The NANOGrav 11 yr Data Set: Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

In this Letter, we carry out the first systematic investigation of the expected gravitational wave (GW) background generated by supermassive black hole (SMBH) binaries in the nHz frequency band accessible to pulsar timing arrays (PTAs). We take from the literature several estimates of the redshift-dependent galaxy mass function and of the fraction of close galaxy pairs to derive a wide range of galaxy merger rates. We then exploit empirical black hole–host relations to populate merging galaxies with SMBHs. The result of our procedure is a collection of a large number of phenomenological SMBH binary merger rates consistent with current observational constraints on the galaxy assembly at z < 1.5. For each merger rate we compute the associated GW signal, eventually producing a large set of estimates of the nHz GW background that we use to infer confidence intervals of its expected amplitude. When considering the most recent SMBH–host relations, accounting for overmassive black holes in brightest cluster galaxies, we find that the nominal 1σ interval of the expected GW signal is only a factor of 3–10 below current PTA limits, implying a non-negligible chance of detection in the next few years.

The gravitational waves (GWs) from supermassive binary black holes (BBHs) have long been sought by pulsar timing array (PTA) experiments, in the forms of both a stochastic GW background (GWB) and individual sources. Evidence for a GWB was reported recently by several PTAs with origins to be determined. Here we use a BBH population synthesis model to investigate the detection probability of individual BBHs by the Chinese PTA (CPTA) and the constraint on the GWB origin that may be obtained by PTA observations of both GWB and individual BBHs. If the detected GWB signal is entirely due to BBHs, a significantly positive redshift evolution (∝ (1 + z)2.07) of the mass scaling relation between supermassive black holes and their host galaxies is required. In this case, we find that the detection probability of individual BBHs is ∼85% or 64% if using a period of 3.4 yr of CPTA observation data, with an expectation of ∼1.9 or 1.0 BBHs detectable with a signal-to-noise ratio ≥3 or 5, and it is expected to increase to >95% if the observation period is extended to 5 yr or longer. Even if the contribution from BBHs to the GWB power signal is as small as ∼10%, a positive detection of individual BBHs can still be expected within an observation period of ∼10 yr. A nondetection of individual BBHs within several years from now jointly with the detected GWB signal can put a strong constraint on the upper limit of the BBH contribution to the GWB signal and help identify/falsify a cosmological origin.

We search for an isotropic stochastic gravitational-wave background (GWB) in the newly released 11 year data set from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). While we find no evidence for a GWB, we place constraints on a population of inspiraling supermassive black hole (SMBH) binaries, a network of decaying cosmic strings, and a primordial GWB. For the first time, we find that the GWB constraints are sensitive to the solar system ephemeris (SSE) model used and that SSE errors can mimic a GWB signal. We developed an approach that bridges systematic SSE differences, producing the first pulsar-timing array (PTA) constraints that are robust against SSE errors. We thus place a 95% upper limit on the GW-strain amplitude of A GWB < 1.45 × 10−15 at a frequency of f = 1 yr−1 for a fiducial f −2/3 power-law spectrum and with interpulsar correlations modeled. This is a factor of ∼2 improvement over the NANOGrav nine-year limit calculated using the same procedure. Previous PTA upper limits on the GWB (as well as their astrophysical and cosmological interpretations) will need revision in light of SSE systematic errors. We use our constraints to characterize the combined influence on the GWB of the stellar mass density in galactic cores, the eccentricity of SMBH binaries, and SMBH–galactic-bulge scaling relationships. We constrain the cosmic-string tension using recent simulations, yielding an SSE-marginalized 95% upper limit of Gμ < 5.3 × 10−11—a factor of ∼2 better than the published NANOGrav nine-year constraints. Our SSE-marginalized 95% upper limit on the energy density of a primordial GWB (for a radiation-dominated post-inflation universe) is ΩGWB(f) h 2 < 3.4 × 10−10.

Large-area sky surveys show that massive galaxies undergo at least one major merger in a Hubble time. Ongoing pulsar timing array (PTA) experiments are aimed at measuring the gravitational-wave (GW) emission from binary supermassive black holes (SMBHs) at the centres of galaxy merger remnants. In this paper, using the latest observational estimates for a range of galaxy properties and scaling relations, we predict the amplitude of the GW background generated by the binary SMBH population. We also predict the numbers of individual binary SMBH GW sources. We predict the characteristic strain amplitude of the GW background to lie in the range 5.1 × 10−16 < Ayr < 2.4 × 10−15 at a frequency of (1 yr)−1, with 95 per cent confidence. Higher values within this range, which correspond to the more commonly preferred choice of galaxy merger time-scale, will fall within the expected sensitivity ranges of existing PTA projects in the next few years. In contrast, we find that a PTA consisting of at least 100 pulsars observed with next-generation radio telescopes will be required to detect continuous-wave GWs from binary SMBHs. We further suggest that GW memory bursts from coalescing SMBH pairs are not viable sources for PTAs. Both the GW background and individual GW source counts are dominated by binaries formed in mergers between early-type galaxies of masses ≳5 × 1010 M⊙ at redshifts ≲1.5. Uncertainties in the galaxy merger time-scale and the SMBH mass–galaxy bulge mass relation dominate the uncertainty in our predictions.

We assess the effects of super-massive black hole (SMBH) environments on the gravitational-wave (GW) signal from binary SMBHs. To date, searches with pulsar timing arrays for GWs from binary SMBHs, in the frequency band $\sim1-100$\,nHz, include the assumptions that all binaries are circular and evolve only through GW emission. However, dynamical studies have shown that the only way that binary SMBH orbits can decay to separations where GW emission dominates the evolution is through interactions with their environments. We augment an existing galaxy and SMBH formation and evolution model with calculations of binary SMBH evolution in stellar environments, accounting for non-zero binary eccentricities. We find that coupling between binaries and their environments causes the expected GW spectral energy distribution to be reduced with respect to the standard assumption of circular, GW-driven binaries, for frequencies up to $\sim20$\,nHz. Larger eccentricities at binary formation further reduce the signal in this regime. We also find that GW bursts from individual eccentric binary SMBHs are unlikely to be detectable with current pulsar timing arrays. The uncertainties in these predictions are large, owing to observational uncertainty in SMBH-galaxy scaling relations and the galaxy stellar mass function, uncertainty in the nature of binary-environment coupling, and uncertainty in the numbers of the most massive binary SMBHs. We conclude, however, that low-frequency GWs from binary SMBHs may be more difficult to detect with pulsar timing arrays than currently thought.

Supermassive binary black holes (SMBBHs) in galactic centers may radiate gravitational waves (GW) in the nano-Hertz frequency band, which are expected to be detected by pulsar timing arrays (PTAs) in the near future. GW signals from individual SMBBHs at cosmic distances, if detected by PTAs, are potentially powerful standard sirens that can be used to independently measure distances and thus put constraints on cosmological parameters. In this paper, we investigate the constraint that may be obtained on the equation of state (w) of dark energy by using those SMBBHs, expected to be detected by the PTAs in the Square Kilometre Array (SKA) era. By considering both the currently available SMBBH candidates and mock SMBBHs in the universe resulting from a simple galaxy major merger model, we find that ∼200–3000 SMBBHs with chirp mass &gt;109 M ⊙ are expected to be detected with a signal-to-noise ratio &gt;10 by SKA–PTA with conservative and optimistic settings and they can be used to put a constraint on w to an uncertainty of Δw ∼ 0.02–0.1. If further information on the mass and mass ratio of those SMBBHs can be provided by electromagnetic observations (e.g., chirp mass uncertainty ≲50%), the constraint may be further improved to a ≲0.01 level, as many more SMBBHs will be detected by SKA–PTA with relatively better distance measurements and can be used as the standard sirens.

Pulsar timing arrays (PTAs) are anticipated to detect continuous gravitational waves (GWs) from individual supermassive black hole binaries (SMBHBs) in the near future. To identify the host galaxy of a GW source, PTAs require significantly improved angular resolution beyond the typical range of 100–1000 square degrees achieved by recent continuous GW searches. In this study, we investigate how precise pulsar distance measurements can enhance the localization of a single GW source. Accurate distance information, comparable to or better than the GW wavelength (typically 1 pc) can refine GW source localization. In the near future, with the advent of Square Kilometre Array (SKA), such high-precision distance measurements will be feasible for a few nearby pulsars. We focus on the relatively nearby pulsars J0437-4715 (156 pc) and J 0030 + 0451 (331 pc), incorporating their actual distance uncertainties based on current very long baseline interferometry measurements and the anticipated precision of the SKA-era. By simulating 87 pulsars with the GW signal and Gaussian white noise in the timing residuals, we assess the impact of the pulsar distance information on GW source localization. Our results show that without precise distance information, localization remains insufficient to identify host galaxies under 10 ns noise. However, incorporating SKA-era distance precision for nearby pulsars J0437-4715 and J 0030 + 0451 can reduce localization uncertainties to the required level of 10 − 3 deg 2 under 10 ns noise. Localization accuracy strongly depends on the geometric configuration of pulsars with well-measured distances and improves notably near and between such pulsars. The improvement of the localization will greatly aid in identifying the host galaxy of a GW source and constructing an SMBHB catalog. It will further enable follow-up electromagnetic observations to investigate the SMBHB in greater detail.

The continuous nanohertz gravitational waves (GWs) from individual supermassive binary black holes (SMBBHs) can be encoded in the timing residuals of pulsar timing arrays (PTAs). For each pulsar, the residuals actually contain an Earth term and a pulsar term, but usually only the Earth term is considered as a signal and the pulsar term is dropped. This leads to parameter-estimation biases (PEBs) for the SMBBHs, and currently there are no convenient evaluations of the PEBs. In this article, we formulate the PEBs for a SMBBH with an eccentric orbit. In our analyses, the unknown phases of pulsar terms are treated as random variables obeying the uniform distribution U[0, 2π), due to the fact that pulsar distances are generally poorly measured. Our analytical results are in accordance with the numerical work by Zhu et al. at 1.5σ level, which implies that our formulae are effective in estimating magnitudes of the PEBs. Additionally, we find that the biases Δφ E and Δe/e for two parameters—that is, Earth-term phase φ E and orbital eccentricity e—monotonically decrease as e increases, which partly confirms a hypothesis in our previous work. Furthermore, we also calculate the PEBs caused by the recently observed common-spectrum process (CSP). We find that if the strain amplitude of the continuous GW is significantly stronger (three times larger, in our cases) than the stochastic GW background, then the PEBs from pulsar terms are larger than those from the CSP. Our formulae of the PEBs can be conveniently applied in the future PTA data analyses.

We present KETJU, a new extension of the widely used smoothed particle hydrodynamics simulation code GADGET-3. The key feature of the code is the inclusion of algorithmically regularized regions around every supermassive black hole (SMBH). This allows for simultaneously following global galactic-scale dynamical and astrophysical processes, while solving the dynamics of SMBHs, SMBH binaries, and surrounding stellar systems at subparsec scales. The KETJU code includes post-Newtonian terms in the equations of motions of the SMBHs, which enables a new SMBH merger criterion based on the gravitational wave coalescence timescale, pushing the merger separation of SMBHs down to ∼0.005 pc. We test the performance of our code by comparison to NBODY7 and rVINE. We set up dynamically stable multicomponent merger progenitor galaxies to study the SMBH binary evolution during galaxy mergers. In our simulation sample the SMBH binaries do not suffer from the final-parsec problem, which we attribute to the nonspherical shape of the merger remnants. For bulge-only models, the hardening rate decreases with increasing resolution, whereas for models that in addition include massive dark matter halos, the SMBH binary hardening rate becomes practically independent of the mass resolution of the stellar bulge. The SMBHs coalesce on average 200 Myr after the formation of the SMBH binary. However, small differences in the initial SMBH binary eccentricities can result in large differences in the SMBH coalescence times. Finally, we discuss the future prospects of KETJU, which allows for a straightforward inclusion of gas physics in the simulations.

In this study of the ‘Resolving supermAssive Black hole Binaries In galacTic hydrodynamical Simulations’ (RABBITS) series, we focus on the hardening and coalescing process of supermassive black hole (SMBH) binaries in galaxy mergers. For simulations including different galaxy formation processes (i.e. gas cooling, star formation, SMBH accretion, stellar, and AGN feedback), we systematically control the effect of stochastic eccentricity by fixing it to similar values during the SMBH hardening phase. We find a strong correlation between the SMBH merger time-scales and the presence of nuclear star formation. Throughout the galaxy merging process, gas condenses at the centre due to cooling and tidal torques, leading to nuclear star formation. These recently formed stars, which inherit low angular momenta from the gas, contribute to the loss cone and assist in the SMBH hardening via three-body interactions. Compared to non-radiative hydrodynamical runs, the SMBH merger time-scales measured from the runs including cooling, stellar, and SMBH physical processes tend to be shortened by a factor of ∼1.7. After fixing the eccentricity to the range of e ∼ 0.6–0.8 during the hardening phase, the simulations with AGN feedback reveal merger time-scales of ∼100–500 Myr for disc mergers and ∼1–2 Gyr for elliptical mergers. With a semi-analytical approach, we find that the torque interaction between the binary and its circumbinary disc has minimal impact on the shrinking of the binary orbit in our retrograde galaxy merger. Our results are useful in improving the modelling of SMBH merger time-scales and gravitational-wave event rates.

While supermassive black hole (SMBH) binaries are not the only viable source for the low-frequency gravitational wave background (GWB) signal evidenced by the most recent pulsar timing array (PTA) data sets, they are expected to be the most likely. Thus, connecting the measured PTA GWB spectrum and the underlying physics governing the demographics and dynamics of SMBH binaries is extremely important. Previously, Gaussian processes (GPs) and dense neural networks have been used to make such a connection by being built as conditional emulators; their input is some selected evolution or environmental SMBH binary parameters and their output is the emulated mean and standard deviation of the GWB strain ensemble distribution over many Universes. In this paper, we use a normalizing flow (NF) emulator that is trained on the entirety of the GWB strain ensemble distribution, rather than only mean and standard deviation. As a result, we can predict strain distributions that mirror underlying simulations very closely while also capturing frequency covariances in the strain distributions as well as statistical complexities such as tails, non-Gaussianities, and multimodalities that are otherwise not learnable by existing techniques. In particular, we feature various comparisons between the NF-based emulator and the GP approach used extensively in past efforts. Our analyses conclude that the NF-based emulator not only outperforms GPs in the ease and computational cost of training but also outperforms in the fidelity of the emulated GWB strain ensemble distributions.

Galaxy mergers at high redshifts trigger activity of their central supermassive black holes, eventually also leading to their coalescence as well as a potential source of low-frequency gravitational waves detectable by the Square Kilometre Array’s pulsar timing array (SKA PTA). Two key parameters related to the fueling of black holes are the Eddington ratio of quasar accretion,ηEdd, and the radiative efficiency of the accretion process,ϵ(which affects the so-called active lifetime of the quasar,tQSO). Here, we forecast the regime of detectability of gravitational wave events with SKA PTA. We find the associated binaries to have orbital periods of the order of weeks to years, observable via relativistic Doppler velocity boosting and/or optical variability of their light curves. Combining the SKA regime of detectability with the latest observational constraints on high-redshift black hole mass and luminosity functions, as well as theoretically motivated prescriptions for the merger rates of dark matter halos, we forecast the number of active counterparts of SKA PTA events expected as a function of primary black hole mass atz ≳ 6. We find that the quasar counterpart of the most massive black holes will be uniquely localizable within the SKA PTA error ellipse atz ≳ 6. We also forecast the number of expected counterparts as a function of the quasars’ Eddington ratios and active lifetimes. Our results show that SKA PTA detections can place robust constraints on the seeding and growth mechanisms of the first supermassive black holes.

With projects such as Laser Interferometer Space Antenna (LISA) and Pulsar Timing Arrays (PTAs) expected to detect gravitational waves from supermassive black hole mergers in the near future, it is key that we understand what we expect those detections to be, and maximize what we can learn from them. To address this, we study the mergers of supermassive black holes in the Illustris simulation, the overall rate of mergers, and the correlation between merging black holes and their host galaxies. We find these mergers occur in typical galaxies along the MBH−M* relation, and that between LISA and PTAs we expect to probe the full range of galaxy masses. As galaxy mergers can trigger star formation, we find that galaxies hosting low-mass black hole mergers tend to show a slight increase in star formation rates compared to a mass-matched sample. However, high-mass merger hosts have typical star formation rates, due to a combination of low gas fractions and powerful active galactic nucleus feedback. Although minor black hole mergers do not correlate with disturbed morphologies, major mergers (especially at high-masses) tend to show morphological evidence of recent galaxy mergers which survive for ∼500 Myr. This is on the same scale as the infall/hardening time of merging black holes, suggesting that electromagnetic follow-ups to gravitational wave signals may not be able to observe this correlation. We further find that incorporating a realistic time-scale delay for the black hole mergers could shift the merger distribution towards higher masses, decreasing the rate of LISA detections while increasing the rate of PTA detections.

The elusive supermassive black hole binaries (SMBHBs) are thought to be the penultimate stage of galaxy mergers, preceding a final coalescence phase. SMBHBs are sources of continuous gravitational waves, possibly detectable by pulsar timing arrays; the identification of candidates could help in performing targeted gravitational wave searches. Due to SMBHBs’ origin in the innermost parts of active galactic nuclei (AGN), X-rays are a promising tool for unveiling their presence, by means of either double Fe Kα emission lines or periodicity in their light curve. Here we report on a new method for selecting SMBHBs by means of the presence of a periodic signal in their Swift Burst Alert Telescope (BAT) 105 month light curves. Our technique is based on Fisher’s exact g-test and takes into account the possible presence of colored noise. Among the 553 AGN selected for our investigation, only the Seyfert 1.5 galaxy Mrk 915 emerges as a candidate SMBHB; from subsequent analysis of its light curve we find a period P 0 = 35 ± 2 months, and the null hypothesis is rejected at the 3.7σ confidence level. We also present a detailed analysis of the BAT light curve of the only previously X-ray-selected binary candidate source in the literature, the Seyfert 2 galaxy MCG+11-11-032. We find P 0 = 26.3 ± 0.6 months, consistent with the one inferred from previously reported double Fe Kα emission lines.

The observations from pulsar timing arrays (PTAs), led by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), have provided opportunities to constrain primordial gravitational waves at low frequencies. In this paper, we analyze the best-fit parameter values for different Gauss-Bonnet Inflationary Gravitational Wave (GB-IGW) models with the PTArcade program, and we compare the results with the observations of NANOGrav, European Pulsar Timing Array (EPTA), Parkes Pulsar Timing Array (PPTA), and International Pulsar Timing Array (IPTA). We find the potential parameter n derived from the GB-IGW model is not necessarily positive. Instead, PTA data suggest the possibility of new parameter ranges. Meanwhile, the other parameters' results, such as the spectral indices of the scalar and tensor perturbation also have differences with traditional Cosmic Microwave Background analyses from Planck 2018, showing the reason for the different phenomena of Gravitational Wave power spectra expected. Additionally, the GB-IGW models we calculated are closer to the central values of multiple PTA datasets compared to the standard inflation model, making the GB-IGW model more likely to be detected by future space-based gravitational wave observatories.