ABSTRACT
Massive black hole binaries (MBHBs) form as a consequence of galaxy mergers. However, it is still unclear whether they typically merge within a Hubble time, and how accretion may affect ...their evolution. These questions will be addressed by pulsar timing arrays (PTAs), which aim to detect the gravitational wave (GW) background (GWB) emitted by MBHBs during the last Myr of inspiral. Here, we investigate the influence of differential accretion on MBHB merger rates, chirp masses, and the resulting GWB spectrum. We evolve an MBHB sample from the Illustris hydrodynamic cosmological simulation using semi-analytical models and for the first time self-consistently evolve their masses with binary accretion models. In all models, MBHBs coalesce with median total masses up to 1.5 × 108 M⊙, up to 3−4 times larger than in models neglecting accretion. In our model with the largest plausible impact, the median mass ratio of coalescing MBHBs increases by a factor 3.6, the coalescence rate by $52.3{{\ \rm per\ cent}}$, and the GWB amplitude by a factor 4.0, yielding a dimensionless GWB strain $A_{yr^{-1}} = 1 \times 10^{-15}$. Our model that favours accretion on to the primary MBH reduces the median mass ratio of coalescing MBHBs by a factor of 2.9, and yields a GWB amplitude $A_{yr^{-1}} = 3.1 \times 10^{-16}$. This is nearly indistinguishable from our model neglecting accretion, despite higher MBHB masses at coalescence. We further predict binary separation and mass ratio distributions of stalled MBHBs in the low-redshift Universe, and find that these depend sensitively on binary accretion models. This presents the potential for combined electromagnetic and GW observational constraints on merger rates and accretion models of MBHB populations.
Massive black hole binaries (MBHBs) form as a consequence of galaxy mergers. However, it is still unclear whether they typically merge within a Hubble time, and how accretion may affect their ...evolution. These questions will be addressed by pulsar timing arrays (PTAs), which aim to detect the GW background (GWB) emitted by MBHBs during the last Myrs of inspiral. Here we investigate the influence of differential accretion on MBHB merger rates, chirp masses and the resulting GWB spectrum. We evolve a MBHB sample from the Illustris hydrodynamic cosmological simulation using semi-analytic models and for the first time self-consistently evolve their masses with binary accretion models. In all models, MBHBs coalesce with median total masses up to \(1.5 \times 10^8 M_{\odot}\), up to \(3-4\) times larger than in models neglecting accretion. In our model with the largest plausible impact, the median mass ratio of coalescing MBHBs increases by a factor \(3.6\), the coalescence rate by \(52.3\%\), and the GWB amplitude by a factor \(4.0\), yielding a dimensionless GWB strain \(A_{yr^{-1}} = 1 \times 10^{-15}\). Our model that favours accretion onto the primary MBH reduces the median mass ratio of coalescing MBHBs by a factor of \(2.9\), and yields a GWB amplitude \(A_{yr^{-1}} = 3.1 \times 10^{-16}\). This is nearly indistinguishable from our model neglecting accretion, despite higher MBHB masses at coalescence. \textbf{We further predict binary separation and mass ratio distributions of stalled MBHBs in the low-redshift universe, and find that these depend sensitively on binary accretion models. This presents the potential for combined EM and GW observational constraints on merger rates and accretion models of MBHB populations.}
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.
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.
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.
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.
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.
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.
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.
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