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Table F.1

Properties of a discrete example ensemble

Mi (M) Ni n0,i
(cm−3) Ri (pc) Ni × area (pc2) Vi (cm3) Ni ×Vi (cm3) Ni × Mi (M)
0.001 24250.4 (0.842) 3.7 × 105 0.0030 0.67 (0.084) 3.2 × 1048 7.75 × 1052 (< 10−3) 24.3 (0.024)
0.01 3843.44 (0.133) 1.9 × 105 0.0081 0.78 (0.099) 6.44 × 1049 2.48 × 1053 (0.002) 8.4 (0.0 8)
0.1 609.144 (0.021) 9.2 × 104 0.0219 0.92 (0.116) 1.30 × 1051 7.91 × 1053 (0.006) 60.9 (0.061)
1. 96.5428 (0.003) 4.6 × 104 0.0597 1.08 (0.136) 2.62 × 1052 2.5 × 1054 (0.021) 96.5 (0.097)
10. 15.301 (<10−3) 2.3 × 104 0.162 1.27 (0.159) 5.27 × 1053 8.07 × 1054 (0.067) 15.0 (0.15)
100. 2.42504 (< 10−4) 1.1 × 104 0.442 1.49 (0.187) 1.06 × 1055 2.58 × 1055 (0.215) 242.5 (0.24)
1000. 0.384344 (< 10−5) 5.6 × 103 1.2 1.75 (0.22) 2.14 × 1056 8.2 × 1055 (0.687) 84. (0. 84)

total 28817.7 7.96 1.2 × 1056 1000.0

Notes. We use the following ensemble parameters: Mens = 1000 M, nens = 104 cm−3, α = 1.8, and γ = 2.3. Numbers in parenthesis indicate the fraction in the column total.

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