Table 1.
Variations of the physical assumptions and initial conditions considered and their impact on the fraction of each evolutionary channel for SN II progenitors and on the ratio of stripped-envelope to Type II SNe, Rstripped/II.
| Model | Description | Effectively | Mass | MS+MS | postMS+MS | Reverse | Spiraled-in | Partially | Rstripped/II |
|---|---|---|---|---|---|---|---|---|---|
| in Z17 | singles | gainers | mergers | mergers | mergers | during CEE | stripped | ||
| [——————————————-%————————————————-] | |||||||||
| – | Standard assumptions (1) | 54.3 | 13.7 | 5.6 | 13.9 | 11.3 | 1.0 | 0.1 | 0.53 |
| – | Simple analytical estimate (Sect. 3) | ∼56.0 | ∼16.0 | ∼8.5 | ∼15.0 | ∼4.0 | – | – | ∼0.52 |
| Physical assumptions | |||||||||
| 01 | Accretion efficiency β = 0 | 57.6 | 13.8 | 5.8 | 14.6 | 7.1 | 1.1 | 0.1 | 0.49 |
| 02 | Accretion efficiency β = 0.2 | 55.3 | 17.6 | 5.4 | 14.1 | 6.6 | 1.0 | 0.1 | 0.49 |
| 03 | Accretion efficiency β = 1 | 51.8 | 13.7 | 5.4 | 13.1 | 15.0 | 0.9 | 0.0 | 0.61 |
| 04 | Angular momentum loss γ = 0 | 54.0 | 13.3 | 5.7 | 14.0 | 11.5 | 1.4 | 0.1 | 0.53 |
| 05 | Angular momentum loss γ:circumbinary disk | 49.3 | 2.8 | 5.2 | 28.4 | 13.5 | 0.8 | 0.0 | 0.34 |
| 06 | Merger μloss = 0 | 57.3 | 15.3 | 6.0 | 8.3 | 12.1 | 1.0 | 0.1 | 0.59 |
| 07 | Merger μloss = 0.25 | 54.1 | 13.7 | 5.7 | 13.9 | 11.5 | 1.0 | 0.1 | 0.52 |
| 08 | Merger μmix = 0 | 54.2 | 13.6 | 5.7 | 14.1 | 11.4 | 1.0 | 0.1 | 0.53 |
| 09 | Merger μmix = 1 | 54.2 | 13.7 | 5.6 | 13.9 | 11.6 | 1.0 | 0.1 | 0.53 |
| 10 | No natal kick in SN, σkick = 0 | 61.1 | 3.6 | 6.4 | 15.7 | 13.0 | 0.1 | 0.1 | 0.61 |
| 11 | Extremely high kick in SN, σkick = ∞ | 53.7 | 14.0 | 5.7 | 14.1 | 11.4 | 1.0 | 0.1 | 0.53 |
| 12 | αCEE = 0.1 | 47.4 | 12.0 | 5.0 | 19.4 | 15.9 | 0.3 | 0.1 | 0.42 |
| 13 | αCEE = 0.2 | 49.5 | 12.5 | 5.2 | 18.2 | 14.0 | 0.6 | 0.1 | 0.49 |
| 14 | αCEE = 0.5 | 55.4 | 14.8 | 5.8 | 9.0 | 14.1 | 0.9 | 0.1 | 0.56 |
| 15 | αCEE = 2.0 | 58.5 | 14.7 | 6.1 | 13.8 | 5.6 | 1.2 | 0.1 | 0.62 |
| 16 | αCEE = 5.0 | 63.7 | 16.2 | 6.7 | 10.1 | 1.6 | 1.6 | 0.1 | 0.69 |
| 17 | αCEE = 10.0 | 67.1 | 17.1 | 7.0 | 5.5 | 1.1 | 2.0 | 0.1 | 0.75 |
| 18 | λCEE = 0.5 | 57.5 | 14.6 | 6.0 | 14.2 | 6.7 | 1.0 | 0.1 | 0.65 |
| 19 | qcrit, MS = 0.25 | 54.3 | 13.7 | 5.4 | 13.9 | 11.7 | 1.0 | 0.1 | 0.53 |
| 20 | qcrit, MS = 0.8 | 54.1 | 13.6 | 7.0 | 14.1 | 10.3 | 1.0 | 0.1 | 0.53 |
| 21 | qcrit, HG = 0.0 | 56.6 | 15.1 | 5.9 | 8.1 | 13.2 | 1.0 | 0.1 | 0.58 |
| 22 | qcrit, HG = 0.25 | 57.3 | 15.2 | 6.0 | 8.3 | 12.1 | 1.0 | 0.1 | 0.58 |
| 23 | qcrit, HG = 0.8 | 48.8 | 6.5 | 5.1 | 30.8 | 7.7 | 0.9 | 0.1 | 0.41 |
| 24 | qcrit, HG = 1.0 | 46.4 | 3.6 | 4.9 | 38.7 | 5.5 | 0.9 | 0.1 | 0.33 |
| – | Wind factor η = 0.1 | 56.2 | 15.5 | 6.9 | 8.2 | 11.6 | 1.1 | 0.5 | 0.37 |
| 25 | Wind factor η = 0.33 | 53.0 | 14.2 | 6.6 | 14.0 | 10.9 | 1.0 | 0.3 | 0.38 |
| 26 | Wind factor η = 3.0 | 56.0 | 9.3 | 4.0 | 14.6 | 15.2 | 0.9 | 0.0 | 1.35 |
| 29 | Exclusion of failed SNe (Mmax, ccSN = 20 M⊙) | 54.6 | 12.7 | 4.7 | 14.5 | 12.4 | 1.1 | 0.0 | 0.30 |
| 30 | Mmin, ccSN ∼ 7 M⊙ | 54.7 | 13.3 | 5.4 | 14.0 | 11.4 | 1.1 | 0.1 | 0.48 |
| 31 | Mmin, ccSN ∼ 8 M⊙ | 53.8 | 14.0 | 5.9 | 14.2 | 11.1 | 0.9 | 0.1 | 0.58 |
| Initial conditions | |||||||||
| 32 | IMF slope for massive stars αIMF = −1.6 | 56.1 | 16.5 | 5.6 | 12.4 | 8.3 | 1.0 | 0.1 | 0.95 |
| 33 | IMF slope for massive stars αIMF = −2.7 | 52.9 | 12.2 | 5.7 | 14.7 | 13.5 | 0.9 | 0.1 | 0.41 |
| 34 | IMF slope for massive stars αIMF = −3.0 | 51.7 | 11.1 | 5.8 | 15.3 | 15.1 | 0.9 | 0.0 | 0.35 |
| 35 | Initial q distr. slope κ = −1 | 54.6 | 8.0 | 6.7 | 24.1 | 5.9 | 0.5 | 0.1 | 0.42 |
| 36 | Initial q distr. slope κ = +1 | 52.9 | 17.4 | 4.6 | 7.6 | 16.2 | 1.3 | 0.1 | 0.61 |
| 37 | Initial period distr. slope π = +1 | 58.1 | 17.5 | 0.8 | 12.8 | 8.6 | 2.0 | 0.2 | 0.60 |
| 38 | Initial period distr. slope π = −1 | 47.0 | 8.6 | 16.8 | 11.3 | 15.9 | 0.3 | 0.0 | 0.41 |
| 39 | Z = 0.0002 | 56.4 | 13.6 | 1.2 | 14.1 | 8.0 | 1.6 | 5.0 | 0.32 |
| 40 | Z = 0.001 | 56.9 | 13.4 | 2.3 | 15.0 | 7.9 | 2.0 | 2.5 | 0.36 |
| 41 | Z = 0.004 | 56.8 | 13.7 | 4.1 | 14.3 | 8.9 | 1.7 | 0.5 | 0.39 |
| 42 | Z = 0.008 | 55.5 | 13.7 | 4.8 | 14.2 | 10.1 | 1.4 | 0.2 | 0.45 |
| 43 | Z = 0.02 | 56.7 | 12.9 | 6.7 | 13.9 | 8.5 | 1.4 | 0.0 | 0.67 |
| 44 | Z = 0.03 | 56.7 | 11.3 | 7.1 | 13.4 | 10.0 | 1.5 | 0.0 | 1.04 |
| Binary fractions (not taken into account in the uncertainty range presented in this study) | |||||||||
| 45 | fbin = 0.3 | 73.0 | 8.0 | 3.2 | 8.3 | 6.8 | 0.6 | 0.0 | 0.39 |
| 00 | fbin = 0.7 | 34.8 | 19.6 | 8.0 | 19.9 | 16.2 | 1.5 | 0.1 | 0.67 |
| 46 | fbin = 0.99 | 5.3 | 28.2 | 11.8 | 29.1 | 23.6 | 2.0 | 0.1 | 0.88 |
| 47 | Mass dependent binary fraction, fbin (M) | 42.0 | 18.2 | 7.1 | 17.7 | 13.6 | 1.3 | 0.1 | 0.64 |
Notes. In the first column we link each varied parameter with the corresponding simulation of Z17 whenever possible, although we assume fbin = 0.5 as standard in this study. Results from the simple analytical estimate in Sect. 3 are also shown.
The standard assumptions of our numerical model are discussed in Sect. 4.1. In summary: β:10*(accretor’s thermal rate), γ:specific angular momentum of the accretor, μloss = μmix = 0.1, σkick = 265 km s−1, αCEE = 1.0, λCEE: Dewi & Tauris (2000) & Tauris & Dewi (2001), qcrit, HG = 0.4, qcrit, MS = 0.65, η = 1.0, no failed SNe, αIMF = −2.3, κ = 0, π = −0.55 (for O-type primaries) & 0 (for the rest), Z = 0.014, fbin = 0.5.
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