We explore hierarchical black hole (BH) mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs), accounting for both original and dynamically assembled binary BHs (BBHs). We find that the median mass of both first- and nth-generation dynamical mergers is larger in GCs and YSCs with respect to NSCs, because the lighter BHs are ejected by supernova kicks from the lower-mass clusters. Also, first- and nth-generation BH masses are strongly affected by the metallicity of the progenitor stars: the median mass of the primary BH of a nth-generation merger is ∼24 − 38 M⊙ (∼9 − 15 M⊙) in metal-poor (metal-rich) NSCs. The maximum BH mass mainly depends on the escape velocity: BHs with mass up to several thousand M⊙ form in NSCs, while YSCs and GCs host BHs with mass up to several hundred M⊙. Furthermore, we calculate the fraction of mergers with at least one component in the pair-instability mass gap (fPI) and in the intermediate-mass BH regime (fIMBH). In the fiducial model for dynamical BBHs with metallicity Z = 0.002, we find fPI ≈ 0.05, 0.02 and 0.007 (fIMBH ≈ 0.01, 0.002 and 0.001) in NSCs, GCs and YSCs, respectively. Both fPI and fIMBH drop by at least one order of magnitude at solar metallicity. Finally, we investigate the formation of GW190521 by assuming that it is either a nearly equal-mass BBH or an intermediate-mass ratio inspiral.

Intermediate-mass black holes (IMBHs) in the mass range $10^2\!-\!10^5\, \mathrm{M_{\odot }}$ bridge the gap between stellar black holes (BHs) and supermassive BHs. Here, we investigate the possibility that IMBHs form in young star clusters via runaway collisions and BH mergers. We analyse 104 simulations of dense young star clusters, featuring up-to-date stellar wind models and prescriptions for core collapse and (pulsational) pair instability. In our simulations, only nine IMBHs out of 218 form via binary BH mergers, with a mass ∼100–140 M⊙. This channel is strongly suppressed by the low escape velocity of our star clusters. In contrast, IMBHs with masses up to ∼438 M⊙ efficiently form via runaway stellar collisions, especially at low metallicity. Up to ∼0.2 per cent of all the simulated BHs are IMBHs, depending on progenitor’s metallicity. The runaway formation channel is strongly suppressed in metal-rich (Z = 0.02) star clusters, because of stellar winds. IMBHs are extremely efficient in pairing with other BHs: ∼70 per cent of them are members of a binary BH at the end of the simulations. However, we do not find any IMBH–BH merger. More massive star clusters are more efficient in forming IMBHs: ∼8 per cent (∼1 per cent) of the simulated clusters with initial mass 104–3 × 104 M⊙ (103–5 × 103 M⊙) host at least one IMBH.

GW190521 is the most massive binary black hole (BBH) merger observed to date, and its primary component lies in the pair-instability (PI) mass gap. Here, we investigate the formation of GW190521-like systems via three-body encounters in young massive star clusters. We performed 2× 105 simulations of binary-single interactions between a BBH and a massive ≥60 M⊙ black hole (BH), including post-Newtonian terms up to the 2.5 order and a prescription for relativistic kicks. In our initial conditions, we take into account the possibility of forming BHs in the PI mass gap via stellar collisions. If we assume that first-generation BHs have low spins, $\sim {0.17}{{\ \rm per\ cent}}$ of all the simulated BBH mergers have component masses, effective and precessing spin, and remnant mass and spin inside the $90{{\ \rm per\ cent}}$ credible intervals of GW190521. Seven of these systems are first-generation exchanged binaries, while five are second-generation BBHs. We estimate a merger rate density $\mathcal {R}_{\rm GW190521}\sim {0.03}\,$Gpc−3 yr−1 for GW190521-like binaries formed via binary-single interactions in young star clusters. This rate is extremely sensitive to the spin distribution of first-generation BBHs. Stellar collisions, second-generation mergers and dynamical exchanges are the key ingredients to produce GW190521-like systems in young star clusters.

Population-synthesis codes are an unique tool to explore the parameter space of massive binary star evolution and binary compact object (BCO) formation. Most population-synthesis codes are based on the same stellar evolution model, limiting our ability to explore the main uncertainties. Here, we present the new version of the code sevn, which overcomes this issue by interpolating the main stellar properties from a set of pre-computed evolutionary tracks. We describe the new interpolation and adaptive time-step algorithms of sevn, and the main upgrades on single and binary evolution. With sevn, we evolved 1.2 × 109 binaries in the metallicity range 0.0001 ≤ Z ≤ 0.03, exploring a number of models for electron-capture, core-collapse and pair-instability supernovae, different assumptions for common envelope, stability of mass transfer, quasi-homogeneous evolution and stellar tides. We find that stellar evolution has a dramatic impact on the formation of single and binary compact objects. Just by slightly changing the overshooting parameter (λov = 0.4, 0.5) and the pair-instability model, the maximum mass of a black hole can vary from ≈60 to ≈100 M⊙. Furthermore, the formation channels of BCOs and the merger efficiency we obtain with sevn show significant differences with respect to the results of other population-synthesis codes, even when the same binary-evolution parameters are used. For example, the main traditional formation channel of BCOs is strongly suppressed in our models: at high metallicity (Z ≳ 0.01) only <20% of the merging binary black holes and binary neutron stars form via this channel, while other authors found fractions >70%.