Table B.8
Fit coefficients (for our main fit and scatter fit) and fit quality for line intensity ratios in cold dense medium conditions.
| Line intensity ratio | Main fit coefficients | R2 | RMSE | Max. abs. error | Scatter fit coefficients | Validity limits | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| a0 | a1 | a2 | a3 | a4 | a5 | dex | (equ. factor) | dex | (equ. factor) | b0 | b1 | b2 | b3 | b4 | b5 | min. | max. | ||
| CF+ (1−0)/DCO+ (1−0) | –6.135(0) | 3.377(–1) | –2.109(–1) | 1.007(–1) | 1.967(–2) | –9.665(–3) | 0.85 | 0.31 | (2.05) | 1.56 | (36.47) | –2.594(–2) | 8.830(–2) | –1.892(–2) | –2.429(–2) | 1.676(–3) | 2.274(–3) | –2.595 | 2.655 |
| 13CO (1−0)/HCO+ (1−0) | –7.891(0) | 1.249(0) | 2.200(0) | –3.222(0) | 1.556(0) | –2.556(–1) | 0.86 | 0.31 | (2.03) | 1.48 | (30.31) | 1.278(–1) | 4.071(–2) | –2.886(–1) | 2.660(–1) | –9.483(–2) | 1.212(–2) | –0.256 | 2.245 |
| CN (1−0)/N2H+ (1−0) | –6.192(0) | 5.913(–1) | –2.320(–1) | 2.217(–2) | 4.920(–2) | 5.057(–3) | 0.86 | 0.30 | (2.01) | 1.76 | (57.06) | –7.328(–3) | 9.392(–2) | –6.054(–2) | –3.017(–2) | 1.027(–2) | 3.238(–3) | –2.724 | 1.569 |
| C2H (1−0)/N2H+ (1−0) | –5.845(0) | 6.220(–2) | 1.010(–1) | 1.101(–1) | 1.754(–2) | 5.489(–4) | 0.81 | 0.36 | (2.28) | 1.53 | (34.06) | –3.781(–2) | 8.024(–2) | 6.650(–2) | 2.219(–3) | –2.629(–3) | –2.851(–4) | –4.812 | 0.850 |
| HCO+ (1−0)/CF+ (1−0) | –4.345(0) | –4.877(0) | 5.810(0) | –3.156(0) | 7.136(–1) | –5.632(–2) | 0.83 | 0.34 | (2.17) | 1.20 | (15.83) | 1.481(–1) | –2.119(–1) | –2.246(–2) | 1.454(–1) | –5.678(–2) | 6.267(–3) | 0.394 | 3.633 |
| C2H (1−0)/HCN (1−0) | –1.549(0) | 7.331(0) | 5.080(0) | 1.688(0) | 2.482(–1) | 1.316(–2) | 0.81 | 0.35 | (2.25) | 1.62 | (41.39) | –1.069(0) | –1.616(0) | –9.046(–1) | –2.325(–1) | –2.917(–2) | –1.464(–3) | –5.536 | –1.255 |
| 13CO (1−0)/DCO+ (1−0) | –7.370(0) | –2.501(0) | 3.053(0) | –1.165(0) | 1.927(–1) | –1.172(–2) | 0.82 | 0.35 | (2.23) | 1.86 | (73.12) | –7.237(–1) | 1.605(0) | –9.307(–1) | 2.022(–1) | –1.423(–2) | –1.181(–4) | 0.756 | 5.025 |
| C2H (1−0)/HNC (1−0) | –1.028(–2) | 9.830(0) | 6.576(0) | 2.094(0) | 2.993(–1) | 1.558(–2) | 0.80 | 0.36 | (2.32) | 1.47 | (29.19) | –1.383(0) | –2.176(0) | –1.200(0) | –2.985(–1) | –3.579(–2) | –1.708(–3) | –5.182 | –1.288 |
| C18O (1−0)/DCO+ (1−0) | –7.844(0) | –4.830(–1) | 1.819(0) | –9.231(–1) | 1.932(–1) | –1.474(–2) | 0.81 | 0.35 | (2.26) | 1.74 | (54.66) | 2.188(–2) | 5.469(–1) | –5.232(–1) | 1.525(–1) | –9.905(–3) | –9.963(–4) | 0.092 | 3.865 |
| C2H (1−0)/DCO+ (1−0) | –6.040(0) | 1.684(–1) | –7.619(–2) | 2.643(–2) | 8.393(–3) | 4.276(–4) | 0.80 | 0.37 | (2.33) | 1.51 | (32.15) | 1.618(–2) | 5.016(–2) | –3.621(–2) | –3.914(–3) | 3.470(–3) | 5.088(–4) | –5.195 | 2.316 |
| CF+ (1−0)/N2H+ (1−0) | –5.718(0) | 6.358(–2) | –8.785(–2) | 1.745(–1) | 2.604(–2) | –5.295(–3) | 0.77 | 0.39 | (2.45) | 1.85 | (70.03) | 6.231(–2) | –9.758(–2) | –1.812(–1) | 4.513(–2) | 6.121(–2) | 1.077(–2) | –3.235 | 0.988 |
| C2H (1−0)/HCO+ (1−0) | –5.226(0) | 1.683(0) | 1.393(0) | 5.332(–1) | 8.166(–2) | 4.315(–3) | 0.78 | 0.38 | (2.39) | 1.13 | (13.61) | –1.098(–1) | –2.630(–1) | –1.013(–1) | 1.043(–2) | 6.635(–3) | 5.457(–4) | –6.029 | –0.182 |
| CN (1−0)/DCO+ (1−0) | –6.975(0) | 5.955(–1) | 1.245(–2) | –2.396(–2) | –5.134(–4) | 1.198(–3) | 0.78 | 0.38 | (2.40) | 1.59 | (38.68) | 2.178(–1) | –6.718(–2) | –6.819(–2) | 2.032(–2) | 6.423(–3) | –1.715(–3) | –2.563 | 3.009 |
| C18O (1−0)/HCO+ (1−0) | –7.081(0) | 1.597(0) | 3.871(–1) | –8.281(–1) | –1.822(–1) | 2.346(–1) | 0.75 | 0.40 | (2.53) | 1.33 | (21.38) | 2.098(–1) | –1.281(–1) | –1.887(–1) | 1.840(–1) | 6.022(–2) | –6.323(–2) | –1.069 | 1.247 |
| HCO+ (1−0)/CN (1−0) | –6.004(0) | –7.336(–1) | –1.856(–1) | 1.466(–1) | –3.290(–2) | 2.461(–3) | 0.75 | 0.41 | (2.54) | 1.85 | (70.06) | 7.670(–2) | 1.316(–1) | 6.624(–2) | –5.588(–2) | 2.769(–4) | 1.978(–3) | –0.758 | 3.627 |
| HCN (1−0)/CN (1−0) | –1.018(1) | 1.609(1) | –2.134(1) | 1.173(1) | –2.950(0) | 2.796(–1) | 0.75 | 0.41 | (2.54) | 2.12 | (130.92) | –3.482(0) | 9.487(0) | –8.900(0) | 3.847(0) | –7.821(–1) | 6.019(–2) | 0.709 | 3.254 |
| HNC (1−0)/CN (1−0) | –1.461(1) | 2.959(1) | –3.630(1) | 1.954(1) | –4.900(0) | 4.671(–1) | 0.75 | 0.41 | (2.55) | 1.65 | (44.57) | –1.763(0) | 4.808(0) | –4.132(0) | 1.530(0) | –2.379(–1) | 1.035(–2) | 0.790 | 3.186 |
| SO (3−2)/C2H (1−0) | –5.883(0) | 1.034(–1) | 3.381(–2) | –9.485(–2) | 1.943(–2) | –1.108(–3) | 0.72 | 0.43 | (2.69) | 1.33 | (21.50) | 9.812(–2) | –5.068(–2) | –4.320(–2) | 4.111(–2) | –8.104(–3) | 4.591(–4) | –1.179 | 6.475 |
| SO (3−2)/CN (1−0) | –5.963(0) | –3.237(–1) | –3.231(–1) | 2.195(–2) | 4.249(–2) | –8.218(–3) | 0.70 | 0.45 | (2.80) | 1.52 | (33.48) | 1.028(–1) | 8.595(–2) | 4.488(–2) | –1.190(–2) | –8.902(–3) | 1.850(–3) | –2.035 | 3.640 |
| CS (2−1)/C2H (1−0) | –5.861(0) | 3.386(–2) | –6.629(–2) | –6.863(–2) | 2.034(–2) | –1.455(–3) | 0.70 | 0.45 | (2.79) | 1.42 | (26.59) | 6.795(–2) | –1.756(–2) | 2.382(–3) | 2.284(–2) | –6.713(–3) | 4.937(–4) | –1.434 | 6.536 |
| SO (3−2)/13CO (1−0) | –7.396(0) | –1.359(0) | 5.844(–1) | 1.010(0) | 3.542(–1) | 3.815(–2) | 0.67 | 0.47 | (2.94) | 1.51 | (32.26) | 2.849(–1) | 7.080(–2) | –2.698(–1) | –2.670(–1) | –8.877(–2) | –9.795(–3) | –3.128 | 0.524 |
| H2CS (3−2)/C2H (1−0) | –6.136(0) | –4.376(–1) | –1.052(–1) | 2.297(–2) | 4.201(–3) | –7.259(–4) | 0.68 | 0.46 | (2.90) | 1.48 | (30.37) | 8.699(–2) | 1.545(–1) | –3.579(–3) | –1.589(–2) | 2.899(–3) | –1.406(–4) | –2.233 | 5.002 |
| 13CO (1−0)/N2H+ (1−0) | –7.687(0) | –3.644(–1) | 1.591(0) | –6.888(–1) | 1.063(–1) | –4.774(–3) | 0.65 | 0.48 | (3.02) | 2.24 | (172.53) | 9.971(–2) | 2.723(–1) | 3.714(–1) | –5.808(–1) | 2.048(–1) | –2.165(–2) | –0.090 | 3.179 |
| SO (3−2)/CF+ (1−0) | –5.838(0) | 2.436(–1) | –1.341(–1) | –1.769(–1) | 5.994(–2) | –4.735(–3) | 0.63 | 0.49 | (3.12) | 1.51 | (32.21) | 5.810(–2) | –6.434(–3) | 1.630(–2) | 7.035(–3) | 2.821(–3) | –1.160(–3) | –0.838 | 3.612 |
| CS (2−1)/CN (1−0) | –6.269(0) | –4.353(–1) | –2.154(–1) | 3.254(–2) | 2.412(–2) | –5.177(–3) | 0.64 | 0.49 | (3.06) | 1.61 | (41.05) | 2.456(–1) | 1.704(–1) | –6.298(–2) | –2.131(–2) | 7.203(–3) | –3.129(–4) | –2.125 | 3.381 |
| C2H (1−0)/CF+ (1−0) | –5.877(0) | 7.235(–1) | –1.044(0) | –1.034(0) | –3.814(–1) | –4.969(–2) | 0.63 | 0.49 | (3.11) | 1.67 | (46.37) | 4.812(–2) | –3.066(–2) | 4.094(–1) | 1.477(–1) | –6.908(–2) | –2.336(–2) | –2.231 | 0.380 |
| HNC (1−0)/DCO+ (1−0) | –7.445(0) | –9.709(–1) | 1.543(0) | –5.990(–1) | 1.047(–1) | –7.187(–3) | 0.60 | 0.52 | (3.27) | 1.96 | (91.56) | 7.342(–2) | 2.833(–1) | 2.507(–1) | –3.250(–1) | 9.346(–2) | –8.171(–3) | 0.152 | 3.964 |
| SO (3−2)/HNC (1−0) | –7.068(0) | –1.115(0) | 4.761(–1) | 4.592(–1) | –5.606(–3) | –2.580(–2) | 0.52 | 0.56 | (3.66) | 1.93 | (85.05) | 3.942(–1) | 7.041(–2) | –2.838(–1) | –2.959(–2) | 9.907(–2) | 2.645(–2) | –1.408 | 1.023 |
| SO (3− 2)/HCN (1− 0) | –7.078(0) | –1.083(0) | 5.829(–1) | 4.300(–1) | –7.650(–2) | –4.289(–2) | 0.50 | 0.57 | (3.74) | 1.78 | (60.45) | 4.082(–1) | 1.217(–1) | –2.744(–1) | –9.133(–2) | 6.756(–2) | 2.311(–2) | –1.864 | 1.181 |
| H2 CS (3− 2)/CN (1− 0) | –7.083(0) | –6.115(–1) | 2.391(–2) | 7.134(–2) | –3.526(–3) | –4.954(–3) | 0.56 | 0.54 | (3.43) | 1.77 | (58.42) | 4.373(–1) | –1.234(–1) | –1.023(–1) | 4.550(–2) | 5.825(–3) | –3.198(–3) | –3.134 | 2.190 |
| HCN (1− 0)/DCO+ (1− 0) | –7.472(0) | –3.954(–1) | 5.704(–1) | –1.092(–2) | –4.384(–2) | 6.173(–3) | 0.56 | 0.54 | (3.45) | 1.96 | (92.06) | 1.076(–1) | 3.150(–1) | 2.249(–1) | –3.267(–1) | 9.620(–2) | –8.474(–3) | 0.057 | 3.979 |
| C2 H (1− 0)/13CO (1− 0) | –2.520(1) | –2.705(1) | –1.383(1) | –3.247(0) | –3.614(–1) | –1.540(–2) | 0.54 | 0.55 | (3.54) | 1.37 | (23.61) | –9.851(–1) | –9.986(–1) | –5.750(–1) | –2.002(–1) | –3.112(–2) | –1.668(–3) | –5.006 | –2.101 |
| SO (3− 2)/C18O (1− 0) | –6.758(0) | –1.072(0) | –1.279(–1) | 2.362(–1) | 6.525(–2) | –2.967(–4) | 0.54 | 0.55 | (3.55) | 2.14 | (138.67) | 3.792(–1) | 2.370(–1) | –3.064(–1) | –1.103(–1) | 6.841(–2) | 2.218(–2) | –2.133 | 1.288 |
| C18O (1− 0)/N2 H+ (1− 0) | –7.435(0) | 5.433(–1) | 4.916(–1) | 4.396(–2) | –1.683(–1) | 3.367(–2) | 0.55 | 0.54 | (3.49) | 2.35 | (223.45) | 3.622(–1) | 3.660(–1) | –3.032(–1) | –2.749(–1) | 2.035(–1) | –3.178(–2) | –0.869 | 2.399 |
| HNC (1− 0)/N2 H+ (1− 0) | –7.479(0) | –1.201(–1) | 2.498(0) | –1.729(0) | 4.207(–1) | –2.895(–2) | 0.55 | 0.54 | (3.50) | 2.03 | (107.25) | 9.170(–2) | 1.183(0) | 1.686(–1) | –2.126(0) | 1.303(0) | –2.215(–1) | –0.178 | 2.560 |
| HCS+ (2− 1)/C2 H (1− 0) | –6.910(0) | –4.969(–1) | 9.186(–2) | 1.739(–2) | –8.200(–3) | 4.164(–4) | 0.52 | 0.56 | (3.66) | 1.72 | (52.43) | 4.306(–1) | 4.465(–2) | –7.944(–2) | 3.195(–3) | 4.950(–3) | –6.888(–4) | –2.785 | 3.211 |
| HCO+ (1− 0)/HNC (1− 0) | –7.297(0) | –1.051(0) | 1.048(0) | 6.128(–1) | –3.643(–1) | –1.887(–1) | 0.54 | 0.55 | (3.56) | 2.03 | (107.01) | 3.815(–1) | 1.841(–1) | –2.198(–1) | –2.694(–1) | –1.498(–1) | –3.694(–2) | –1.683 | 0.721 |
| C2 H (1− 0)/C18O (1− 0) | –7.648(0) | –5.022(0) | –3.999(0) | –1.225(0) | –1.670(–1) | –8.382(–3) | 0.50 | 0.57 | (3.73) | 1.41 | (25.63) | 4.605(–1) | 5.719(–1) | 2.782(–1) | 1.040(–1) | 1.839(–2) | 1.092(–3) | –4.824 | –1.091 |
| CS (2− 1)/CF+ (1− 0) | –5.922(0) | –1.527(–1) | –2.376(–1) | –5.469(–2) | 4.886(–2) | –6.188(–3) | 0.52 | 0.56 | (3.64) | 2.05 | (111.81) | 1.150(–2) | 2.021(–1) | 8.627(–2) | –4.137(–2) | –2.773(–3) | 1.295(–3) | –1.449 | 3.578 |
| HCO+ (1− 0)/DCO+ (1− 0) | –1.911(0) | –2.238(1) | 3.036(1) | –1.799(1) | 5.000(0) | –5.278(–1) | 0.52 | 0.57 | (3.67) | 2.53 | (341.17) | –1.131(0) | 3.237(0) | –3.531(0) | 2.419(0) | –8.588(–1) | 1.124(–1) | 0.735 | 1.721 |
| HCO+ (1− 0)/HCN (1− 0) | –7.307(0) | –9.731(–1) | 1.345(0) | 6.279(–1) | –5.966(–1) | –2.808(–1) | 0.51 | 0.57 | (3.69) | 2.06 | (115.42) | 4.043(–1) | 1.953(–1) | –2.770(–1) | –2.153(–1) | –2.202(–2) | 5.842(–3) | –1.646 | 0.759 |
| CS (2− 1)/HCS+ (2− 1) | –2.476(1) | 4.266(1) | –3.509(1) | 1.376(1) | –2.687(0) | 2.108(–1) | 0.51 | 0.57 | (3.72) | 1.86 | (72.47) | 1.533(1) | –3.793(1) | 3.431(1) | –1.445(1) | 2.903(0) | –2.257(–1) | 1.659 | 3.594 |
Notes. We list the fit coefficients for predicting log10(x(e−) (according to the fit formula given in Eq. (2)), the quality of this fit estimated as the (cross-validated) R2, root mean square error (RMSE) on log10(x(e−) and corresponding error factor on x(e−), maximum absolute error factor on log10(x(e−)) and corresponding error factor on x(e−), the fit coefficients for estimating the uncertainty on the prediction (according to the fit formula given in Eq. (4)), and the validity range of the fit (given as log10 of the ratio values).
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