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Table 1.

Analytical fits to the CR-IGIMF.

SFR ΣSFR/ΣMW αI mI αII mII αIII mIII αIV mIV αV f dg ⋆ $ f^{\star}_{\mathrm{dg}} $ (1 − fret)⋆ f SN 2 ⋆ $ f^{\star}_{\mathrm{SN2}} $
(M⊙ yr−1) (M⊙) (M⊙) (M⊙) (M⊙)
10−3 0.1 −1.28 0.31 −1.35 1.30 −2.92 5.18 −3.70 20.99 −14.65 0.89 0.95 0.27
0.01 −1.42 0.34 −1.63 1.38 −2.81 7.96 −3.46 55.94 −14.64 0.96 1.00 0.39
0.1 −1.34 0.21 −1.72 1.25 −2.46 1.89 −2.79 76.84 −4.10 1.01 1.03 0.58
1 −1.54 0.21 −1.80 1.48 −2.73 5.11 −2.57 20.04 −2.40 1.03 1.02 0.70
10 −1.84 0.25 −1.97 1.50 −2.42 6.52 −2.20 25.23 −2.05 1.08 0.96 1.06
100 −1.98 0.24 −2.21 0.45 −2.09 6.88 −1.90 24.31 −1.79 1.13 0.82 1.51
103 −2.16 0.25 −2.27 0.97 −1.83 5.18 −1.67 21.74 −1.57 1.17 0.61 1.97
10−3 1 −1.30 0.45 −1.37 1.52 −3.10 9.33 −4.19 21.98 −17.42 0.89 0.91 0.29
0.01 −1.30 0.25 −1.54 1.36 −2.85 11.46 −3.59 56.34 −14.73 0.95 0.96 0.42
0.1 −1.30 0.27 −1.71 1.32 −2.50 2.13 −2.80 76.99 −4.13 0.98 1.00 0.61
1 −1.51 0.26 −1.79 1.58 −2.74 5.09 −2.59 20.38 −2.41 1.02 0.99 0.73
10 −1.80 0.31 −1.95 1.58 −2.42 6.80 −2.22 24.39 −2.06 1.08 0.94 1.08
100 −2.00 0.27 −2.09 6.33 −1.96 13.00 −1.87 31.57 −1.79 1.12 0.81 1.53
103 −2.16 0.34 −2.27 0.97 −1.83 5.20 −1.67 21.64 −1.57 1.17 0.61 1.98
10−3 10 −1.30 1.16 −2.02 3.34 −3.29 13.08 −4.95 22.67 −19.82 0.88 0.76 0.52
0.01 −1.30 0.57 −1.50 1.25 −2.22 5.20 −3.50 55.67 −14.37 0.90 0.81 0.63
0.1 −1.30 0.61 −1.68 1.23 −2.09 3.05 −2.85 77.40 −4.12 0.91 0.81 0.81
1 −1.50 0.71 −1.73 1.25 −2.14 3.13 −2.69 23.52 −2.45 0.95 0.83 0.92
10 −1.75 0.97 −2.01 3.07 −2.46 8.00 −2.31 24.39 −2.10 1.02 0.81 1.24
100 −1.99 0.70 −1.95 3.05 −2.12 8.80 −1.95 26.45 −1.81 1.09 0.72 1.63
103 −2.08 0.63 −2.20 1.04 −1.79 9.00 −1.66 25.90 −1.57 1.14 0.57 2.03
10−3 100 −1.30 0.26 −1.28 1.27 −2.26 9.42 −4.53 22.30 −18.68 0.87 0.71 0.95
0.01 −1.30 0.43 −1.34 1.66 −2.38 11.39 −3.87 58.87 −18.11 0.89 0.67 1.11
0.1 −1.30 0.33 −1.32 1.51 −2.22 7.08 −2.94 78.04 −4.24 0.88 0.62 1.25
1 −1.30 0.35 −1.47 1.64 −2.20 7.05 −2.78 25.12 −2.53 0.92 0.64 1.35
10 −1.30 0.35 −1.67 2.06 −2.12 7.25 −2.43 24.79 −2.15 0.96 0.62 1.62
100 −1.30 0.35 −1.96 0.90 −1.60 2.10 −2.03 24.89 −1.85 1.02 0.56 1.93
103 −1.30 0.35 −2.15 0.82 −1.74 18.08 −1.64 36.40 −1.58 1.05 0.45 2.23
10−3 103 −1.30 1.37 −2.31 9.37 −3.20 18.75 −8.04 24.44 −37.78 0.88 0.71 1.12
0.01 −1.30 1.35 −2.17 13.37 −3.83 50.00 −7.68 65.52 −40.60 0.88 0.62 1.46
0.1 −1.30 1.18 −1.89 5.47 −2.42 13.20 −3.00 77.98 −4.40 0.88 0.56 1.70
1 −1.30 1.20 −1.89 5.79 −2.41 15.85 −2.94 25.35 −2.59 0.88 0.54 1.79
10 −1.30 1.25 −1.78 5.73 −2.24 16.22 −2.51 26.27 −2.20 0.88 0.45 2.09
100 −1.30 1.30 −1.70 5.22 −2.00 13.44 −2.04 30.19 −1.87 0.88 0.37 2.34
103 −1.30 1.32 −1.62 4.82 −1.74 23.13 −1.64 43.16 −1.59 0.88 0.29 2.52
10−3 104 −1.30 1.41 −2.34 10.67 −3.45 19.35 −7.39 24.35 −34.27 0.88 0.71 1.11
0.01 −1.30 1.31 −2.13 12.65 −2.40 31.59 −4.91 62.55 −26.49 0.88 0.59 1.79
0.1 −1.30 1.18 −2.02 4.00 −2.00 27.97 −3.12 73.28 −4.39 0.88 0.52 2.08
1 −1.30 1.19 −1.94 11.94 −1.97 27.27 −2.77 77.57 −3.19 0.88 0.48 2.21
10 −1.30 1.19 −1.74 2.09 −1.68 6.29 −1.85 26.43 −2.39 0.88 0.37 2.56
100 −1.30 1.14 −1.48 6.18 −1.75 26.88 −2.06 44.84 −1.98 0.88 0.30 2.75
103 −1.30 1.18 −1.36 5.91 −1.62 27.85 −1.72 44.22 −1.65 0.88 0.24 2.77

Notes. The quantities f dg ⋆ $ f^{\star}_{\mathrm{dg}} $, (1–fret)⋆ and f SN 2 ⋆ $ f^{\star}_{\mathrm{SN2}} $ represent the value of the dwarf-to-giant ratio, of the mass fraction locked in low-mass stars, and of the Type II SNe fraction, respectively, relative to the same quantities computed for an MW-like IMF with a Kroupa (2001) multislope functional form.

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