The cosmic merger rate density of black hole binaries (BHBs) can give us an essential clue to constraining the formation channels of BHBs, in light of current and forthcoming gravitational wave detections. Following a Monte Carlo approach, we couple new population-synthesis models of BHBs with the Illustris cosmological simulation, to study the cosmic history of BHB mergers. We explore six population-synthesis models, varying the prescriptions for supernovae, common envelope, and natal kicks. In most considered models, the cosmic BHB merger rate follows the same trend as the cosmic star formation rate. The normalization of the cosmic BHB merger rate strongly depends on the treatment of common envelope and on the distribution of natal kicks. We find that most BHBs merging within LIGO's instrumental horizon come from relatively metal-poor progenitors (< 0.2 Z ). The total masses of merging BHBs span a large range of values, from ∼ 6 to ∼ 82 M . In our fiducial model, merging BHBs consistent with GW150914, GW151226 and GW170104 represent ∼ 6, 3, and 12 per cent of all BHBs merging within the LIGO horizon, respectively. The heavy systems, like GW150914, come from metal-poor progenitors (< 0.15 Z ). Most GW150914-like systems merging in the local Universe appear to have formed at high redshift, with a long delay time. In contrast, GW151226-like systems form and merge all the way through the cosmic history, from progenitors with a broad range of metallicities. Future detections will be crucial to put constraints on common envelope, on natal kicks, and on the BHB mass function.

The first four gravitational wave events detected by LIGO were all interpreted as merging black hole binaries (BHBs), opening a new perspective on the study of such systems. Here we use our new population-synthesis code MOBSE, an upgraded version of BSE (Hurley et al. 2002), to investigate the demography of merging BHBs. MOBSE includes metallicity-dependent prescriptions for mass loss of massive hot stars. It also accounts for the impact of the electron-scattering Eddington factor on mass loss. We perform > 10 8 simulations of isolated massive binaries, with 12 different metallicities, to study the impact of mass loss, core-collapse supernovae and common envelope on merging BHBs. Accounting for the dependence of stellar winds on the Eddington factor leads to the formation of black holes (BHs) with mass up to 65 M at metallicity Z ∼ 0.0002. However, most BHs in merging BHBs have masses 40 M . We find merging BHBs with mass ratios in the 0.1−1.0 range, even if mass ratios > 0.6 are more likely. We predict that systems like GW150914, GW170814 and GW170104 can form only from progenitors with metallicity Z ≤ 0.006, Z ≤ 0.008 and Z ≤ 0.012, respectively. Most merging BHBs have gone through a common envelope phase, but up to ∼ 17 per cent merging BHBs at low metallicity did not undergo any common envelope phase. We find a much higher number of mergers from metal-poor progenitors than from metalrich ones: the number of BHB mergers per unit mass is ∼ 10 −4 M −1 at low metallicity (Z = 0.0002 − 0.002) and drops to ∼ 10 −7 M −1 at high metallicity (Z ∼ 0.02).

Searching for distinctive signatures, which characterize different formation channels of binary black holes (BBHs), is a crucial step towards the interpretation of current and future gravitational wave detections. Here, we investigate the demography of merging BBHs in young star clusters (SCs), which are the nursery of massive stars. We performed 4 × 10 3 N-body simulations of SCs with metallicity Z = 0.002, initial binary fraction 0.4 and fractal initial conditions, to mimic the clumpiness of star forming regions. Our simulations include a novel population-synthesis approach based on the code MOBSE. We find that SC dynamics does not affect the merger rate significantly, but leaves a strong fingerprint on the properties of merging BBHs. More than 50 % of merging BBHs in young SCs form by dynamical exchanges in the first few Myr. Dynamically formed merging BBHs are significantly heavier than merging BBHs in isolated binaries: merging BBHs with total mass up to ∼ 120 M form in young SCs, while the maximum total mass of merging BBHs in isolated binaries with the same metallicity is only ∼ 70 M . Merging BBHs born via dynamical exchanges tend to have smaller mass ratios than BBHs in isolated binaries. Furthermore, SC dynamics speeds up the merger: the delay time between star formation and coalescence is significantly shorter in young SCs. In our simulations, massive systems such as GW170729 form only via dynamical exchanges. Finally ∼ 2 % of merging BBHs in young SCs have mass in the pair-instability mass gap (∼ 60 − 120 M ). This represents a unique fingerprint of merging BBHs in SCs.