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Table 1.

Formation and retention of stellar-remnant BHs in a Mcl(0) ≈ 5.0 × 104M model cluster (Sect. 3) as a function of metallicity (Col. 1) and SN–remnant-formation scheme (Col. 2; Sect. 2.2; “+MB” implies the cluster model includes a population of massive primordial binaries as described in Sect. 4).

Metallicity Z Remnant scheme FBH, m/10−2 fret, BH, m FBH, n/10−3 fret, BH, n
0.0001 F12-rapid+B16-PPSN/PSN 6.130 0.771 1.833 0.656
0.0001 F12-rapid 6.562 0.786 1.844 0.658
0.0001 F12-delayed 6.973 0.601 2.580 0.353
0.0001 B08 7.493 0.835 2.055 0.682

0.002 F12-rapid+B16-PPSN/PSN 4.999 0.777 1.751 0.633
0.002 F12-rapid 5.018 0.777 1.751 0.633
0.002 F12-delayed 5.334 0.566 2.533 0.318
0.002 B08 5.604 0.808 1.938 0.675

0.02 F12-rapid 2.117 0.594 1.564 0.530
0.02 F12-delayed 1.944 0.185 2.055 0.074
0.02 B08 2.220 0.538 1.716 0.374

0.0001 F12-rapid+B16-PPSN/PSN (+MB) 6.152 0.793 1.167 0.700
0.0001 F12-rapid (+MB) 7.418 0.813 1.249 0.710
0.0001 F12-delayed (+MB) 7.563 0.736 1.447 0.564
0.0001 B08 (+MB) 7.992 0.881 1.296 0.793

Notes. Columns 3–6 give the fraction, FBH, m, of the cluster’s initial stellar mass that is converted into BHs; the fraction, fret, BH, m, of those retained in the cluster owing to sufficiently low natal kicks; the fraction, FBH, n, of the cluster’s initial number of stars that is converted into BHs; and the fraction, fret, BH, n, of those retained in the cluster, respectively. In this table, fret, BH, m and fret, BH, n correspond to the standard, fallback-controlled natal kicks (Sect. 3.1) – Sect. 3.2 discusses how the retentions are affected by alternative natal-kick prescriptions, namely, the convection-asymmetry-driven kick results in nearly the same retention fractions, the collapse-asymmetry-driven kick leads to all retention fractions ≈1.0 and the neutrino-driven kick leads to all retention fractions ≈0.0. Such BH retention fractions are representative of those in a typical young massive or an open cluster or a low-mass GC in the Milky Way or a local-group galaxy.

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