Active Galactic Nuclei Disks Research Articles

Exploring the connection between AGN radiative feedback and massive black hole spin

We present a novel implementation for active galactic nucleus (AGN) feedback through ultrafast winds in the code GIZMO. Our feedback recipe accounts for the angular dependence of radiative feedback on black hole spin. We self-consistently evolve in time (i) the gas-accretion process from resolved scales to a smaller scale unresolved (subgrid) AGN disk, (ii) the evolution of the spin of the massive black hole (MBH), (iii) the injection of AGN-driven winds into the resolved scales, and (iv) the spin-induced anisotropy of the overall feedback process. We tested our implementation by following the propagation of the wind-driven outflow into an homogeneous medium, and here we present a comparison of the results against simple analytical models. We also considered an isolated galaxy setup, where the galaxy is thought to be formed from the collapse of a spinning gaseous halo, and there we studied the impact of the AGN feedback on the evolution of the MBH and of the host galaxy. We find that: (i) AGN feedback limits the gas inflow that powers the MBH, with a consequent weak impact on the host galaxy characterized by a suppression of star formation by about a factor of two in the nuclear (≲kpc) region; (ii) the impact of AGN feedback on the host galaxy and on MBH growth is primarily determined by the AGN luminosity rather than by its angular pattern set by the MBH spin (i.e., more luminous AGNs more efficiently suppress central star formation (SF), clearing wider central cavities and driving outflows with larger semiopening angles); (iii) the imprint of the angular pattern of AGN radiation emission is detected more clearly at high (i.e., Eddington) accretion rates. At such high rates, the more isotropic angular patterns, as occur for high spin values, sweep away gas in the nuclear region more easily, therefore causing a slower MBH mass and spin growths and a higher quenching of SF. We argue that the influence of spin-dependent anisotropy of AGN feedback on MBH and galaxy evolution is likely to be relevant in those scenarios characterized by high and prolonged MBH accretion episodes and by high AGN wind–galaxy coupling. Such conditions are more frequently met in galaxy mergers and/or high-redshift galaxies.

Radiation Hydrodynamic Simulations of Massive Stars in Gas-rich Environments: Accretion of AGN Stars Suppressed by Thermal Feedback

Massive stars may form in or be captured into active galactic nuclei (AGN) disks. Recent 1D studies employing stellar-evolution codes have demonstrated the potential for rapid growth of such stars through accretion up to a few hundred solar masses. We perform 3D radiation hydrodynamic simulations of moderately massive stars’ envelopes in order to determine the rate and critical radius R crit of their accretion process in an isotropic gas-rich environment in the absence of luminosity-driven mass loss. We find that in the “fast-diffusion” regime where characteristic radiative diffusion speed c/τ is faster than the gas sound speed c s , the accretion rate is suppressed by feedback from gravitational and radiative advection energy flux, in addition to the stellar luminosity. Alternatively, in the “slow-diffusion” regime where c/τ < c s , due to adiabatic accretion, the stellar envelope expands quickly to become hydrostatic and further net accretion occurs on thermal timescales in the absence of self-gravity. When the radiation entropy of the medium is less than that of the star, however, this hydrostatic envelope can become more massive than the star itself. Within this subregime, the self-gravity of the envelope excites runaway growth. Applying our results to realistic environments, moderately massive stars (≲100M ⊙) embedded in AGN disks typically accrete in the fast-diffusion regime, leading to a reduction of steady-state accretion rate 1–2 orders of magnitudes lower than expected by previous 1D calculations and R crit smaller than the disk scale height, except in the opacity window at temperature T ∼ 2000 K. Accretion in slow diffusion regime occurs in regions with very high density ρ ≳ 10−9 g cm−3, and needs to be treated with caution in 1D long-term calculations.

Studying Binary Formation under Dynamical Friction Using Hill’s Problem

Using the equations of motion from Hill’s problem, with added accelerations for different forms of dynamical friction, we provide the (to-date) broadest scale-free study of friction-driven binary formation in gaseous disks and stellar clusters. We focus mainly on binary formation between stellar-mass black holes in active galactic nuclei (AGNs), considering both gas dynamical friction (GDF) from AGN disks and stellar dynamical friction (SDF) from the nuclear star cluster. We first find simple, dimensionless friction coefficients that approximate the effects of standard models for GDF and SDF. We perform extensive simulations of Hill’s problem under such friction, and we present a picture of binary formation through encounters between single stars on nearby orbits, as a function of friction parameter, eccentricity, and inclination. Notably, we find that the local binary formation rate is a linear function of the friction coefficient so long as the friction is weak. Due to the dimensionless nature of our model problem, our findings are generalizable to binary formation at all scales (e.g., intermediate-mass black holes in a star cluster, planetesimals in a gaseous disk).

Afterglows from Binary Neutron Star Postmerger Systems Embedded in Active Galactic Nuclei Disks

The observability of afterglows from binary neutron star mergers occurring within active galactic nuclei (AGN) disks is investigated. We perform 3D GRMHD simulations of a postmerger system and follow the jet launched from the compact object. We use semianalytic techniques to study the propagation of the blast wave powered by the jet through an AGN disk-like external environment, extending to distances beyond the disk scale height. The synchrotron emission produced by the jet-driven forward shock is calculated to obtain the afterglow emission. The observability of this emission at different frequencies is assessed by comparing it to the quiescent AGN emission. In the scenarios where the afterglow could temporarily outshine the AGN, we find that detection will be more feasible at higher frequencies (≳1014 Hz) and the electromagnetic counterpart could manifest as a fast variability in the AGN emission, on timescales less than a day.

Disc novae: thermodynamics of gas-assisted binary black hole formation in AGN discs

ABSTRACT We investigate the thermodynamics of close encounters between stellar mass black holes (BHs) in the gaseous discs of active galactic nuclei (AGNs), during which binary black holes (BBHs) may form. We consider a suite of 2D viscous hydrodynamical simulations within a shearing box prescription using the Eulerian grid code athena++. We study formation scenarios where the fluid is either an isothermal gas or an adiabatic mixture of gas and radiation in local thermal equilibrium. We include the effects of viscous and shock heating, as well as optically thick cooling. We co-evolve the embedded BHs with the gas, keeping track of the energetic dissipation and torquing of the BBH by gas and inertial forces. We find that compared to the isothermal case, the minidiscs formed around each BH are significantly hotter and more diffuse, though BBH formation is still efficient. We observe massive blast waves arising from collisions between the radiative minidiscs during both the initial close encounter and subsequent periapsis periods for successfully bound BBHs. These ‘disc novae’ have a profound effect, depleting the BBH Hill sphere of gas and injecting energy into the surrounding medium. In analysing the thermal emission from these events, we observe periodic peaks in local luminosity associated with close encounters/periapses, with emission peaking in the optical/near-infrared (IR). In the AGN outskirts, these outbursts can reach 4 per cent of the AGN luminosity in the IR band, with flares rising over 0.5–1 yr. Collisions in different disc regions, or when treated in 3D with magnetism, may produce more prominent flares.

Concurrent Accretion and Migration of Giant Planets in Their Natal Disks with Consistent Accretion Torque

Migration commonly occurs during the epoch of planet formation. For emerging gas giant planets, it proceeds concurrently with their growth through the accretion of gas from their natal protoplanetary disks. A similar migration process should also be applied to the stellar-mass black holes embedded in active galactic nucleus disks. In this work, we perform high-resolution 3D and 2D numerical hydrodynamical simulations to study the migration dynamics for accreting embedded objects over the disk viscous timescales in a self-consistent manner. We find that an accreting planet embedded in a predominantly viscous disk has a tendency to migrate outward, in contrast to the inward orbital decay of nonaccreting planets. 3D and 2D simulations find the consistent outward migration results for the accreting planets. Under this circumstance, the accreting planet’s outward migration is mainly due to the asymmetric spiral arms feeding from the global disk into the Hill radius. This is analogous to the unsaturated corotation torque although the imbalance is due to material accretion within the libration timescale rather than diffusion onto the inner disk. In a disk with a relatively small viscosity, the accreting planets clear deep gaps near their orbits. The tendency of inward migration is recovered, albeit with suppressed rates. By performing a parameter survey with a range of disks’ viscosity, we find that the transition from outward to inward migration occurs with the effective viscous efficiency factor α ∼ 0.003 for Jupiter-mass planets.

High-energy Neutrinos from Outflows Powered by the Kicked Remnants of Binary Black Hole Mergers in Active Galactic Nucleus Accretion Disks

Merging of stellar-mass binary black holes (BBHs) could take place within the accretion disks of active galactic nuclei (AGN). The resulting BH remnant is likely to accrete the disk gas at a super-Eddington rate, launching a fast, quasi-spherical outflow (wind). Particles will be accelerated by shocks driven by the wind, subsequently interacting with the shocked disk gas or radiation field through hadronic processes and resulting in the production of high-energy neutrinos and potential electromagnetic (EM) emission. This study delves into the intricate evolution of the shock driven by a merged BH wind within an AGN disk. Subsequently, we calculated the production of neutrinos and the expected detection numbers for a single event, along with their contributions to the overall diffuse neutrino background. Our analysis, which considers various scenarios, reveals considerable neutrino production and possible detection by IceCube for nearby events. The contribution of merged BH winds on the diffuse neutrino background is minor due to the low event rate density, but it can be improved to some extent for some optimistic parameters. We also propose that there could be two neutrino/EM bursts, one originating from the premerger BBH wind and the other from the merged BH wind, with the latter typically having a delay to the gravitational wave (GW) event of around tens of days. When combined with the anticipated GWs emitted during the BBH merger, such a system emerges as a promising candidate for joint observations involving neutrinos, GWs, and EM signals.

Super-Eddington Magnetized Neutron Star Accretion Flows: A Self-similar Analysis

The properties of super-Eddington accretion disks exhibit substantial distinctions from the sub-Eddington ones. In this paper, we investigate the accretion process of a magnetized neutron star (NS) surrounded by a super-Eddington disk. By constructing self-similar solutions for the disk structure, we study in detail an interaction between the NS magnetosphere and the inner region of the disk, revealing that this interaction takes place within a thin boundary layer. The magnetosphere truncation radius is found to be approximately proportional to the Alfvén radius, with a coefficient ranging between 0.34–0.71, influenced by the advection and twisting of a magnetic field, NS rotation, and radiation emitted from an NS accretion column. Under super-Eddington accretion, the NS can readily spin up to become a rapid rotator. The proposed model can be employed to explore the accretion and evolution of NSs in diverse astrophysical contexts, such as ultraluminous X-ray binaries or active galactic nucleus disks.

Runaway Eccentricity Growth: A Pathway for Binary Black Hole Mergers in AGN Disks

Binary black holes (BBHs) embedded within the accretion disks that fuel active galactic nuclei (AGN) are promising progenitors for the source of gravitational wave (GW) events detected by LIGO/VIRGO. Several recent studies have shown that when these binaries form, they are likely to be highly eccentric and retrograde. However, many uncertainties remain concerning the orbital evolution of these binaries as they either inspiral toward merger or disassociate. Previous hydrodynamical simulations exploring their orbital evolution have been predominantly two-dimensional or have been restricted to binaries on nearly circular orbits. We present the first high-resolution, three-dimensional local shearing-box simulations of both prograde and retrograde eccentric BBHs embedded in AGN disks. We find that retrograde binaries shrink several times faster than their prograde counterparts and exhibit significant orbital eccentricity growth, the rate of which monotonically increases with binary eccentricity. Our results suggest that retrograde binaries may experience runaway orbital eccentricity growth, which may bring them close enough together at pericenter for GW emission to drive them to coalescence. Although their eccentricity is damped, prograde binaries shrink much faster than their orbital eccentricity decays, suggesting they should remain modestly eccentric as they contract toward merger. Finally, binary precession driven by the AGN disk may dominate over precession induced by the supermassive black hole depending on the binary accretion rate and its location in the AGN disk, which can subdue the evection resonance and von Ziepel–Lidov–Kozai cycles.

Inferring the iron K emissivity profiles of accretion discs irradiated by extended coronae

ABSTRACT One of the most promising methods to measure the spin of an accreting black hole is fitting the broad iron K$\alpha$ line in the X-ray spectrum. The line profile also depends on the geometry of the hard X-ray emitting corona. To put constraints on the black hole spin and corona geometry, it is essential to understand how do they affect the iron K$\alpha$ line emissivity profile. In this work, we present calculations of the illumination and the iron K$\alpha$ emissivity profiles performed with the Monte Carlo GR radiative transfer code monk. We focus on distinction between the illumination and emissivity profiles, which is in most previous studies neglected. We show that especially for the case of black hole X-ray binaries (BHXRBs), the difference is very large. For active galactic nuclei (AGNs), the emissivity profile has a more similar shape as the illumination profile, but it is notably steeper in the innermost region within a few gravitational radii. We find out that the different behaviour between AGN and BHXRB discs is due to the different energy spectra of the illuminating radiation. This suggests that the emissivity profile of the iron K$\alpha$ line cannot be determined by black hole spin and corona geometry alone and the energy spectrum of the illuminating radiation has to be taken into account. We also examined the effect of including the self-irradiation, and find it to be more important than the corona emission in BHXRBs.

Neutron star accretion events in AGN discs: mutimessenger implications

ABSTRACT This paper investigates the accretion of neutron stars (NSs) in active galactic nucleus (AGN) accretion discs. We classify potential accretion modes of NSs in AGN discs, proposing a hierarchical model of NS accretion: accretion flow from the Bondi sphere to accretion columns. The accretion of NSs in AGN discs differs from that of BHs, especially within the scale of the NS’s magnetosphere due to its hard surface and magnetic field. As the accretion flow approaches the magnetosphere, the magnetic fields guide the accretion flow to form accretion columns, primarily dominated by neutrinos. While neutrinos generated from single NS accretion may not have observable effects, considering the all-sky background, they contribute to the neutrino background in the sub-MeV energy range comparable to that of supernova explosions. NS accretion may also lead to the generation of mass quadrupole moments, consequently generating gravitational waves (GWs). The GWs, which exhibit characteristic effects like periodic modulations and echoes, could be observed by third-generation GW detectors. The emission of neutrinos and GWs carries away energy and angular momentum brought by accretion, reducing the feedback effect on the AGN disc. This results in an exceptionally high NS accretion rate, leading to a collapse time-scale shorter than the migration-merge time-scale, making it less likely that binary NS mergers originate from AGN discs.

Accretion-modified Stars in Accretion Disks of Active Galactic Nuclei: Observational Characteristics in Different Regions of the Disks

Stars and compact objects embedded in accretion disks of active galactic nuclei (AGNs), dubbed accretion-modified stars (AMSs), often experience hyper-Eddington accretion in the dense gas environment, resulting in powerful outflows as the Bondi explosion and formation of cavities. The varying gas properties across different regions of the AGN disk can give rise to diverse and intriguing phenomena. In this paper, we conduct a study on the characteristics of AMSs situated in the outer, middle, and inner regions of the AGN disk, where the growth of the AMSs during the shift inward is considered. We calculate their multiwavelength spectral energy distributions (SEDs) and thermal light curves. Our results reveal that the thermal luminosity of the Bondi explosion occurring in the middle region leads to UV flares with a luminosity of ∼1044 erg s−1. The synchrotron radiation of Bondi explosion in the middle and inner regions peaks at the X-ray band with luminosities of ∼1043 and ∼1042 erg s−1, respectively. The γ-ray luminosity of inverse Compton radiation spans from 1042–1043 erg s−1 peaked at the ∼10 MeV (outer region) and ∼GeV (middle and inner regions) bands. The observable flares of AMS in the middle region exhibit a slow rise and rapid Gaussian decay with a duration of months, while in the inner region, it exhibits a fast rise and slow Gaussian decay with a duration of several hours. These various SED and light-curve features provide valuable insights into the various astronomical transient timescales associated with AGNs.

Gas assisted binary black hole formation in AGN discs

ABSTRACT We investigate close encounters by stellar mass black holes (BHs) in the gaseous discs of active galactic nuclei (AGNs) as a potential formation channel of binary black holes (BBHs). We perform a series of 2D isothermal viscous hydrodynamical simulations within a shearing box prescription using the Eulerian grid code Athena++. We co-evolve the embedded BHs with the gas keeping track of the energetic dissipation and torquing of the BBH by gas gravitation and inertial forces. To probe the dependence of capture on the initial conditions, we discuss a suite of 345 simulations spanning BBH impact parameter (b) and local AGN disc density (ρ0). We identify a clear region in b − ρ0 space where gas assisted BBH capture is efficient. We find that the presence of gas leads to strong energetic dissipation during close encounters between unbound BHs, forming stably bound eccentric BBHs. We find that the gas dissipation during close encounters increases for systems with increased disc density and deeper periapsis passages rp, fitting a power law such that $\Delta E \propto \rho _0^{\alpha }r_{\mathrm{p}}^{\beta }$, where {α, β} = {1.01 ± 0.04, −0.43 ± 0.03}. Alternatively, the gas dissipation is approximately ΔE = 4.3MdvHvp, where Md is the mass of a single BH minidisc just prior to the encounter when the binary separation is 2rH (two binary Hill radii), vH and vp are the relative BH velocities at 2rH and at the first closest approach, respectively. We derive a prescription for capture which can be used in semi-analytical models of AGN. We do not find the dissipative dynamics observed in these systems to be in agreement with the simple gas dynamical friction models often used in the literature.

Soft No More: Gas Shielding Protects Soft Binaries from Disruption in Gas-rich Environments

Binaries in dense environments are traditionally classified as soft or hard based on their binding energy relative to the kinetic energy of surrounding stars. Heggie’s law suggests that stellar encounters tend to soften soft binaries and harden hard binaries, altering their separations. However, interactions with gas in such environments can significantly modify this behavior. This study investigates the impact of gas on binary softening and its consequences. We find that gas interactions can actually harden binaries, extending the soft–hard boundary to larger separations. This introduces a “shielding radius” within which binaries are likely to harden due to gas interactions, surpassing the traditional soft–hard limit. Consequently, a notable portion of binaries initially classified as “soft” may become “hard” when both gas and stars are considered. We propose a two-stage formation process for hard binaries: initial soft binary formation, either dynamically or through gas-assisted capture, followed by gas-induced hardening before eventual disruption. In environments with low gas density but high gas content, the shielding radius could exceed the typical hard–soft limit by 1 order of magnitude, leading to a significant fraction of originally soft binaries effectively becoming hard. Conversely, in high-gas-density environments, gas-induced hardening may dominate, potentially rendering the entire binary population hard. Gas hardening emerges as a crucial factor in shaping binary populations in gas-rich settings, such as clusters, star-forming regions, and possibly active galactic nucleus disks. This highlights the complex interplay between gas dynamics and stellar interactions in binary evolution within dense environments.

Determining the Hubble constant with AGN-assisted black hole mergers

ABSTRACT Gravitational waves from neutron star mergers have long been considered a promising way to measure the Hubble constant, H0, which describes the local expansion rate of the Universe. While black hole mergers are more abundantly observed, their expected lack of electromagnetic emission and poor gravitational-wave localization make them less well suited for measuring H0. Black hole mergers within the discs of Active Galactic Nuclei (AGN) could be an exception. Accretion from the AGN disc may produce an electromagnetic signal, pointing observers to the host galaxy. Alternatively, the low number density of AGNs could help identify the host galaxy of $1{\!-\!}5~{{\ \rm per\ cent}}$ of mergers. Here we show that black hole mergers in AGN discs may be a sensitive way to determine H0 with gravitational waves. If 1 per cent (10 per cent) of LIGO’s observations occur in AGN discs with identified host galaxies, we could measure H0 with 12 per cent (4 per cent) uncertainty in five years, possibly comparable to the sensitivity of neutron star mergers and set to considerably improve current gravitational wave measurements.

Constraining the LVK AGN channel with black hole spins

ABSTRACT Merging black holes (BHs) are expected to produce remnants with large dimensionless spin parameters (aspin ∼ 0.7). However, gravitational wave (GW) observations with LIGO–Virgo–Kagra (LVK) suggest that merging BHs are consistent with modestly positive but not high spin (aspin ∼ 0.2), causing tension with models suggesting that high-mass mergers are produced by hierarchical merger channels. Some BHs also show evidence for strong in-plane spin components. Here, we point out that spin-down of BHs due to eccentric prograde post-merger orbits within the gas of an active galactic nucleus (AGN) disc can yield BHs with masses in the upper mass gap, but only modestly positive aspin, and thus observations of BHs with low spin do not rule out hierarchical models. We also point out that the fraction of binary black hole (BBH) mergers with significant in-plane spin components is a strong test of interactions between disc BBHs and nuclear spheroid orbiters. Spin magnitude and spin tilt constraints from LVK observations of BBHs are an excellent test of dynamics of BHs in AGN discs, disc properties, and the nuclear clusters interacting with AGNs.

The Population of Massive Stars in Active Galactic Nuclei Disks

Gravitational instability in the outskirts of active galactic nuclei (AGN) disks leads to disk fragmentation and formation of ∼300 M ⊙ supermassive stars with potentially long lifetimes. Alternatively, stars can be captured ex situ and grow from gas accretion in the AGN disk. However, the number density distribution throughout the disk is limited by thermal feedback as their luminosities provide the dominant heating source. We derive equilibrium stellar surface density profiles under two limiting contexts: in the case where the stellar lifetimes are prolonged, due to the recycling of hydrogen-rich disk gas, only the fraction of gas converted into heat is removed from the disk accretion flow. Alternatively, if stellar composition recycling is inefficient and stars can evolve off the main sequence, the disk accretion rate is quenched toward smaller radii resembling a classical starburst disk, albeit the effective removal rate depends not only on the stellar lifetime, but also the mass of stellar remnants. For AGNs with central supermassive black hole masses of ∼106–108 M ⊙ accreting at ∼0.1 Eddington efficiency, we estimate a total number of 103–105 massive stars and the rate of stellar mergers to be 10−3 to 1 yr−1. We initiate the detailed study of the interaction between a swarm of massive stars through hydro and N-body simulations to provide better prescriptions of dynamical processes in AGN disks, and to constrain more accurate estimates of the stellar population.

Tidal disruption events from three-body scatterings and eccentricity pumping in the disks of active galactic nuclei

ABSTRACT Tidal disruption events (TDEs) are routinely observed in quiescent galaxies, as stars from the nuclear star cluster are scattered into the loss cone of the central supermassive black hole (SMBH). TDEs are also expected to occur in active galactic nuclei (AGNs), due to scattering or orbital eccentricity pumping of stars embedded in the innermost regions of the AGN accretion disc. Encounters with embedded stellar-mass black holes (BH) can result in AGN μTDEs. AGN TDEs and μTDEs could therefore account for a fraction of observed AGN variability. Here, by performing scattering experiments with the few-body code SpaceHub, we compute the probability of AGN TDEs and μTDEs as a result of 3-body interactions between stars and binary BHs. We find that AGN TDEs are more probable during the early life of the AGNs, when rates are $\sim (6\times 10^{-5}-5 \times 10^{-2}) (f_\bullet /0.01)\, \rm {AGN}^{-1}$ yr−1 (where f• is the ratio between the number density of BHs and stars), generally higher than in quiescent galactic nuclei. By contrast, μTDEs should occur throughout the AGN lifetime at a rate of $\sim (1\times 10^{-4} - 4\times 10^{-2})(f_\bullet /0.01)\, \rm {AGN}^{-1}$ yr−1. Detection and characterization of AGN TDEs and μAGN TDEs with future surveys using Rubin and Roman will help constrain the populations of stars and compact objects embedded in AGN discs, a key input for the LVK AGN channel.

GRB Afterglows with Energy Injections in AGN Accretion Disks

Active galactic nucleus (AGN) disks are widely considered potential hosts for various high-energy transients, including gamma-ray bursts (GRBs). The reactivation of GRB central engines can provide additional energy to shocks formed during the interaction of the initially ejected GRB jets with the circumburst material, commonly referred to as energy injections. In this paper, we study GRBs occurring in AGN disks within the context of energy injections. We adopt the standard external forward shock (EFS) model and consider both short- and long-duration GRB scenarios. Light curves for two types of radiation, namely, the radiation from the heated disk material (RHDM) and GRB afterglows, are computed. We find that the energy injection facilitates the EFS to break out from the photosphere of the low-density AGN disk at relativistic velocity. Moreover, the energy injection almost does not affect the RHDM but significantly enhances the peak flux of the GRB afterglows.

Impact of gas hardening on the population properties of hierarchical black hole mergers in active galactic nucleus disks

Hierarchical black hole (BH) mergers in active galactic nuclei (AGNs) are unique among formation channels of binary black holes (BBHs) because they are likely associated with electromagnetic counterparts and can efficiently lead to the mass growth of BHs. Here, we explore the impact of gas accretion and migration traps on the evolution of BBHs in AGNs. We have developed a new fast semi-analytic model, that allows us to explore the parameter space while capturing the main physical processes involved. We find that an effective exchange of energy and angular momentum between the BBH and the surrounding gas (i.e., gas hardening) during inspiral greatly enhances the efficiency of hierarchical mergers, leading to the formation of intermediate-mass BHs (up to 104 M⊙) and triggering spin alignment. Moreover, our models with efficient gas hardening show both an anticorrelation between the BBH mass ratio and the effective spin and a correlation between the primary BH mass and the effective spin. In contrast, if gas hardening is inefficient, the hierarchical merger chain is already truncated after the first two or three generations. We compare the BBH population in AGNs with other dynamical channels as well as isolated binary evolution.