It arises a puzzle in \NGC\, how to secularly maintain the counter-rotating disc from $0.2$ to $7\,$pc unambiguously detected by recent ALMA observations of molecular gas. Upon further analysis of disc dynamics, we find that the Kelvin-Helmholtz (KH) instability (KHI) results in an unavoidable catastrophe of the disc developed at the interface between the reversely rotating parts, and demonstrate that a close binary of supermassive black holes provides tidal torques as the unique external sources to prevent the disc from the KH catastrophe. We are led to the inescapable conclusion that there must be a binary black hole at the center of NGC 1068, to prevent it from the KH catastrophe. The binary is composed of black holes with a separation of $0.1\,$pc from GRAVITY/VLTI observations, a total mass of $1.3\times 10^{7}\:M_{\odot}$ and a mass ratio of $\sim 0.3$ estimated from the angular momentum budge of the global system. The KHI gives rise to forming a gap without cold gas at the velocity interface which overlaps with the observed gap of hot and cold dust regions. Releases of kinematic energies from the KHI of the disc are in agreement with observed emissions in radio and $γ$-rays. Such a binary is shrinking with a timescale much longer than the local Hubble time via gravitational waves, however, the KHI leads to an efficient annihilation of the orbital angular momentum and speed up merge of the binary, providing a new paradigm of solving the long term issue of "final parsec problem". Future observations of GRAVITY+/VLTI are expected to be able to spatially resolve the CB-SMBHs suggested in this paper.
During a galaxy merger, the supermassive black hole (SMBH) in each galaxy is thought to sink to the center of the potential and form a supermassive black hole binary; this binary can eject stars via 3-body scattering, bringing the SMBHs ever closer. In a static spherical galaxy model, the binary stalls at a separation of about a parsec after ejecting all the stars in its loss cone -- this is the well-known final parsec problem. Earlier work has shown that the centrophilic orbits in triaxial galaxy models are key in refilling the loss cone at a high enough rate to prevent the black holes from s…
I review the evolution of binary supermassive black holes and focus on the stellar-dynamical mechanisms that may help to overcome the final-parsec problem - the possible stalling of the binary at a separation much larger than is required for an efficient gravitational wave emission. Recent N-body simulations have suggested that a departure from spherical symmetry in the nucleus of the galaxy may keep the rate of interaction of stars with the binary at a high enough level so that the binary continues to shrink rather rapidly. However, a major problem of all these simulations is that they do not…
Radial velocity monitoring has revealed the presence of moving broad emission lines in some quasars, potentially indicating the presence of a sub-parsec binary system. Phase-referenced, near-infrared interferometric observations could map out the binary orbit by measuring the photocenter difference between a broad emission line and the hot dust continuum. We show that astrometric data over several years may be able to detect proper motions and accelerations, confirming the presence of a binary and constraining system parameters. The brightness, redshifts, and astrometric sizes of current candi…
As a natural consequence of cosmological hierarchical structure formation, sub-parsec supermassive black hole binaries (SMBHBs) should be common in galaxies but thus far have eluded spectroscopic identification. Based on four decades of optical spectroscopic monitoring, we report that the nucleus of NGC 5548, a nearby Seyfert galaxy long suspected to have experienced a major merger about one billion years ago, exhibits long-term variability with a period of 14 years in the optical continuum and broad Hbeta emission line. Remarkably, the double-peaked profile of Hbeta shows systematic velocity …
We study the formation of a supermassive black hole (SMBH) binary and the shrinking of the separation of the two holes to sub-pc scales starting from a realistic major merger between two gas-rich spiral galaxies with mass comparable to our Milky Way. The simulations, carried out with the Adaptive Mesh Refinement (AMR) code RAMSES, are capable of resolving separations as small as 0.1 pc. The collision of the two galaxies produces a gravo-turbulent rotating nuclear disk with mass (10^9 Msun) and size (60 pc) in excellent agreement with previous SPH simulations with particle splitting that used a…
Using few-body simulations, we investigate the evolution of supermassive black holes (SMBHs) in galaxies ($M_{\star}=10^{10}-10^{12}{\rm M}_{\odot}$ at $z=0$) at $0<z<4$. Following galaxy merger trees from the Millennium simulation, we model BH mergers with two extreme binary decay scenarios for the `hard binary' stage: a full or an empty loss cone. These two models should bracket the true evolution, and allow us to separately explore the role of dynamical friction and that of multi-body BH interactions on BH mergers. Using the computed merger rates, we infer the stochastic gravitational wave …
We identify SDSS J153636.22+044127.0, a QSO discovered in the Sloan Digital Sky Survey, as a promising candidate for a binary black hole system. This QSO has two broad-line emission systems separated by 3500 km/sec. The redder system at z=0.3889 also has a typical set of narrow forbidden lines. The bluer system (z=0.3727) shows only broad Balmer lines and UV Fe II emission, making it highly unusual in its lack of narrow lines. A third system, which includes only unresolved absorption lines, is seen at a redshift, z=0.3878, intermediate between the two emission-line systems. While the observati…
The jet in active galactic nuclei (AGN) is a key ingredient in understanding the co-evolution of galaxies and their central supermassive black holes (SMBHs). Unfortunately, the mechanism of jet launching and collimation is still elusive. The observational evidence of decreasing radio loudness with increasing Eddington ratio implies that the jet should be coupled with the accretion process. To further explore the relationship between the jet and accretion, it is necessary to extend our knowledge of the jet to an extreme end of the Eddington ratio distribution of AGN. Using Very Long Baseline Ar…
We study the connection between the large-scale dynamics and the gas fueling toward a central black hole via the analysis of a Milky Way-like simulation at sub-parsec resolution. This allows us to follow a set of processes at various scales (e.g., the triggering of inward gas motion towards inner resonances via the large-scale bar, the connection to the central black hole via mini spirals) in a self-consistent manner. This simulation provides further insights on the role of shear for the inhibition of star formation within the bar in regions with significant amount of gas. We also witness the …
One of the most intriguing scenarios proposed to explain how active galactic nuclei are triggered involves the existence of a supermassive binary black hole system in their cores. Here we present an observational evidence for the first spectroscopically resolved sub-parsec orbit of a such system in the core of Seyfert galaxy NGC 4151. Using a method similar to those typically applied for spectroscopic binary stars we obtained radial velocity curves of the supermassive binary system, from which we calculated orbital elements and made estimates about the masses of components. Our analysis shows …
We simulate shells created by supernovae expanding into the interstellar medium (ISM) of the nuclear region of a galaxy, and analyze how the shell evolution is influenced by the supernova (SN) position relative to the galactic center, by the interstellar matter (ISM) density, and by the combined gravitational pull of the nuclear star cluster (NSC) and supermassive black hole (SMBH).We adopted simplified hydrodynamical simulations using the infinitesimally thin layer approximation in 3D (code RING) and determined whether and where the shell expansion may bring new gas into the inner parsec arou…
We present analysis of Chandra X-ray observations of seven quasars that were identified as candidate sub-parsec binary supermassive black hole (SMBH) systems in the Catalina Real-Time Transient Survey (CRTS) based on apparent periodicity in their optical light curves. Simulations predict close-separation accreting SMBH binaries will have different X-ray spectra than single accreting SMBHs, including harder or softer X-ray spectra, ripple-like profiles in the Fe K-$α$ line, and distinct peaks in the spectrum due to the separation of the accretion disk into a circumbinary disk and mini-disks aro…
The formation of massive black hole binaries (MBHBs) is an unavoidable outcome of galaxy evolution via successive mergers. However, the mechanism that drives their orbital evolution from parsec separations down to the gravitational wave (GW) dominated regime is poorly understood, and their final fate is still unclear. If such binaries are embedded in gas-rich and turbulent environments, as observed in remnants of galaxy mergers, the interaction with gas clumps (such as molecular clouds) may efficiently drive their orbital evolution. Using numerical simulations, we test this hypothesis by study…
We present a high resolution simulation of an idealized model to explain the origin of the two young, counter-rotating, sub-parsec scale stellar disks around the supermassive black hole SgrA* at the Center of the Milky Way. In our model, the collision of a single molecular cloud with a circum-nuclear gas disk (similar to the one observed presently) leads to multiple streams of gas flowing towards the black hole and creating accretion disks with angular momentum depending on the ratio of cloud and circum-nuclear disk material. The infalling gas creates two inclined, counter-rotating sub-parsec …
We simulate an equal-mass merger of two Milky Way-size galaxy discs with moderate gas fractions at parsec-scale resolution including a new model for radiative cooling and heating in a multi-phase medium, as well as star formation and feedback from supernovae. The two discs initially have a $2.6\times10^6\mathrm{~M_{\odot}}$ supermassive black hole (SMBH) embedded in their centers. As the merger completes and the two galactic cores merge, the SMBHs form a a pair with a separation of a few hundred pc that gradually decays. Due to the stochastic nature of the system immediately following the merg…
Motivated by advances in observational searches for sub-parsec supermassive black hole binaries (SBHBs) made in the past few years we develop a semi-analytic model to describe spectral emission line signatures of these systems. The goal of this study is to aid the interpretation of spectroscopic searches for binaries and help test one of the leading models of binary accretion flows in the literature: SBHB in a circumbinary disk. In this work we present the methodology and a comparison of the preliminary model with the data. We model SBHB accretion flows as a set of three accretion disks: two m…
NGC 3115 is known as the low-luminosity active galactic nucleus which hosts the nearest ($z\sim0.002$) billion solar mass supermassive black hole ($\sim1.5\times10^9~M_\odot$). Its Bondi radius $r_\mathrm{B}$ ($\sim3\farcs6$) can be readily resolved with Chandra, which offers us an excellent opportunity to investigate the accretion flow onto a supermassive black hole. In this paper, we perform two-dimensional hydrodynamical numerical simulations, tailored for NGC 3115, on the mass flow across the Bondi radius. Our best fittings for the density and temperature agree well with the observations o…
Supermassive binary black holes (BBHs) are unavoidable products of galaxy mergers and are expected to exist in the cores of many quasars. Great effort has been made during the past several decades to search for BBHs among quasars; however, observational evidence for BBHs remains elusive and ambiguous, which is difficult to reconcile with theoretical expectations. In this paper, we show that the distinct optical-to-UV spectrum of Mrk 231 can be well interpreted as emission from accretion flows onto a BBH, with a semimajor axis of ~590AU and an orbital period of ~1.2 year. The flat optical and U…
The processes driving gas accretion on to supermassive black holes (SMBHs) are still poorly understood. Angular momentum conservation prevents gas within $\sim10\,$pc of the black hole from reaching radii $\sim10^{-3}\,$pc where viscous accretion becomes efficient. Here we present simulations of the collapse of a clumpy shell of swept-up isothermal gas, which is assumed to have formed as a result of feedback from a previous episode of AGN activity. The gas falls towards the SMBH forming clumps and streams, which intersect, collide, and often form a disc. These collisions promote partial cancel…
We present an improved semi-analytic model for calculation of the broad optical emission-line signatures from sub-parsec supermassive black hole binaries (SBHBs) in circumbinary disks. The second-generation model improves upon the treatment of radiative transfer by taking into account the effect of the radiation driven accretion disk wind on the properties of the emission-line profiles. Analysis of 42.5 million modeled emission-line profiles shows that correlations between the profile properties and SBHB parameters identified in the first-generation model are preserved, indicating that their d…
We present a method for comparing the H$β$ emission-line profiles of observed supermassive black hole (SBHB) candidates and models of sub-parsec SBHBs in circumbinary disks. Using the approach based on principal component analysis we infer the values of the binary parameters for the spectroscopic SBHB candidates and evaluate the parameter degeneracies, representative of the uncertainties intrinsic to such measurements. We find that as a population, the SBHB candidates favor the average value of the semimajor axis corresponding to $\log(a/M) \approx 4.20\pm 0.42$ and comparable mass ratios, $q>…
We consider the interaction between a binary system (e.g. two supermassive black holes or two stars) and an external accretion disc with misaligned angular momentum. This situation occurs in galaxy merger events involving supermassive black holes, and in the formation of stellar--mass binaries in star clusters. We work out the gravitational torque between the binary and disc, and show that their angular momenta J_b, J_d stably counteralign if their initial orientation is sufficiently retrograde, specifically if the angle theta between them obeys cos(theta) < -J_d/2J_b, on a time short compared…
Supermassive binary black holes (BBHs) on sub-parsec scales are prime targets for gravitational wave experiments. They also provide insights on close binary evolution and hierarchical structure formation. Sub-parsec BBHs cannot be spatially resolved but indirect methods can identify candidates. In 2015 Liu et al. reported an optical-continuum periodicity in the quasar PSO J334.2028+01.4075, with the estimated mass and rest-frame period suggesting an orbital separation of about 0.006 pc (0.7 micro-arcsec). The persistence of the quasar's optical periodicity has recently been disfavored over an …
The broadening of atomic emission lines by high-velocity motion of gas near accreting supermassive black holes is an observational hallmark of quasars. Observations of broad emission lines could potentially constrain the mechanism for transporting gas inwards through accretion disks or outwards through winds. The size of this broad-line region has been estimated by measuring the light travel time delay between the variable nuclear continuum and the emission lines - a method known as reverberation mapping. In some models the emission lines arise from a continuous outflow, whereas in others they…
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$α$ emission lines or periodicity in their light curve. Here we report on a new method to s…
The supermassive black holes originally in the nuclei of two merging galaxies will form a binary in the remnant core. The early evolution of the massive binary is driven by dynamical friction before the binary becomes "hard" and eventually reaches coalescence through gravitational wave emission. { We consider the dynamical friction evolution of massive binaries consisting of a secondary hole orbiting inside a stellar cusp dominated by a more massive central black hole.} In our treatment we include the frictional force from stars moving faster than the inspiralling object which is neglected in …
Motivated by observational searches for sub-parsec supermassive black hole binaries (SBHBs) we develop a modular analytic model to determine the likelihood for detection of SBHBs by ongoing spectroscopic surveys. The model combines the parametrized rate of orbital evolution of SBHBs in circumbinary disks with the selection effects of spectroscopic surveys and returns a multivariate likelihood for SBHB detection. Based on this model we find that in order to evolve into the detection window of the spectroscopic searches from larger separations in less than a Hubble time, $10^8M_\odot$ SBHBs must…
Quasars whose broad emission lines show temporal, bulk radial velocity (RV) shifts have been proposed as candidate sub-parsec (sub-pc), binary supermassive black holes (BSBHs). We identified a sample of 16 BSBH candidates based on two-epoch spectroscopy among 52 quasars with significant RV shifts over a few rest-frame years. The candidates showed consistent velocity shifts independently measured from two broad lines (H$β$ and H$α$ or Mg${\rm \,II}$) without significant changes in the broad-line profiles. Here in the third paper of the series, we present further third- and fourth-epoch spectros…
During a galaxy merger, the supermassive black hole (SMBH) in each galaxy is thought to sink to the center of the potential and form a supermassive black hole binary; this binary can eject stars via 3-body scattering, bringing the SMBHs ever closer. In a static spherical galaxy model, the binary stalls at a separation of about a parsec after ejecting all the stars in its loss cone -- this is the well-known final parsec problem. However it has been shown that SMBH binaries in non-spherical galactic nuclei harden at a nearly constant rate until reaching the gravitational wave regime. Here we use…
We investigate the dynamics of supermassive black holes (SMBHs) in galactic cores by means of a semi-analytic model based on the Langevin equation, including dynamical friction and stochastic noise accounting for the gravitational interactions with stars. The model is validated against direct $N$-body simulations of intermediate-mass black holes in stellar clusters where a realistic number of particles is accessible. For the galactic case, we find that the SMBH experiences a Brownian-like motion with a typical displacement from the geometric center of the Galaxy of a few parsecs, for system pa…
The dynamical evolution of supermassive black-hole binary systems is tethered on large scales to the merger rate of massive galaxies, and on small scales to the stellar and gaseous environments of galactic cores. The population of these systems will create an ensemble gravitational-wave signal at nanohertz frequencies that is detectable by Pulsar Timing Arrays (PTA), such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). By measuring nanohertz gravitational waves, we will be able to definitively demonstrate that supermassive black-hole binaries reach milliparsec s…
Radio galaxy phenomenon is directly connected to mass accreting, spinning supermassive black holes found in the active galactic nuclei (AGN). It is still unclear how the collimated jets of relativistic plasma on hundreds to thousands of kpc scale form, and why nearly always they are launched from the nuclei of bulge dominated elliptical galaxies and not flat spirals. Here we present the discovery of giant radio source J2345-0449 (z=0.0755), a clear and extremely rare counter example where relativistic jets are ejected from a luminous and massive spiral galaxy on scale of ~1.6 Mpc, the largest …
We present KETJU, a new extension of the widely-used smoothed particle hydrodynamics simulation code GADGET-3. The key feature of the code is the inclusion of algorithmically regularized regions around every supermassive black hole (SMBH). This allows for simultaneously following global galactic-scale dynamical and astrophysical processes, while solving the dynamics of SMBHs, SMBH binaries and surrounding stellar systems at sub-parsec scales. The KETJU code includes Post-Newtonian terms in the equations of motions of the SMBHs which enables a new SMBH merger criterion based on the gravitationa…
Blazars are a sub-class of quasars with Doppler boosted jets oriented close to the line of sight, and thus efficient probes of supermassive black hole growth and their environment, especially at high redshifts. Here we report on Very Long Baseline Interferometry observations of a blazar J0906+6930 at z = 5.47, which enabled the detection of polarised emission and measurement of jet proper motion at parsec scales. The observations suggest a less powerful jet compared with the general blazar population, including lower proper motion and bulk Lorentz factor. This coupled with a previously inferre…
Galaxies are believed to evolve through merging, which should lead to multiple supermassive black holes in some. There are four known triple black hole systems, with the closest pair being 2.4 kiloparsecs apart (the third component is more distant at 3 kiloparsecs), which is far from the gravitational sphere of influence of a black hole with mass $\sim$10$^9$ M$_\odot$ (about 100 parsecs). Previous searches for compact black hole systems concluded that they were rare, with the tightest binary system having a separation of 7 parsecs. Here we report observations of a triple black hole system at …
The existence of binary supermassive black holes (SBHs) is predicted by models of hierarchical galaxy formation. To date, only a single binary SBH has been imaged, at a projected separation of 7.3 parsecs. Here we report the detection of a candidate dual SBH with projected separation of 0.35 pc in the gas-rich interacting spiral galaxy NGC 7674 (Mrk 533). This peculiar Seyfert galaxy possesses a $\sim$0.7 kpc Z-shaped radio jet; the leading model for the formation of such sources postulates the presence of an uncoalesced binary SBH created during the infall of a satellite galaxy. Using very lo…
The capture and disruption of stars by supermassive black holes (SMBHs), and the formation and coalescence of binaries, are inevitable consequences of the presence of SMBHs at the cores of galaxies. Pairs of active galactic nuclei (AGN) and binary SMBHs are important stages in the evolution of galaxy mergers, and an intense search for these systems is currently ongoing. In the early and advanced stages of galaxy merging, observations of the triggering of accretion onto one or both BHs inform us about feedback processes and BH growth. Identification of the compact binary SMBHs at parsec and sub…
Effects of dark dipole radiation on eccentric supermassive black hole binary inspirals
School of Astronomy and Space Science, University of Chinese Academy of Sciences (UCAS)（中国科学院大学天文与空间科学学院）；School of Physics, Nanjing University（南京大学物理学院）
We show that a 10 year Gaia mission could astrometrically detect the orbital motion of ~1 sub-parsec separation supermassive black hole binary in the heart of nearby, bright active galactic nuclei (AGN). Candidate AGN lie out to a redshift of z=0.02 and in the V-band magnitude range $10 \lesssim m_V \lesssim 13$. The distribution of detectable binary masses peaks at a few times $10^7$ solar masses and is truncated above a few times $10^8$ solar masses.
We present 1.4 pc resolution observations of 256 GHz nuclear radio continuum and HCN ($J=3 \to 2$) in the molecular torus of NGC 1068. The integrated radio continuum emission has a flat spectrum consistent with free-free emission and resolves into an X-shaped structure resembling an edge-brightened bicone. HCN is detected in absorption against the continuum, and the absorption spectrum shows a pronounced blue wing that suggests a high-velocity molecular outflow with speeds reaching 450 km/s. Analysis of the off-nucleus emission line kinematics and morphology reveals two nested, rotating disk c…
A binary supermassive black hole loses energy via ejection of stars in a galactic nucleus, until emission of gravitational waves becomes strong enough to induce rapid coalescence. Evolution via the gravitational slingshot requires that stars be continuously supplied to the binary, and it is known that in spherical galaxies the reservoir of such stars is quickly depleted, leading to stalling of the binary at parsec-scale separations. Recent N-body simulations of galaxy mergers and isolated nonspherical galaxies suggest that this stalling may not occur in less idealized systems. However, it rema…
Jet precession can reveal the presence of binary systems of supermassive black holes. The ability to accurately measure the parameters of jet precession from radio-loud AGN is important for constraining the binary supermassive black hole population, which are expected as a result of hierarchical galaxy evolution. The age, morphology, and orientation along the line of sight of a given source often result in uncertainties regarding jet path. This paper presents a new approach for efficient determination of precession parameters using a 2D MCMC curve-fitting algorithm which provides us a full pos…
Most large galaxies harbor supermassive black holes (SMBHs) in their centers, and galaxies merge. Consequently, binary SMBHs should be common in galactic nuclei. However, close binaries of SMBH (CB-SMBHs) with sub-parsec separation cannot be imaged directly using current facilities. Some indirect signatures, such as periodic signals in light curves and double peaks in emission-line profile, have been used to find CB-SMBH candidates, but ambiguities still exist and no definitive conclusions can be made. We have recently proposed a new method focusing on kinematic signatures that can be derived …
Ultracompact dwarf galaxies (UCDs) are among the densest stellar systems in the universe. These systems have masses up to 200 million solar masses, but half light radii of just 3-50 parsecs. Dynamical mass estimates show that many UCDs are more massive than expected from their luminosity. It remains unclear whether these high dynamical mass estimates are due to the presence of supermassive black holes or result from a non-standard stellar initial mass function that causes the average stellar mass to be higher than expected. Here we present the detection of a supermassive black hole in a massiv…
Supermassive black hole binaries (SMBHBs) in the 10 million to 10 billion $M_\odot$ range form in galaxy mergers, and live in galactic nuclei with large and poorly constrained concentrations of gas and stars. There are currently no observations of merging SMBHBs--- it is in fact possible that they stall at their final parsec of separation and never merge. While LIGO has detected high frequency GWs, SMBHBs emit GWs in the nanohertz to millihertz band. This is inaccessible to ground-based interferometers, but possible with Pulsar Timing Arrays (PTAs). Using data from local galaxies in the 2 Micr…
Multiphase Gas Nature in the Sub-parsec Region of the Active Galactic Nuclei. III. Eddington Ratio Dependence on the Structures of Dusty and Dust-free Outflows
We produce radiation hydrodynamics models of an AGN 'torus' plus outflow on 1-100 pc scales. This large scale permits direct comparison with observations, provides justification for configurations used in radiation transfer models, and tests the sensitivity of results of smaller scale dynamical models. We find that anisotropic radiation from an AGN accretion disk can cause an outflow to evolve to become more polar, agreeing with the ubiquity of polar extended mid-IR emission, and the general geometry predicted by radiative transfer models. We also find the velocity maps can reproduce many feat…
The gravitational interaction at parsec to sub-parsec scales between a circumbinary gas disc and a super massive black hole binary (SMBHB) is a promising mechanism to drive the migration of SMBHBs toward coalescence. The typical dynamical evolution can be separated in two main regimes: I) Slow migration ($T_{\rm mig}$ $\sim$ $10^{3-4}\times T_{\rm orb}$), where viscous torques are not efficient enough to redistribute the extracted angular momentum from the binary, leading to the formation of a low density cavity around the binary. II) Fast migration ($T_{\rm mig}$ $\sim$ $10^{1-2} \times T_{\r…
Jet-torus interaction revealed by sub-parsec SO absorption in NGC 1052
Graduate School of Science, Osaka Metropolitan University（大阪公立大学大学院理学研究科）；Faculty of Engineering, Fukui University of Technology（福井工业大学工学部）；Joint ALMA Observatory（ALMA联合天文台）；National Astronomical Observatory of Japan（日本国立天文台）；Department of Astronomy, School of Science, Graduate University for Advanced Studies (SOKENDAI)（高级研究院天文学系）；National Institute of Technology, Kure College（国立高等专门学校呉高专）；Korea Astronomy and Space Science Institute（韩国天文与空间科学院）；University of Science and Technology（科学技术联合研究生院）
We consider the evolution of supermassive black hole binaries at the center of spherical, axisymmetric, and triaxial galaxies, using direct N-body integrations as well as analytic estimates. We find that the rates of binary hardening exhibit a significant N-dependence in all the models, at least for N in the investigated range of 10^5<=N<=10^6. Binary hardening rates are also substantially lower than would be expected if the binary loss cone remained full, as it would be if the orbits supplying stars to the binary were being efficiently replenished. The difference in binary hardening rates bet…
