Table B.7
Fit coefficients (for our main fit and scatter fit) and fit quality for column density ratios in cold dense medium conditions.
| Column density | Main fit coefficients | R2 | RMSE | Max. abs. error | Scatter fit coefficients | Validity limits | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ratio | a0 | a1 | a2 | a3 | a4 | a5 | dex | (equ. factor) | dex | (equ. factor) | b0 | b1 | b2 | b3 | b4 | b5 | min. | max. | |
| CN/N2H+ | –7.561(0) | 7.191(–1) | 4.245(–2) | –5.030(–2) | 1.433(–3) | 1.432(–3) | 0.92 | 0.23 | (1.69) | 1.44 | (27.85) | 8.041(–2) | –7.902(–3) | –3.071(–2) | 1.565(–2) | –2.670(–3) | 1.433(–4) | –1.163 | 4.105 |
| HNC/CN | –6.688(0) | –1.441(0) | 2.400(–1) | 3.289(–1) | –2.172(–1) | 3.518(–2) | 0.89 | 0.27 | (1.88) | 1.14 | (13.87) | 8.695(–2) | –5.348(–2) | –2.167(–2) | 9.789(–2) | –5.606(–2) | 7.240(–3) | –0.867 | 2.167 |
| SO/HCS+ | –1.164(1) | 4.093(1) | –3.472(1) | 1.154(1) | –1.706(0) | 9.336(–2) | 0.83 | 0.33 | (2.16) | 1.77 | (58.35) | 1.986(1) | –2.280(1) | 1.065(1) | –2.512(0) | 2.960(–1) | –1.378(–2) | 3.190 | 5.651 |
| CN/DCO+ | –7.932(0) | 3.588(–1) | 4.656(–2) | 2.160(–2) | –1.182(–2) | 1.250(–3) | 0.88 | 0.28 | (1.92) | 1.17 | (14.69) | 7.834(–2) | 6.037(–2) | –9.351(–3) | –1.152(–2) | 3.247(–3) | –2.249(–4) | –1.046 | 5.488 |
| HCN/CN | –6.429(0) | –1.311(0) | –2.158(–2) | 2.582(–1) | –6.006(–2) | –3.863(–3) | 0.88 | 0.29 | (1.93) | 1.28 | (19.02) | 1.110(–1) | –1.312(–2) | –1.223(–1) | 9.218(–2) | –1.380(–3) | –7.957(–3) | –0.752 | 2.434 |
| HCO+/CN | –7.272(0) | –5.440(–1) | 5.703(–2) | 2.188(–2) | –4.248(–3) | –1.607(–3) | 0.82 | 0.34 | (2.20) | 1.61 | (41.13) | 1.712(–1) | 3.642(–3) | –3.996(–2) | –6.869(–3) | 3.220(–3) | 8.277(–4) | –3.149 | 2.640 |
| C2H/N2H+ | –6.105(0) | 3.568(–1) | –1.771(–1) | 9.534(–3) | 1.147(–2) | –7.543(–5) | 0.77 | 0.39 | (2.43) | 1.25 | (17.67) | 2.364(–2) | 1.214(–1) | –5.300(–2) | –2.543(–2) | 4.519(–3) | 1.639(–3) | –3.400 | 2.847 |
| C2H/DCO+ | –6.781(0) | 5.614(–1) | –6.852(–2) | –2.464(–2) | 4.068(–3) | 4.588(–4) | 0.81 | 0.35 | (2.25) | 1.47 | (29.48) | 1.484(–1) | –5.616(–2) | –2.227(–2) | 7.746(–3) | 1.215(–3) | –3.250(–4) | –3.210 | 4.432 |
| C18O/CN | –6.033(0) | –5.206(–1) | –7.988(–2) | 3.017(–3) | 1.172(–2) | –1.748(–3) | 0.81 | 0.36 | (2.27) | 1.24 | (17.32) | 7.942(–2) | 8.908(–2) | 1.171(–2) | –2.295(–2) | 4.440(–3) | –2.265(–4) | –0.940 | 5.042 |
| CF+/DCO+ | –6.565(0) | 8.365(–1) | –3.588(–1) | –2.491(–2) | 7.078(–2) | –1.264(–2) | 0.79 | 0.37 | (2.35) | 1.76 | (57.35) | 1.608(–1) | –1.133(–1) | –8.819(–2) | 3.772(–2) | 1.686(–2) | –5.617(–3) | –1.640 | 3.318 |
| 13CO/CN | –5.790(0) | 1.174(–1) | –4.659(–1) | 1.035(–1) | –4.918(–3) | –3.338(–4) | 0.79 | 0.37 | (2.36) | 1.75 | (56.62) | –1.861(–1) | 4.377(–1) | –1.777(–1) | 3.415(–2) | –3.900(–3) | 2.118(–4) | 0.385 | 5.961 |
| C2H/CF+ | –7.099(0) | 1.254(0) | 1.560(–2) | –3.191(–1) | 1.035(–2) | 4.254(–2) | 0.78 | 0.38 | (2.40) | 1.18 | (15.19) | 1.911(–1) | –1.025(–1) | –1.367(–1) | 9.891(–2) | 2.349(–2) | –1.613(–2) | –1.699 | 1.797 |
| SO/CN | –6.333(0) | –3.618(–1) | –6.588(–2) | 1.401(–2) | 2.745(–3) | –5.273(–4) | 0.78 | 0.38 | (2.40) | 1.22 | (16.73) | 1.287(–1) | 1.902(–2) | 4.003(–3) | 8.329(–4) | –7.636(–4) | 4.753(–5) | –3.358 | 5.549 |
| C2H/HCO+ | –6.097(0) | 1.859(–1) | –1.136(–1) | 5.531(–2) | 2.500(–2) | 2.227(–3) | 0.77 | 0.39 | (2.46) | 1.19 | (15.35) | 5.314(–2) | 4.352(–2) | –8.102(–2) | 1.599(–3) | 1.375(–2) | 1.961(–3) | –4.577 | 1.813 |
| CS/SO | –5.713(0) | 3.742(–1) | –1.150(0) | –1.653(0) | –1.125(0) | –2.430(–1) | 0.76 | 0.40 | (2.49) | 1.79 | (62.25) | 6.368(–2) | 2.650(–1) | 1.343(0) | 1.135(0) | 2.714(–1) | 5.662(–3) | –2.357 | –0.002 |
| C2H/C18O | –5.166(0) | 1.292(0) | 9.232(–1) | 3.319(–1) | 4.751(–2) | 2.334(–3) | 0.75 | 0.41 | (2.55) | 1.31 | (20.65) | –1.130(–1) | –3.125(–1) | –1.545(–1) | –1.194(–2) | 2.417(–3) | 2.642(–4) | –6.608 | –0.143 |
| C2H/13CO | –1.759(0) | 5.082(0) | 2.513(0) | 6.058(–1) | 6.581(–2) | 2.618(–3) | 0.75 | 0.41 | (2.55) | 1.30 | (20.14) | 4.727(–1) | 3.387(–1) | 1.868(–2) | –3.289(–2) | –6.941(–3) | –3.864(–4) | –7.591 | –1.542 |
| SO/C2H | –5.851(0) | –6.810(–2) | –6.714(–2) | –1.468(–2) | 5.136(–3) | –3.241(–4) | 0.71 | 0.44 | (2.72) | 1.37 | (23.66) | 5.503(–2) | –2.381(–2) | 1.215(–2) | 9.070(–3) | –2.495(–3) | 1.532(–4) | –2.114 | 8.543 |
| HCO+/CF+ | –5.631(0) | –6.854(–1) | 3.847(–1) | –1.052(–1) | –1.078(–1) | 3.214(–2) | 0.71 | 0.44 | (2.74) | 1.34 | (21.79) | 6.275(–2) | –7.457(–2) | –5.731(–1) | 8.260(–1) | –3.242(–1) | 3.815(–2) | –0.351 | 2.934 |
| H2CS/C2H | –6.798(0) | –5.504(–1) | 3.614(–3) | 2.847(–2) | –2.113(–4) | –5.451(–4) | 0.69 | 0.45 | (2.82) | 1.43 | (26.95) | 2.221(–1) | 7.335(–2) | –1.322(–2) | –5.414(–3) | 4.551(–4) | 7.322(–5) | –3.475 | 4.518 |
| H2CS/CN | –7.685(0) | –2.746(–1) | 1.395(–1) | –2.263(–2) | –2.562(–2) | –3.222(–3) | 0.70 | 0.45 | (2.80) | 1.37 | (23.30) | 1.732(–1) | –2.424(–2) | 3.817(–2) | –1.308(–2) | –1.419(–2) | –1.907(–3) | –4.966 | 1.603 |
| C2H/HCN | –5.412(0) | 4.796(–1) | 5.142(–1) | 4.294(–1) | 1.026(–1) | 7.489(–3) | 0.68 | 0.46 | (2.88) | 1.24 | (17.25) | –2.534(–1) | –1.044(0) | –1.024(0) | –3.568(–1) | –5.272(–2) | –2.858(–3) | –4.447 | –0.266 |
| HCS+/CN | –8.384(0) | –9.575(–1) | –7.642(–1) | –3.411(–1) | –5.939(–2) | –3.510(–3) | 0.69 | 0.46 | (2.85) | 1.57 | (37.23) | –9.782(–2) | –5.297(–1) | –4.655(–1) | –1.963(–1) | –3.530(–2) | –2.185(–3) | –6.784 | –0.246 |
| C2H/HNC | –5.444(0) | 5.237(–1) | 5.572(–1) | 4.900(–1) | 1.239(–1) | 9.559(–3) | 0.67 | 0.47 | (2.93) | 1.25 | (17.80) | –1.168(–1) | –7.700(–1) | –9.054(–1) | –3.404(–1) | –5.148(–2) | –2.703(–3) | –4.146 | –0.105 |
| HNC/DCO+ | –7.494(0) | –1.407(0) | 1.530(0) | –5.464(–1) | 9.408(–2) | –6.335(–3) | 0.67 | 0.47 | (2.92) | 1.76 | (58.10) | –1.085(–2) | –1.019(–1) | 5.482(–1) | –3.220(–1) | 6.689(–2) | –4.698(–3) | 0.764 | 5.131 |
| C18O/CF+ | 1.388(1) | –3.218(1) | 2.018(1) | –5.967(0) | 8.227(–1) | –4.278(–2) | 0.66 | 0.47 | (2.96) | 1.44 | (27.36) | –2.665(0) | 6.118(0) | –4.845(0) | 1.697(0) | –2.677(–1) | 1.557(–2) | 1.779 | 5.227 |
| 13CO/CF+ | 1.006(2) | –1.260(2) | 5.833(1) | –1.309(1) | 1.419(0) | –5.957(–2) | 0.66 | 0.48 | (2.99) | 1.43 | (26.82) | 4.435(0) | 5.410(–1) | –2.778(0) | 1.140(0) | –1.736(–1) | 9.169(–3) | 3.069 | 6.033 |
| HCN/DCO+ | –6.217(0) | –3.979(0) | 3.334(0) | –1.153(0) | 1.913(–1) | –1.224(–2) | 0.65 | 0.48 | (3.01) | 1.81 | (64.85) | –5.703(–1) | 8.276(–1) | –1.108(–1) | –7.561(–2) | 2.159(–2) | –1.533(–3) | 1.009 | 5.207 |
| CS/CN | –6.863(0) | –5.631(–1) | –1.615(–2) | 4.874(–2) | 1.232(–3) | –2.008(–3) | 0.65 | 0.48 | (3.01) | 1.46 | (29.04) | 3.074(–1) | 1.578(–2) | –3.348(–2) | 4.549(–3) | 1.180(–3) | –3.663(–4) | –3.742 | 3.316 |
| HCS+ /C2 H | –7.555(0) | –2.507(–1) | 1.150(–1) | –3.825(–3) | –8.251(–3) | –7.183(–4) | 0.64 | 0.49 | (3.08) | 1.57 | (36.90) | 3.142(–1) | –7.090(–2) | –4.661(–2) | 5.577(–3) | 3.154(–3) | 2.290(–4) | –5.144 | 2.446 |
| HNC/N2 H+ | –6.822(0) | –3.863(0) | 5.578(0) | –2.720(0) | 5.725(–1) | –4.307(–2) | 0.63 | 0.49 | (3.10) | 2.29 | (195.89) | –3.782(–1) | 2.183(0) | –2.288(0) | 1.006(0) | –2.056(–1) | 1.618(–2) | 0.298 | 3.465 |
| CN/CF+ | –8.292(0) | 4.875(–1) | 7.130(–2) | –4.240(–1) | 2.855(–1) | –4.862(–2) | 0.64 | 0.48 | (3.05) | 2.38 | (240.38) | 1.685(–3) | 8.331(–1) | –1.956(0) | 1.580(0) | –4.845(–1) | 4.920(–2) | –0.065 | 3.401 |
| SO/HNC | –6.355(0) | –5.639(–1) | –1.313(–1) | 6.174(–2) | 1.050(–2) | –3.664(–3) | 0.62 | 0.50 | (3.18) | 1.54 | (34.41) | 2.206(–1) | 1.144(–1) | –4.656(–3) | –1.157(–2) | –3.395(–4) | 3.928(–4) | –2.846 | 3.755 |
| SO/HCN | –6.466(0) | –6.205(–1) | –9.568(–2) | 7.446(–2) | 7.301(–3) | –4.182(–3) | 0.61 | 0.51 | (3.21) | 1.53 | (33.98) | 2.492(–1) | 1.161(–1) | –1.390(–2) | –1.235(–2) | 2.439(–4) | 3.870(–4) | –2.974 | 3.415 |
| CS/C2 H | –6.028(0) | –3.536(–1) | –9.409(–2) | 1.801(–2) | 2.176(–3) | –3.588(–4) | 0.60 | 0.52 | (3.28) | 1.59 | (39.23) | 5.485(–2) | 1.789(–1) | 9.862(–3) | –1.936(–2) | 3.054(–3) | –1.403(–4) | –2.127 | 5.830 |
| SO/CF+ | –5.813(0) | 3.743(–2) | 4.544(–2) | –1.101(–1) | 2.504(–2) | –1.587(–3) | 0.60 | 0.52 | (3.28) | 1.75 | (56.20) | 4.402(–2) | –2.032(–2) | 5.045(–3) | 2.516(–2) | –6.924(–3) | 4.744(–4) | –0.735 | 7.064 |
| HCN/N2 H+ | –6.045(0) | –5.187(0) | 5.600(0) | –2.231(0) | 3.893(–1) | –2.431(–2) | 0.59 | 0.52 | (3.30) | 2.37 | (231.91) | –8.023(–1) | 2.766(0) | –2.301(0) | 8.246(–1) | –1.379(–1) | 8.904(–3) | 0.506 | 3.553 |
| HCO+ /DCO+ | 8.131(0) | –4.927(1) | 5.478(1) | –2.793(1) | 6.803(0) | –6.392(–1) | 0.57 | 0.53 | (3.41) | 2.42 | (264.65) | –9.194(0) | 2.540(1) | –2.786(1) | 1.525(1) | –4.070(0) | 4.175(–1) | 1.074 | 2.103 |
| CF+ /N2 H+ | –5.896(0) | 4.777(–1) | –2.300(–1) | 3.024(–2) | 2.751(–2) | –1.222(–3) | 0.54 | 0.55 | (3.55) | 2.13 | (134.90) | 4.794(–2) | –6.315(–1) | 2.671(–1) | 3.412(–1) | –6.066(–2) | –4.304(–2) | –2.535 | 1.680 |
| HCO+ /HNC | –7.496(0) | –4.396(–1) | 7.013(–2) | –1.139(–1) | –3.859(–2) | 9.718(–4) | 0.53 | 0.56 | (3.61) | 2.48 | (302.40) | 3.875(–1) | –1.868(–1) | –2.885(–1) | –8.864(–2) | –6.456(–3) | 1.098(–3) | –2.711 | 0.660 |
| SO/H2 CS | 1.413(1) | –4.647(1) | 4.143(1) | –1.749(1) | 3.456(0) | –2.577(–1) | 0.51 | 0.57 | (3.68) | 1.81 | (64.14) | –1.221(1) | 2.515(1) | –1.995(1) | 7.625(0) | –1.397(0) | 9.857(–2) | 1.502 | 3.882 |
| HCO+ /HCN | –7.578(0) | –4.133(–1) | 5.389(–2) | –2.386(–2) | 3.404(–2) | 1.376(–2) | 0.50 | 0.57 | (3.73) | 2.55 | (357.99) | 3.530(–1) | –3.288(–1) | –4.007(–1) | –1.360(–1) | –1.345(–2) | 1.319(–3) | –2.769 | 0.427 |
| DCO+ /N2 H+ | –8.336(0) | –6.084(–2) | 1.634(0) | –3.723(–2) | –6.371(–1) | –1.646(–1) | 0.50 | 0.57 | (3.75) | 2.16 | (146.16) | –1.468(–2) | 1.147(0) | 4.358(0) | 4.314(0) | 1.752(0) | 2.586(–1) | –1.747 | 0.004 |
| C18O/HNC | –5.902(0) | –8.434(–1) | –5.550(–1) | 6.929(–1) | –2.584(–1) | 3.151(–2) | 0.50 | 0.58 | (3.76) | 1.96 | (90.47) | –2.582(–3) | 4.299(–1) | 5.236(–1) | –7.059(–1) | 2.471(–1) | –2.807(–2) | –0.418 | 2.894 |
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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