Young dense massive star clusters are promising environments for the formation of intermediate mass black holes (IMBHs) through collisions. We present a set of 80 simulations carried out with Nbody6++GPU of 10 models of compact ∼7 × 104M⊙ star clusters with half-mass radii Rh ≲ 1pc, central densities ρcore ≳ 105M⊙pc−3, and resolved stellar populations with 10% primordial binaries. Very massive stars (VMSs) up to ∼400M⊙ grow rapidly by binary exchange and three-body scattering with stars in hard binaries. Assuming that in VMS - stellar BH collisions all stellar material is accreted onto the BH, IMBHs with masses up to MBH ∼ 350M⊙ can form on timescales of ≲ 15 Myr, as qualitatively predicted from Monte Carlo MOCCA simulations. One model forms an IMBH of 140 M⊙ by three BH mergers with masses of 17 : 28, 25 : 45, 68 : 70 M⊙ within ∼90 Myr. Despite the stochastic nature of the process, formation efficiencies are higher in more compact clusters. Lower accretion fractions of 0.5 also result in IMBH formation. The process might fail for values as low as 0.1. The IMBHs can merge with stellar mass BHs in intermediate mass-ratio inspiral events (IMRIs) on a 100 Myr timescale. With 105 stars, 10 % binaries, stellar evolution, all relevant dynamical processes, and 300 Myr simulation time, our large suite of 80 simulations indicate another rapid IMBH formation channel in young and compact massive star clusters.

We present direct N-body simulations, carried out with nbody6++gpu, of young and compact low-metallicity (Z = 0.0002) star clusters with 1.1 × 105 stars, a velocity dispersion of ∼ 15 km s−1, a half mass radius Rh = 0.6 pc, and a binary fraction of $10{\rm {per\ cent}}$ including updated evolution models for stellar winds and (pulsation) pair-instability supernovae ((P)PSNe). Within the first tens of megayears, each cluster hosts several black hole (BH) merger events which nearly cover the complete mass range of primary and secondary BH masses for current LIGO-Virgo-KAGRA gravitational wave detections. The importance of gravitational recoil is estimated statistically during post-processing analysis. We present possible formation paths of massive BHs above the assumed lower PSN mass-gap limit (45 M⊙) into the intermediate-mass BH (IMBH) regime (>100 M⊙) which include collisions of stars, BHs and the direct collapse of stellar merger remnants with low core masses. The stellar evolution updates result in the early formation of heavier stellar BHs compared to the previous model. The resulting higher collision rates with massive stars support the rapid formation of massive BHs. For models assuming a high accretion efficiency for star-BH mergers, we present a first-generation formation scenario for GW190521-like events: a merger of two BHs which reached the PSN mass-gap merging with massive stars. This event is independent of gravitational recoil and therefore conceivable in dense stellar systems with low escape velocities. One simulated cluster even forms an IMBH binary (153 M⊙, 173 M⊙) which is expected to merge within a Hubble time.

The LIGO-Virgo-Kagra collaboration (LVC) discovered recently GW190521, a gravitational wave (GW) source associated with the merger between two black holes (BHs) with mass 66 M and > 85 M . GW190521 represents the first BH binary (BBH) merger with a primary mass falling in the "upper mass-gap" and the first leaving behind a ∼ 150 M remnant. So far, the LVC reported the discovery of four further mergers having a total mass > 100 M , i.e. in the intermediate-mass black holes (IMBH) mass range. Here, we discuss results from a series of 80 N -body simulations of young massive clusters (YMCs) that implement relativistic corrections to follow compact object mergers. We discover the development of a GW190521-like system as the result of a 3rd-generation merger, and four IMBH-BH mergers with total mass (300 − 350) M . We show that these IMBH-BH mergers are low-frequency GW sources detectable with LISA and DECIGO out to redshift z = 0.01 − 0.1 and z > 100, and we discuss how their detection could help unravelling IMBH natal spins. For the GW190521 test case, we show that the 3rd-generation merger remnant has a spin and effective spin parameter that matches the 90% credible interval measured for GW190521 better than a simpler double merger and comparably to a single merger. Due to GW recoil kicks, we show that retaining the products of these mergers require birth-sites with escape velocities 50 − 100 km s −1 , values typically attained in galactic nuclei and massive clusters with steep density profiles.

The flat stellar density cores of massive elliptical galaxies form rapidly due to sinking supermassive black holes (SMBH) in gas-poor galaxy mergers. After the SMBHs form a bound binary, gravitational slingshot interactions with nearby stars drive the core regions towards a tangentially biased stellar velocity distribution. We use collisionless galaxy merger simulations with accurate collisional orbit integration around the central SMBHs to demonstrate that the removal of stars from the centre by slingshot kicks accounts for the entire change in velocity anisotropy. The rate of strong (unbinding) kicks is constant over several hundred Myr at $\sim 3 \ M_\odot \rm yr^{-1}$ for our most massive SMBH binary (MBH = 1.7 × 1010M⊙). Using a frequency-based orbit classification scheme (box, x-tube, z-tube, rosette) we demonstrate that slingshot kicks mostly affect box orbits with small pericentre distances, leading to a velocity anisotropy of β ≲ −0.6 within several hundred Myr as observed in massive ellipticals with large cores. We show how different SMBH masses affect the orbital structure of the merger remnants and present a kinematic tomography connecting orbit families to integral field kinematic features. Our direct orbit classification agrees remarkably well with a modern triaxial Schwarzschild analysis applied to simulated mock kinematic maps.

We present N-body simulations, including post-Newtonian dynamics, of dense clusters of low-mass stars harbouring central black holes (BHs) with initial masses of 50, 300, and 2000 M⊙. The models are evolved with the N-body code bifrost to investigate the possible formation and growth of massive BHs by the tidal capture of stars and tidal disruption events (TDEs). We model star-BH tidal interactions using a velocity-dependent drag force, which causes orbital energy and angular momentum loss near the BH. About ∼20 − 30 per cent of the stars within the spheres of influence of the black holes form Bahcall-Wolf cusps and prevent the systems from core collapse. Within the first 40 Myr of evolution, the systems experience 500–1300 TDEs, depending on the initial cluster structure. Most (>95 per cent) of the TDEs originate from stars in the Bahcall-Wolf cusp. We derive an analytical formula for the TDE rate as a function of the central BH mass, density and velocity dispersion of the clusters ($\dot{N}_{\mathrm{TDE}} \propto M\mathrm{_{BH}}\rho \sigma ^{-3}$). We find that TDEs can lead a 300 M⊙ BH to reach ∼7000 M⊙ within a Gyr. This indicates that TDEs can drive the formation and growth of massive BHs in sufficiently dense environments, which might be present in the central regions of nuclear star clusters.