Search

We investigate the coalescence of massive black hole ($M_{\rm BH}\gtrsim 10^{6}~\rm {\rm M}_{\odot }$) binaries (MBHBs) at 6 < z < 10 by adopting a suite of cosmological hydrodynamical simulations of galaxy formation, zoomed-in on biased (>3σ) overdense regions (Mh ∼ 1012 M⊙ dark matter haloes at z = 6) of the Universe. We first analyse the impact of different resolutions and AGN feedback prescriptions on the merger rate, assuming instantaneous mergers. Then, we compute the halo bias correction factor due to the overdense simulated region. Our simulations predict merger rates that range between 3 and 15 $\rm yr^{-1}$ at z ∼6, depending on the run considered, and after correcting for a bias factor of ∼20−30. For our fiducial model, we further consider the effect of delay in the MBHB coalescence due to dynamical friction. We find that 83 per cent of MBHBs will merge within the Hubble time, and 21 per cent within 1 Gyr, namely the age of the Universe at z > 6. We finally compute the expected properties of the gravitational wave (GW) signals and find the fraction of LISA detectable events with high signal-to-noise ratio (SNR > 5) to range between 66 per cent and 69 per cent. However, identifying the electro-magnetic counterpart of these events remains challenging due to the poor LISA sky localization that, for the loudest signals ($\mathcal {M}_c\sim 10^6~{{\rm M}_{\odot }}$ at z = 6), is around 10 $\rm deg^2$.

The authors wish to thank J.M. Torrejón for the organization of the Athena-multi-messenger Workshops, held on November 27 - 29, 2018, in Alicante, Spain and on 5 May 2020 - 6 May 2020 in videoconference., In this paper we explore the scientific synergies between Athena and some of the key multi-messenger facilities that should be operative concurrently with Athena. These facilities include LIGO A+, Advanced Virgo+ and future detectors for ground-based observation of gravitational waves (GW), LISA for space-based observations of GW, IceCube and KM3NeT for neutrino observations, and CTA for very high energy observations. These science themes encompass pressing issues in astrophysics, cosmology and fundamental physics such as: the central engine and jet physics in compact binary mergers, accretion processes and jet physics in Super-Massive Binary Black Holes (SMBBHs) and in compact stellar binaries, the equation of state of neutron stars, cosmic accelerators and the origin of Cosmic Rays (CRs), the origin of intermediate and high-Z elements in the Universe, the Cosmic distance scale and tests of General Relativity and the Standard Model. Observational strategies for implementing the identified science topics are also discussed. A significant part of the sources targeted by multi-messenger facilities is of transient nature. We have thus also discussed the synergy of Athena with wide-field high-energy facilities, taking THESEUS as a case study for transient discovery. This discussion covers all the Athena science goals that rely on follow-up observations of high-energy transients identified by external observatories, and includes also topics that are not based on multi-messenger observations, such as the search for missing baryons or the observation of early star populations and metal enrichment at the cosmic dawn with Gamma-Ray Bursts (GRBs)., Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature., This research has been supported by the European Union’s Horizon 2020 programme under the AHEAD (grant agreement number 654215) and AHEAD2020 project (grant agreement n. 871158). FJC and SMN acknowledges funding under project RTI2018-096686-B-C21 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, and by the Unidad de Excelencia María de Maeztu, ref. MDM-2017-0765.

The shrinking of a binary orbit driven by the interaction with a gaseous circumbinary disc, initially advocated as a potential way to catalyze the binary merger, has been recently debated in the case of geometrically thick (i.e. with $H/R\gtrsim 0.1$) discs. However, a clear consensus is still missing mainly owing to numerical limitations, such as fixed orbit binaries or lack of resolution inside the cavity carved by the binary in its circumbinary disc. In this work, we asses the importance of evolving the binary orbit by means of hydrodynamic simulations performed with the code {\sc gizmo} in meshless-finite-mass mode. In order to model the interaction between equal mass circular binaries and their locally isothermal circumbinary discs, we enforce hyper-Lagrangian resolution inside the cavity. We find that fixing the binary orbit ultimately leads to an overestimate of the gravitational torque that the gas exerts on the binary, and in an underestimate of the torque due to the accretion of material onto the binary components. Furthermore, we find that the modulation of the accretion rate on the binary orbital period is strongly suppressed in the fixed orbit simulation, while it is clearly present in the live binary simulations. This has potential implications for the prediction of the observable periodicities in massive black hole binary candidates., Comment: 7 pages, 8 figures, accepted for publication in MNRAS

Parsec-scale massive black hole binaries (MBHBs) are expected to form in hierarchical models of structure formation. Even though different observational strategies have been designed to detect these systems, a theoretical study is a further guide for their search and identification. In this work, we investigate the hosts properties and the electromagnetic signatures of massive black holes gravitationally bound on parsec-scales with primary mass $\rm {>}\,10^7\,M_{\odot}$. For that, we construct a full-sky lightcone by the use of the semi-analytical model L-Galaxies in which physically motivated prescriptions for the formation and evolution of MBHBs have been included. Our predictions show that the large majority of the MBHBs are placed either in spiral galaxies with a classical bulge structure or in elliptical galaxies. Besides, the scaling relations followed by MBHBs are indistinguishable from the ones of single massive black holes. We find that the occupation fraction of parsec-scale MBHBs reaches up to ${\sim}\,50\%$ in galaxies with $\rm M_{stellar}\,{>}\,10^{11}\, M_{\odot}$ and drops below 10\% for $\rm M_{stellar}\,{}\,1$ but the number of binaries per $\rm deg^2$ is ${\lesssim}\,0.01$ at $\rm L_{\rm bol}\,{>}\,10^{45} \rm erg/s$., 19 pages, 16 Figures, Accepted by MNRAS

The Laser Interferometer Space Antenna (LISA) will open the mHz frequency window of the gravitational wave (GW) landscape. Among all the new GW sources expected to emit in this frequency band, extreme mass-ratio inspirals (EMRIs) constitute a unique laboratory for astrophysics and fundamental physics. Here we show that EMRIs can also be used to extract relevant cosmological information, complementary to both electromagnetic (EM) and other GW observations. By using the loudest EMRIs (SNR$>$100) detected by LISA as dark standard sirens, statistically matching their sky localisation region with mock galaxy catalogs, we find that constraints on $H_0$ can reach $\sim$1.1% ($\sim$3.6%) accuracy, at the 90% credible level, in our best (worst) case scenario. By considering a dynamical dark energy (DE) cosmological model, with $\Lambda$CDM parameters fixed by other observations, we further show that in our best (worst) case scenario $\sim$5.9% ($\sim$12.3%) relative uncertainties at the 90% credible level can be obtained on $w_0$, the DE equation of state parameter. Besides being relevant in their own right, EMRI measurements will be affected by different systematics compared to both EM and ground-based GW observations. Cross validation with complementary cosmological measurements will therefore be of paramount importance, especially if convincing evidence of physics beyond $\Lambda$CDM emerges from future observations., Comment: 22 pages, 9 figures. v2: new author in author list, new sub-Appendix with additional results, new Fig. A1; some explicative paragraphs added, Fig. 3 updated. Matches the journal version

The search for gravitational waves using Pulsar Timing Arrays (PTAs) is a computationally expensive complex analysis that involves source-specific noise studies. As more pulsars are added to the arrays, this stage of PTA analysis will become increasingly challenging. Therefore, optimizing the number of included pulsars is crucial to reduce the computational burden of data analysis. Here, we present a suite of methods to rank pulsars for use within the scope of PTA analysis. First, we use the maximization of the signal-to-noise ratio as a proxy to select pulsars. With this method, we target the detection of stochastic and continuous gravitational wave signals. Next, we present a ranking that minimizes the coupling between spatial correlation signatures, namely monopolar, dipolar, and Hellings & Downs correlations. Finally, we also explore how to combine these two methods. We test these approaches against mock data using frequentist and Bayesian hypothesis testing. For equal-noise pulsars, we find that an optimal selection leads to an increase in the log-Bayes factor two times steeper than a random selection for the hypothesis test of a gravitational wave background versus a common uncorrelated red noise process. For the same test but for a realistic European PTA (EPTA) data set, a subset of 25 pulsars selected out of 40 can provide a log-likelihood ratio that is 89 % of the total, implying that an optimally selected subset of pulsars can yield results comparable to those obtained from the whole array. We expect these selection methods to play a crucial role in future PTA data combinations.

LISA will extend the search for gravitational waves (GWs) at $0.1\,{-}\,100$ mHz where loud signals from coalescing binary black holes of $ 10^4 \,{-}\,10^7\,\rm M_{\odot}$ are expected. Depending on their mass and luminosity distance, the uncertainty in the LISA sky-localization decreases from hundreds of deg$^2$ during the inspiral phase to fractions of a deg$^2$ after the merger. By using the semi-analytical model L-Galaxies applied to the Millennium-I merger trees, we generate a simulated Universe to identify the hosts of $z\,{\leq}\,3$ coalescing binaries with total mass of $3\,{\times}\,10^{5}$, $3\,{\times}\,10^6$ and $3\,{\times}\,10^7\rm M_{\odot}$, and varying mass ratio. We find that, even at the time of merger, the number of galaxies around the LISA sources is too large (${\gtrsim}\,10^2$) to allow direct host identification. However, if an X-ray counterpart is associated to the GW sources at $z\,{, 25 pages, 14 Figures, To be submitted to MNRAS

In this paper we develop a computationally efficient, two-population, time-dependent Fokker-Plank approach in the two dimensions of energy and angular momentum to study the rates of tidal disruption events (TDEs), extreme mass ratio inspirals (EMRIs) and direct plunges occurring around massive black holes (MBHs) in galactic nuclei. We test our code by exploring a wide range of the astrophysically relevant parameter space, including MBH masses, galaxy central densities and inner density slopes. We find that mass segregation and, more in general, the time dependency of the distribution function regulate the event rate: TDEs always decline with time, whereas EMRIs and plunges reach a maximum and undergo a subsequent nearly exponential decay. Once suitably normalized, the rates associated to different choices of MBH mass and galaxy density overlap nearly perfectly. Based on this, we provide a simple scaling that allows to reproduce the time-dependent event rates for any MBH mass and underlying galactic nucleus. Although our peak rates are in general agreement with the literature relying on the steady-state (non-time dependent) assumption, those can be sustained on a timescale that strongly depends on the properties of the system. In particular this can be much shorter than a Gyr for relatively light MBHs residing in dense systems. This warns against using steady state models to compute global TDE, EMRI and plunge rates and calls for a more sophisticated, time dependent treatment of the problem., 14 pages, 10 figures, submitted to MNRAS

The observation of a population of massive black hole binaries (MBHBs) is key for our complete understanding of galaxy mergers and for the characterization of the expected gravitational waves (GWs) signal. However, MBHBs still remain elusive with only a few candidates proposed to date. Among these, SDSSJ143016.05+230344.4 ('tick-tock' hereafter) is the only candidate with a remarkably well sampled light curve showing a clear reduction of the modulation period and amplitude over three years of observations. This particular feature has been recently claimed to be the signature of a MBHB that is about to merge. In this paper, we provide an optical follow-up of the tick-tock source using the Rapid Eye Mount (REM) telescope. The decreasing luminosity observed in our follow up is hardly explained within the binary scenario. We speculate about an alternative scenario that might explain the observed light curve through relativistic Lense-Thirring precession of an accretion disc around a single massive black hole., 9 pages, 2 figure, accepted for publication in MNRAS

The study of the interaction of a massive black hole binary with its gaseous environment is crucial in order to be able to predict merger rates and possible electromagnetic counterparts of gravitational wave signals. The evolution of the binary semi-major axis resulting from this interaction has been recently debated, and a clear consensus is still missing, also because of several numerical limitations, i.e. fixed orbit binaries or lack of resolution inside the cavity carved by the binary in its circumbinary disc. Using on-the-fly particle-splitting in the 3D meshless code gizmo, we achieve hyper-Lagrangian resolution, which allows us to properly resolve the dynamics inside the cavity, and in particular for the first time the discs that form around the two components of a live binary surrounded by a locally isothermal gaseous circumbinary disc. We show that the binary orbit decays with time for very cold and very warm discs and that the result of the interaction in the intermediate regime is strongly in uenced by the disc viscosity as this essentially regulates the fraction of mass contained in the discs around the binary components as well as the fraction that is accreted by the binary. We find the balance between these two quantities to determine whether the binary semi-major axis decreases with time., 8 pages, published in ApJL

Coalescing supermassive black hole binaries (BHBs) are expected to be the loudest sources of gravitational waves (GWs) in the Universe. Detection rates for ground or space-based detectors based on cosmological simulations and semi-analytic models are highly uncertain. A major difficulty stems from the necessity to model the BHB from the scale of the merger to that of inspiral. Of particular relevance to the GW merger timescale is the binary eccentricity. Here we present a self-consistent numerical study of the eccentricity of BHBs formed in massive gas-free mergers from the early stages of the merger to the hardening phase, followed by a semi-analytical model down to coalescence. We find that the early eccentricity of the unbound black hole pair is largely determined by the initial orbit. It systematically decreases during the dynamical friction phase. The eccentricity at binary formation is affected by stochasticity and noise owing to encounters with stars, but preserves a strong correlation with the initial orbital eccentricity. Binding of the black holes is a phase characterised by strong perturbations, and we present a quantitative definition of the time of binary formation. During hardening the eccentricity increases in minor mergers, unless the binary is approximately circular, but remains largely unchanged in major mergers, in agreement with predictions from semi-analytical models based on isotropic scattering experiments. Coalescence times due to hardening and GW emission in gas-poor non-rotating ellipticals are, Comment: 15 pages, 13 figures, accepted for publication in MNRAS

Extreme mass ratio inspirals (EMRIs) are compact binary systems characterized by a mass-ratio $q=m/M$ in the range $~10^{-9}-10^{-4}$ and represent primary gravitational wave (GW) sources for the forthcoming Laser Interferometer Space Antenna (LISA). While their standard formation channel involves relaxation processes deflecting compact objects on very low angular momentum orbits around the central massive black hole, a number of alternative formation channels has been proposed, including binary tidal break-up, migration in accretion disks and secular and chaotic dynamics around a massive black hole binary (MBHB). In this work, we take an extensive closer look at this latter scenario, investigating how EMRIs can be triggered by a MBHBs, formed in the aftermath of galaxy mergers. By employing a suite of relativistic three-body simulations, we evaluate the efficiency of EMRI formation for different parameters of the MBHB, assessing the importance of both secular and chaotic dynamics. By modelling the distribution of compact objects in galaxy nuclei, we estimate the resulting EMRI formation rate, finding that EMRI are produced in a sharp burst, with peak rates that are 10-100 times higher than the standard two-body relaxation channel, lasting for 10$^6$--10$^8$ years. By coupling our results with an estimate of the cosmic MBHB merger rate, we finally forecast that LISA could observe ${\cal O}(10)$ EMRIs per year formed by this channel., 18 pages, 15 figures, accepted for publication in MNRAS

Binaries of relatively massive black holes like GW190521 have been proposed to form in dense gas environments, such as the disks of Active Galactic Nuclei (AGNs), and they might be associated with transient electromagnetic counterparts. The interactions of this putative environment with the binary could leave a significant imprint at the low gravitational wave frequencies observable with the Laser Interferometer Space Antenna (LISA). We show that LISA will be able to detect up to ten GW190521-like black hole binaries, with sky position errors $\lesssim1$ deg$^2$. Moreover, it will measure directly various effects due to the orbital motion around the supermassive black hole at the center of the AGN, especially the Doppler modulation and the Shapiro time delay. Thanks to a careful treatment of their frequency domain signal, we were able to perform the full parameter estimation of Doppler and Shapiro-modulated binaries as seen by LISA. We find that the Doppler and Shapiro effects will allow for measuring the AGN parameters (radius and inclination of the orbit around the AGN, central black hole mass) with up to percent-level precision. Properly modeling these low-frequency environmental effects is crucial to determine the binary formation history, as well as to avoid biases in the reconstruction of the source parameters and in tests of general relativity with gravitational waves., 13+4 pages, 7+1 figures v3: corrected typo in Fig 5

To report complications and long-term outcomes after submucosal resections of benign and malignant epithelial rectal masses.Retrospective multicentric study.Medical records of 93 dogs at 7 referral hospitals.Records were reviewed for surgical time, diagnosis, margins, complications, and recurrences. Survival of dogs was evaluated based on tumor types, categorized as benign, carcinoma in situ, and carcinoma. The Kaplan-Meier survival curve and Cox proportional hazards analysis were used to determine the association of a range of variables with recurrence and survival time.Duration of follow up was 708 days (range, 25-4383). Twenty-seven dogs (29%) developed complications. Recurrence was identified in 20/93 (21%), with 12/20 recurrent masses treated with repeat submucosal resection. Median survival was not reached in any group. The 1-,2-, 5-year survival rates for carcinomas were 95%, 89%, and 73% respectively. However, overall survival was longer for benign tumors than carcinomas (P = .001). Recurrence was more likely when complications (P = .032) or incomplete margins (P = .023) were present. Recurrence was associated with an increased risk of death (P = .046).Submucosal resection of both benign and malignant rectal masses was associated with a low rate of severe complications and prolonged survival in the 93 dogs described here.Submucosal resection is a suitable technique for resection of selected rectal masses.

In this work we characterize the expected gravitational wave signal detectable by the planned space-borne interferometer LISA and the proposed next generation space-borne interferometer $\mu$Ares arising from a population of primordial black holes orbiting Sgr A*, the super-massive black hole at the Galactic center. Assuming that such objects indeed form the entire diffuse mass allowed by the observed orbit of S2 in the Galactic center, under the simplified assumption of circular orbits and monochromatic mass function, we assess the expected signal in gravitational waves, either from resolved and non-resolved sources. We estimate a small but non negligible chance of $\simeq$ 10% of detecting one single 1 M$_{\odot}$ primordial black hole with LISA in a 10-year-long data stream, while the background signal due to unresolved sources would essentially elude any reasonable chance of detection. On the contrary, $\mu$Ares, with a $\simeq$ 3 orders-of-magnitude better sensitivity at $\simeq$ 10$^{-5}$ Hz, would be able to resolve $\simeq$ 140 solar mass primordial black holes in the same amount of time, while the unresolved background should be observable with an integrated signal-to-noise ratio $\gtrsim$ 100. Allowing the typical PBH mass to be in the range 0.01-10 M$_{\odot}$ would increase LISA chance of detection to $\simeq$ 40% towards the lower limit of the mass spectrum. In the case of $\mu$Ares, instead, we find a "sweet spot" just about 1 M$_{\odot}$, a mass for which the number of resolvable events is indeed maximized., Comment: 10 pages, 11 figures; Referee reviewed

We estimate the properties of the double neutron star (DNS) population that will be observable by the planned space-based interferometer LISA. By following the gravitational radiation driven evolution of DNSs generated from rapid population synthesis of massive binary stars, we estimate that around 35 DNSs will accumulate a signal-to-noise ratio above 8 over a four-year LISA mission. The observed population mainly comprises Galactic DNSs (94 per cent), but detections in the LMC (5 per cent) and SMC (1 per cent) may also be expected. The median orbital frequency of detected DNSs is expected to be 0.8 mHz, and many of them will be eccentric (median eccentricity of $0.11$). The orbital properties will provide insights into DNS progenitors and formation channels. LISA is expected to localise these DNSs to a typical angular resolution of $2^\circ$, with best-constrained sources localised to a few arcminutes. These localisations may allow neutron star natal kick magnitudes to be constrained through the Galactic distribution of DNSs, and make it possible to follow up the sources with radio pulsar searches. However, LISA is also expected to resolve $\sim 10^4$ Galactic double white dwarfs, many of which may have binary parameters that resemble DNSs; we discuss how the combined measurement of binary eccentricity, chirp mass, and sky location may aid the identification of a DNS. We expect the best-constrained DNSs to have eccentricities known to a few parts in a thousand, chirp masses measured to better than 1 per cent fractional uncertainty, and sky localisation at the level of a few arcminutes., Accepted by the Monthly Notices of the Royal Astronomical Society, added comparison with two more binary evolution prescriptions

We propose a space-based interferometer surveying the gravitational wave (GW) sky in the milli-Hz to $\mu$-Hz frequency range. By the 2040s', the $\mu$-Hz frequency band, bracketed in between the Laser Interferometer Space Antenna (LISA) and pulsar timing arrays, will constitute the largest gap in the coverage of the astrophysically relevant GW spectrum. Yet many outstanding questions related to astrophysics and cosmology are best answered by GW observations in this band. We show that a $\mu$-Hz GW detector will be a truly overarching observatory for the scientific community at large, greatly extending the potential of LISA. Conceived to detect massive black hole binaries from their early inspiral with high signal-to-noise ratio, and low-frequency stellar binaries in the Galaxy, this instrument will be a cornerstone for multimessenger astronomy from the solar neighbourhood to the high-redshift Universe., Comment: 28 pages, 8 figures; White Paper submitted to ESA's Voyage 2050 call for papers on behalf of the LISA Consortium 2050 Task Force

The 100 years since the publication of Albert Einstein’s theory of general relativity saw significant development of the understanding of the theory, the identification of potential astrophysical sources of sufficiently strong gravitational waves and development of key technologies for gravitational-wave detectors. In 2015, the first gravitational-wave signals were detected by the two US Advanced LIGO instruments. In 2017, Advanced LIGO and the European Advanced Virgo detectors pinpointed a binary neutron star coalescence that was also seen across the electromagnetic spectrum. The field of gravitational-wave astronomy is just starting, and this Roadmap of future developments surveys the potential for growth in bandwidth and sensitivity of future gravitational-wave detectors, and discusses the science results anticipated to come from upcoming instruments.

Massive black hole binaries (MBHBs) with masses of ~ 10^4 to ~ 10^10 of solar masses are one of the main targets for currently operating and forthcoming space-borne gravitational wave observatories. In this paper, we explore the effect of the stellar host rotation on the bound binary hardening efficiency, driven by three-body stellar interactions. As seen in previous studies, we find that the centre of mass (CoM) of a prograde MBHB embedded in a rotating environment starts moving on a nearly circular orbit about the centre of the system shortly after the MBHB binding. In our runs, the oscillation radius is approximately 0.25 ( approximately 0.1) times the binary influence radius for equal mass MBHBs (MBHBs with mass ratio 1:4). Conversely, retrograde binaries remain anchored about the centre of the host. The binary shrinking rate is twice as fast when the binary CoM exhibits a net orbital motion, owing to a more efficient loss cone repopulation even in our spherical stellar systems. We develop a model that captures the CoM oscillations of prograde binaries; we argue that the CoM angular momentum gain per time unit scales with the internal binary angular momentum, so that most of the displacement is induced by stellar interactions occurring around the time of MBHB binding, while the subsequent angular momentum enhancement gets eventually quashed by the effect of dynamical friction. The effect of the background rotation on the MBHB evolution may be relevant for LISA sources, that are expected to form in significantly rotating stellar systems., 10 pages, 9 figures, 2 tables. Accepted for publication on MNRAS

We compute the expected cosmic rates of tidal disruption events induced by individual massive black holes (MBHs) and by MBH binaries (MBHBs) - with a specific focus on the latter class - to explore the potential of TDEs to probe the cosmic population of sub-pc MBHBs. Rates are computed by combining MBH and MBHB population models derived from large cosmological simulations with estimates of the induced TDE rates for each class of objects. We construct empirical TDE spectra that fit a large number of observations in the optical, UV and X-ray and consider their observability by current and future survey instruments. Consistent with results in the literature, and depending on the detailed assumption of the model, we find that LSST and Gaia in optical and eROSITA in X-ray will observe a total of 3000-6000, 80-180 and 600-900 TDEs per year, respectively. Depending on the survey, one to several percent of these are prompted by MBHBs. In particular both LSST and eROSITA are expected to see 150-450 MBHB induced TDEs in their respective mission lifetimes, including 5-100 repeated flares. The latter provide an observational sample of binary candidates with relatively low contamination and have the potential of unveiling the sub-pc population of MBHBs in the mass range $10^5M_\odot, Comment: 19 pages, 15 figures, 4 tables. Accepted for publication in MNRAS

GW190521 is the compact binary with the largest masses observed to date, with at least one in the pair-instability gap. This event has also been claimed to be associated with an optical flare observed by the Zwicky Transient Facility in an Active Galactic Nucleus (AGN), possibly due to the post-merger motion of the merger remnant in the AGN gaseous disk. We show that the Laser Interferometer Space Antenna (LISA) will detect up to ten of such gas-rich black hole binaries months to years before their detection by LIGO/Virgo-like interferometers, localizing them in the sky within $\approx1$ deg$^2$. LISA will also measure directly deviations from purely vacuum and stationary waveforms, arising from gas accretion, dynamical friction, and orbital motion around the AGN's massive black hole (acceleration, strong lensing, and Doppler modulation). LISA will therefore be crucial to alert and point electromagnetic telescopes ahead of time on this novel class of gas-rich sources, to gain direct insight on their physics, and to disentangle environmental effects from corrections to General Relativity that may also appear in the waveforms at low frequencies., 6 pages, 4 figures. Matches published version

Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the $\sim 10$-$10^3~\mathrm{Hz}$ band of ground-based observatories and the $\sim10^{-4}$-$10^{-1}~\mathrm{Hz}$ band of LISA lies the uncharted decihertz gravitational-wave band. We propose a Decihertz Observatory to study this frequency range, and to complement observations made by other detectors. Decihertz observatories are well suited to observation of intermediate-mass ($\sim10^2$-$10^4 M_\odot$) black holes; they will be able to detect stellar-mass binaries days to years before they merge, providing early warning of nearby binary neutron star mergers and measurements of the eccentricity of binary black holes, and they will enable new tests of general relativity and the Standard Model of particle physics. Here we summarise how a Decihertz Observatory could provide unique insights into how black holes form and evolve across cosmic time, improve prospects for both multimessenger astronomy and multiband gravitational-wave astronomy, and enable new probes of gravity, particle physics and cosmology., Comment: 13 pages, 1 figure. Published in Experimental Astronomy. Summarising white paper arXiv:1908.11375

Massive stellar origin black hole binaries (SBHBs), originating from stars above the pair-instability mass gap, are primary candidates for multiband gravitational wave (GW) observations. Here we study the possibility to use them as effective dark standard sirens to constrain cosmological parameters. The long lasting inspiral signal emitted by these systems is accessible by the future $Laser \; Interferometer \; Space \; Antenna$ (LISA), while the late inspiral and merger are eventually detected by third generation ground-based telescopes such as the $Einstein \; Telescope$ (ET). The direct measurement of the luminosity distance and the sky position to the source, together with the inhomogeneous redshift distribution of possible host galaxies, allow us to infer cosmological parameters by probabilistic means. The efficiency of this statistical method relies in high parameter estimation performances. We show that this multiband approach allows a precise determination of the Hubble constant H$_0$ with just ${\cal O}(10)$ detected sources. For selected SBHB population models, assuming $4$ ($10$) years of LISA observations, we find that H$_0$ is typically determined at $\sim 2\%$ ($\sim 1.5\%$), whereas $\Omega_m$ is only mildly constrained with a typical precision of $30\%$ ($20\%$). We discuss the origin of some outliers in our final estimates and we comment on ways to reduce their presence., Comment: Updated results. 18 pages, 9 figures. Accepted for publication in PRD

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported evidence for the presence of a common stochastic signal across their array of pulsars. The origin of this signal is still unclear. One of the possibilities is that it is due to a stochastic gravitational wave background (SGWB) in the $\sim 1-10\,{\rm nHz}$ frequency region. Taking the NANOGrav observational result at face value, we show that this signal would be fully consistent with a SGWB produced by an unresolved population of in-spiralling massive black hole binaries (MBHBs) predicted by current theoretical models. Considering an astrophysically agnostic model we find that the MBHB merger rate is loosely constrained to the range $10^{-11} - 2$ $\mathrm{Mpc}^{-3}\,\mathrm{Gyr}^{-1}$. Including additional constraints from galaxy pairing fractions and MBH-bulge scaling relations, we find that the MBHB merger rate is $10^{-5} - 5\times10^{-4}$ $\mathrm{Mpc}^{-3}\,\mathrm{Gyr}^{-1}$, the MBHB merger time-scale is $\le 3\,\mathrm{Gyr}$ and the norm of the $M_\mathrm{BH}-M_\mathrm{bulge}$ relation $\ge 1.2\times 10^{8}\,M_\odot$ (all intervals quoted at 90\% confidence). Regardless of the astrophysical details of MBHB assembly, this result would imply that a sufficiently large population of massive black holes pair up, form binaries and merge within a Hubble time., Comment: 6 pages, 4 figures, to be submitted

Third Generation ground based Gravitational Wave Interferometers, like the Einstein Telescope (ET), Cosmic Explorer (CE), and the Laser Interferometer Space Antenna (LISA) will detectcoalescing binary black holes over a wide mass spectrum and across all cosmic epochs. We track the cosmological growth of the earliest light and heavy seeds that swiftly transit into the supermassive domain using a semi analytical model for the formation of quasars at $z=6.4$, 2 and $0.2$, in which we follow black hole coalescences driven by triple interactions. We find that light seed binaries of several $10^2$ M$_\odot$ are accessible to ET with a signal-to-noise ratio ($S/N$) of $10-20$ at $620$). Mergers involving heavy seeds ($\sim 10^5 M_\odot - 10^6 M_\odot$) would be within reach up to $z=20$ in the LISA frequency domain. The lower-z model predicts $11.25(18.7)$ ET(LISA) events per year, overall., Comment: 16 pages, 8 figures accepted for publication in MNRAS

Understanding the interaction of massive black hole binaries with their gaseous environment is crucial since at sub-parsec scales the binary is too wide for gravitational wave emission to take over and to drive the two black holes to merge. We here investigate the interaction between a massive black hole binary and a self-gravitating circumbinary disc using 3D smoothed particle hydrodynamics simulations. We find that, when the disc self-gravity regulates the angular momentum transport, the binary semi-major axis decreases regardless the choice of disc masses and temperatures, within the range we explored. In particular, we find that the disc initial temperature (hence the disc aspect ratio) has little effect on the evolution of the binary since discs with the same mass self-regulate towards the same temperature. Initially warmer discs cause the binary to shrink on a slightly shorter timescale until the disc has reached the self-regulated equilibrium temperature. More massive discs drive the binary semi-major axis to decrease at a faster pace compared to less massive discs and result in faster binary eccentricity growth even after the initial-condition-dependent transient evolution. Finally we investigate the effect that the initial cavity size has on the binary-disc interaction and we find that, in the self-gravitating regime, an initially smaller cavity leads to a much faster binary shrinking, as expected. Our results are especially important for very massive black hole binaries such as those in the PTA band, for which gas self gravity cannot be neglected., Comment: 9 pages, submitted to MNRAS on June 1st 2021

We present results from the search for a stochastic gravitational-wave background (GWB) as predicted by the theory of General Relativity using six radio millisecond pulsars from the Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA) covering a timespan up to 24 years. A GWB manifests itself as a long-term low-frequency stochastic signal common to all pulsars, a common red signal (CRS), with the characteristic Hellings-Downs (HD) spatial correlation. Our analysis is performed with two independent pipelines, \eprise{} and \tn{}+\ftwo{}, which produce consistent results. A search for a CRS with simultaneous estimation of its spatial correlations yields spectral properties compatible with theoretical GWB predictions, but does not result in the required measurement of the HD correlation, as required for GWB detection. Further Bayesian model comparison between different types of CRSs, including a GWB, finds the most favoured model to be the common uncorrelated red noise described by a power-law with $A = 5.13_{-2.73}^{+4.20} \times 10^{-15}$ and $\gamma = 3.78_{-0.59}^{+0.69}$ (95\% credible regions). Fixing the spectral index to $\gamma=13/3$ as expected from the GWB by circular, inspiralling supermassive black-hole binaries results in an amplitude of $A =2.95_{-0.72}^{+0.89} \times 10^{-15}$. We implement three different models, BAYESEPHEM, LINIMOSS and EPHEMGP, to address possible Solar-system ephemeris (SSE) systematics and conclude that our results may only marginally depend on these effects. This work builds on the methods and models from the studies on the EPTA DR1. We show that under the same analysis framework the results remain consistent after the data set extension., Comment: 25 pages, 10 figures, 7 tables, 2 appendix tables and 1 appendix figure

Within the next several years, pulsar-timing array programs will likely usher in the next era of gravitational-wave astronomy through the detection of a stochastic background of nanohertz-frequency gravitational waves, originating from a cosmological population of inspiraling supermassive binary black holes. While the source positions will likely be isotropic to a good approximation, the gravitational-wave angular power distribution will be anisotropic, with the most massive and/or nearby binaries producing signals that may resound above the background. We study such a realistic angular power distribution, developing fast and accurate sky-mapping strategies to localize pixels and extended regions of excess power while simultaneously modeling the background signal from the less massive and more distant ensemble. We find that power anisotropy will be challenging to discriminate from isotropy for realistic gravitational-wave skies, requiring SNR $>10$ in order to favor anisotropy with $10:1$ posterior odds in our case study. Amongst our techniques, modeling the population signal with multiple point sources in addition to an isotropic background provides the most physically-motivated and easily interpreted maps, while spherical-harmonic modeling of the square-root power distribution, $P(\hat\Omega)^{1/2}$, performs best in discriminating from overall isotropy. Our techniques are modular and easily incorporated into existing pulsar-timing array analysis pipelines., Comment: 19 pages, 7 figures. Code available at https://github.com/stevertaylor/gworf. Matches version accepted by PRD

TianQin is a planned space-based gravitational wave (GW) observatory consisting of three earth orbiting satellites with an orbital radius of about $10^5~{\rm km}$. The satellites will form a equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4}~{\rm Hz}$ and $1~{\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe or exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new generation $17~{\rm cm}$ single-body hollow corner-cube retro-reflector which has been launched with the QueQiao satellite on 21 May 2018; a new laser ranging station equipped with a $1.2~{\rm m}$ telescope has been constructed and the station has successfully ranged to all the five retro-reflectors on the Moon; and the TianQin-1 experimental satellite has been launched on 20 December 2019 and the first round result shows that the satellite has exceeded all of its mission requirements., 16 pages, 1 figure, invited article to a special section in PTEP

We study the dynamical evolution of eccentric massive black hole binaries (MBHBs) interacting with unbound stars by means of an extensive set of three body scattering experiments. Compared to previous studies, we extend the investigation down to a MBHB mass ratio of $q=m_2/m_1=10^{-4}$, where $m_1$ and $m_2$ are the masses of the primary and secondary hole respectively. Contrary to a simple extrapolation from higher mass ratios, we find that for $q\lesssim 10^{-3}$ the eccentricity growth rate becomes negative, i.e., the binary {\it circularises} as it shrinks. This behaviour is due to the subset of interacting stars captured in metastable counter-rotating orbits; those stars tend to extract angular momentum from the binary, promoting eccentricity growth for $q>10^{-3}$, but tend to inject angular momentum into the binary driving it towards circularisation for $q, 6 pages, 5 figures; accepted for publication in MNRAS

The evolution of cosmic structures, the formation and growth of the first black holes and the connection to their baryonic environment are key unsolved problems in astrophysics. The X-ray Athena mission and the gravitational-wave Laser Interferometer Space Antenna (LISA) offer independent and complementary angles on these problems. We show that up to 10 black hole binaries in the mass range 10^5 - 10^8 Msun discovered by LISA at redshift, Comment: Published in Nature Astronomy

Extreme mass ratio inspirals (EMRIs), i.e. binary systems comprised by a compact stellar-mass object orbiting a massive black hole, are expected to be among the primary gravitational wave (GW) sources for the forthcoming LISA mission. The astrophysical processes leading to the formation of such systems still remain poorly understood, resulting into large uncertainties in the predicted cosmic rate of these sources, spanning at least three orders of magnitude. As LISA can individually resolve mostly EMRIs up to $z\gtrsim1$, the ensemble of signals below its detection threshold will add up incoherently forming an unresolved confusion noise, which can be formally described as a stochastic background. We perform an extensive study of this background by considering a collection of astrophysically motivated EMRI formation scenarios, spanning current uncertainties. We find that, for most astrophysical models, this signal is easily detectable by LISA, with signal to noise ratios of several hundreds. In fiducial EMRI models -- predicting hundreds of EMRI detections during mission operations -- the background level is comparable to the LISA noise, affecting the performance of the instrument around 3 mHz. In extreme cases, this background can even "erase" the whole LISA sensitivity bucket in the 2-10 mHz frequency range. This points to the need of a better understanding of EMRIs' astrophysics for a full assessment of the LISA mission potential., Comment: 19 pages, 12 figures, accepted for publication in PRD

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 their origin in the innermost parts of active galactic nuclei (AGN), X-rays are a promising tool to unveil the presence of SMBHBs, by means of either double Fe K$\alpha$ emission lines or periodicity in their light curve. Here we report on a new method to select SMBHBs by means of the presence of a periodic signal in their Swift-BAT 105-months light curves. Our technique is based on the 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 Mrk 915 emerged as possible candidate for a SMBHB; from the subsequent analysis of its light curve we find a period $P_0=35\pm2$ months, and the null hypothesis is rejected at the $3.7\sigma$ 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 $P_0=26.3\pm0.6$ months, consistent with the one inferred from previously reported double Fe K$\alpha$ emission lines., Comment: 11 pages, 10 figures; accepted for publication in The Astrophysical Journal

We have constructed a new timescale, TT(IPTA16), based on observations of radio pulsars presented in the first data release from the International Pulsar Timing Array (IPTA). We used two analysis techniques with independent estimates of the noise models for the pulsar observations and different algorithms for obtaining the pulsar timescale. The two analyses agree within the estimated uncertainties and both agree with TT(BIPM17), a post-corrected timescale produced by the Bureau International des Poids et Mesures (BIPM). We show that both methods could detect significant errors in TT(BIPM17) if they were present. We estimate the stability of the atomic clocks from which TT(BIPM17) is derived using observations of four rubidium fountain clocks at the US Naval Observatory. Comparing the power spectrum of TT(IPTA16) with that of these fountain clocks suggests that pulsar-based timescales are unlikely to contribute to the stability of the best timescales over the next decade, but they will remain a valuable independent check on atomic timescales. We also find that the stability of the pulsar-based timescale is likely to be limited by our knowledge of solar-system dynamics, and that errors in TT(BIPM17) will not be a limiting factor for the primary goal of the IPTA, which is to search for the signatures of nano-Hertz gravitational waves., Comment: accepted by MNRAS

We estimate the merger timescale of spectroscopically-selected, subparsec supermassive black hole binary (SMBHB) candidates by comparing their expected contribution to the gravitational wave background (GWB) with the sensitivity of current pulsar timing array (PTA) experiments and in particular, with the latest upper limit placed by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). We find that the average timescale to coalescence of such SMBHBs is $\langle t_{\rm evol} \rangle > 6\times 10^4\,$yr, assuming that their orbital evolution in the PTA frequency band is driven by emission of gravitational waves. If some fraction of SMBHBs do not reside in spectroscopically detected active galaxies, and their incidence in active and inactive galaxies is similar, then the merger timescale could be $\sim 10$ times longer, $\langle t_{\rm evol} \rangle > 6\times 10^5\,$yr. These limits are consistent with the range of timescales predicted by theoretical models and imply that all the SMBHB candidates in our spectroscopic sample could be binaries without violating the observational constraints on the GWB. This result illustrates the power of the multi-messenger approach, facilitated by the PTAs, in providing an independent statistical test of the nature of SMBHB candidates discovered in electromagnetic searches., Published in ApJL (9 pages, 3 figures)

Pulsar timing arrays provide a means to observe the nano-Hertz gravitational wave background from the population of merging massive black hole binaries. Observations are placing increasingly stringent upper limits on the gravitational wave background. Upper limits and future detections will enable the study of the properties of the merging population. Recent upper limits have cast doubt on current predictions of the gravitational wave background. Here we perform a Bayesian analysis comparing upper limits to astrophysical prediction. So far models are consistent with observation. These proceedings summarise previous work in Ref. [1].

The gravitational-wave astronomical revolution began in 2015 with LIGO's observation of the coalescence of two stellar-mass black holes. Over the coming decades, ground-based detectors like LIGO will extend their reach, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will enable gravitational-wave observations of the massive black holes in galactic centres. Between LISA and ground-based observatories lies the unexplored decihertz gravitational-wave frequency band. Here, we propose a Decihertz Observatory to cover this band, and complement observations made by other gravitational-wave observatories. The decihertz band is uniquely suited to observation of intermediate-mass ($\sim 10^2$-$10^4 M_\odot$) black holes, which may form the missing link between stellar-mass and massive black holes, offering a unique opportunity to measure their properties. Decihertz observations will be able to detect stellar-mass binaries days to years before they merge and are observed by ground-based detectors, providing early warning of nearby binary neutron star mergers, and enabling measurements of the eccentricity of binary black holes, providing revealing insights into their formation. Observing decihertz gravitational-waves also opens the possibility of testing fundamental physics in a new laboratory, permitting unique tests of general relativity and the Standard Model of particle physics. Overall, a Decihertz Observatory will answer key questions about how black holes form and evolve across cosmic time, open new avenues for multimessenger astronomy, and advance our understanding of gravitation, particle physics and cosmology., 52 pages, 5 figures, 4 tables. Submitted to Classical & Quantum Gravity. Based upon a white paper for ESA's Voyage 2050 on behalf of the LISA Consortium 2050 Task Force

Systems consisting of a massive black hole and a stellar-origin compact object (CO), known as extreme-mass-ratio inspirals (EMRIs), are of great significance for space-based gravitational-wave detectors, as they will allow for testing gravitational theories in the strong field regime, and for checking the validity of the black hole no-hair theorem. In this work, we present a calculation of the EMRI rate and parameter estimation capabilities of the TianQin observatory, for various astrophysical models for these sources. We find that TianQin can observe EMRIs involving COs with mass of 10$M_\odot$ up to redshift $\sim2$. We also find that detections could reach tens or hundreds per year in the most optimistic astrophysical scenarios. Intrinsic parameters are expected to be recovered to within fractional errors of $\sim 10^{-6}$, while typical errors on the luminosity distance and sky localization are 10% and 10 deg$^2$, respectively. TianQin observation of EMRIs can also constrain possible deviations from the Kerr quadrupole moment to within fractional errors $\lesssim10^{-4}$. We also find that a network of multiple detectors would allow for improvements in both detection rates (by a factor $\sim 1.5$ -$3$) and in parameter estimation precision (20-fold improvement for the sky localization and fivefold improvement for the other parameters)., Comment: 13 pages, 5 figures

Massive black hole binaries (MBHBs) of $10^5 \, \rm M_\odot - 3 \times 10^7 \, \rm M_\odot $ merging in low redshift galaxies ($z\le4$) are sufficiently loud to be detected weeks before coalescence with the Laser Interferometer Space Antenna (LISA). This allows us to perform the parameter estimation $on$ $the$ $fly$, i.e. as a function of the time to coalescence during the inspiral phase, relevant for early warning of the planned LISA protected periods and for searches of electromagnetic signals. In this work, we study the evolution of the sky position, luminosity distance, chirp mass and mass ratio uncertainties as function of time left before merger. Overall, light systems with total intrinsic mass $\rm M_{\rm tot} = 3 \times 10^5 \, \rm M_\odot$ are characterized by smaller uncertainties than heavy ones ($\rm M_{\rm tot} = 10^7 \, \rm M_\odot$) during the inspiral. Luminosity distance, chirp mass and mass ratio are well constrained at the end of the inspiral. Concerning sky position, at $z=1$, MBHBs with $\rm M_{\rm tot} = 3 \times 10^5 \, \rm M_\odot$ can be localized with a median precision of $\simeq 10^2 \, \rm deg^2 (\simeq 1 \, \rm deg^2)$ at 1 month (1 hour) from merger, while the sky position of heavy MBHBs can be determined to $10 \, \rm deg^2$ only 1 hour before merger. However the uncertainty around the median values broadens with time, ranging in between 0.04 -- 20 $\rm deg^2$ (0.3 -- 3 $\times 10^3 \, \rm deg^2$) for light (heavy) systems at 1 hour before merger. At merger the sky localization improves down to $\simeq 10^{-1} \, \rm deg^2$ for all masses. For the benefit of the observer community, we provide the full set of data from our simulations and simple and ready-to-use analytical fits to describe the time evolution of uncertainties in the aforementioned parameters, valid for systems with total mass between $10^5$--$10^7 \, \rm M_\odot$ and redshift $0.3$--$3$., Comment: 31 pages, 24 figures and 6 tables. Accepted for publication in Physical Review D

We determine the main properties of the Galactic binary black hole (BBH) population detectable by LISA and strategies to distinguish them from the much more numerous white dwarf binaries. We simulate BBH populations based on cosmological simulations of Milky Way-like galaxies and binary evolution models. We then determine their gravitational wave emission as observed by LISA and build mock catalogs. According to our model LISA will detect $\approx4(6)$ binary black holes assuming 4(10) years of operations. Those figures grow to $\approx6(9)$ when models are re-normalized to the inferred LIGO/Virgo merger rates. About 40\%(70\%) of the sources will have a good enough chirp mass measurement to separate them from the much lighter white dwarf and neutron star binaries. Most of the remaining sources should be identifiable by their lack of electromagnetic counterpart within $\approx100$ pc. These results are robust with respect to the current uncertainties of the BBH merger rate as measured by LIGO/Virgo as well as the global mass spectrum of the binaries. We determine there is a 94 per cent chance that LISA finds at least one of these systems, which will allow us to pinpoint the conditions where they were formed and possibly find unique electromagnetic signatures., 6 pages, 5 figures, submitted to MNRAS Letters

69 pages, 21 figures. Accepted for publication in New Astronomy Reviews © 2020 Elsevier B.V., The quest for binary and dual supermassive black holes (SMBHs) at the dawn of the multi-messenger era is compelling. Detecting dual active galactic nuclei (AGN) -- active SMBHs at projected separations larger than several parsecs -- and binary AGN -- probing the scale where SMBHs are bound in a Keplerian binary -- is an observational challenge. The study of AGN pairs (either dual or binary) also represents an overarching theoretical problem in cosmology and astrophysics. The AGN triggering calls for detailed knowledge of the hydrodynamical conditions of gas in the imminent surroundings of the SMBHs and, at the same time, their duality calls for detailed knowledge on how galaxies assemble through major and minor mergers and grow fed by matter along the filaments of the cosmic web. This review describes the techniques used across the electromagnetic spectrum to detect dual and binary AGN candidates and proposes new avenues for their search. The current observational status is compared with the state-of-the-art numerical simulations and models for formation of dual and binary AGN. Binary SMBHs are among the loudest sources of gravitational waves (GWs) in the Universe. The search for a background of GWs at nHz frequencies from inspiralling SMBHs at low redshifts, and the direct detection of signals from their coalescence by the Laser Interferometer Space Antenna in the next decade, make this a theme of major interest for multi-messenger astrophysics. This review discusses the future facilities and observational strategies that are likely to significantly advance this fascinating field.© 2020 Elsevier B.V., All authors acknowledge the hospitality of the Lorentz Center for international workshops (Leiden, The Netherlands), where the idea of this work was born, and acknowledge the support of the International Space Science Institute (ISSI Bern, Switzerland), where the collaboration was originated. We thank the reviewers for having provided valuable and constructive comments that improved the clarity of the manuscript, and J.E. Barnes, L. Blecha, M. Eracleous, B.D. Farris, H. Fu, X. Liu, R. Pfeifle, L.C. Popovic, C. Ricci, S. Rodriguez, S. Tang, G. B. Taylor for their kind permission to reuse figures from their publications. ADR, CV and SB acknowledge financial support from ASI under grant ASI-INAF I/037/12/0 , and from the agreement ASI-INAF n. 2017-14-H.O . TB acknowledges support by the National Aeronautics and Space Administration under Grant No. NNX15AK84G and 80NSSC19K0319 issued through the Astrophysics Theory Program and by the Research Corporation for Science Advancement through a Cottrell Scholar Award. SF and KÉG thank the Hungarian National Research, Development, and Innovation Office ( OTKA NN110333 ) for support. KÉG was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the ÚNKP-19-4 New National Excellence Program of the Ministry for Innovation and Technology. BH acknowledges financial support by the DFG grant GE625/17-1 . EL is supported by a European Union COFUND/Durham Junior Research Fellowship (under EU grant agreement no. 609412). DL acknowledges support from the European Research Council (ERC) under grant 647208 (PI Jonker). AS is supported by the ERC CoG grant 818691 (B Massive). MGi is supported by the “Programa de Atracción de Talento” of the Comunidad de Madrid grant 2018-T1/TIC-11733 for the project: “Unveiling Black Hole Winds from Space”, and by the Spanish State Research Agency (AEI) grant MDM-2017-0737 Unidad de Excelencia “María de Maeztu” - Centro de Astrobiología (INTA-CSIC). PRC and LM acknowledge support from the Swiss National Science Foundation under the Grant 200020_178949 . MC acknowledges support from the National Science Foundation (NSF) NANOGrav Physics Frontier Center, award number 1430284 . NHR acknowledges support from the BMBF Verbundforschung under FKZ: 05A17PC1 and FKZ: 05A17PC2. ZH acknowledges support from NASA grants NNX17AL82G and 80NSSC19K0149 and NSF grant 1715661 . KI acknowledges support by the Spanish MINECO under grant AYA2016-76012-C3-1-P and MDM-2014-0369 of ICCUB (Unidad de Excelencia ’María de Maeztu’). MPT acknowledges financial support from the Spanish MCIU through the “Center of Excellence Severo Ochoa” award for the Instituto de Astrofísica de Andalucía ( SEV-2017-0709 ) and through the MINECO grants AYA2012-38491-C02-02 and AYA2015-63939-C2-1-P .

Super-massive black hole binaries are expected to produce a GW signal in the nano-Hertz frequency band which may be detected by PTAs in the coming years. The signal is composed of both stochastic and individually resolvable components. Here we develop a generic Bayesian method for the analysis of resolvable sources based on the construction of `null-streams' which cancel the part of the signal held in common for each pulsar (the Earth-term). For an array of $N$ pulsars there are $N-2$ independent null-streams that cancel the GW signal from a particular sky location. This method is applied to the localisation of quasi-circular binaries undergoing adiabatic inspiral. We carry out a systematic investigation of the scaling of the localisation accuracy with signal strength and number of pulsars in the PTA. Additionally, we find that source sky localisation with the International PTA data release one is vastly superior than what is achieved by its constituent regional PTAs., Comment: 13 pages, 7 figures, 1 appendix. Edited Figures 5, 6, 7 due to a bug in the plotting script (results unchanged). Additional edit to fix a type in equation 4