Supermassive Black Hole Mergers Research Articles

Detectability of Modulated X-Rays from LISA’s Supermassive Black Hole Mergers

Abstract One of the central goals of the Laser Interferometer Space Antenna (LISA) is the detection of gravitational waves from the merger of supermassive black holes. Contrary to stellar-mass black hole mergers, such events are expected to be rich X-ray sources due to the accretion of material from the circumbinary disks onto the black holes. The orbital dynamics before merger is also expected to modulate the resulting X-ray emission via Doppler boosting in a quasiperiodic way and in a simple phase relation with the gravitational wave from the inspiral of the black holes. Detecting the X-ray source would enable a precise and early localization of the binary, thus allowing many telescopes to observe the very moment of the merger. Although identifying the correct X-ray source in the relatively large LISA sky localization will be challenging due to the presence of many confounding point sources, the quasiperiodic modulation may aid in the identification. We explore the practical feasibility of such idea. We simulate populations of merging supermassive black holes, their detection with LISA, and their X-ray light curves using a simple model. Taking the parameters of the X-ray telescope on the proposed NASA Transient Astrophysics Probe, we then design and simulate an observation campaign that searches for the modulated X-ray source while LISA is still observing the inspiral of the black holes. Assuming a fiducial LISA detection rate of 10 mergers per year at redshift closer than 3.5, we expect a few detections of modulated X-ray counterparts over the nominal duration of the LISA mission.

The X-Ray Halo Scaling Relations of Supermassive Black Holes

Abstract We carry out a comprehensive Bayesian correlation analysis between hot halos and direct masses of supermassive black holes (SMBHs), by retrieving the X-ray plasma properties (temperature, luminosity, density, pressure, and masses) over galactic to cluster scales for 85 diverse systems. We find new key scalings, with the tightest relation being − , followed by − . The tighter scatter (down to 0.2 dex) and stronger correlation coefficient of all the X-ray halo scalings compared with the optical counterparts (as the − ) suggest that plasma halos play a more central role than stars in tracing and growing SMBHs (especially those that are ultramassive). Moreover, correlates better with the gas mass than dark matter mass. We show the important role of the environment, morphology, and relic galaxies/coronae, as well as the main departures from virialization/self-similarity via the optical/X-ray fundamental planes. We test the three major channels for SMBH growth: hot/Bondi-like models have inconsistent anticorrelation with X-ray halos and too low feeding; cosmological simulations find SMBH mergers as subdominant over most of cosmic time and too rare to induce a central-limit-theorem effect; the scalings are consistent with chaotic cold accretion, the rain of matter condensing out of the turbulent X-ray halos that sustains a long-term self-regulated feedback loop. The new correlations are major observational constraints for models of SMBH feeding/feedback in galaxies, groups, and clusters (e.g., to test cosmological hydrodynamical simulations), and enable the study of SMBHs not only through X-rays, but also via the Sunyaev–Zel’dovich effect (Compton parameter), lensing (total masses), and cosmology (gas fractions).

Recoiling supermassive black holes in analytical and numerical galaxy potential

ABSTRACTWe follow trajectories of recoiling supermassive black holes (SMBHs) in analytical and numerical models of galaxy merger remnants with masses of 1011 M⊙ and 1012 M⊙. We construct various merger remnant galaxies in order to investigate how the central SMBH mass and the mass ratio of progenitor galaxies influence escape velocities of recoiling SMBHs. Our results show that static analytical models of major merger remnant galaxies overestimate the SMBHs escape velocities. During major mergers violent relaxation leads to the decrease of galaxy mass and lower potential at large remnant radii. This process is not depicted in static analytical potential but clearly seen in our numerical models. Thus, the evolving numerical model is a more realistic description of dynamical processes in galaxies with merging SMBHs. We find that SMBH escape velocities in numerical major merger remnant galaxies can be up to 25 per cent lower compared to those in analytical models. Consequently, SMBHs in numerical models generally reach greater galactocentric distances and spend more time on bound orbits outside of the galactic nuclei. Thus, numerical models predict a greater number of spatially offset active galactic nuclei (AGNs).

On the Prevalence of Supermassive Black Holes over Cosmic Time

Abstract We investigate the abundance of supermassive black hole (SMBH) seeds in primordial galaxy halos. We explore the assumption that dark matter halos outgrowing a critical halo mass M c have some probability p of having spawned an SMBH seed. Current observations of local, intermediate-mass galaxies constrain these parameters: for M c = 1011 M ⊙, all halos must be seeded, but when adopting smaller M c masses the seeding can be much less efficient. The constraints simultaneously put lower limits on the number density of black holes in the local and high-redshift universe. Reproducing z ∼ 6 quasar space densities depends on their typical halo mass, which can be constrained by counting nearby Lyman Break Galaxies and Lyman-alpha emitters. For both observables, our simulations demonstrate that single-field predictions are too diverse to make definitive statements, in agreement with mixed claims in the literature. If quasars are not limited to the most massive host halos, they may represent a tiny fraction (≈10−5) of the SMBH population. Finally, we produce a wide range of predictions for gravitational events from SMBH mergers. We define a new diagnostic diagram for the Laser Interferometer Space Antenna to measure both SMBH space density and the typical delay between halo merger and black hole merger. While previous works have explored specific scenarios, our results hold independent of the seed mechanism, seed mass, obscuration, fueling methods and duty cycle.

The Simultaneous Formation of Cored, Tangentially Biased, and Kinematically Decoupled Centers in Massive Early-type Galaxies

Abstract We study the impact of merging supermassive black holes (SMBHs) on the central regions of massive early-type galaxies (ETGs) using a series of merger simulations with varying mass ratios. The ETG models include realistic stellar and dark matter components and are evolved with the gadget-3 based regularized tree code ketju. We show that observed key properties of the nuclear stellar populations of massive ETGs, namely flat stellar density distributions (cores), tangentially biased velocity distributions, and kinematically decoupled (counter-)rotation, can naturally result from a single process—the scouring by SMBHs. Major mergers with mass ratios of q > 1/3 produce flat, tangentially biased cores with kinematically distinct components. These kinematic features originate from reversals of the SMBH orbits caused by gravitational torques after pericenter passages. Minor mergers (q ≲ 1/3), on the other hand, form non-rotating cores and the orbit reversal becomes less important. Low-density stellar cores scoured in (multiple) minor mergers are less tangentially biased. This implies that the nuclear stellar properties of massive ETGs can be solely explained by stellar dynamical processes during their final assembly without any need for “feedback” from accreting black holes. We predict a strong correlation between decoupled cores, central anisotropy, and merger history: decoupled cores form in binary mergers and we predict them to occur in elliptical galaxies with the strongest central anisotropy. Measurements of the central orbital structure are the key to understanding the number of mergers that a given galaxy has experienced.

Hydrodynamics of Circumbinary Accretion: Angular Momentum Transfer and Binary Orbital Evolution

Abstract We carry out 2D viscous hydrodynamical simulations of circumbinary accretion using the moving-mesh code AREPO. We self-consistently compute the accretion flow over a wide range of spatial scales, from the circumbinary disk (CBD) far from the central binary, through accretion streamers, to the disks around individual binary components, resolving the flow down to 2% of the binary separation. We focus on equal-mass binaries with arbitrary eccentricities. We evolve the flow over long (viscous) timescales until a quasi-steady state is reached, in which the mass supply rate at large distances (assumed constant) equals the time-averaged mass transfer rate across the disk and the total mass accretion rate onto the binary components. This quasi-steady state allows us to compute the secular angular momentum transfer rate onto the binary, , and the resulting orbital evolution. Through direct computation of the gravitational and accretional torques on the binary, we find that is consistently positive (i.e., the binary gains angular momentum), with in the range of , depending on the binary eccentricity (where are the binary semimajor axis and angular frequency); we also find that this is equal to the net angular momentum current across the CBD, indicating that global angular momentum balance is achieved in our simulations. In addition, we compute the time-averaged rate of change of the binary orbital energy for eccentric binaries and thus obtain the secular rates and . In all cases, is positive; that is, the binary expands while accreting. We discuss the implications of our results for the merger of supermassive binary black holes and for the formation of close stellar binaries.

Probing supermassive black hole binaries with pulsar timing

The observation of gravitational-waves from merging supermassive black holes will be transformative: the detection of a low-frequency gravitational-wave background can tell us if and how supermassive black holes merge, inform our knowledge of galaxy merger rates and supermassive black hole masses, and enable the possibility of detecting new physics at nanohertz frequencies. All we have to do is time pulsars.

Misaligned snowplough effect and the electromagnetic counterpart to black hole binary mergers

We estimate the accretion rates produced when a circumprimary gas disc is pushed into the primary supermassive black hole (SMBH) by the tidal force of the decaying secondary during a SMBH merger. Using the 3D Smoothed Particle Hydrodynamics (SPH) code {\sc phantom}, we extend previous investigations of co-planar discs to the case where the disc and binary orbital planes are misaligned. We consider a geometrically thin disc with inclination angles varying from 1 to 180 degrees and a binary with mass ratio $q$=$10^{-3}$. We find that discs with small inclination angles (< 10 degrees) produce an increase in luminosity exceeding the Eddington rate. By contrast, discs with inclinations between 20 and 30 degrees show a less pronounced rise in the accretion rate, whilst discs inclined by 180 degrees show no peak in the mass accretion rate. While previous analytic work predicted that the effective tidal torque drops with increasing inclination angle, we show that the misaligned snowplough effect remains important even for angles larger than the disc aspect ratio. The rise in the accretion rate produced by discs inclined at small angles to the binary orbit can produce an electromagnetic counterpart to the gravitational wave signal emitted from final stages of the binary orbital decay.

Dynamical Evolution and Merger Timescales of LISA Massive Black Hole Binaries in Disk Galaxy Mergers

Abstract The Laser Interferometer Space Antenna (LISA) will detect gravitational-wave (GW) signals from merging supermassive black holes (BHs) with masses below 107 M ⊙. It is thus of paramount importance to understand the orbital dynamics of these relatively light central BHs, which typically reside in disk-dominated galaxies, in order to produce reliable forecasts of merger rates. To this aim, realistic simulations probing BH dynamics in unequal-mass disk galaxy mergers, into and beyond the binary hardening stage, are performed by combining smooth particle hydrodynamics and direct N-body codes. The structural properties and orbits of the galaxies are chosen to be consistent with the results of galaxy formation simulations. Stellar and dark matter distributions are triaxial down to the central 100 pc of the merger remnant. In all cases, a BH binary forms and hardens on timescales of at most 100 Myr, coalescing on another few-hundred-megayear timescale, depending on the characteristic density and orbital eccentricity. Overall, the sinking of the BH binary takes no more than ∼0.5 Gyr after the merger of the two galaxies is completed, but it can be much faster for very plunging orbits. Comparing with previous numerical simulations following the decay of BHs in massive early-type galaxies at z ∼ 3, we confirm that the characteristic density is the most crucial parameter determining the overall BH merging timescale, despite the structural diversity of the host galaxies. Our results lay down the basis for robust forecasts of LISA event rates in the case of merging BHs.

Co-evolution of supermassive black holes with galaxies from semi-analytic model: stochastic gravitational wave background and black hole clustering

We study the co-evolution of supermassive black holes (SMBHs) with galaxies by means of semi-analytic model (SAM) of galaxy formation based on sub-halo merger trees built from Millennium and Millennium-II simulation. We utilize the simulation results from Guo 2013 and Henriques 2015 to study two aspects of the co-evolution, \emph{i.e.} the stochastic gravitational wave (GW) background generated by SMBH merger and the SMBH/galaxy clustering. The characteristic strain amplitude of GW background predicted by Guo 2013 and Henriques 2015 models are $A_{yr^{-1}}=5.00\times10^{-16}$ and $A_{yr^{-1}}=9.42\times10^{-17}$, respectively. We find the GW amplitude is very sensitive to the galaxy merger rate. The difference in the galaxy merger rate between Guo 2013 and Henriques 2015, results in a factor $5$ deviation in the GW strain amplitude. For clusterings, we calculate the spatially isotropic two point auto- and cross-correlation functions (2PCFs) for both SMBHs and galaxies by using the mock catalogs generated from Guo 2013 model. We find that all 2PCFs have positive dependence on both SMBH and galaxy mass. And there exist a significant time evolution in 2PCFs, namely, the clustering effect is enhanced at lower redshifts. Interestingly, this result is not reported in the active galactic nuclei samples in SDSS. Our analysis also shows that, roughly, SMBHs and galaxies, with galaxy mass $10^2\sim10^3$ larger than SMBH mass, have similar pattern of clustering, which is a reflection of the co-evolution of SMBH and galaxy. Finally, we calculate the first ten multiples of the angular power spectrum of the energy density of GW background. We find the amplitude of angular power spectrum of the first ten multiples is about $10\%$ to $60\%$ of the monopole component in the whole frequency range.

The Formation of Extremely Diffuse Galaxy Cores by Merging Supermassive Black Holes

Abstract Given its velocity dispersion, the early-type galaxy NGC 1600 has an unusually massive (M • = 1.7 × 1010 M ⊙) central supermassive black hole (SMBH) surrounded by a large core (r b = 0.7 kpc) with a tangentially biased stellar distribution. We present high-resolution equal-mass merger simulations including SMBHs to study the formation of such systems. The structural parameters of the progenitor ellipticals were chosen to produce merger remnants resembling NGC 1600. We test initial stellar density slopes of ρ ∝ r −1 and ρ ∝ r −3/2 and vary the initial SMBH masses from 8.5 × 108 to 8.5 × 109 M ⊙. With increasing SMBH mass, the merger remnants show a systematic decrease in central surface brightness, an increasing core size, and an increasingly tangentially biased central velocity anisotropy. Two-dimensional kinematic maps reveal decoupled, rotating core regions for the most massive SMBHs. The stellar cores form rapidly as the SMBHs become bound, while the velocity anisotropy develops more slowly after the SMBH binaries become hard. The simulated merger remnants follow distinct relations between the core radius and the sphere of influence, and the SMBH mass, similar to observed systems. We find a systematic change in the relations as a function of the progenitor density slope and present a simple scouring model reproducing this behavior. Finally, we find the best agreement with NGC 1600 using SMBH masses totaling the observed value of M • = 1.7 × 1010 M ⊙. In general, density slopes of ρ ∝ r −3/2 for the progenitor galaxies are strongly favored for the equal-mass merger scenario.

A Population of Bona Fide Intermediate-mass Black Holes Identified as Low-luminosity Active Galactic Nuclei

Abstract Nearly every massive galaxy harbors a supermassive black hole (SMBH) in its nucleus. SMBH masses are millions to billions of solar mass, and they correlate with properties of spheroids of their host galaxies. While the SMBH growth channels, mergers, and gas accretion are well established, their origin remains uncertain: they could have emerged either from massive “seeds” (105–106 M ⊙) formed by direct collapse of gas clouds in the early universe or from smaller (100 M ⊙) BHs, end products of first stars. The latter channel would leave behind numerous intermediate-mass BHs (IMBHs, 102–105 M ⊙). Although many IMBH candidates have been identified, none are accepted as definitive; thus, their very existence is still debated. Using data mining in wide-field sky surveys and applying dedicated analysis to archival and follow-up optical spectra, we identified a sample of 305 IMBH candidates having masses 3 × 10 4 M ⊙ &lt; M BH &lt; 2 × 10 5 M ⊙ , which reside in galaxy centers and are accreting gas that creates characteristic signatures of a type I active galactic nucleus (AGN). We confirmed the AGN nature of 10 sources (including five previously known objects that validate our method) by detecting the X-ray emission from their accretion disks, thus defining the first bona fide sample of IMBHs in galactic nuclei. All IMBH host galaxies possess small bulges and sit on the low-mass extension of the M BH – M bulge scaling relation, suggesting that they must have experienced very few if any major mergers over their lifetime. The very existence of nuclear IMBHs supports the stellar-mass seed scenario of the massive BH formation.

Gravitational wave driven mergers and coalescence time of supermassive black holes

Aims. The evolution of supermassive black holes (SMBHs) initially embedded in the centres of merging galaxies realised with a stellar mass function (SMF) is studied from the onset of galaxy mergers until coalescence. Coalescence times of SMBH binaries are of great importance for black hole evolution and gravitational wave detection studies. Methods. We performed direct N-body simulations using the highly efficient and massively parallel phi-GRAPE+GPU code capable of running on high-performance computer clusters supported by graphic processing units (GPUs). Post-Newtonian terms up to order 3.5 are used to drive the SMBH binary evolution in the relativistic regime. We performed a large set of simulations with three different slopes of the central stellar cusp and different random seeds. The impact of a SMF on the hardening rate and the coalescence time is investigated. Results. We find that SMBH binaries coalesce well within one billion years when our models are scaled to galaxies with a steep cusp at low redshift. Here higher central densities provide a larger supply of stars to efficiently extract energy from the SMBH binary orbit and shrink it to the phase where gravitational wave (GW) emission becomes dominant, leading to the coalescence of the SMBHs. Mergers of models with shallow cusps that are representative of giant elliptical galaxies having central cores result in less efficient extraction of the binary’s orbital energy, due to the lower stellar densities in the centre. However, high values of eccentricity witnessed for SMBH binaries in such galaxy mergers ensure that the GW emission dominated phase sets in earlier at larger values of the semi-major axis. This helps to compensate for the less efficient energy extraction during the phase dominated by stellar encounters resulting in mergers of SMBHs in about 1 Gyr after the formation of the binary. Additionally, we witness mass segregation in the merger remnant resulting in enhanced SMBH binary hardening rates. We show that at least the final phase of the merger in cuspy low-mass galaxies would be observable with the GW detector eLISA.

Supermassive black holes and their feedback effects in the IllustrisTNG simulation

We study the population of supermassive black holes (SMBHs) and their effects on massive central galaxies in the IllustrisTNG cosmological hydrodynamical simulations of galaxy formation. The employed model for SMBH growth and feedback assumes a two-mode scenario in which the feedback from active galactic nuclei occurs through a kinetic, comparatively efficient mode at low accretion rates relative to the Eddington limit, and in the form of a thermal, less efficient mode at high accretion rates. We show that the quenching of massive central galaxies happens coincidently with kinetic-mode feedback, consistent with the notion that active supermassive black cause the low specific star formation rates observed in massive galaxies. However, major galaxy mergers are not responsible for initiating most of the quenching events in our model. Up to black hole masses of about $10^{8.5}\,{\rm M}_\odot$, the dominant growth channel for SMBHs is in the thermal mode. Higher mass black holes stay mainly in the kinetic mode and gas accretion is self-regulated via their feedback, which causes their Eddington ratios to drop, with SMBH mergers becoming the main channel for residual mass growth. As a consequence, the quasar luminosity function is dominated by rapidly accreting, moderately massive black holes in the thermal mode. We show that the associated growth history of SMBHs produces a low-redshift quasar luminosity function and a redshift zero black hole mass-stellar bulge mass relation in good agreement with observations, whereas the simulation tends to over-predict the high-redshift quasar luminosity function.

The late inspiral of supermassive black hole binaries with circumbinary gas discs in the LISA band

We present the results of 2D, moving-mesh, viscous hydrodynamical simulations of an accretion disc around a merging supermassive black hole binary (SMBHB). The simulation is pseudo-Newtonian, with the BHs modeled as point masses with a Paczynski-Wiita potential, and includes viscous heating, shock heating, and radiative cooling. We follow the gravitational inspiral of an equal-mass binary with a component mass M_bh=10^6 M_sun from an initial separation of 60r_g (where r_g=GM_bh/c^2 is the gravitational radius) to the merger. We find that a central, low-density cavity forms around the binary, as in previous work, but that the BHs capture gas from the circumbinary disc and accrete efficiently via their own minidiscs, well after their inspiral outpaces the viscous evolution of the disc. The system remains luminous, displaying strong periodicity at twice the binary orbital frequency throughout the entire inspiral process, all the way to the merger. In the soft X-ray band, the thermal emission is dominated by the inner edge of the circumbinary disc with especially clear periodicity in the early inspiral. By comparison, harder X-ray emission is dominated by the minidiscs, and the light curve is initially more noisy but develops a clear periodicity in the late inspiral stage. This variability pattern should help identify the EM counterparts of SMBHBs detected by the space-based gravitational-wave detector LISA.

Dancing to changa: a self-consistent prediction for close SMBH pair formation time-scales following galaxy mergers

We present the first self-consistent prediction for the distribution of formation timescales for close Supermassive Black Hole (SMBH) pairs following galaxy mergers. Using ROMULUS25, the first large-scale cosmological simulation to accurately track the orbital evolution of SMBHs within their host galaxies down to sub-kpc scales, we predict an average formation rate density of close SMBH pairs of 0.013 cMpc^-3 Gyr^-1. We find that it is relatively rare for galaxy mergers to result in the formation of close SMBH pairs with sub-kpc separation and those that do form are often the result of Gyrs of orbital evolution following the galaxy merger. The likelihood and timescale to form a close SMBH pair depends strongly on the mass ratio of the merging galaxies, as well as the presence of dense stellar cores. Low stellar mass ratio mergers with galaxies that lack a dense stellar core are more likely to become tidally disrupted and deposit their SMBH at large radii without any stellar core to aid in their orbital decay, resulting in a population of long-lived 'wandering' SMBHs. Conversely, SMBHs in galaxies that remain embedded within a stellar core form close pairs in much shorter timescales on average. This timescale is a crucial, though often ignored or very simplified, ingredient to models predicting SMBH mergers rates and the connection between SMBH and star formation activity.

Pulsar timing arrays are poised to reveal gravitational waves

Radio observatories are accumulating data to detect mergers of supermassive black holes.

Galaxy rotation and supermassive black hole binary evolution

Supermassive black hole (SMBH) binaries residing at the core of merging galaxies are recently found to be strongly affected by the rotation of their host galaxies. The highly eccentric orbits that form when the host is counterrotating emit strong bursts of gravitational waves that propel rapid SMBH binary coalescence. Most prior work, however, focused on planar orbits and a uniform rotation profile, an unlikely interaction configuration. However, the coupling between rotation and SMBH binary evolution appears to be such a strong dynamical process that it warrants further investigation. This study uses direct N-body simulations to isolate the effect of galaxy rotation in more realistic interactions. In particular, we systematically vary the SMBH orbital plane with respect to the galaxy rotation axis, the radial extent of the rotating component, and the initial eccentricity of the SMBH binary orbit. We find that the initial orbital plane orientation and eccentricity alone can change the inspiral time by an order of magnitude. Because SMBH binary inspiral and merger is such a loud gravitational wave source, these studies are critical for the future gravitational wave detector, LISA, an ESA/NASA mission currently set to launch by 2034.

The Romulus cosmological simulations: a physical approach to the formation, dynamics and accretion models of SMBHs

We present a novel implementation of supermassive black hole (SMBH) formation, dynamics, and accretion in the massively parallel tree+SPH code, ChaNGa. This approach improves the modeling of SMBHs in fully cosmological simulations, allowing for a more de- tailed analysis of SMBH-galaxy co-evolution throughout cosmic time. Our scheme includes novel, physically motivated models for SMBH formation, dynamics and sinking timescales within galaxies, and SMBH accretion of rotationally supported gas. The sub-grid parameters that regulate star formation (SF) and feedback from SMBHs and SNe are optimized against a comprehensive set of z = 0 galaxy scaling relations using a novel, multi-dimensional parameter search. We have incorporated our new SMBH implementation and parameter optimization into a new set of high resolution, large-scale cosmological simulations called Romulus. We present initial results from our flagship simulation, Romulus25, showing that our SMBH model results in SF efficiency, SMBH masses, and global SF and SMBH accretion histories at high redshift that are consistent with observations. We discuss the importance of SMBH physics in shaping the evolution of massive galaxies and show how SMBH feedback is much more effective at regulating star formation compared to SNe feedback in this regime. Further, we show how each aspect of our SMBH model impacts this evolution compared to more common approaches. Finally, we present a science application of this scheme studying the properties and time evolution of an example dual AGN system, highlighting how our approach allows simulations to better study galaxy interactions and SMBH mergers in the context of galaxy-BH co-evolution.

On the orbital evolution of supermassive black hole binaries with circumbinary accretion discs

Gaseous circumbinary accretion discs provide a promising mechanism to facilitate the mergers of supermassive black holes (SMBHs) in galactic nuclei. We measure the torques exerted on accreting SMBH binaries, using 2D, isothermal, moving-mesh, viscous hydrodynamical simulations of circumbinary accretion discs. Our computational domain includes the entire inner region of the circumbinary disk with the individual black holes (BHs) included as point masses on the grid and a sink prescription to model accretion onto each BH. The BHs each acquire their own well-resolved accretion discs ("minidiscs"). We explore a range of mass removal rates for the sink prescription removing gas from the central regions of the minidiscs. We find that the torque exerted on the binary is primarily gravitational, and dominated by the gas orbiting close behind and ahead of the individual BHs. The torques from the distorted circumbinary disc farther out and from the direct accretion of angular momentum are subdominant. The torques are sensitive to the sink prescription: slower sinks result in more gas accumulating near the BHs and more negative torques, driving the binary to merger more rapidly. For faster sinks, the torques are less negative and eventually turn positive (for unphysically fast sinks). When the minidiscs are modeled as standard alpha discs, our results are insensitive to the choice of sink radius. Scaling the simulations to a binary orbital period tbin = 1yr and background disc accretion rate Mdot = 0.3MEdd in Eddington units, the binary inspirals on a timescale of 3X10^6 years, irrespective of the SMBH masses. For binaries with total mass <10^7Msun, this is shorter than the inspiral time due to gravitational wave (GW) emission alone, implying that gas discs will have a significant impact on the SMBH binary population and can affect the GW signal for Pulsar Timing Arrays.