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Table A.1.

Model variations of the assumptions that affect the binary population specifically as well as our whole stellar population.

Model Description Slope of Slope of equivalent Ratio of hydrogen-rich 103 × prob. of
in Z17 MHe, preSN single-star progenitors with 0 high mass
distribution, IMF distribution, high mass cores, detections,
αHe αsingle_IMF Rmassive P0, massive × 103
– FIDUCIAL POPULATION (standard set of assumptions) –1.89 –2.20 0.2 4.6
– Population of only single stars (standard set of assumptions) −2.01 −2.35 0.18 9.0
Variations of assumptions affecting the binary population
– Parameters of stable mass transfer
01 Accretion efficiency β = 0 −2.22 −2.62 0.16 12.6
02 Accretion efficiency β = 0.2 −2.04 −2.38 0.18 8.6
03 Accretion efficiency β = 1 −1.34 −1.50 0.26 1.0
04 Angular momentum loss γ = 0 −1.80 −2.08 0.22 3.0
05 Angular momentum loss γ: circumbinary disk −1.91 −2.22 0.19 6.1
– SN kick
10 No natal kick in SNe, σkick = 0 −2.25 −2.66 0.17 11.3
11 Extremely high kick in SNe, σkick = ∞ −1.88 −2.19 0.21 4.2
– Common envelope evolution
12 αCE = 0.1 −2.26 −2.66 0.16 12.4
13 αCE = 0.2 −2.12 −2.49 0.18 8.6
14 αCE = 0.5 −1.87 −2.17 0.21 4.0
15 αCE = 2.0 −1.86 −2.16 0.21 3.6
16 αCE = 5.0 −1.60 −1.83 0.24 1.6
17 αCE = 10.0 −1.47 −1.67 0.26 1.1
18 λCE = 0.5 −2.02 −2.36 0.20 4.9
– Parameter space for unstable mass transfer and mergers
19 qcrit, MS = 0.25 −1.90 −2.21 0.20 4.5
20 qcrit, MS = 0.8 −1.90 −2.21 0.20 4.5
21 qcrit, HG = 0.0 −1.90 −2.20 0.20 4.6
22 qcrit, HG = 0.25 −1.83 −2.12 0.21 3.5
23 qcrit, HG = 0.8 −1.94 −2.26 0.18 8.6
24 qcrit, HG = 1.0 −1.95 −2.28 0.17 10.2
06 Merger μloss = 0 −1.86 −2.15 0.21 3.8
07 Merger μloss = 0.25 −1.87 −2.17 0.20 4.4
08 Merger μmix = 0 −1.90 −2.21 0.20 4.5
09 Merger μmix = 1 −1.89 −2.20 0.20 4.4
27 WD mergers exclusion if not massive companion −1.75 −2.02 0.22 3.1
– Initial binary distributions
35 Initial q distr. slope κ = −1 −1.90 −2.20 0.20 5.1
36 Initial q distr. slope κ = +1 −1.87 −2.17 0.21 3.8
37 Initial period distr. slope π = +1 −1.97 −2.30 0.19 6.8
38 Initial period distr. slope π = −1 −1.88 −2.18 0.20 5.2
– Binary fraction
45 fbin = 0.3 −1.98 −2.32 0.18 7.6
(55) fbin = 0.5 −1.96 −2.28 0.19 6.6
00 fbin = 0.7 −1.93 −2.22 0.19 5.8
47 Mass dependent binary fraction, fbin(M) −1.96 −2.29 0.19 6.3
Variations of assumptions affecting the entire population
– Exclusion of failed SNe
(52) Mmax, ccSN ∼ 15 M⊙ −2.02 −2.45 0.29 (a) 1000.0 (b)
(53) Mmax, ccSN ∼ 16.5 M⊙ −2.02 −2.42 0.2 (a) 1000.0 (b)
(54) Mmax, ccSN ∼ 18 M⊙ −2.01 −2,40 0.18 (a) 580.7 (b)
29 Mmax, ccSN ∼ 20 M⊙ −1.97 −2.33 0.13 (a) 67.8 (b)
– Minimum mass for SNe
30 Mmin, ccSN ∼ 7 M⊙ −1.88 −2.20 0.19 7.9
31 Mmin, ccSN ∼ 8 M⊙ −1.89 −2.18 0.22 3.0
– IMF slope for massive stars
32 αIMF = −1.6 −1.36 −1.53 0.28 0.6
33 αIMF = −2.7 −2.21 −2.61 0.17 11.9
34 αIMF = −3.0 −2.44 −2.90 0.14 22.6
– Wind efficiency
(51) Wind factor η = 0.1 −1.76 −1.98 0.32 0.3
25 Wind factor η = 0.33 −1.80 −2.04 0.30 0.4
(52) Wind factor η = 0.5 −1.80 −2.04 0.30 0.4
(53) Wind factor η = 1.5 −2.12 −2.50 0.12 48.7
(54) Wind factor η = 2.0 −3.56 −4.35 0.01 875.5
26 Wind factor η = 3.0 −4.02 −4.95 0.00 879.1
– Metallicity
40 Z = 0.001 −1.80 −2.07 0.29 0.6
42 Z = 0.008 −1.78 −2.05 0.27 1.0
44 Z = 0.03 −2.59 −3.10 0.03 404.2

Notes. We show the slope of the distribution of final helium cores, αHe, as well as the corresponding IMF slope of a single-star population, αsingle_IMF. Rmassive is the fraction of hydrogen-rich stars at collapse with cores more massive than 5.75 M⊙ that corresponds to a single star of 16.5 M⊙ (Smartt et al. 2009), which has been suggested lead to “failed” SNe. P0, massive is the possibility of having zero progenitor detections of these high core mass progenitors out of 26 observational trials by chance. In the first column we show the model number of each variation, which corresponds to a simulation of Z17 in case it is not in parenthesis. Bold values represent the fiducial simulation that is used as a reference throughout the study.

(a)

The mass threshold of 16.5 M⊙ to calculate Rmassive is replaced by Mmax, ccSN.

(b)

The maximum equivalent single-star mass for Type II SNe to calculate this possibility is replaced by Mmax, ccSN, thus by definition increasing the possibility of zero detections of progenitors above 16.5 M⊙.

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