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Home All issues Volume 645 (January 2021) A&A, 645 (2021) A28 Full HTML

Table B.4

Ranking of line intensity ratios according to their usefulness to predict the ionization fraction in dense cold medium conditions (measured through the R2 of a fitted Random Forest model).

Line intensity ratio Random Forest model Analytical fit
R2 Root mean square error Maximum absolute error R2
dex (equ. factor) dex (equ. factor)
CF+ (1− 0)/DCO+ (1−0) 0.86 0.30 (2.00) 1.57 (36.93) 0.85
13CO (1− 0)/HCO+ (1−0) 0.86 0.30 (2.01) 1.45 (27.93) 0.86
CN (1− 0)/N2 H+ (1−0) 0.86 0.30 (2.01) 1.83 (66.88) 0.86
C2 H (1− 0)/N2 H+ (1−0) 0.86 0.31 (2.04) 1.09 (12.29) 0.81
HCO+ (1− 0)/CF+ (1−0) 0.84 0.33 (2.12) 1.14 (13.75) 0.83
C2 H (1− 0)/HCN (1− 0) 0.83 0.34 (2.19) 1.32 (20.69) 0.81
13CO (1− 0)/DCO+ (1−0) 0.81 0.35 (2.24) 1.92 (82.34) 0.82
C2 H (1− 0)/HNC (1− 0) 0.81 0.35 (2.24) 1.35 (22.14) 0.80
C18O (1− 0)/DCO+ (1−0) 0.81 0.35 (2.26) 1.77 (58.68) 0.81
C2 H (1− 0)/DCO+ (1−0) 0.80 0.36 (2.30) 1.58 (38.36) 0.80
CF+ (1− 0)/N2 H+ (1−0) 0.80 0.37 (2.32) 2.09 (122.49) 0.77
C2 H (1− 0)/HCO+ (1−0) 0.79 0.37 (2.37) 1.19 (15.64) 0.78
CN (1− 0)/DCO+ (1− 0) 0.78 0.38 (2.41) 1.58 (37.69) 0.78
C18O (1− 0)/HCO+ (1−0) 0.76 0.40 (2.52) 1.30 (20.13) 0.75
HCO+ (1− 0)/CN (1− 0) 0.75 0.41 (2.55) 1.83 (67.50) 0.75
HCN (1− 0)/CN (1− 0) 0.75 0.41 (2.56) 2.18 (152.46) 0.75
HNC (1− 0)/CN (1− 0) 0.75 0.41 (2.57) 1.64 (43.67) 0.75
SO (3− 2)/C2 H (1− 0) 0.73 0.43 (2.66) 1.36 (22.71) 0.72
SO (3− 2)/CN (1− 0) 0.70 0.44 (2.78) 1.42 (26.59) 0.70
CS (2− 1)/C2 H (1− 0) 0.70 0.44 (2.79) 1.41 (25.43) 0.70
SO (3− 2)/13CO (1− 0) 0.69 0.45 (2.83) 1.71 (51.83) 0.67
H2 CS (3− 2)/C2 H (1−0) 0.68 0.46 (2.86) 1.45 (28.31) 0.68
13CO (1− 0)/N2 H+ (1−0) 0.65 0.48 (3.00) 2.30 (201.04) 0.65
SO (3− 2)/CF+ (1− 0) 0.64 0.49 (3.06) 1.46 (29.17) 0.63
CS (2− 1)/CN (1− 0) 0.64 0.49 (3.06) 1.62 (42.00) 0.64
C2 H (1− 0)/CF+ (1−0) 0.64 0.49 (3.09) 1.37 (23.67) 0.63
HNC (1− 0)/DCO+ (1− 0) 0.60 0.52 (3.28) 2.00 (99.15) 0.60
SO (3− 2)/HNC (1− 0) 0.58 0.53 (3.36) 1.64 (44.11) 0.52
SO (3− 2)/HCN (1− 0) 0.57 0.53 (3.41) 1.66 (45.48) 0.50
H2 CS (3− 2)/CN (1− 0) 0.56 0.54 (3.44) 1.86 (72.28) 0.56
HCN (1− 0)/DCO+ (1− 0) 0.56 0.54 (3.45) 1.99 (98.14) 0.56
C2 H (1− 0)/13CO (1−0) 0.56 0.54 (3.47) 1.38 (23.81) 0.54
SO (3− 2)/C18O (1− 0) 0.56 0.54 (3.47) 2.15 (140.92) 0.54
C18O (1− 0)/N2 H+ (1−0) 0.55 0.54 (3.48) 2.40 (248.83) 0.55
HNC (1− 0)/N2 H+ (1−0) 0.55 0.55 (3.52) 2.14 (138.57) 0.55
HCS+ (2− 1)/C2 H (1−0) 0.54 0.55 (3.53) 1.64 (43.65) 0.52
HCO+ (1− 0)/HNC (1− 0) 0.54 0.55 (3.57) 2.09 (123.36) 0.54
C2 H (1− 0)/C18O (1−0) 0.53 0.56 (3.61) 1.40 (25.06) 0.50
CS (2− 1)/CF+ (1− 0) 0.52 0.56 (3.64) 2.11 (127.92) 0.52
HCO+ (1− 0)/DCO+ (1−0) 0.52 0.57 (3.68) 2.71 (509.55) 0.52
HCO+ (1− 0)/HCN (1− 0) 0.51 0.57 (3.69) 2.16 (143.66) 0.51
CS (2− 1)/HCS+ (2− 1) 0.51 0.57 (3.73) 1.79 (61.10) 0.51

Notes. Additional error measures of the Random Forest model (root mean square error and maximum absolute errors) are also given. As these errors concern the logarithm of the ionization fraction, we also provide the equivalent error factors on the ionization fraction. For comparison, the R2 obtained with the analytical fit described in Sect. 5 is also listed in the last column.

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