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  1. Abstract

    Pulsar timing array experiments have recently uncovered evidence for a nanohertz gravitational wave background by precisely timing an ensemble of millisecond pulsars. The next significant milestones for these experiments include characterizing the detected background with greater precision, identifying its source(s), and detecting continuous gravitational waves from individual supermassive black hole binaries. To achieve these objectives, generating accurate and precise times of arrival of pulses from pulsar observations is crucial. Incorrect polarization calibration of the observed pulsar profiles may introduce errors in the measured times of arrival. Further, previous studies have demonstrated that robust polarization calibration of pulsar profiles can reduce noise in the pulsar timing data and improve timing solutions. In this paper, we investigate and compare the impact of different polarization calibration methods on pulsar timing precision using three distinct calibration techniques: the Ideal Feed Assumption (IFA), Measurement Equation Modeling (MEM), and Measurement Equation Template Matching (METM). Three NANOGrav pulsars—PSRs J1643−1224, J1744−1134, and J1909−3744—observed with the 800 MHz and 1.5 GHz receivers at the Green Bank Telescope (GBT) are utilized for our analysis. Our findings reveal that all three calibration methods enhance timing precision compared to scenarios where no polarization calibration is performed. Additionally, among the three calibration methods, the IFA approach generally provides the best results for timing analysis of pulsars observed with the GBT receiver system. We attribute the comparatively poorer performance of the MEM and METM methods to potential instabilities in the reference noise diode coupled to the receiver and temporal variations in the profile of the reference pulsar, respectively.

     
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  2. Abstract

    PINTis a pure-Python framework for high-precision pulsar timing developed on top of widely used and well-tested Python libraries, supporting both interactive and programmatic data analysis workflows. We present a new frequentist framework withinPINTto characterize the single-pulsar noise processes present in pulsar timing data sets. This framework enables parameter estimation for both uncorrelated and correlated noise processes, as well as model comparison between different timing and noise models in a computationally inexpensive way. We demonstrate the efficacy of the new framework by applying it to simulated data sets as well as a real data set of PSR B1855+09. We also describe the new features implemented inPINTsince it was first described in the literature.

     
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  3. Abstract

    The cosmic merger history of supermassive black hole binaries (SMBHBs) is expected to produce a low-frequency gravitational wave background (GWB). Here we investigate how signs of the discrete nature of this GWB can manifest in pulsar timing arrays (PTAs) through excursions from, and breaks in, the expectedfGW2/3power law of the GWB strain spectrum. To do this, we create a semianalytic SMBHB population model, fit to North American Nanohertz Observatory for Gravitational Waves (NANOGrav’s) 15 yr GWB amplitude, and with 1000 realizations, we study the populations’ characteristic strain and residual spectra. Comparing our models to the NANOGrav 15 yr spectrum, we find two interesting excursions from the power law. The first, at 2 nHz, is below our GWB realizations with ap-value significancep= 0.05–0.06 (≈1.8σ–1.9σ). The second, at 16 nHz, is above our GWB realizations withp= 0.04–0.15 (≈1.4σ–2.1σ). We explore the properties of a loud SMBHB that could cause such an excursion. Our simulations also show that the expected number of SMBHBs decreases by 3 orders of magnitude, from ∼106to ∼103, between 2 and 20 nHz. This causes a break in the strain spectrum as the stochasticity of the background breaks down at2619+28nHz, consistent with predictions pre-dating GWB measurements. The diminished GWB signal from SMBHBs at frequencies above the 26 nHz break opens a window for PTAs to detect continuous GWs from individual SMBHBs or GWs from the early Universe.

     
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  4. 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,γrun(f)=γ+βlnf/fref. 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,β0.80,2.96, and an inconclusive Bayes factor,BRPLversusCPL=0.69±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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  5. 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 fromlog10ARN=14.10.1+0.1to14.70.5+0.3, and the spectral index broadens fromγRN=2.60.4+0.5toγRN=3.50.9+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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  6. Abstract

    Recently we found compelling evidence for a gravitational-wave background with Hellings and Downs (HD) correlations in our 15 yr data set. These correlations describe gravitational waves as predicted by general relativity, which has two transverse polarization modes. However, more general metric theories of gravity can have additional polarization modes, which produce different interpulsar correlations. In this work, we search the NANOGrav 15 yr data set for evidence of a gravitational-wave background with quadrupolar HD and scalar-transverse (ST) correlations. We find that HD correlations are the best fit to the data and no significant evidence in favor of ST correlations. While Bayes factors show strong evidence for a correlated signal, the data does not strongly prefer either correlation signature, with Bayes factors ∼2 when comparing HD to ST correlations, and ∼1 for HD plus ST correlations to HD correlations alone. However, when modeled alongside HD correlations, the amplitude and spectral index posteriors for ST correlations are uninformative, with the HD process accounting for the vast majority of the total signal. Using the optimal statistic, a frequentist technique that focuses on the pulsar-pair cross-correlations, we find median signal-to-noise ratios of 5.0 for HD and 4.6 for ST correlations when fit for separately, and median signal-to-noise ratios of 3.5 for HD and 3.0 for ST correlations when fit for simultaneously. While the signal-to-noise ratios for each of the correlations are comparable, the estimated amplitude and spectral index for HD are a significantly better fit to the total signal, in agreement with our Bayesian analysis.

     
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    Free, publicly-accessible full text available March 1, 2025
  7. Abstract

    Analyses of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nanohertz frequency band. The most plausible source of this background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for this background and assess its significance make several simplifying assumptions, namely (i) Gaussianity, (ii) isotropy, and most often, (iii) a power-law spectrum. However, a stochastic background from a finite collection of binaries does not exactly satisfy any of these assumptions. To understand the effect of these assumptions, we test standard analysis techniques on a large collection of realistic simulated data sets. The data-set length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15 yr data set. Simulated signals from millions of binaries drawn from models based on the Illustris cosmological hydrodynamical simulation were added to the data. We find that the standard statistical methods perform remarkably well on these simulated data sets, even though their fundamental assumptions are not strictly met. They are able to achieve a confident detection of the background. However, even for a fixed set of astrophysical parameters, different realizations of the universe result in a large variance in the significance and recovered parameters of the background. We also find that the presence of loud individual binaries can bias the spectral recovery of the background if we do not account for them.

     
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  8. Abstract

    The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has reported evidence for the presence of an isotropic nanohertz gravitational-wave background (GWB) in its 15 yr data set. However, if the GWB is produced by a population of inspiraling supermassive black hole binary (SMBHB) systems, then the background is predicted to be anisotropic, depending on the distribution of these systems in the local Universe and the statistical properties of the SMBHB population. In this work, we search for anisotropy in the GWB using multiple methods and bases to describe the distribution of the GWB power on the sky. We do not find significant evidence of anisotropy. By modeling the angular power distribution as a sum over spherical harmonics (where the coefficients are not bound to always generate positive power everywhere), we find that the Bayesian 95% upper limit on the level of dipole anisotropy is (Cl=1/Cl=0) < 27%. This is similar to the upper limit derived under the constraint of positive power everywhere, indicating that the dipole may be close to the data-informed regime. By contrast, the constraints on anisotropy at higher spherical-harmonic multipoles are strongly prior dominated. We also derive conservative estimates on the anisotropy expected from a random distribution of SMBHB systems using astrophysical simulations conditioned on the isotropic GWB inferred in the 15 yr data set and show that this data set has sufficient sensitivity to probe a large fraction of the predicted level of anisotropy. We end by highlighting the opportunities and challenges in searching for anisotropy in pulsar timing array data.

     
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  9. Abstract

    The radio galaxy 3C 66B has been hypothesized to host a supermassive black hole binary (SMBHB) at its center based on electromagnetic observations. Its apparent 1.05 yr period and low redshift (∼0.02) make it an interesting testbed to search for low-frequency gravitational waves (GWs) using pulsar timing array (PTA) experiments. This source has been subjected to multiple searches for continuous GWs from a circular SMBHB, resulting in progressively more stringent constraints on its GW amplitude and chirp mass. In this paper, we develop a pipeline for performing Bayesian targeted searches for eccentric SMBHBs in PTA data sets, and test its efficacy by applying it to simulated data sets with varying injected signal strengths. We also search for a realistic eccentric SMBHB source in 3C 66B using the NANOGrav 12.5 yr data set employing PTA signal models containing Earth term-only as well as Earth+pulsar term contributions using this pipeline. Due to limitations in our PTA signal model, we get meaningful results only when the initial eccentricitye0< 0.5 and the symmetric mass ratioη> 0.1. We find no evidence for an eccentric SMBHB signal in our data, and therefore place 95% upper limits on the PTA signal amplitude of 88.1 ± 3.7 ns for the Earth term-only and 81.74 ± 0.86 ns for the Earth+pulsar term searches fore0< 0.5 andη> 0.1. Similar 95% upper limits on the chirp mass are (1.98 ± 0.05) × 109and (1.81 ± 0.01) × 109M. These upper limits, while less stringent than those calculated from a circular binary search in the NANOGrav 12.5 yr data set, are consistent with the SMBHB model of 3C 66B developed from electromagnetic observations.

     
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