In this paper, we revisit the issue of estimating the "fossil" disc mass in the circumprimary disc, during the merger of a supermassive black hole binary. As the binary orbital decay speeds up due to the emission of gravitational waves, the gas in the circumprimary disc might be forced to accrete rapidly and could in principle provide a significant electromagnetic counterpart to the gravitational wave emission. Since the luminosity of such flare is proportional to the gaseous mass in the circumprimary disc, estimating such mass accurately is important. Previous investigations of this issue have produced contradictory results, with some authors estimating super-Eddington flares and large disc mass, while others suggesting that the "fossil" disc mass is very low, even less than a Jupiter mass. Here, we perform simple 1D calculations to show that such very low estimates of the disc mass are an artifact of the specific implementation of the tidal torque in 1D models. In particular, for moderate mass ratios of the binary, the usual formula for the torque used in 1D models significantly overestimates the width of the gap induced by the secondary and this artificially leads to a very small leftover circumprimary disc. Using a modified torque, calibrated to reproduce the correct gap width as estimated by 3D models, leads to fossil disc masses of the order of one solar mass. The rapid accretion of the whole circumprimary disc would produce peak luminosities of the order of 1-20 times the Eddington luminosity. Even if a significant fraction of the gas escapes accretion by flowing out the secondary orbit during the merger (an effect not included in our calculations), we would still predict close to Eddington luminosities that might be easily detected.
Using a one-dimensional height integrated model, we calculate the evolution of an unequal mass binary black hole with a coplanar gas disk that contains a gap due to the presence of the secondary black hole. Viscous evolution of the outer circumbinary disk initially hardens the binary, while the inner disk drains onto the primary (central) black hole. As long as the inner disk remains cool and thin at low $\dot{M}_{\rm ext}$ (rather than becoming hot and geometrically thick), the mass of the inner disk reaches an asymptotic mass typically $\sim 10^{-3}-10^{-4}\Msun$. Once the semimajor axis shr…
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")…
The merger rate of stellar-mass black hole binaries (sBHBs) inferred by the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) suggests the need for an efficient source of sBHB formation. Active galactic nucleus (AGN) disks are a promising location for the formation of these sBHBs, as well as binaries of other compact objects, because of powerful torques exerted by the gas disk. These gas torques cause orbiting compact objects to migrate towards regions in the disk where inward and outward torques cancel, known as migration traps. We simulate the migration of stellar mass blac…
An extraordinary recent development in astrophysics was the discovery of the fossil relationship between central black hole mass and the stellar mass of galactic bulges. The physical process underpinning this relationship has become known as feedback. The Chandra X-ray Observatory was instrumental in realizing the physical basis for feedback, by demonstrating a tight coupling between the energy released by supermassive black holes and the gaseous structures surrounding them. This white paper discusses how a great leap forward in X-ray collecting area and spectral resolution will allow a qualit…
Accretion disks around supermassive black holes (SMBHs) in active galactic nuclei contain stars, stellar mass black holes, and other stellar remnants, which perturb the disk gas gravitationally. The resulting density perturbations in turn exert torques on the embedded masses causing them to migrate through the disk in a manner analogous to the behavior of planets in protoplanetary disks. We determine the strength and direction of these torques using an empirical analytic description dependent on local disk gradients, applied to two different analytic, steady-state disk models of SMBH accretion…
We propose a new spectral signature for supermassive black hole binaries (SMBHBs) with circumbinary gas disks: a sharp drop in flux blueward of the Lyman limit. A prominent edge is produced if the gas dominating the emission in the Lyman continuum region of the spectrum is sufficiently cold (T < 20,000 K) to contain significant neutral hydrogen. Circumbinary disks may be in this regime if the binary torques open a central cavity in the disk and clear most of the hot gas from the inner region, and if any residual UV emission from the individual BHs is either dim or intermittent. We model the ve…
We consider warped equilibrium configurations for stellar and gaseous disks in the Keplerian force-field of a supermassive black hole, assuming that the self-gravity of the disk provides the only acting torques. Modeling the disk as a collection of concentric circular rings, and computing the torques in the non-linear regime, we show that stable, strongly warped precessing equilibria are possible. These solutions exist for a wide range of disk-to-black hole mass ratios $M_d/M_{bh}$, can span large warp angles of up to $\pm\sim 120°$, have inner and outer boundaries, and extend over a radial ra…
The transient Swift J1644+57 is believed to have been produced by an unlucky star wandering too close to a supermassive black hole (BH) leading to a tidal disruption event. This unusual flare displayed highly super-Eddington X-ray emission which likely originated in a relativistic, collimated jet. This presents challenges to modern accretion and jet theory as upper limits of prior BH activity, which we obtain from the radio afterglow of this event, imply that both the pre-disruption BH and stellar magnetic fluxes fall many orders of magnitude short of what is required to power the observed X-r…
Accretion discs are common in binary systems, and they are often found to be misaligned with respect to the binary orbit. The gravitational torque from a companion induces nodal precession in misaligned disc orbits. We calculate whether this precession is strong enough to overcome the internal disc torques communicating angular momentum. For typical parameters precession wins: the disc breaks into distinct planes that precess effectively independently. We run hydrodynamical simulations to check these results, and confirm that disc breaking is widespread and generally enhances accretion on to t…
Many galaxies are expected to harbor binary supermassive black holes (SMBHs) in their centers. Their interaction with the surrounding gas results in accretion and exchange of angular momentum via tidal torques, facilitating binary inspiral. Here we explore the non-trivial coupling between these two processes and analyze how the global properties of externally supplied circumbinary disks depend on the binary accretion rate. By formulating our results in terms of the angular momentum flux driven by internal stresses, we come up with a very simple classification of the possible global disk struct…
The physics of angular momentum transport from galactic scales (~10-100 pc) to much smaller radii is one of the oustanding problems in our understanding of the formation and evolution of super-massive black holes (BHs). Seemingly unrelated observations have discovered that there is a lopsided stellar disk of unknown origin orbiting the BH in M31, and possibly many other systems. We show that these nominally independent puzzles are in fact closely related. Multi-scale simulations of gas inflow from galactic to BH scales show that when sufficient gas is driven towards a BH, gravitational instabi…
After the Tidal Disruption Event (TDE) of a star around a SuperMassive Black Hole (SMBH), the bound stellar debris rapidly forms an accretion disk. If the accretion disk is not aligned with the spinning SMBH's equatorial plane, the disk will be driven into Lense-Thirring precession around the SMBH's spin axis, possibly affecting the TDE's light curve. We carry out an eigenmode analysis of such a disk to understand how the disk's warp structure, precession, and inclination evolution are influenced by the disk's and SMBH's properties. We find an oscillatory warp may develop as a result of strong…
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…
We consider the evolution of a supermassive black hole binary (SMBHB) surrounded by a retrograde accretion disk. Assuming the disk is exactly in the binary plane and transfers energy and angular momentum to the binary via direct gas accretion, we calculate the time evolution of the binary's semi-major axis $a$ and eccentricity $e$. Because the gas is predominantly transferred when the binary is at apocenter, we find the eccentricity grows rapidly while maintaining constant $a(1+e)$. After accreting only a fraction of the secondary's mass, the eccentricity grows to nearly unity; from then on, g…
The population of stellar black holes (SBHs) in the Galaxy and galaxies generally is poorly known in both number and distribution. SBHs are the fossil record of the massive stars in galaxy evolution and may have produced some (if not all) of the intermediate mass (\gsim100\Msun) black holes (IMBHs) and, in turn, the central supermassive black holes (SMBHs) in galactic nuclei. For the first time, a Galaxy-wide census of accreting black holes, and their more readily recognizable tracer population, accreting neutron stars (NSs), could be measured with a wide-field hard X-ray imaging survey and so…
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…
Accretion discs are present around both stellar-mass black holes in X-ray binaries and supermassive black holes in active galactic nuclei. A wide variety of circumstantial evidence implies that many of these discs are warped. The standard Bardeen--Petterson model attributes the shape of the warp to the competition between Lense--Thirring torque from the central black hole and viscous angular-momentum transport within the disc. We show that this description is incomplete, and that torques from the companion star (for X-ray binaries) or the self-gravity of the disc (for active galactic nuclei) c…
Orbital Migration of Interacting Stellar Mass Black Holes in Disks around Supermassive Black Holes. III. Mass Distribution of Hierarchical Mergers
Lunar and Planetary Laboratory, University of Arizona（亚利桑那大学）；Center for Computational Astrophysics, Flatiron Institute（平顿研究所计算天体物理学中心）；Department of Astrophysics, American Museum of Natural History（美国自然历史博物馆天体物理系）；Department of Science, CUNY Borough of Manhattan Community College（纽约市立大学曼哈顿社区学院科学系）；Physics Program, CUNY Graduate Center（纽约市立大学研究生中心物理项目）；Heidelberg Institute for Theoretical Studies（海德堡理论研究所）；Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut（海德堡大学天文中心天文计算研究所）
We study the circularization of tidally disrupted stars on bound orbits around spinning supermassive black holes by performing three-dimensional smoothed particle hydrodynamic simulations with Post-Newtonian corrections. Our simulations reveal that debris circularization depends sensitively on the efficiency of radiative cooling. There are two stages in debris circularization if radiative cooling is inefficient: first, the stellar debris streams self-intersect due to relativistic apsidal precession; shocks at the intersection points thermalize orbital energy and the debris forms a geometricall…
We study the warping and tearing of a geometrically thin, non-self-gravitating disk surrounding binary supermassive black holes on an eccentric orbit. The circumbinary disk is significantly misaligned with the binary orbital plane, and is subject to the time-dependent tidal torques. In principle, such a disk is warped and precesses, and is torn into mutually misaligned rings in the region, where the tidal precession torques are stronger than the local viscous torques. We derive the tidal-warp and tearing radii of the misaligned circumbinary disks around eccentric SMBH binaries. We find that in…
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>…
Among the potential milliHz gravitational wave (GW) sources for the upcoming space-based interferometer LISA are extreme- or intermediate-mass ratio inspirals (EMRI/IMRIs). These events involve the coalescence of supermassive black holes in the mass range $10^5 M_{\odot} \lesssim M \lesssim 10^7 M_{\odot}$ with companion BHs of much lower masses. A subset of E/IMRIs are expected to occur in the accretion discs of active galactic nuclei (AGN), where torques exerted by the disc can interfere with the inspiral and cause a phase shift in the GW waveform. Here we use a suite of two-dimensional hydr…
Since the seminal work of Penrose (1969) and Blandford & Znajek (1977), it has been realized that black hole spin may be an important energy source in astrophysics. The radio-loud/radio-quiet dichotomy in the AGN population is usually attributed to differences in black hole spin, with correlations between black hole spin and host galaxy morphology being hypothesized in order to explain why radio-loud AGN occur in early-type galaxies. X-ray observations are uniquely able to answer: Does black hole spin play a crucial role in powering relativistic jets such as those seen from radio-loud active g…
The masses, rates, and spins of merging stellar-mass binary black holes (BBHs) detected by aLIGO and Virgo provide challenges to traditional BBH formation and merger scenarios. An active galactic nucleus (AGN) disk provides a promising additional merger channel, because of the powerful influence of the gas that drives orbital evolution, makes encounters dissipative, and leads to migration. Previous work showed that stellar mass black holes (sBHs) in an AGN disk migrate to regions of the disk, known as migration traps, where positive and negative gas torques cancel out, leading to frequent BBH …
Pulsar timing arrays (PTAs) are expected to detect gravitational waves (GWs) from individual low-redshift (z<1.5) compact supermassive (M>10^9 Msun) black hole (SMBH) binaries with orbital periods of approx. 0.1 - 10 yrs. Identifying the electromagnetic (EM) counterparts of these sources would provide confirmation of putative direct detections of GWs, present a rare opportunity to study the environments of compact SMBH binaries, and could enable the use of these sources as standard sirens for cosmology. Here we consider the feasibility of such an EM identification. We show that because the hos…
We study the interaction of a supermassive black hole (SMBH) binary and a standard radiatively efficient thin accretion disk. We examine steady-state configurations of the disk and migrating SMBH system, self-consistently accounting for tidal and viscous torques and heating, radiative diffusion limited cooling, gas and radiation pressure, and the decay of the binary's orbit. We obtain a "phase diagram" of the system as a function of binary parameters, showing regimes in which both the disk structure and migration have a different character. Although massive binaries can create a central gap in…
The coalescence of a compact object with a $10^{4}-10^{7} {\rm M_\odot}$ supermassive black hole (SMBH) produces mHz gravitational waves (GWs) detectable by the future Laser Interferometer Space Antenna (LISA). If such an inspiral occurs in the accretion disc of an active galactic nucleus (AGN), the gas torques imprint a small deviation in the GW waveform. Here we present two-dimensional hydrodynamical simulations with the moving-mesh code DISCO of a BH inspiraling at the GW rate in a binary system with a mass ratio $q\!=\!M_2/M_1\!=\!10^{-3}$, embedded in an accretion disc. We assume a locall…
We study the effects of a thin gaseous accretion disk on the inspiral of a stellar--mass black hole into a supermassive black hole. We construct a phenomenological angular momentum transport equation that reproduces known disk effects. Disk torques modify the gravitational wave phase evolution to detectable levels with LISA for reasonable disk parameters. The Fourier transform of disk-modified waveforms acquires a correction with a different frequency trend than post-Newtonian vacuum terms. Such inspirals could be used to detect accretion disks with LISA and to probe their physical parameters.
Electromagnetic alignment and jet precession around supermassive black holes: Quasi-periodic oscillations in tidal disruption events
Universitat Politècnica de València（瓦伦西亚理工大学）；Max Planck Institute for Extraterrestrial Physics（马克斯·普朗克地外物理研究所）；The Kavli Institute for Astronomy and Astrophysics（卡弗里天文学与天体物理研究所）；Beijing Institute of Mathematical Sciences and Applications（北京数学与应用科学研究所有限公司）；Department of Astronomy, School of Physics, Peking University（北京大学物理学院天文学系）
We present three-dimensional Smoothed Particle Hydrodynamics (SPH) simulations investigating the dependence of the accretion rate on the disc thickness around an equal-mass, circular black hole binary system. We find that for thick/hot discs, with $H/R\gtrsim 0.1$, the binary torque does not prevent the gas from penetrating the cavity formed in the disc by the binary (in line with previous investigations). The situation drastically changes for thinner discs, in this case the mass accretion rate is suppressed, such that only a fraction (linearly dependent on $H/R$) of the available gas is able …
Much of the parameter space relevant to the evolution of astrophysical circumbinary accretion discs remains unexplored. We have carried out a suite of circumbinary disc simulations surveying both disc thickness and kinematic viscosity, using both constant-$ν$ and constant-$α$ prescriptions. We focus primarily on disc aspect ratios between $0.1$ and $0.033$, and on viscosities between $ν=0.0005$ and $ν=0.008$ (in units of binary semi-major axis and orbital frequency), and specialise to circular equal-mass binaries. Both factors strongly influence the evolution of the binary semi-major axis: at …
In this work, we report a radio galaxy with precessing jets, double-peaked emission lines and the presence of two compact radio components with a projected separation of ~6 parsec in Very Long Baseline Interferometry (VLBI) observations. The emission line peak separations could be suggesting the presence of a supermassive black hole binary (BBH) with a separation of 6.3 parsec, matching the VLBI results. The kinematic jet precession model applied to the jets of J1328+2751 indicates that if it is a BBH, the accretion disk of the primary black hole is not coplanar with the binary system orbit, m…
I review accretion and outflow in active galactic nuclei. Accretion appears to occur in a series of very small--scale, chaotic events, whose gas flows have no correlation with the large--scale structure of the galaxy or with each other. The accreting gas has extremely low specific angular momentum and probably represents only a small fraction of the gas involved in a galaxy merger, which may be the underlying driver. Eddington accretion episodes in AGN must be common in order for the supermassive black holes to grow. I show that they produce winds with velocities $v \sim 0.1c$ and ionization p…
We compute the effect of an orbiting gas disc in promoting the coalescence of a central supermassive black hole binary. Unlike earlier studies, we consider a finite mass of gas with explicit time dependence: we do not assume that the gas necessarily adopts a steady state or a spatially constant accretion rate, i.e. that the merging black hole was somehow inserted into a pre--existing accretion disc. We consider the tidal torque of the binary on the disc, and the binary's gravitational radiation. We study the effects of star formation in the gas disc in a simple energy feedback framework. The d…
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 …
Accretion disks around supermassive black holes (SMBH) are promising sites for stellar mass black hole (BH) mergers due to mass segregation and merger acceleration by disk gas torques. Here we show that a GW-kick at BH merger causes ram-pressure stripping of gas within the BH Hill sphere. If $R_{H}\geq H$, the disk height, an off-center UV flare at $a_{\rm BH} \sim 10^{3}r_{g}$ emerges within $t_{\rm UV} \sim \rm{O}(2 {\rm days})(a_{\rm BH}/10^{3}r_{g})(M_{\rm SMBH}/10^{8}M_{\odot})(v_{\rm kick}/10^{2}\rm{km/s})$ post-merger and lasts O$(R_{H}/v_{\rm kick}) \sim \rm{O}(5 t_{\rm UV}$). The flar…
We investigate the role of the Keplerian tidal field generated by a supermassive black hole (SMBH) on the three-body dynamics of stellar mass black holes. We consider two scenarios occurring close to the SMBH: the breakup of unstable triples and three-body encounters between a binary and a single. These two cases correspond to the hard and soft binary cases, respectively. The tidal field affects the breakup of triples by tidally limiting the system, so that the triples break earlier with lower breakup velocity, leaving behind slightly larger binaries (relative to the isolated case). The breaku…
The recent advanced LIGO/Virgo detections of gravitational waves (GWs) from stellar binary black hole (BBH) mergers, in particular GW190521, which is potentially associated with a quasar, have stimulated renewed interest in active galactic nuclei (AGNs) as factories of merging BBHs. Compact objects evolving from massive stars are unavoidably enshrouded by a massive envelope to form accretion-modified stars (AMSs) in the dense gaseous environment of a supermassive black hole (SMBH) accretion disk. We show that most AMSs form binaries due to gravitational interaction with each other during radia…
The astrophysical origin of gravitational wave (GW) transients is a timely open question in the wake of discoveries by LIGO/Virgo. In active galactic nuclei (AGNs), binaries form and evolve efficiently by interaction with a dense population of stars and the gaseous AGN disk. Previous studies have shown that stellar-mass black hole (BH) mergers in such environments can explain the merger rate and the number of suspected hierarchical mergers observed by LIGO/Virgo. The binary eccentricity distribution can provide further information to distinguish between astrophysical models. Here we derive the…
Gravitational torques among objects orbiting a supermassive black hole drive the rapid reorientation of orbital planes in nuclear star clusters (NSCs), a process known as vector resonant relaxation. In this Letter, we determine the statistical equilibrium of systems with a distribution of masses, semimajor axes, and eccentricities. We average the interaction over the apsidal precession time and construct a Monte Carlo Markov chain method to sample the microcanonical ensemble of the NSC. We examine the case of NSCs formed by 16 episodes of star formation or globular cluster infall. We find that…
We consider misaligned accretion discs formed after tidal disruption events occurring when a star encounters a supermassive rotating black hole. We use the linear theory of warped accretion discs to find the disc shape when the stream produced by the disrupted star provides a source of mass and angular momentum that is misaligned with the black hole. The evolution of the surface density and aspect ratio is found from a one dimensional vertically averaged model. We extend previous work which assumed a quasi-stationary disc to allow unrestricted dynamical propagation of disc tilt and twist throu…
We carry out 2D viscous hydrodynamical simulations of circumbinary accretion using the AREPO code. 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 is reached, in which the mass supply rate at large distances $\dot{M}_0$ (assumed con…
We carry out 2D viscous hydrodynamics simulations of circumbinary disk (CBD) accretion using {\footnotesize AREPO}. We resolve the accretion flow from a large-scale CBD down to the streamers and disks around individual binary components. Extending our recent studies \citep{mun19}, we consider circular binaries with various mass ratios ($0.1\leq q_{\rm{b}}\leq1$) and study accretion from ``infinite'', steady-supply disks and from finite-sized, viscously spreading tori. For ``infinite'' disks, a global steady state can be reached, and the accretion variability has a dominant frequency ${\sim}0.2…
