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The NANOGrav 15-year data provides 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 in a simple power-law fit involving two parameters: an amplitude A and a spectral index \gamma. In this paper, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, \gamma_run(f) = \gamma + \beta \ln(f/f_ref). We fit this running-power-law (RPL) model to the NANOGrav 15-year data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter \beta consistent with no running, \beta \in [-0.80,2.96], and an inconclusive Bayes factor, B(RPL vs. CPL) = 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 nonzero \beta. 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., Comment: 17 pages, 4 figures, 2 tables

In this paper, we present a unique multi-functional super-resolution instrument, the SuperNANO system, which integrates real-time super-resolution imaging with direct laser nanofabrication capabilities. Central to the func-tionality of the SuperNANO system is its capacity for simultaneous nanoimaging and nanopatterning, enabling the creation of anti-counterfeiting markings and precision cutting with exceptional accuracy. The SuperNANO system, featuring a unibody superlens objective, achieves a resolution ranging from 50 to 320 nm. We showcase the instrument's versatility through its application in generating high-security anti-counterfeiting features on an aluminum film. These 'invisible' security features, which are nanoscale in dimension, can be crafted with arbi-trary shapes at designated locations. Moreover, the system's precision is further evidenced by its ability to cut silver nanowires to a minimum width of 50 nm. The integrated imaging and fabricating functions of the Su-perNANO make it a pivotal tool for a variety of applications, including nano trapping, sensing, cutting, weld-ing, drilling, signal enhancement, detection, and nano laser treatment., Comment: super resolution system

Pulsar-timing-array experiments have reported evidence for a stochastic background of nanohertz gravitational waves consistent with the signal expected from a population of supermassive--black-hole binaries. Those analyses assume power-law spectra for intrinsic pulsar noise and for the background, as well as a Hellings--Downs cross-correlation pattern among the gravitational-wave--induced residuals across pulsars. These assumptions are idealizations that may not be realized in actuality. We test them in the NANOGrav 15 yr data set using Bayesian posterior predictive checks: after fitting our fiducial model to real data, we generate a population of simulated data-set replications, and use them to assess whether the optimal-statistic significance, inter-pulsar correlations, and spectral coefficients assume extreme values for the real data when compared to the replications. We confirm that the NANOGrav 15 yr data set is consistent with power-law and Hellings--Downs assumptions. We also evaluate the evidence for the stochastic background using posterior-predictive versions of the frequentist optimal statistic and of Bayesian model comparison, and find comparable significance (3.2\ $\sigma$ and 3\ $\sigma$ respectively) to what was previously reported for the standard statistics. We conclude with novel visualizations of the reconstructed gravitational waveforms that enter the residuals for each pulsar. Our analysis strengthens confidence in the identification and characterization of the gravitational-wave background as reported by NANOGrav., Comment: 20 pages, 14 Figures

Based on the rate of change of its orbital period, PSR J2043+1711 has a substantial peculiar acceleration of 3.5 $\pm$ 0.8 mm/s/yr, which deviates from the acceleration predicted by equilibrium Milky Way models at a $4\sigma$ level. The magnitude of the peculiar acceleration is too large to be explained by disequilibrium effects of the Milky Way interacting with orbiting dwarf galaxies ($\sim$1 mm/s/yr), and too small to be caused by period variations due to the pulsar being a redback. We identify and examine two plausible causes for the anomalous acceleration: a stellar flyby, and a long-period orbital companion. We identify a main-sequence star in \textit{Gaia} DR3 and Pan-STARRS DR2 with the correct mass, distance, and on-sky position to potentially explain the observed peculiar acceleration. However, the star and the pulsar system have substantially different proper motions, indicating that they are not gravitationally bound. However, it is possible that this is an unrelated star that just happens to be located near J2043+1711 along our line of sight (chance probability of 1.6\%). Therefore, we also constrain possible orbital parameters for a circumbinary companion in a hierarchical triple system with J2043+1711; the changes in the spindown rate of the pulsar are consistent with an outer object that has an orbital period of 80 kyr, a companion mass of 0.3 $M_\odot$ (indicative of a white dwarf or low-mass star), and a semi-major axis of 2000 AU. Continued timing and/or future faint optical observations of J2043+1711 may eventually allow us to differentiate between these scenarios.

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 (e.g., van Straten 2013; Manchester et al. 2013) 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., Comment: 21 pages, 6 figures, 1 table, submitted to Astrophysical Journal

Energy-efficient spintronic devices require a large spin-orbit torque (SOT) and low damping to excite magnetic precession. In conventional devices with heavy-metal/ferromagnet bilayers, reducing the ferromagnet thickness to $\sim$1 nm enhances the SOT but dramatically increases damping. Here, we investigate an alternative approach based on a 10 nm thick single-layer ferromagnet to attain both low damping and a sizable SOT. Instead of relying on a single interface, we continuously break the bulk inversion symmetry with a vertical compositional gradient of two ferromagnetic elements: Fe with low intrinsic damping and Ni with sizable spin-orbit coupling. We find low effective damping parameters of $\alpha_\mathrm{eff} < 5\times10^{-3}$ in the FeNi alloy films, despite the steep compositional gradients. Moreover, we reveal a sizable anti-damping SOT efficiency of $\theta_\mathrm{AD} \approx 0.05$, even without an intentional compositional gradient. Through depth-resolved x-ray diffraction, we identify a lattice strain gradient as crucial symmetry breaking that underpins the SOT. Our findings provide fresh insights into damping and SOTs in single-layer ferromagnets for power-efficient spintronic devices.

As generative AI continues to evolve, educators face the challenge of preparing students for a future where AI-assisted work is integral to professional success. This paper introduces ChatISA, an in-house, multi-model chatbot designed to support students in an Information Systems and Analytics department. ChatISA comprises four primary modules-Coding Companion, Project Coach, Exam Ally, and Interview Mentor-each tailored to enhance different aspects of the educational experience. Through iterative development, student feedback, and leveraging open-source frameworks, we created a robust tool that addresses coding inquiries, project management, exam preparation, and interview readiness. The implementation of ChatISA revealed significant insights and challenges, including the necessity of ethical guidelines and balancing AI usage with maintaining student agency. Our findings underscore the importance of adaptive pedagogy and proactive engagement with AI tools to maximize their educational benefits. To support broader adoption and innovation, all code for ChatISA is made publicly available on GitHub, enabling other institutions to customize and integrate similar AI-driven educational tools within their curricula., Comment: 18 pages

A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the elements of the response, the precision matrix is reparameterized so it can be estimated with univariate-response linear regression techniques. A novel generalized bridge regression prior that accommodates both sparse and dense settings and is competitive with alternative methods for univariate-response regression is proposed and used in this framework. Two component-wise Markov chain Monte Carlo algorithms are developed for sampling, including a data augmentation algorithm based on a scale mixture of normals representation. Numerical examples demonstrate that the proposed method is competitive with comparable joint mean-covariance models, particularly in estimation of the precision matrix. The method is also used to estimate the 253 by 253 precision matrices of two classes of spectra extracted from images taken by the Hubble Space Telescope. Some interesting structural patterns in the estimates are discussed., Comment: 49 pages, 11 figures

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 achromatic noise properties in each pulsar. The models we compare include existing DM models used by 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 dataset. 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 $\log_{10}A_{\text{RN}} = -14.1^{+0.1}_{-0.1}$ to $-14.7^{+0.3}_{-0.5}$, and the spectral index broadens from $\gamma_{\text{RN}} = 2.6^{+0.5}_{-0.4}$ to $\gamma_{\text{RN}} = 3.5^{+1.2}_{-0.9}$. 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.

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 through excursions from, and breaks in, the expected $f_{\mathrm{GW}}^{-2/3}$ power-law of the GWB strain spectrum. To do this, we create a semi-analytic SMBHB population model, fit to NANOGrav's 15 yr GWB amplitude, and with 1,000 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 $2 \; \mathrm{nHz}$, is below our GWB realizations with $p$-value significance $p = 0.05$ to $0.06$ ($\approx 1.8 \sigma - 1.9 \sigma$). The second, at $16 \; \mathrm{nHz}$, is above our GWB realizations with $p = 0.04$ to $0.15$ ($\approx 1.4 \sigma - 2.1 \sigma$). We explore the properties of a loud SMBHB which could cause such an excursion. Our simulations also show that the expected number of SMBHBs decreases by three orders of magnitude, from $\sim 10^6$ to $\sim 10^3$, between $2\; \mathrm{nHz}$ and $20 \; \mathrm{nHz}$. This causes a break in the strain spectrum as the stochasticity of the background breaks down at $26^{+28}_{-19} \; \mathrm{nHz}$, 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., Comment: 10 pages, 8 figures, 1 appendix, submitted to ApJ

There has been a surge of recent interest in the Wigner's friend paradox, sparking several novel thought experiments and no-go theorems. The main narrative has been that Wigner's friend highlights a counterintuitive feature that is unique to quantum theory, and which is closely related to the quantum measurement problem. Here, we challenge this view. We argue that the gist of the Wigner's friend paradox can be reproduced without assuming quantum physics, and that it underlies a much broader class of enigmas in the foundations of physics and philosophy. To show this, we first consider several recently proposed extended Wigner's friend scenarios, and demonstrate that their implications for the absoluteness of observations can be reproduced by classical thought experiments that involve the duplication of agents. Crucially, some of these classical scenarios are technologically much easier to implement than their quantum counterparts. Then, we argue that the essential structural ingredient of all these scenarios is a feature that we call "Restriction A": essentially, that a physical theory cannot give us a probabilistic description of the observations of all agents. Finally, we argue that this difficulty is at the core of other puzzles in the foundations of physics and philosophy, and demonstrate this explicitly for cosmology's Boltzmann brain problem. Our analysis suggests that Wigner's friend should be studied in a larger context, addressing a frontier of human knowledge that exceeds the boundaries of quantum physics: to obtain reliable predictions for experiments in which these predictions can be privately but not intersubjectively verified., Comment: 21+8 pages, 3 figures

How can detector click probabilities respond to spatial rotations around a fixed axis, in any possible physical theory? Here, we give a thorough mathematical analysis of this question in terms of "rotation boxes", which are analogous to the well-known notion of non-local boxes. We prove that quantum theory admits the most general rotational correlations for spins 0, 1/2, and 1, but we describe a metrological game where beyond-quantum resources of spin 3/2 outperform all quantum resources of the same spin. We prove a multitude of fundamental results about these correlations, including an exact convex characterization of the spin-1 correlations, a Tsirelson-type inequality for spins 3/2 and higher, and a proof that the general spin-J correlations provide an efficient outer SDP approximation to the quantum set. Furthermore, we review and consolidate earlier results that hint at a wealth of applications of this formalism: a theory-agnostic semi-device-independent randomness generator, an exact characterization of the quantum (2,2,2)-Bell correlations in terms of local symmetries, and the derivation of multipartite Bell witnesses. Our results illuminate the foundational question of how space constrains the structure of quantum theory, they build a bridge between semi-device-independent quantum information and spacetime physics, and they demonstrate interesting relations to topics such as entanglement witnesses, spectrahedra, and orbitopes., Comment: 27+22 pages, 9 figures

Recently we found compelling evidence for a gravitational wave background with Hellings and Downs (HD) correlations in our 15-year 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-year data set for evidence of a gravitational wave background with quadrupolar Hellings and Downs (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 $\sim 2$ when comparing HD to ST correlations, and $\sim 1$ 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., Comment: 11 pages, 5 figures

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-year period and low redshift ($\sim0.02$) 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 on 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-year 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 eccentricity $e_0<0.5$ and the symmetric mass ratio $\eta>0.1$. We find no evidence for an eccentric SMBHB signal in our data, and therefore place 95% upper limits on the PTA signal amplitude of $88.1\pm3.7$ ns for the Earth term-only and $81.74\pm0.86$ ns for the Earth+Pulsar term searches for $e_0<0.5$ and $\eta>0.1$. Similar 95% upper limits on the chirp mass are $(1.98 \pm 0.05) \times 10^9\,M_{\odot}$ and $(1.81 \pm 0.01) \times 10^9\,M_{\odot}$. These upper limits, while less stringent than those calculated from a circular binary search in the NANOGrav 12.5-year data set, are consistent with the SMBHB model of 3C 66B developed from electromagnetic observations., Comment: 27 Pages, 10 Figures, 1 Table, Accepted for publication in ApJ

The structure of the unbound nucleus $^{13}$Be is important to understanding the Borromean, two-neutron halo nucleus $^{14}$Be. The experimental studies conducted over the last four decades are reviewed in the context of the beryllium chain of isotopes and some significant theoretical studies. One focus of this paper is the comparison of new data from a $^{12}$Be(d,p) reaction in inverse kinematics, which was analyzed using GEANT4 simulations and a Bayesian fitting procedure, with previous measurements. Two possible scenarios to explain the strength below 1~MeV above the neutron separation energy were proposed in that study: a single $p$-wave resonance, or a mixture of an $s$-wave virtual state with a weaker either $p$-wave or $d$-wave resonance. Comparisons of recent invariant mass and the (d,p) experiments show good agreement between the transfer measurement and the two most recent high-energy nucleon removal measurements., Comment: 10 pages 2 figures

The low-lying structure of $^{13}$Be has remained an enigma for decades. Despite numerous experimental and theoretical studies, large inconsistencies remain. Being both unbound, and one neutron away from $^{14}$Be, the heaviest bound beryllium nucleus, $^{13}$Be is difficult to study through simple reactions with weak radioactive ion beams or more complex reactions with stable-ion beams. Here, we present the results of a study using the $^{12}$Be(d,p)$^{13}$Be reaction in inverse kinematics using a 9.5~MeV per nucleon $^{12}$Be beam from the ISAC-II facility. The solid deuteron target of IRIS was used to achieve an increased areal thickness compared to conventional deuterated polyethylene targets. The Q-value spectrum below -4.4~MeV was analyzed using a Bayesian method with GEANT4 simulations. A three-point angular distribution with the same Q-value gate was fit with a mixture of $s$- and $p$-wave, $s$- and $d$-wave, or pure $p$-wave transfer. The Q-value spectrum was also compared with GEANT simulations obtained using the energies and widths of states reported in four previous works. It was found that our results are incompatible with works that revealed a wide $5/2^+$ resonance but shows better agreement with ones that reported a narrower width., Comment: 10 pages, 5 figures

Analysis of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nHz frequency band. The most plausible source of such a background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for such a 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 datasets. The dataset length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15-year dataset. 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 datasets, despite their fundamental assumptions not being 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., Comment: 14 pages, 8 figures, version matching published paper

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 $1\sigma$. 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 and 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 as single PTA., Comment: 21 pages, 9 figures, submitted to ApJ

We introduce ChatSQC, an innovative chatbot system that combines the power of OpenAI's Large Language Models (LLM) with a specific knowledge base in Statistical Quality Control (SQC). Our research focuses on enhancing LLMs using specific SQC references, shedding light on how data preprocessing parameters and LLM selection impact the quality of generated responses. By illustrating this process, we hope to motivate wider community engagement to refine LLM design and output appraisal techniques. We also highlight potential research opportunities within the SQC domain that can be facilitated by leveraging ChatSQC, thereby broadening the application spectrum of SQC. A primary goal of our work is to provide a template and proof-of-concept on how LLMs can be utilized by our community. To continuously improve ChatSQC, we ask the SQC community to provide feedback, highlight potential issues, request additional features, and/or contribute via pull requests through our public GitHub repository. Additionally, the team will continue to explore adding supplementary reference material that would further improve the contextual understanding of the chatbot. Overall, ChatSQC serves as a testament to the transformative potential of AI within SQC, and we hope it will spur further advancements in the integration of AI in this field., Comment: 24 pages

We present the detection of 661 known pulsars observed with the Australian SKA Pathfinder (ASKAP) telescope at 888 MHz as a part of the Rapid ASKAP Continuum Survey (RACS). Detections were made through astrometric coincidence and we estimate the false alarm rate of our sample to be ~0.5%. Using archival data at 400 and 1400 MHz, we estimate the power law spectral indices for the pulsars in our sample and find that the mean spectral index is -1.78 +/- 0.6. However, we also find that a single power law is inadequate to model all the observed spectra. With the addition of the flux densities between 150 MHz and 3 GHz from various imaging surveys, we find that up to 40% of our sample shows deviations from a simple power law model. Using Stokes V measurements from the RACS data, we measured the circular polarization fraction for 9% of our sample and find that the mean polarization fraction is ~10% (consistent between detections and upper limits). Using the dispersion measure (DM) derived distance we estimate the pseudo luminosity of the pulsars and do not find any strong evidence for a correlation with the pulsars' intrinsic properties., Comment: Accepted for publication in ApJ (18 pages, 16 figures), comments are welcome

We present the results of a Bayesian search for gravitational wave (GW) memory in the NANOGrav 12.5-yr data set. We find no convincing evidence for any gravitational wave memory signals in this data set (Bayes factor = 2.8). As such, we go on to place upper limits on the strain amplitude of GW memory events as a function of sky location and event epoch. These upper limits are computed using a signal model that assumes the existence of a common, spatially uncorrelated red noise in addition to a GW memory signal. The median strain upper limit as a function of sky position is approximately $3.3 \times 10^{-14}$. We also find that there are some differences in the upper limits as a function of sky position centered around PSR J0613$-$0200. This suggests that this pulsar has some excess noise which can be confounded with GW memory. Finally, the upper limits as a function of burst epoch continue to improve at later epochs. This improvement is attributable to the continued growth of the pulsar timing array., Comment: 29 pages, 5 figures

Noise characterization for pulsar-timing applications accounts for interstellar dispersion by assuming a known frequency-dependence of the delay it introduces in the times of arrival (TOAs). However, calculations of this delay suffer from mis-estimations due to other chromatic effects in the observations. The precision in modeling dispersion is dependent on the observed bandwidth. In this work, we calculate the offsets in infinite-frequency TOAs due to mis-estimations in the modeling of dispersion when using varying bandwidths at the Green Bank Telescope. We use a set of broadband observations of PSR J1643-1224, a pulsar with an excess of chromatic noise in its timing residuals. We artificially restricted these observations to a narrowband frequency range, then used both data sets to calculate residuals with a timing model that does not include short-scale dispersion variations. By fitting the resulting residuals to a dispersion model, and comparing the ensuing fitted parameters, we quantify the dispersion mis-estimations. Moreover, by calculating the autocovariance function of the parameters we obtained a characteristic timescale over which the dispersion mis-estimations are correlated. For PSR J1643-1224, which has one of the highest dispersion measures (DM) in the NANOGrav pulsar timing array, we find that the infinite-frequency TOAs suffer from a systematic offset of ~22 microseconds due to DM mis-estimations, with correlations over ~1 month. For lower-DM pulsars, the offset is ~7 microseconds. This error quantification can be used to provide more robust noise modeling in NANOGrav's data, thereby increasing sensitivity and improving parameter estimation in gravitational wave searches.

Convergence rate analyses of random walk Metropolis-Hastings Markov chains on general state spaces have largely focused on establishing sufficient conditions for geometric ergodicity or on analysis of mixing times. Geometric ergodicity is a key sufficient condition for the Markov chain Central Limit Theorem and allows rigorous approaches to assessing Monte Carlo error. The sufficient conditions for geometric ergodicity of the random walk Metropolis-Hastings Markov chain are refined and extended, which allows the analysis of previously inaccessible settings such as Bayesian Poisson regression. The key technical innovation is the development of explicit drift and minorization conditions for random walk Metropolis-Hastings, which allows explicit upper and lower bounds on the geometric rate of convergence. Further, lower bounds on the geometric rate of convergence are also developed using spectral theory. The existing sufficient conditions for geometric ergodicity, to date, have not provided explicit constraints on the rate of geometric rate of convergence because the method used only implies the existence of drift and minorization conditions. The theoretical results are applied to random walk Metropolis-Hastings algorithms for a class of exponential families and generalized linear models that address Bayesian Regression problems.

This paper presents rigorous tests of pulsar timing array methods and software, examining their consistency across a wide range of injected parameters and signal strength. We discuss updates to the 15-year isotropic gravitational-wave background analyses and their corresponding code representations. Descriptions of the internal structure of the flagship algorithms \texttt{Enterprise} and \texttt{PTMCMCSampler} are given to facilitate understanding of the PTA likelihood structure, how models are built, and what methods are currently used in sampling the high-dimensional PTA parameter space. We introduce a novel version of the PTA likelihood that uses a two-step marginalization procedure that performs much faster when the white noise parameters remain fixed. We perform stringent tests of consistency and correctness of the Bayesian and frequentist analysis software. For the Bayesian analysis, we test prior recovery, injection recovery, and Bayes factors. For the frequentist analysis, we test that the cross-correlation-based optimal statistic, when modified to account for a non-negligible gravitational-wave background, accurately recovers the amplitude of the background. We also summarize recent advances and tests performed on the optimal statistic in the literature from both GWB detection and parameter estimation perspectives. The tests presented here validate current and future analyses of PTA data., Comment: 30 pages, 10 figures, 1 table; Companion paper to "The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background"; For questions or comments, please email comments@nanograv.org

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 dataset. 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, and place a Bayesian $95\%$ upper limit on the level of broadband anisotropy such that $(C_{l>0} / C_{l=0}) < 20\%$. 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 dataset, and show that this dataset 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., Comment: 19 pages, 11 figures; submitted to Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

The NANOGrav 15-year data set shows evidence for the presence of a low-frequency gravitational-wave background (GWB). While many physical processes can source such low-frequency gravitational waves, here we analyze the signal as coming from a population of supermassive black hole (SMBH) binaries distributed throughout the Universe. We show that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency gravitational-wave spectrum. While multiple model variations are able to reproduce the GWB spectrum at our current measurement precision, our results highlight the importance of accurately modeling binary evolution for producing realistic GWB spectra. Additionally, while reasonable parameters are able to reproduce the 15-year observations, the implied GWB amplitude necessitates either a large number of parameters to be at the edges of expected values, or a small number of parameters to be notably different from standard expectations. While we are not yet able to definitively establish the origin of the inferred GWB signal, the consistency of the signal with astrophysical expectations offers a tantalizing prospect for confirming that SMBH binaries are able to form, reach sub-parsec separations, and eventually coalesce. As the significance grows over time, higher-order features of the GWB spectrum will definitively determine the nature of the GWB and allow for novel constraints on SMBH populations., Comment: Accepted by Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org. Edited to fix two equation typos (Eq.13 & 21), and minor text typos

The 15-year pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) shows positive evidence for the presence of a low-frequency gravitational-wave (GW) background. In this paper, we investigate potential cosmological interpretations of this signal, specifically cosmic inflation, scalar-induced GWs, first-order phase transitions, cosmic strings, and domain walls. We find that, with the exception of stable cosmic strings of field theory origin, all these models can reproduce the observed signal. When compared to the standard interpretation in terms of inspiraling supermassive black hole binaries (SMBHBs), many cosmological models seem to provide a better fit resulting in Bayes factors in the range from 10 to 100. However, these results strongly depend on modeling assumptions about the cosmic SMBHB population and, at this stage, should not be regarded as evidence for new physics. Furthermore, we identify excluded parameter regions where the predicted GW signal from cosmological sources significantly exceeds the NANOGrav signal. These parameter constraints are independent of the origin of the NANOGrav signal and illustrate how pulsar timing data provide a new way to constrain the parameter space of these models. Finally, we search for deterministic signals produced by models of ultralight dark matter (ULDM) and dark matter substructures in the Milky Way. We find no evidence for either of these signals and thus report updated constraints on these models. In the case of ULDM, these constraints outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons., Comment: 74 pages, 31 figures, 4 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

Pulsar timing arrays (PTAs) are galactic-scale gravitational wave detectors. Each individual arm, composed of a millisecond pulsar, a radio telescope, and a kiloparsecs-long path, differs in its properties but, in aggregate, can be used to extract low-frequency gravitational wave (GW) signals. We present a noise and sensitivity analysis to accompany the NANOGrav 15-year data release and associated papers, along with an in-depth introduction to PTA noise models. As a first step in our analysis, we characterize each individual pulsar data set with three types of white noise parameters and two red noise parameters. These parameters, along with the timing model and, particularly, a piecewise-constant model for the time-variable dispersion measure, determine the sensitivity curve over the low-frequency GW band we are searching. We tabulate information for all of the pulsars in this data release and present some representative sensitivity curves. We then combine the individual pulsar sensitivities using a signal-to-noise-ratio statistic to calculate the global sensitivity of the PTA to a stochastic background of GWs, obtaining a minimum noise characteristic strain of $7\times 10^{-15}$ at 5 nHz. A power law-integrated analysis shows rough agreement with the amplitudes recovered in NANOGrav's 15-year GW background analysis. While our phenomenological noise model does not model all known physical effects explicitly, it provides an accurate characterization of the noise in the data while preserving sensitivity to multiple classes of GW signals., Comment: 67 pages, 73 figures, 3 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

We present observations and timing analyses of 68 millisecond pulsars (MSPs) comprising the 15-year data set of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). NANOGrav is a pulsar timing array (PTA) experiment that is sensitive to low-frequency gravitational waves. This is NANOGrav's fifth public data release, including both "narrowband" and "wideband" time-of-arrival (TOA) measurements and corresponding pulsar timing models. We have added 21 MSPs and extended our timing baselines by three years, now spanning nearly 16 years for some of our sources. The data were collected using the Arecibo Observatory, the Green Bank Telescope, and the Very Large Array between frequencies of 327 MHz and 3 GHz, with most sources observed approximately monthly. A number of notable methodological and procedural changes were made compared to our previous data sets. These improve the overall quality of the TOA data set and are part of the transition to new pulsar timing and PTA analysis software packages. For the first time, our data products are accompanied by a full suite of software to reproduce data reduction, analysis, and results. Our timing models include a variety of newly detected astrometric and binary pulsar parameters, including several significant improvements to pulsar mass constraints. We find that the time series of 23 pulsars contain detectable levels of red noise, 10 of which are new measurements. In this data set, we find evidence for a stochastic gravitational-wave background., Comment: 90 pages, 74 figures, 6 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org