Search

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.

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 eccentricity e _0 < 0.5 and the symmetric mass ratio η > 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 for e _0 < 0.5 and η > 0.1. Similar 95% upper limits on the chirp mass are (1.98 ± 0.05) × 10 ^9 and (1.81 ± 0.01) × 10 ^9 M _☉ . 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.

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. We find a Bayes factor of 2.8 in favor of a model that includes a memory signal and common spatially uncorrelated red noise (CURN) compared to a model including only a CURN. However, further investigation shows that a disproportionate amount of support for the memory signal comes from three dubious pulsars. Using a more flexible red-noise model in these pulsars reduces the Bayes factor to 1.3. Having found no compelling evidence, 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 × 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 that 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.

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 ( C _l _=1 / C _l _=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.

The NANOGrav 15 yr 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 yr 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 subparsec 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.

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 data sets. Here we present the search for individual supermassive black hole binaries in the NANOGrav 15 yr data set. 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 ∼4 nHz, and another at ∼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. At our most sensitive frequency of 6 nHz, we place a sky-averaged 95% upper limit of 8 × 10 ^−15 on the strain amplitude. We also calculate an exclusion volume and a corresponding effective radius, within which we can rule out the presence of black hole binaries emitting at a given frequency.

Pulsar timing array collaborations, such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), are seeking to detect nanohertz gravitational waves emitted by supermassive black hole binaries formed in the aftermath of galaxy mergers. We have searched for continuous waves from individual circular supermassive black hole binaries using NANOGrav’s recent 12.5 yr data set. We created new methods to accurately model the uncertainties on pulsar distances in our analysis, and we implemented new techniques to account for a common red-noise process in pulsar timing array data sets while searching for deterministic gravitational wave signals, including continuous waves. As we found no evidence for continuous waves in our data, we placed 95% upper limits on the strain amplitude of continuous waves emitted by these sources. At our most sensitive frequency of 7.65 nHz, we placed a sky-averaged limit of h _0 < (6.82 ± 0.35) × 10 ^−15 , and h _0 < (2.66 ± 0.15) × 10 ^−15 in our most sensitive sky location. Finally, we placed a multimessenger limit of ${ \mathcal M }\lt (1.41\pm 0.02)\times {10}^{9}\,{M}_{\odot }$ on the chirp mass of the supermassive black hole binary candidate 3C 66B.

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

We present observations and timing analyses of 68 millisecond pulsars (MSPs) comprising the 15 yr 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 (GWs). 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 3 yr, now spanning nearly 16 yr 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 GW background.

Pulsar timing arrays (PTAs) are galactic-scale gravitational wave (GW) 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 GW signals. We present a noise and sensitivity analysis to accompany the NANOGrav 15 yr 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 × 10 ^−15 at 5 nHz. A power-law-integrated analysis shows rough agreement with the amplitudes recovered in NANOGrav’s 15 yr 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.

The 15 yr 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.

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.

We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ∼ 10^{-5} – 1 Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational-wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from binary mergers and ringdowns; the true nature of astrophysical black holes; and much more. The strength of this science alone calls for the swift implementation of a space-based detector; the remarkable richness of astrophysics, astronomy, and cosmology in the low-frequency gravitational-wave band make the case even stronger.

Gravitational waves from the inspiral and coalescence of supermassive black-hole (SMBH) binaries with masses m1 [?] m2 [?] 106M[?] are likely to be among the strongest sources for the Laser Interferometer Space Antenna (LISA). We describe a three-stage data-analysis pipeline designed to search for and measure the parameters of SMBH binaries in LISA data. The first stage uses a time-frequency track-search method to search for inspiral signals and provide a coarse estimate of the black-hole masses m1, m2 and the coalescence time of the binary tc. The second stage uses a sequence of matched-filter template banks, seeded by the first stage, to improve the measurement accuracy of the masses and coalescence time. Finally, a Markov chain Monte Carlo search is used to estimate all nine physical parameters of the binary (masses, coalescence time, distance, initial phase, sky position and orientation). Using results from the second stage substantially shortens the Markov chain burn-in time and allows us to determine the number of SMBH-binary signals in the data before starting parameter estimation. We demonstrate our analysis pipeline using simulated data from the first Mock LISA Data Challenge. We discuss our plan for improving this pipeline and the challenges that will be faced in real LISA data analysis. [ABSTRACT FROM AUTHOR]

The Mock LISA Data Challenges are a programme to demonstrate and encourage the development of LISA data-analysis capabilities, tools and techniques. At the time of this workshop, three rounds of challenges had been completed, and the next was about to start. In this paper we provide a critical analysis of the entries to the latest completed round, Challenge 1B. The entries confirm the consolidation of a range of data-analysis techniques for galactic and massive-black-hole binaries, and they include the first convincing examples of detection and parameter estimation of extreme-mass-ratio inspiral sources. In this paper we also introduce the next round, Challenge 3. Its data sets feature more realistic waveform models (e.g., galactic binaries may now chirp, and massive-black-hole binaries may precess due to spin interactions), as well as new source classes (bursts from cosmic strings, isotropic stochastic backgrounds) and more complicated nonsymmetric instrument noise. [ABSTRACT FROM AUTHOR]

The Mock LISA data challenges are a program to demonstrate LISA data-analysis capabilities and to encourage their development. Each round of challenges consists of several data sets containing simulated instrument noise and gravitational waves from sources of undisclosed parameters. Participants are asked to analyze the data sets and report the maximum information about the source parameters. The challenges are being released in rounds of increasing complexity and realism: here we present the results of Challenge 2, issued in Jan 2007, which successfully demonstrated the recovery of signals from nonspinning supermassive-black-hole binaries with optimal SNRs between [?]10 and 2000, from [?]20 000 overlapping galactic white-dwarf binaries (among a realistically distributed population of 26 million), and from the extreme-mass-ratio inspirals of compact objects into central galactic black holes with optimal SNRs [?]100. [ABSTRACT FROM AUTHOR]

We describe a simple framework to assess the LISA scientific performance (more specifically, its sensitivity and expected parameter-estimation precision for prescribed gravitational-wave signals) under the assumption of failure of one or two inter-spacecraft laser measurements (links) and of one to four intra-spacecraft laser measurements. We apply the framework to the simple case of measuring the LISA sensitivity to monochromatic circular binaries, and the LISA parameter-estimation precision for the gravitational-wave polarization angle of these systems. Compared to the six-link baseline configuration, the five-link case is characterized by a small loss in signal-to-noise ratio (SNR) in the high-frequency section of the LISA band; the four-link case shows a reduction by a factor of \sqrt{2} at low frequencies, and by up to [?]2 at high frequencies. The uncertainty in the estimate of polarization, as computed in the Fisher-matrix formalism, also worsens when moving from six to five, and then to four links: this can be explained by the reduced SNR available in those configurations (except for observations shorter than three months, where five and six links do better than four even with the same SNR). In addition, we prove (for generic signals) that the SNR and Fisher matrix are invariant with respect to the choice of a basis of TDI observables; rather, they depend only on which inter-spacecraft and intra-spacecraft measurements are available. [ABSTRACT FROM AUTHOR]