We evaluate the redshift distribution of binary black hole (BBH), black hole – neutron star binary (BHNS) and binary neutron star (BNS) mergers, exploring the main sources of uncertainty: star formation rate (SFR) density, metallicity evolution, common envelope, mass transfer via Roche lobe overflow, natal kicks, core-collapse supernova model and initial mass function. Among binary evolution processes, uncertainties on common envelope ejection have a major impact: the local merger rate density of BNSs varies from ∼103 to ∼20 Gpc−3 yr−1 if we change the common envelope efficiency parameter from αCE = 7 to 0.5, while the local merger rates of BBHs and BHNSs vary by a factor of ∼2 − 3. The BBH merger rate changes by one order of magnitude, when 1σ uncertainties on metallicity evolution are taken into account. In contrast, the BNS merger rate is almost insensitive to metallicity. Hence, BNSs are the ideal test bed to put constraints on uncertain binary evolution processes, such as common envelope and natal kicks. Only models assuming values of αCE ≳ 2 and moderately low natal kicks (depending on the ejected mass and the SN mechanism), result in a local BNS merger rate density within the 90% credible interval inferred from the second gravitational-wave transient catalogue.
Young star clusters are the most common birth-place of massive stars and are dynamically active environments. Here, we study the formation of black holes (BHs) and binary black holes (BBHs) in young star clusters, by means of 6000 N-body simulations coupled with binary population synthesis. We probe three different stellar metallicities (Z = 0.02, 0.002 and 0.0002) and two initial density regimes (density at the half-mass radius ρh ≥ 3.4 × 104 and ≥1.5 × 102 M⊙ pc−3 in dense and loose star clusters, respectively). Metal-poor clusters tend to form more massive BHs than metal-rich ones. We find ∼6, ∼2, and <1 % of BHs with mass mBH > 60 M⊙ at Z = 0.0002, 0.002 and 0.02, respectively. In metal-poor clusters, we form intermediate-mass BHs with mass up to ∼320 M⊙. BBH mergers born via dynamical exchanges (exchanged BBHs) can be more massive than BBH mergers formed from binary evolution: the former (latter) reach total mass up to ∼140 M⊙ (∼80 M⊙). The most massive BBH merger in our simulations has primary mass ∼88 M⊙, inside the pair-instability mass gap, and a mass ratio of ∼0.5. Only BBHs born in young star clusters from metal-poor progenitors can match the masses of GW170729, the most massive event in O1 and O2, and those of GW190412, the first unequal-mass merger. We estimate a local BBH merger rate density ∼110 and ∼55 Gpc−3 yr−1, if we assume that all stars form in loose and dense star clusters, respectively.
Pair instability (PI) and pulsational PI prevent the formation of black holes (BHs) with mass ${\gtrsim}\,\, 60$ M⊙ from single star evolution. Here, we investigate the possibility that BHs with mass in the PI gap form via stellar mergers and multiple stellar mergers, facilitated by dynamical encounters in young star clusters. We analyze 104 simulations, run with the direct N-body code nbody6++gpu coupled with the population synthesis code mobse. We find that up to ∼6 % of all simulated BHs have mass in the PI gap, depending on progenitor’s metallicity. This formation channel is strongly suppressed in metal-rich (Z = 0.02) star clusters, because of stellar winds. BHs with mass in the PI gap are initially single BHs but can efficiently acquire companions through dynamical exchanges. We find that ∼21%, 10% and 0.5% of all binary BHs have at least one component in the PI mass gap at metallicity Z = 0.0002, 0.002 and 0.02, respectively. Based on the evolution of the cosmic star formation rate and metallicity, and under the assumption that all stars form in young star clusters, we predict that ∼5 % of all binary BH mergers detectable by advanced LIGO and Virgo at their design sensitivity have at least one component in the PI mass gap.
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