Supermassive stars (SMSs) with mass $\sim10^{5}~\rm{M}_{\odot}$ are promising candidates for the origin of supermassive black holes observed at redshift $\gtrsim6$. They are supposed to form as a result of rapid accretion of primordial gas, although it can be obstructed by the time variation caused by circum-stellar disc fragmentation due to gravitational instability. To assess the occurrence of fragmentation, we study the structure of marginally gravitationally unstable accretion discs, by using a steady one-dimensional thin disc model with detailed treatment of chemical and thermal processes. Motivated by two SMS formation scenarios, i.e., those with strong ultraviolet radiation background or with large velocity difference between the baryon and the dark matter, we consider two types of flows, i.e., atomic and molecular flows, respectively, for a wide range of the central stellar mass $10-10^5~\rm{M}_{\odot}$ and the accretion rate $10^{-3}-1~\rm{M}_{\odot}~\rm{yr}^{-1}$. In the case of a mostly atomic gas flowing to the disc outer boundary, the fragmentation condition is expressed as the accretion rate being higher than the critical value of $10^{-1}~\rm{M}_{\odot}~\rm{yr}^{-1}$ regardless of the central stellar mass. On the other hand, in the case of molecular flows, there is a critical disc radius outside of which the disc becomes unstable. Those conditions appears to be marginally satisfied according to numerical simulations, suggesting that disc fragmentation can be common during SMS formation.
The ngVLA will facilitate deep surveys capable of detecting the faint and compact signatures of accreting supermassive black holes (SMBHs) with masses below one million solar-masses hosted by low-mass ($< 10^9$ solar-masses) galaxies. This will provide important new insights on both the origins of supermassive black holes and the possible impact of active galactic nucleus-driven feedback in a currently unexplored mass regime.
In hierarchical structure formation scenarios, merging galaxies are expected to be seen in different phases of their coalescence. Simulations suggest that simultaneous activity of the supermassive black holes (SMBHs) in the centres of the merging galaxies may be expected at kpc-scale separations. Currently, there are no direct observational methods which allow the selection of a large number of such dual active galactic nuclei (AGN) candidates. SDSS J142507.32+323137.4 was reported as a promising candidate source based on its optical spectrum. Here we report on our sensitive e-MERLIN observati…
The impact of Active Galactic Nuclei (AGN) on star formation has implications for our understanding of the relationships between supermassive black holes and their galaxies, as well as for the growth of galaxies over the history of the Universe. We report on a high-resolution multi-phase study of the nuclear environment in the nearby Seyfert galaxy NGC 2110 using the Atacama Large Millimeter Array (ALMA), Hubble and Spitzer Space Telescopes, and the Very Large Telescope/SINFONI. We identify a region that is markedly weak in low-excitation CO $2\rightarrow1$ emission from cold molecular gas, bu…
Distinguishing the photon output of an accreting supermassive black hole binary system from that of a single supermassive black hole accreting at the same rate is intrinsically difficult because the majority of the light emerges from near the ISCOs of the black holes. However, there are two possible signals that can distinctively mark binaries, both arising from the gap formed in circumbinary accretion flows inside approximately twice the binary separation. One of these is a "notch" cut into the thermal spectra of these systems in the IR/optical/UV, the other a periodically-varying excess hard…
Supermassive stars (SMSs) with $\sim10^{4-5}~\mathrm{M}_{\odot}$ are candidate objects for the origin of supermassive black holes observed at redshift $z$>6. They are supposed to form in primordial-gas clouds that provide the central stars with gas at a high accretion rate, but their growth may be terminated in the middle due to the stellar ionizing radiation if the accretion is intermittent and its quiescent periods are longer than the Kelvin-Helmholtz (KH) timescales at the stellar surfaces. In this paper, we examine the role of the ionizing radiation feedback based on the accretion history …
Major mergers of gas-rich galaxies provide promising conditions for the formation of supermassive black holes (SMBHs; $\gtrsim10^5$ M$_\odot$) by direct collapse because they can trigger mass inflows as high as $10^4-10^5$ M$_\odot$ yr$^{-1}$ on sub-parsec scales. However, the channel of SMBH formation in this case, either dark collapse (direct collapse without prior stellar phase) or supermassive star (SMS; $\gtrsim10^4$ M$_\odot$), remains unknown. Here, we investigate the limit in accretion rate up to which stars can maintain hydrostatic equilibrium. We compute hydrostatic models of SMSs ac…
Supermassive stars born in pristine environments in the early Universe hold the promise of being the seeds for the supermassive black holes observed as high redshift quasars shortly after the epoch of reionisation. H$_2$ suppression is thought to be crucial in order to negate normal Population III star formation and allow high accretion rates to drive the formation of supermassive stars. Only in the cases where vigorous fragmentation is avoided will a monolithic collapse be successful giving rise to a single massive central object. We investigate the number of fragmentation sites formed in col…
Supermassive stars (SMSs; >10^5 Msun) formed in the first protogalaxies with virial temperature T_vir>10^4 K are expected to collapse into seeds of supermassive black hole (SMBHs) in the high-redshift universe (z>7). Fragmentation of the primordial gas is, however, a possible obstacle to SMS formation. We discuss the expected properties of a compact, metal-free, marginally unstable nuclear protogalactic disk, and the fate of the clumps formed in the disk by gravitational instability. Interior to a characteristic radius R_f=few*10^{-2} pc, the disk fragments into massive clumps with M_c~30 Msun…
The vast majority of supermassive black holes (SMBHs) in the local universe exhibit levels of activity much lower than those expected from gas supplying rates onto the galactic nuclei, and only a small fraction of silent SMBHs can turn into active galactic nuclei. Revisiting observational data of very nearby SMBHs whose gravitational spheres of influence are spatially reached by the Chandra X-ray satellite, we find that the level of BH activity drastically increases from the quiescent phase when the inflow rate outside of the BH influence radius is higher than 0.1% of the Eddington accretion r…
The formation of supermassive stars (SMSs) is a possible pathway to seed supermassive black holes in the early universe. This chapter summarizes recent theoretical efforts to understand their evolution, highlighting effects of very rapid accretion at the rates of $\dot{M}_* \gtrsim 0.1~$M$_\odot$ yr$^{-1}$. Stellar evolution calculations predict that such an accreting SMS has a characteristic feature, i.e., a very large radius that monotonically increases as the stellar mass increases. The radius exceeds $7000$ R$_\odot$ (or $30$ AU) after the star accretes the gas of more than $10^3$ M$_\odot…
Disc-driven migration is a key evolutionary stage of supermassive black-hole binaries hosted in gas-rich galaxies. Besides promoting the inspiral, viscous interactions tend to align the spins of the black holes with the orbital angular momentum of the disc. We present a critical and systematic investigation of this problem, also known as the Bardeen-Petterson effect. We design a new iterative scheme to solve the non-linear dynamics of warped accretion discs under the influence of both relativistic frame dragging and binary companion. We characterize the impact of the disc "critical obliquity",…
The origin of supermassive black holes (with $\gtrsim\!10^9\,M_{\odot}$) in the early universe (redshift $z \sim 7$) remains poorly understood. Gravitational collapse of a massive primordial gas cloud is a promising initial process, but theoretical studies have difficulty growing the black hole fast enough. We focus on the magnetic effects on star formation that occurs in an atomic-cooling gas cloud. Using a set of three-dimensional magnetohydrodynamic (MHD) simulations, we investigate the star formation process in the magnetized atomic-cooling gas cloud with different initial magnetic field s…
Accreting supermassive black holes (SMBHs) can exhibit variable emission across the electromagnetic spectrum and over a broad range of timescales. The variability of active galactic nuclei (AGNs) in the ultraviolet and optical is usually at the few tens of per cent level over timescales of hours to weeks. Recently, rare, more dramatic changes to the emission from accreting SMBHs have been observed, including tidal disruption events, 'changing look' AGNs and other extreme variability objects. The physics behind the 're-ignition', enhancement and 'shut-down' of accretion onto SMBHs is not entire…
The detection and characterization of supermassive black holes (SMBHs) in local low mass galaxies is crucial to our understanding of the origins of SMBHs. This statement assumes that low mass galaxies have had a relatively quiet cosmic history, so that their black holes have not undergone significant growth and therefore can be treated as relics of the original SMBH seeds. While recent studies have found optical signatures of active galactic nuclei (AGNs) in a growing population of dwarf galaxies, these studies are biased against low metallicity and relatively merger-free galaxies, thus missin…
The close neighbourhood of a supermassive black hole contains not only accreting gas and dust, but also stellar-sized objects like stars, stellar-mass black holes, neutron stars, and dust-enshrouded objects that altogether form a dense nuclear star-cluster. These objects interact with the accreting medium and they perturb the otherwise quasi-stationary configuration of the accretion flow. We investigate how the passages of a star can influence the black hole gaseous environment with GRMHD 2D and 3D simulations. We focus on the changes in the accretion rate and the associated emergence of outfl…
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…
(Abridged) We study stability of gas accretion in Active Galactic Nuclei. Our grid based simulations cover a radial range from 0.1 to 200 pc. Here, as in previous studies by our group, we include gas radiative cooling as well as heating by a sub-Eddington X-ray source near the central supermassive black hole of 10^8 M_{\odot}. Our theoretical estimates and simulations show that for the X-ray luminosity L_X \sim 0.008 L_{Edd}, the gas is thermally and convectivelly unstable within the computational domain. In the simulations, we observe that very tiny fluctuations in an initially smooth, spheri…
The formation of supermassive stars is believed to be an essential intermediate step for the formation of the massive black hole seeds that become the supermassive black holes powering the quasars observed in the early Universe. Numerical simulations have shown that supermassive stars can form in atomic-cooling halos when protostars reach accretion rates higher than $\sim10^{-2}$ M$_\odot$ yr$^{-1}$ and fragmentation is suppressed on pc scales. It is however still uncertain if a supermassive star still emerges when fragmentation occurs at smaller scales and a cluster of stars is formed instead…
Supermassive primordial stars are suspected to be the progenitors of the most massive quasars at z~6. Previous studies of such stars were either unable to resolve hydrodynamical timescales or considered stars in isolation, not in the extreme accretion flows in which they actually form. Therefore, they could not self-consistently predict their final masses at collapse, or those of the resulting supermassive black hole seeds, but rather invoked comparison to simple polytropic models. Here, we systematically examine the birth, evolution and collapse of accreting non-rotating supermassive stars un…
We have performed cosmological hydrodynamic simulations to study the effect of fragmentation on the SMBH seed mass in the direct collapse formation scenario. We considered different background UV intensities, host halo spin, and halo merger histories. Our simulations in low-spin halos, in the presence of a strong UV background are consistent with the Direct Collapse Black Hole model, in which a single massive object $\sim10^5$ M$_{\odot}$ is formed in the center of a proto-galaxy. While in our simulations under the presence of a low UV background, we find fragmentation and the formation of var…
Recent observations have shown that a large portion of the mid--infrared (MIR) spectrum of active galactic nuclei (AGN) stems from the polar regions. In this paper, we investigate the effects of this polar gas on the X-ray spectrum of AGN using ray-tracing simulations. Two geometries for the polar gas are considered, (1) a hollow cone corresponding to the best fit MIR model and (2) a filled cone, both with varying column densities (ranging from $10^{21}-10^{22.5}$ cm$^{-2}$) along with a torus surrounding the central X-ray source. We find that the polar gas leads to an increase in the equivale…
We show results from the radiation hydrodynamics (RHD) simulations of tidal disruption of a star on a parabolic orbit by a supermassive black hole (SMBH) based on a three-dimensional smoothed particle hydrodynamics code with radiative transfer. We find that such a tidally disrupted star fragment and form clumps soon after its tidal disruption. The fragmentation results from the endothermic processes of ionization and dissociation that reduce the gas pressure, leading to local gravitational collapse. Radiative cooling is less effective because the stellar debris is still highly optically thick …
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 …
The effect of pressure confinement on the maximum mass of rapidly accreting supermassive stars
Niels Bohr International Academy, The Niels Bohr Institute（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所）；Center of Gravity, Niels Bohr Institute（引力中心，尼尔斯·玻尔研究所）；Institute of Science and Technology Austria (ISTA)（奥地利科学与技术研究所）
We use smoothed particle hydrodynamic simulations to investigate the growth of perturbations in infinitely long, initially sub-critical but accreting filaments. The growth of these perturbations leads to filament fragmentation and the formation of cores. Most previous work on this subject has been confined to the growth and fragmentation of equilibrium filaments and has found that there exists a preferential fragmentation length scale which is roughly 4 times the filament's diameter. Our results show a more complicated dispersion relation with a series of peaks linking perturbation wavelength …
Variability of active galactic nuclei is not well understood. One possible explanation is existence of supermassive binary black holes (SMBBH) in their centres. It is expected that major mergers are common in the Universe. It is expected that each supermassive black hole of every galaxy eventually finish as a SMBBH system in the core of newly formed galaxy. Here we model the emission line profiles of active galactic nuclei (AGN) assuming that the flux and emission line shapes variation are induced by supermassive binary black hole systems (SMBBH). We assume that accreting gas inside of circumb…
Supermassive primordial stars in hot, atomically-cooling haloes at $z \sim$ 15 - 20 may have given birth to the first quasars in the universe. Most simulations of these rapidly accreting stars suggest that they are red, cool hypergiants, but more recent models indicate that some may have been bluer and hotter, with surface temperatures of 20,000 - 40,000 K. These stars have spectral features that are quite distinct from those of cooler stars and may have different detection limits in the near infrared (NIR) today. Here, we present spectra and AB magnitudes for hot, blue supermassive primordial…
We present 1-second cadence observations of M32 (NGC221) with the CHIMERA instrument at the Hale 200-inch telescope of the Palomar Observatory. Using field stars as a baseline for relative photometry, we are able to construct a light curve of the nucleus in the g-prime and r-prime band with 1sigma=36 milli-mag photometric stability. We derive a temporal power spectrum for the nucleus and find no evidence for a time-variable signal above the noise as would be expected if the nuclear black hole were accreting gas. Thus, we are unable to constrain the spin of the black hole although future work w…
We studied the gravitational collapse of a warm (~8000 K) primordial-gas cloud as a candidate progenitor for a supermassive star (SMS; >10^5 Msun) using a three-dimensional hydrodynamical simulation, including all the relevant cooling processes of both H_2 and H, which can potentially induce cloud fragmentation. This is the first simulation of this kind to resolve protostar formation. We find that the cloud undergoes runaway collapse without a major episode of fragmentation. Although the H_2 fraction jumps by a large factor via the three-body reaction at ~10^-13 g/cm^3, its cooling remains ine…
We have modeled direct collapse of a primordial gas within dark matter halos in the presence of radiative transfer, in high-resolution zoom-in simulations in a cosmological framework, down to the formation of the photosphere and the central object. Radiative transfer has been implemented in the flux-limited diffusion (FLD) approximation. Adiabatic models were run for comparison. We find that (a) the FLD flow forms an irregular central structure and does not exhibit fragmentation, contrary to adiabatic flow which forms a thick disk, driving a pair of spiral shocks, subject to Kelvin-Helmholtz s…
Direct collapse black hole (DCBH) formation with mass $\gtrsim 10^{5}~M_{\odot}$ is a promising scenario for the origin of high-redshift supermassive black holes. It has usually been supposed that the DCBH can only form in the primordial gas since the metal enrichment enhances the cooling ability and causes the fragmentation into smaller pieces. What actually happens in such an environment, however, has not been explored in detail. Here, we study the impact of the metal enrichment on the clouds, conducting hydrodynamical simulations to follow the cloud evolution in cases with different degree …
Little Red Dots as self-gravitating discs accreting on supermassive stars: Spectral appearance and formation pathway of the progenitors to direct collapse black holes
Niels Bohr International Academy, The Niels Bohr Institute（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所）；Center of Gravity, Niels Bohr Institute（引力中心，尼尔斯·玻尔研究所）；Department of Astrophysics, University of Zurich（苏黎世大学天体物理学系）
Disk truncation triggers relativistic jet launching of a highly accreting supermassive black hole
Tohoku University（东北大学）；Nagoya City University（名古屋市立大学）；National Astronomical Observatory of Japan（日本国立天文台）；University of Miyazaki（宫崎大学）；The University of Osaka（大阪大学）；Shibaura Institute of Technology（芝浦工业大学）；National Institute of Technology, Ichinoseki College（国立工学期仙学院）
Determining the mechanisms that formed and grew the first supermassive black holes is one of top priorities in extragalactic astrophysics. Observational clues can be inferred from the demographics of massive black holes (in the ten thousand through million Solar mass range) in nearby low-mass galaxies. This chapter of the next generation Very Large Array (ngVLA) Science Book describes how an ngVLA can play a prominent role in developing large samples of weakly accreting active galactic nuclei in low-mass galaxies (out to nearly 1 Gpc), which will help constrain the types of objects that origin…
We study the gravitational fragmentation of circumstellar discs accreting extremely metal-poor ($Z \leq 10^{-3}$ Zsun) gas, performing a suite of three-dimensional hydrodynamic simulations using the adaptive mesh refinement code Enzo. We systematically follow the long-term evolution for 2000 years after the first protostar's birth, for the cases of $Z = 0$, $10^{-5}$, $10^{-4}$, and $10^{-3}$ Zsun. We show that evolution of number of self-gravitating clumps qualitatively changes with $Z$. Vigorous fragmentation induced by dust cooling occurs in the metal-poor cases, temporarily providing about…
Observational evidence suggests that some very large supermassive black holes (SMBHs) already existed less than 1 Gyr after the Big Bang. Explaining the formation and growth of the 'seeds' of these SMBHs is quite challenging. We explore the formation of such seeds in the direct collapse scenario. Using 3D hydrodynamical simulations, we investigate the impact of turbulence and rotation on the fragmentation behavior of collapsing primordial gas in the presence of a strong UV radiation background, which keeps the gas hot. Additionally, we explore different ways in which the collapsing gas may be …
Major galaxy mergers are thought to play an important part in fuelling the growth of supermassive black holes. However, observational support for this hypothesis is mixed, with some studies showing a correlation between merging galaxies and luminous quasars and others showing no such association. Recent observations have shown that a black hole is likely to become heavily obscured behind merger-driven gas and dust, even in the early stages of the merger, when the galaxies are well separated (5 to 40 kiloparsecs). Merger simulations further suggest that such obscuration and black-hole accretion…
Galaxy-scale outflows powered by actively accreting supermassive black holes are routinely detected, and they have been associated both with suppression and triggering of star formation. Recent observational evidence and simulations are favouring a delayed mechanism that connects outflows and star formation
Under rapid cooling from molecular hydrogen, the accretion disks around Population III (PopIII) stars are believed to fragment, resulting in multiple accreting cores. In this paper, we build a theoretical framework for calculating the optical depth of H$_2$ ro-vibrational line cooling based on the vertical structure in these accretion disks. Applying this physically motivated prescription for the optical depth, we find that cooling in the inner disk with $r \lesssim 10 {\rm\ AU}$ is attenuated significantly as a result of high surface density; $PdV$ heating becomes more efficient than cooling,…
Numerical simulations have shown the occurence of a scenario termed ''super-competitive accretion'', a term that describes a situation where only the central few objects grow supermassive while a larger number of stars compete for the reservoir, with significant accretion flows of $\gtrsim0.1$ M$_\odot$ yr$^{-1}$. This scenario particularly implies that the presence of fragmentation will not necessarily impeed the formation of a central massive object. We here explore this phenomenon using analytical estimates for growth via collisions and accretion, considering accretion due to self-gravity a…
Formation of supermassive stars (SMSs) with mass ~10^4 Msun is a promising pathway to seed the formation of supermassive black holes in the early universe. The so-called direct-collapse (DC) model postulates that such an SMS forms in a hot gas cloud irradiated by a nearby star-forming galaxy. We study the DC SMS formation in a fully cosmological context using three-dimensional radiation hydrodynamics simulations. We initialize our simulations using the outputs of the cosmological simulation of Chon et al. (2016), where two DC gas clouds are identified. The long-term evolution over a hundred th…
The detection of $\rm z>6$ quasars reveals the existence of supermassive black holes of a few $\rm 10^9~M_{\odot}$. One of the potential pathways to explain their formation in the infant universe is the so-called direct collapse model which provides massive seeds of $\rm 10^5-10^6~M_{\odot}$. An isothermal direct collapse mandates that halos should be of a primordial composition and the formation of molecular hydrogen remains suppressed in the presence of a strong Lyman Werner flux. In this study, we perform high resolution cosmological simulations for two massive primordial halos employing a …
In this paper, we investigate the influences of two continuum radiation pressures of the central engines on the black hole mass estimates for 40 active galactic nuclei (AGNs) with high accretion rates. The two continuum radiation pressure forces, usually believed negligible or not considered, are from the free electron Thomson scattering, and the recombination and re-ionization of hydrogen ions that continue to absorb ionizing photons to compensate for the recombination. The masses counteracted by the two radiation pressures $M_{\rm{RP}}$ depend sensitively on the percent of ionized hydrogen i…
The Millimeter/X-ray Relation in Rapidly Accreting Supermassive Black Holes at $z < 0.16$
Universidad Diego Portales（迭戈·波特莱斯大学）；University of Geneva（日内瓦大学）；Peking University（北京大学）；Chalmers University of Technology（查尔姆斯理工大学）；Liège Université（列日大学）；Universiteit Gent（根特大学）；Leibniz-Institut für Astrophysik Potsdam (AIP)（波茨坦阿斯特罗物理学会莱布尼茨研究所）；Joint ALMA Observatory（ALMA联合天文台）
We study the gas accretion onto a supermassive black hole (SMBH) using the 3D SPH code GADGET-3 on scales of 0.1-200 pc. First we test our code with spherically symmetric, adiabatic Bondi accretion problem. We find that our simulation can reproduce the expected Bondi accretion flow very well for a limited amount of time until the effect of outer boundary starts to be visible. We also find artificial heating of gas near the inner accretion boundary due to the artificial viscosity of SPH. Second, we implement radiative cooling and heating due to X-rays, and examine the impact of thermal feedback…
The collapse of supermassive primordial stars in hot, atomically-cooled halos may have given birth to the first quasars at $z \sim$ 15 - 20. Recent numerical simulations of these rapidly accreting stars reveal that they are cool, red hypergiants shrouded by dense envelopes of pristine atomically-cooled gas at 6,000 - 8,000 K, with luminosities $L$ $\gtrsim$ 10$^{10}$ L$_{\odot}$. Could such luminous but cool objects be detected as the first stage of quasar formation in future near infrared (NIR) surveys? We have now calculated the spectra of supermassive primordial stars in their birth envelop…
In this paper we report on the formation of magnetically-levitating accretion disks around supermassive black holes. The structure of these disks is calculated by numerically modelling tidal disruption of magnetized interstellar gas clouds. We find that the resulting disks are entirely supported by the pressure of the magnetic fields against the component of gravitational force directed perpendicular to the disks. The magnetic field shows ordered large-scale geometry that remains stable for the duration of our numerical experiments extending over 10% of the disk lifetime. Strong magnetic press…
Supermassive stars have been proposed as the progenitors of the massive ($\sim 10^{9}\,\rm{M}_{\odot}$) quasars observed at $z\sim7$. Prospects for directly detecting supermassive stars with next-generation facilities depend critically on their intrinsic lifetimes, as well as their formation rates. We use the 1D stellar evolution code Kepler to explore the theoretical limiting case of zero-metallicity, non-rotating stars, formed monolithically with initial masses between $10\,\rm{kM}_{\odot}$ and $190\,\rm{kM}_{\odot}$. We find that stars born with masses between $\sim60\,\rm{kM}_{\odot}$ and …
We simulate recoiling black hole trajectories from $z=20$ to $z=0$ in dark matter halos, quantifying how parameter choices affect escape velocities. These choices include the strength of dynamical friction, the presence of stars and gas, the accelerating expansion of the universe (Hubble acceleration), host halo accretion and motion, and seed black hole mass. $Λ$CDM halo accretion increases escape velocities by up to 0.6 dex and significantly shortens return timescales compared to non-accreting cases. Other parameters change orbit damping rates but have subdominant effects on escape velocities…
