Search

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

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

Neutron stars and white dwarfs are both dense remnants of post-main-sequence stars. Pulsars, magnetars and strongly magnetised white dwarfs have all been seen to been observed to exhibit coherent, pulsed radio emission in relation to their rotational period. Recently, a new type of radio long period transient (LPT) has been discovered. The bright radio emission of LPTs resembles that of radio pulsars and magnetars. However, they pulse on timescales (minutes) much longer than previously seen. While minute timescales are common rotation periods for white dwarfs, LPTs are much brighter than the known pulsating white dwarfs, and dipolar radiation from isolated (as opposed to binary) magnetic white dwarfs has yet to be observed. Here, we report the discovery of a new $\sim$421~s LPT, CHIME J0630+25, using the CHIME/FRB and CHIME/Pulsar instruments. We used standard pulsar timing techniques and obtained a phase-coherent timing solution which yielded limits on the inferred magnetic field and characteristic age. CHIME J0630+25 is remarkably nearby ($170 \pm 80$~pc), making it the closest LPT discovered to date., Comment: Submitted

Studying transient phenomena, such as individual pulses from pulsars, has garnered considerable attention in the era of astronomical big data. Of specific interest to this study are Rotating Radio Transients (RRATs), nulling, and intermittent pulsars. This study introduces a new algorithm named LuNfit, tailored to correct the selection biases originating from the telescope and detection pipelines. Ultimately LuNfit estimates the intrinsic luminosity distribution and nulling fraction of the single pulses emitted by pulsars. LuNfit relies on Bayesian nested sampling so that the parameter space can be fully explored. Bayesian nested sampling also provides the additional benefit of simplifying model comparisons through the Bayes ratio. The robustness of LuNfit is shown through simulations and applying LuNfit onto pulsars with known nulling fractions. LuNfit is then applied to three RRATs, J0012+5431, J1538+1523, and J2355+1523, extracting their intrinsic luminosity distribution and burst rates. We find that their nulling fraction is 0.4(2), 0.749(5) and 0.995(2) respectively. We further find that a log-normal distribution likely describes the single pulse luminosity distribution of J0012+5431 and J1538+1523, while the Bayes ratio for J2355+1523 slightly favors an exponential distribution. We show the conventional method of correcting selection effects by "scaling up" the missed fraction of radio transients can be unreliable when the mean luminosity of the source is faint relative to the telescope sensitivity. Finally, we discuss the limitations of the current implementation of LuNfit while also delving into potential enhancements that would enable LuNfit to be applied to sources with complex pulse morphologies., Comment: Accepted by ApJ

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

We performed near-daily observations on the binary pulsars PSR J0218+4232, PSR J1518+4904 and PSR J2023+2853 with the Canadian Hydrogen Intensity Mapping Experiment (CHIME). For the first time, we detected the Shapiro time delay in all three pulsar-binary systems, using only 2--4 years of CHIME/Pulsar timing data. We measured the pulsar masses to be $1.49^{+0.23}_{-0.20}$ M$_\odot$, $1.470^{+0.030}_{-0.034}$ M$_\odot$ and $1.50^{+0.49}_{-0.38}$ M$_\odot$ respectively. The companion mass to PSR J0218+4232 was found to be $0.179^{+0.018}_{-0.016}$ M$_\odot$. We constrained the mass of the neutron-star companion of PSR J1518+4904 to be $1.248^{+0.035}_{-0.029}$ M$_\odot$, using the observed apsidal motion as a constraint on mass estimation. The binary companion to PSR J2023+2853 was found to have a mass of $0.93^{+0.17}_{-0.14}$ M$_\odot$; in the context of the near-circular orbit, this mass estimate suggests that the companion to PSR J2023+2853 is likely a high-mass white dwarf. By comparing the timing model obtained for PSR J0218+4232 with previous observations, we found a significant change in the observed orbital period of the system of $\dot{P_{\rm b}} = 0.14(2) \times 10^{-12}$; we determined that this variation arises from ``Shklovskii acceleration" due to relative motion of the binary system, and used this measurement to estimate a distance of $d=(6.7 \pm 1.0)$ kpc to PSR J0218+4232. This work demonstrates the capability of high-cadence observations, enabled by the CHIME/Pulsar system, to detect and refine general-relativistic effects of binary pulsars over short observing timescales., Comment: 14 pages, 4 figures, accepted for publication in ApJ

The 5n-vector ensemble method is a multiple test for the targeted search of continuous gravitational waves from an ensemble of known pulsars. This method can improve the detection probability combining the results from individually undetectable pulsars if few signals are near the detection threshold. In this paper, we apply the 5n-vector ensemble method to the O3 data set from the LIGO and Virgo detectors considering an ensemble of 201 known pulsars. We find no evidence for a signal from the ensemble and set a 95% credible upper limit on the mean ellipticity assuming a common exponential distribution for the pulsars' ellipticities. Using two independent hierarchical Bayesian procedures, we find upper limits of $1.2 \times 10^{-9}$ and $2.5 \times 10^{-9}$ on the mean ellipticity for the 201 analyzed pulsars.

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

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

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

Annual variations of interstellar scintillation can be modelled to constrain parameters of the ionized interstellar medium. If a pulsar is in a binary system, then investigating the orbital parameters is possible through analysis of the orbital variation of scintillation. In observations carried out from 2011 January to 2020 August by the European Pulsar Timing Array radio telescopes, PSRs~J0613$-$0200 and J0636+5128 show strong annual variations in their scintillation velocity, while the former additionally exhibits an orbital fluctuation. Bayesian theory and Markov-chain-Monte-Carlo methods are used to interpret these periodic variations. We assume a thin and anisotropic scattering screen model, and discuss the mildly and extremely anisotropic scattering cases. PSR~J0613$-$0200 is best described by mildly anisotropic scattering, while PSR~J0636+5128 exhibits extremely anisotropic scattering. We measure the distance, velocity and degree of anisotropy of the scattering screen for our two pulsars, finding that scattering screen distances from Earth for PSRs~J0613$-$0200 and J0636+5128 are 316$^{+28}_{-20}$\,pc and 262$^{+96}_{-38}$\,pc, respectively. The positions of these scattering screens are coincident with the shell of the Local Bubble towards both pulsars. These associations add to the growing evidence of the Local Bubble shell as a dominant region of scattering along many sightlines., Comment: Accepted by SCIENCE CHINA Physics, Mechanics & Astronomy ( SCPMA)

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

Evidence for a low-frequency stochastic gravitational wave background has recently been reported based on analyses of pulsar timing array data. The most likely source of such a background is a population of supermassive black hole binaries, the loudest of which may be individually detected in these datasets. Here we present the search for individual supermassive black hole binaries in the NANOGrav 15-year dataset. We introduce several new techniques, which enhance the efficiency and modeling accuracy of the analysis. The search uncovered weak evidence for two candidate signals, one with a gravitational-wave frequency of $\sim$4 nHz, and another at $\sim$170 nHz. The significance of the low-frequency candidate was greatly diminished when Hellings-Downs correlations were included in the background model. The high-frequency candidate was discounted due to the lack of a plausible host galaxy, the unlikely astrophysical prior odds of finding such a source, and since most of its support comes from a single pulsar with a commensurate binary period. Finding no compelling evidence for signals from individual binary systems, we place upper limits on the strain amplitude of gravitational waves emitted by such systems., Comment: 23 pages, 13 figures, 2 tables. Accepted for publication 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

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

We report multiple lines of evidence for a stochastic signal that is correlated among 67 pulsars from the 15-year 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 these latter Bayes factors using a method that removes inter-pulsar correlations from our data set, finding $p = 10^{-3}$ (approx. $3\sigma$) for the observed Bayes factors in the null no-correlation scenario. A frequentist test statistic built directly as a weighted sum of inter-pulsar correlations yields $p = 5 \times 10^{-5} - 1.9 \times 10^{-4}$ (approx. $3.5 - 4\sigma$). Assuming a fiducial $f^{-2/3}$ characteristic-strain spectrum, as appropriate for an ensemble of binary supermassive black-hole inspirals, the strain amplitude is $2.4^{+0.7}_{-0.6} \times 10^{-15}$ (median + 90% credible interval) at a reference frequency of 1/(1 yr). 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., Comment: 30 pages, 18 figures. 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

Interstellar scattering (ISS) of radio pulsar emission can be used as a probe of the ionised interstellar medium (IISM) and causes corruptions in pulsar timing experiments. Two types of ISS phenomena (intensity scintillation and pulse broadening) are caused by electron density fluctuations on small scales (< 0.01 AU). Theory predicts that these are related, and both have been widely employed to study the properties of the IISM. Larger scales ($\sim$1-100\,AU) cause measurable changes in dispersion and these can be correlated with ISS observations to estimate the fluctuation spectrum over a very wide scale range. IISM measurements can often be modeled by a homogeneous power-law spatial spectrum of electron density with the Kolmogorov ($-11/3$) spectral exponent. Here we aim to test the validity of using the Kolmogorov exponent with PSR~J0826+2637. We do so using observations of intensity scintillation, pulse broadening and dispersion variations across a wide fractional bandwidth (20 -- 180\,MHz). We present that the frequency dependence of the intensity scintillation in the high frequency band matches the expectations of a Kolmogorov spectral exponent but the pulse broadening in the low frequency band does not change as rapidly as predicted with this assumption. We show that this behavior is due to an inhomogeneity in the scattering region, specifically that the scattering is dominated by a region of transverse size $\sim$40\,AU. The power spectrum of the electron density, however, maintains the Kolmogorov spectral exponent from spatial scales of 5$\times10^{-6}$\,AU to $\sim$100\,AU., Comment: Accepted for publication in MNRAS, typo fixed

The millisecond pulsar J1713+0747 underwent a sudden and significant pulse shape change between April 16 and 17, 2021 (MJDs 59320 and 59321). Subsequently, the pulse shape gradually recovered over the course of several months. We report the results of continued multi-frequency radio observations of the pulsar made using the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and the 100-meter Green Bank Telescope (GBT) in a three-year period encompassing the shape change event, between February 2020 and February 2023. As of February 2023, the pulse shape had returned to a state similar to that seen before the event, but with measurable changes remaining. The amplitude of the shape change and the accompanying TOA residuals display a strong non-monotonic dependence on radio frequency, demonstrating that the event is neither a glitch (the effects of which should be independent of radio frequency, $\nu$) nor a change in dispersion measure (DM) alone (which would produce a delay proportional to $\nu^{-2}$). However, it does bear some resemblance to the two previous "chromatic timing events" observed in J1713+0747 (Demorest et al. 2013; Lam et al. 2016), as well as to a similar event observed in PSR J1643-1224 in 2015 (Shannon et al. 2016)., Comment: 18 pages, 8 figures. Submitted to ApJ. Data available at https://doi.org/10.5281/zenodo.7236459

The Canadian Hydrogen Mapping Experiment (CHIME) is a radio telescope located in British Columbia, Canada. The large FOV allows CHIME/FRB to be an exceptional pulsar and Rotating Radio Transient (RRAT) finding machine, despite saving only the metadata of incoming Galactic events. We have developed a pipeline to search for pulsar/RRAT candidates using DBSCAN, a clustering algorithm. Follow-up observations are then scheduled with the more sensitive CHIME/Pulsar instrument capable of near-daily high time resolution spectra observations. We have developed the CHIME/Pulsar Single Pulse Pipeline to automate the processing of CHIME/Pulsar search-mode data. We report the discovery of 21 new Galactic sources, with 14 RRATs, 6 isolated long-period pulsars and 1 binary system. Owing to CHIME/Pulsar's observations we have obtained timing solutions for 8 of the 14 RRATs along with all the regular pulsars and the binary system. Notably we report that the binary system is in a long orbit of 412 days with a minimum companion mass of 0.1303 solar masses and no evidence of an optical companion within 10" of the pulsar position. This highlights that working synergistically with CHIME/FRB's large survey volume CHIME/Pulsar can obtain arc second localisations for low burst rate RRATs though pulsar timing. We find that the properties of our newly discovered RRATs are consistent with those of the presently known population. They tend to have lower burst rates than those found in previous surveys, which is likely due to survey bias rather than the underlying population.

Interstellar scintillation analysis of pulsars allows us to probe the small-scale distribution and inhomogeneities of the ionized interstellar medium. Our priority is to present the data set and the basic measurements of scintillation parameters of pulsars employing long-term scintillation observations carried out from 2011 January to 2020 August by the European Pulsar Timing Array radio telescopes in the 21-cm and 11-cm bands. Additionally, we aim to identify future possible lines of study using this long-term scintillation dataset. We present the long-term time series of $\nu_{\rm d}$ and $\tau_{\rm d}$ for 13 pulsars. Sanity-checks and comparisons indicate that the scintillation parameters of our work and previously published works are mostly consistent. For two pulsars, PSRs~J1857+0943 and J1939+2134, we were able to obtain measurements of the $\nu_{\rm d}$ at both bands, which allows us to derive the time series of frequency scaling indices with a mean and a standard deviation of 2.82$\pm$1.95 and 3.18$\pm$0.60, respectively. We found some interesting features which will be studied in more detail in subsequent papers in this series: (i) in the time series of PSR~J1939+2134, where the scintillation bandwidth sharply increases or decreases associated with a sharp change of dispersion measure; (ii) PSR~J0613$-$0200 and PSR~J0636+5126 show a strong annual variation in the time series of the $\tau_{\rm d}$; (iii) PSR~J1939+2134 shows a weak anti-correlation between scintillation timescale and dispersion in WSRT data., Comment: 18 pages, 6 figures, 4 tables, accepted for publication in A&A

The interstellar medium hosts a population of scattering screens, most of unknown origin. Scintillation studies of pulsars provides a sensitive tool for resolving these scattering screens and a means of measuring their properties. In this paper, we report our analysis of 34 years of Arecibo observations of PSR B1133+16, from which we have obtained high-quality dynamic spectra and their associated scintillation arcs, arising from the scattering screens located along the line of sight to the pulsar. We have identified six individual scattering screens that are responsible for the observed scintillation arcs, which persist for decades. Using the assumption that the scattering screens have not changed significantly in this time, we have modeled the variations in arc curvature throughout the Earth's orbit and extracted information about the placement, orientation, and velocity of five of the six screens, with the highest-precision distance measurement placing a screen at just $5.46^{+0.54}_{-0.59}$ pc from the Earth. We associate the more distant of these screens with an under-dense region of the Local Bubble., Comment: 16 pages, 9 figures, accepted for publication in ApJ

The CHIME/FRB experiment has detected thousands of Fast Radio Bursts (FRBs) due to its sensitivity and wide field of view; however, its low angular resolution prevents it from localizing events to their host galaxies. Very Long Baseline Interferometry (VLBI), triggered by FRB detections from CHIME/FRB will solve the challenge of localization for non-repeating events. Using a refurbished 10-m radio dish at the Algonquin Radio Observatory located in Ontario Canada, we developed a testbed for a VLBI experiment with a theoretical ~<30 masec precision. We provide an overview of the 10-m system and describe its refurbishment, the data acquisition, and a procedure for fringe fitting that simultaneously estimates the geometric delay used for localization and the dispersive delay from the ionosphere. Using single pulses from the Crab pulsar, we validate the system and localization procedure, and analyze the clock stability between sites, which is critical for phase-referencing an FRB event. We find a localization of 50 masec is possible with the performance of the current system. Furthermore, for sources with insufficient signal or restricted wideband to simultaneously measure both geometric and ionospheric delays, we show that the differential ionospheric contribution between the two sites must be measured to a precision of 1e-8 pc/cc to provide a reasonable localization from a detection in the 400--800 MHz band. Finally we show detection of an FRB observed simultaneously in the CHIME and the Algonquin 10-m telescope, the first FRB cross-correlated in this very long baseline. This project serves as a testbed for the forthcoming CHIME/FRB Outriggers project., Comment: Accepted for publication by AJ

We report results from continued timing observations of PSR J0740+6620, a high-mass, 2.8-ms radio pulsar in orbit with a likely ultra-cool white dwarf companion. Our data set consists of combined pulse arrival-time measurements made with the 100-m Green Bank Telescope and the Canadian Hydrogen Intensity Mapping Experiment telescope. We explore the significance of timing-based phenomena arising from general-relativistic dynamics and variations in pulse dispersion. When using various statistical methods, we find that combining $\sim 1.5$ years of additional, high-cadence timing data with previous measurements confirms and improves upon previous estimates of relativistic effects within the PSR J0740+6620 system, with the pulsar mass $m_{\rm p} = 2.08^{+0.07}_{-0.07}$ M$_\odot$ (68.3\% credibility) determined by the relativistic Shapiro time delay. For the first time, we measure secular variation in the orbital period and argue that this effect arises from apparent acceleration due to significant transverse motion. After incorporating contributions from Galactic differential rotation and off-plane acceleration in the Galactic potential, we obtain a model-dependent distance of $d = 1.14^{+0.17}_{-0.15}$ kpc (68.3\% credibility). This improved distance confirms the ultra-cool nature of the white dwarf companion determined from recent optical observations. We discuss the prospects for future observations with next-generation facilities, which will likely improve the precision on $m_{\rm p}$ for J0740+6620 by an order of magnitude within the next few years., Comment: Final version after minor corrections during referee process. Published in the Astrophysical Journal Letters on 1 July 2021