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The mode of star formation that results in the formation of globular clusters and young massive clusters is difficult to constrain through observations. We present models of massive star cluster formation using the TORCHframework, which uses the Astrophysical MUltipurpose Software Environment (AMUSE) to couple distinct multi-physics codes that handle star formation, stellar evolution and dynamics, radiative transfer, and magnetohydrodynamics. We upgraded TORCHby implementing the N-body code PETAR, thereby enabling TORCHto handle massive clusters forming from 10⁶M_⊙clouds with ≥10⁵individual stars. We present results from TORCHsimulations of star clusters forming from 10⁴,  10⁵, and 10⁶M_⊙turbulent spherical gas clouds (named M4, M5, M6) of radiusR= 11.7 pc. We find that star formation is highly efficient and becomes more so at a higher cloud mass and surface density. For M4, M5, and M6 with initial surface densities 2.325 × 10^1,2,3M_⊙pc⁻², after a free-fall time oft_ff= 6.7,2.1,0.67 Myr, we find that ∼30%, 40%, and 60% of the cloud mass has formed into stars, respectively. The end of simulation-integrated star formation efficiencies for M4, M5, and M6 areϵ_⋆ = M_⋆/M_cloud = 36%, 65%, and 85%. Observations of nearby clusters similar in mass and size to M4 have instantaneous star formation efficiencies ofϵ_inst ≤ 30%, which is slightly lower than the integrated star formation efficiency of M4. The M5 and M6 models represent a different regime of cluster formation that is more appropriate for the conditions in starburst galaxies and gas-rich galaxies at high redshift, and that leads to a significantly higher efficiency of star formation. We argue that young massive clusters build up through short efficient bursts of star formation in regions that are sufficiently dense (Σ ≥ 10²M_⊙pc⁻²) and massive (M_cloud≥ 10⁵M_⊙). In such environments, stellar feedback from winds and radiation is not strong enough to counteract the gravity from gas and stars until a majority of the gas has formed into stars. 

ABSTRACT Two-body scatterings under the potential of a massive object are very common in astrophysics. If the massive body is far enough away that the two small bodies are in their own gravitational sphere of influence, the gravity of the massive body can be temporarily ignored. However, this requires the scattering process to be fast enough that the small objects do not spend too much time at distances near the surface of the sphere of influence. In this paper, we derive the validation criteria for effective two-body scattering and establish a simple analytical solution for this process, which we verify through numerical scattering experiments. We use this solution to study star–black hole scatterings in the discs of active galactic nuclei and planet–planet scatterings in planetary systems, and calculate their one-dimensional cross-section analytically. Our solution will be valuable in reducing computational time when treating two-body scatterings under the potential of a much more massive third body, provided that the problem settings are in the valid parameter space region identified by our study. 

ABSTRACT Stars and stellar remnants orbiting a supermassive black hole (SMBH) can interact with an active galactic nucleus (AGN) disc. Over time, prograde orbiters (inclination i < 90°) decrease inclination, as well as semimajor axis (a) and eccentricity (e) until orbital alignment with the gas disc (‘disc capture’). Captured stellar-origin black holes (sBH) add to the embedded AGN population that drives sBH–sBH mergers detectable in gravitational waves using LIGO–Virgo–KAGRA or sBH–SMBH mergers detectable with Laser Interferometer Space Antenna. Captured stars can be tidally disrupted by sBH or the SMBH or rapidly grow into massive ‘immortal’ stars. Here, we investigate the behaviour of polar and retrograde orbiters (i ≥ 90°) interacting with the disc. We show that retrograde stars are captured faster than prograde stars, flip to prograde orientation (i < 90°) during capture, and decrease a dramatically towards the SMBH. For sBH, we find a critical angle iret ∼ 113°, below which retrograde sBH decay towards embedded prograde orbits (i → 0°), while for io > iret sBH decay towards embedded retrograde orbits (i → 180°). sBH near polar orbits (i ∼ 90°) and stars on nearly embedded retrograde orbits (i ∼ 180°) show the greatest decreases in a. Whether a star is captured by the disc within an AGN lifetime depends primarily on disc density, and secondarily on stellar type and initial a. For sBH, disc capture time is longest for polar orbits, low-mass sBH, and lower density discs. Larger mass sBH should typically spend more time in AGN discs, with implications for the spin distribution of embedded sBH. 

Abstract The accretion disks of active galactic nuclei (AGNs) are promising locations for the merger of compact objects detected by gravitational wave (GW) observatories. Embedded within a baryon-rich, high-density environment, mergers within AGNs are the only GW channel where an electromagnetic (EM) counterpart must occur (whether detectable or not). Considering AGNs with unusual flaring activity observed by the Zwicky Transient Facility (ZTF), we describe a search for candidate EM counterparts to binary black hole (BBH) mergers detected by LIGO/Virgo in O3. After removing probable false positives, we find nine candidate counterparts to BBH mergers during O3 (seven in O3a, two in O3b) with a p -value of 0.0019. Based on ZTF sky coverage, AGN geometry, and merger geometry, we expect ≈3( N BBH /83)( f AGN /0.5) potentially detectable EM counterparts from O3, where N BBH is the total number of observed BBH mergers and f AGN is the fraction originating in AGNs. Further modeling of breakout and flaring phenomena in AGN disks is required to reduce our false-positive rate. Two of the events are also associated with mergers with total masses >100 M ⊙ , which is the expected rate for O3 if hierarchical (large-mass) mergers occur in the AGN channel. Candidate EM counterparts in future GW observing runs can be better constrained by coverage of the Southern sky as well as spectral monitoring of unusual AGN flaring events in LIGO/Virgo alert volumes. A future set of reliable AGN EM counterparts to BBH mergers will yield an independent means of measuring cosmic expansion ( H 0 ) as a function of redshift. 

ABSTRACT Galactic nuclei are promising sites for stellar origin black hole (BH) mergers, as part of merger hierarchies in deep potential wells. We show that binary black hole (BBH) merger rates in active galactic nuclei (AGNs) should always exceed merger rates in quiescent galactic nuclei (nuclear star clusters, NSCs) around supermassive black holes (SMBHs) without accretion discs. This is primarily due to average binary lifetimes in AGNs that are significantly shorter than those in NSCs. The lifetime difference comes from rapid hardening of BBHs in AGNs, such that their semimajor axes are smaller than the hard–soft boundary of their parent NSC; this contrasts with the large average lifetime to merger for BBHs in NSCs around SMBHs, due to binary ionization mechanisms. Secondarily, merger rates in AGNs are enhanced by gas-driven binary formation mechanisms. Formation of new BHs in AGN discs is a minor contributor to the rate differences. With the gravitational wave detection of several BBHs with at least one progenitor in the upper mass gap, and signatures of dynamical formation channels in the χeff distribution, we argue that AGNs could contribute $$\sim 25{\!-\!}80{{\ \rm per\ cent}}$$ of the LIGO–Virgo measured rate of $$\sim 24\, \rm {Gpc}^{-3} \rm {yr}^{-1}$$. 

Abstract Active galactic nuclei (AGNs) are promising environments for the assembly of merging binary black hole (BBH) systems. Interest in AGNs as nurseries for merging BBHs is rising, following the detection of gravitational waves from a BBH system from the purported pair-instability mass gap, most notably GW190521. AGNs have also been invoked to explain the formation of the high-mass-ratio system GW190814. We draw on simulations of BBH systems in AGNs to propose a phenomenological model for the distribution of black hole spins of merging binaries in AGN disks. The model incorporates distinct features that make the AGN channel potentially distinguishable from other channels, such as assembly in the field and in globular clusters. The model parameters can be mapped heuristically to the age and density of the AGN disks. We estimate the extent to which different populations of mergers in AGNs can be distinguished. If the majority of merging black holes are assembled in AGNs, future gravitational-wave observations may provide insights into the dynamics of AGN disks.