pattern expected for a stochastic gravitational-wave background. The presence of such a gravitational-wave background with a power-law spectrum is favored over a model with only independent pulsar noises with a Bayes factor in excess of 10 14 , and this same model is favored over an uncorrelated common power-law spectrum model with Bayes factors of 200–1000, depending on spectral modeling choices. We have built a statistical background distribution for the latter Bayes factors using a method that removes interpulsar correlations from our data set, finding p = 10 −3 (≈3 σ ) for the observed Bayes factors in the null no-correlation scenario. A frequentist test statistic built directly as a weighted sum of interpulsar correlations yields p = 5 × 10 −5 to 1.9 × 10 −4 (≈3.5 σ –4 σ ). Assuming a fiducial f −2/3 characteristic strain spectrum, as appropriate for an ensemble of binary supermassive black hole inspirals, the strain amplitude is 2.4 − 0.6 + 0.7 × 10 − 15 (median + 90% credible interval) at a reference frequency of 1 yr −1 . The inferred gravitational-wave background amplitude and spectrum are consistent with astrophysical expectations for a signal from a population of supermassive black hole binaries, although more exotic cosmological and astrophysical sources cannot be excluded. The observation of Hellings–Downs correlations points to the gravitational-wave origin of this signal. 

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3. The NANOGrav 15 yr Data Set: Harmonic Analysis of the Pulsar Angular Correlations

   https://doi.org/10.3847/1538-4357/adc997  

   Agazie, Gabriella; Anumarlapudi, Akash; Archibald, Anne M; Arzoumanian, Zaven; Baier, Jeremy G; Baker, Paul T; Bécsy, Bence; Blecha, Laura; Boddy, Kimberly K; Brazier, Adam; et al (May 2025, The Astrophysical Journal)

   Abstract Pulsar timing array observations have found evidence for an isotropic gravitational-wave background with the Hellings–Downs angular correlations between pulsar pairs. This interpretation hinges on the measured shape of the angular correlations, which is predominantly quadrupolar under general relativity. Here we explore a more flexible parameterization: we expand the angular correlations into a sum of Legendre polynomials and use a Bayesian analysis to constrain their coefficients with the 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). When including Legendre polynomials with multipolesℓ≥ 2, we only find a significant signal in the quadrupole with an amplitude consistent with general relativity and nonzero at the ∼95% confidence level and a Bayes factor of 200. When we include multipolesℓ≤ 1, the Bayes factor evidence for quadrupole correlations decreases by more than an order of magnitude due to evidence for a monopolar signal at approximately 4 nHz, which has also been noted in previous analyses of the NANOGrav 15 yr data. Further work needs to be done in order to better characterize the properties of this monopolar signal and its effect on the evidence for quadrupolar angular correlations. 

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4. A Detection of Red Noise in PSR J1824–2452A and Projections for PSR B1937+21 Using NICER X-Ray Timing Data

   https://doi.org/10.3847/1538-4357/ac54ae  

   Hazboun, Jeffrey S.; Crump, Jack; Lommen, Andrea N.; Montano, Sergio; Berry, Samantha J. H.; Zeldes, Jesse; Teng, Elizabeth; Ray, Paul S.; Kerr, Matthew; Arzoumanian, Zaven; et al (March 2022, The Astrophysical Journal)

   Abstract We have used X-ray data from the Neutron Star Interior Composition Explorer (NICER) to search for long-timescale temporal correlations (“red noise”) in the pulse times of arrival (TOAs) from the millisecond pulsars PSR J1824−2452A and PSR B1937+21. These data more closely track intrinsic noise because X-rays are unaffected by the radio-frequency-dependent propagation effects of the interstellar medium. Our search yields strong evidence (natural log Bayes factor of 9.634 ± 0.016) for red noise in PSR J1824−2452A, but the search is inconclusive for PSR B1937+21. In the interest of future X-ray missions, we devise and implement a method to simulate longer and higher-precision X-ray data sets to determine the timing baseline necessary to detect red noise. We find that the red noise in PSR B1937+21 can be reliably detected in a 5 yr mission with a TOA error of 2μs and an observing cadence of 20 observations per month compared to the 5μs TOA error and 11 observations per month that NICER currently achieves in PSR B1937+21. We investigate detecting red noise in PSR B1937+21 with other combinations of observing cadences and TOA errors. We also find that time-correlated red noise commensurate with an injected stochastic gravitational-wave background having an amplitude ofA_GWB= 2 × 10⁻¹⁵and spectral index of timing residuals ofγ_GWB= 13/3 can be detected in a pulsar with similar TOA precision to PSR B1937+21. This is with no additional red noise in a 10 yr mission that observes the pulsar 15 times per month and has an average TOA error of 1μs. 

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5. The NANOGrav 15 yr Data Set: Running of the Spectral Index

   https://doi.org/10.3847/2041-8213/ad99d3  

   Agazie, Gabriella; Anumarlapudi, Akash; Archibald, Anne_M; Arzoumanian, Zaven; Baier, Jeremy_G; Baker, Paul_T; Bécsy, Bence; Blecha, Laura; Brazier, Adam; Brook, Paul_R; et al (January 2025, The Astrophysical Journal Letters)

   Abstract The NANOGrav 15 yr data provide compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists of a simple power-law fit involving two parameters: an amplitudeAand a spectral indexγ. In this Letter, we consider the next logical step beyond this minimal spectral model, allowing for arunning(i.e., logarithmic frequency dependence) of the spectral index, ${\gamma }_{\mathrm{run}}\left(f\right)=\gamma +\beta \ln \left(f/f_{\mathrm{ref}}\right)$. We fit this running-power-law (RPL) model to the NANOGrav 15 yr data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameterβconsistent with no running, $\beta \in \left(-0.80,2.96\right)$, and an inconclusive Bayes factor, $B\left(\mathrm{RPL}\mathrm{versus}\mathrm{CPL}\right)=0.69\pm 0.01$. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzeroβ. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from Big Bang nucleosynthesis, the cosmic microwave background, and LIGO–Virgo–KAGRA. 

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