Table B.5
Fit coefficients (for our main fit and scatter fit) and fit quality for column density ratios in translucent medium conditions.
| Column density | Main fit coefficients | R2 | RMSE | Max. abs. error | Scatter fit coefficients | Validity limits | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ratio | fmax | a0 | a1 | a2 | a3 | a4 | a5 | dex | (equ. factor) | dex | (equ. factor) | b0 | b1 | b2 | b3 | b4 | b5 | min. | max. | |
| C2H/HCN | –3.635(0) | –8.370(–1) | 1.213(0) | 2.613(–1) | –7.071(–2) | –4.022(–2) | –3.973(–3) | 0.96 | 0.15 | (1.42) | 0.82 | (6.54) | 4.437(–2) | –2.067(–2) | –3.212(–2) | 3.046(–3) | 6.837(–3) | 1.128(–3) | –3.253 | 0.624 |
| C2H/13CO | –4.031(0) | 2.614(–1) | –8.546(0) | –8.138(0) | –2.676(0) | –3.822(–1) | –2.014(–2) | 0.93 | 0.19 | (1.54) | 1.09 | (12.22) | 2.720(–1) | 6.069(–1) | 5.294(–1) | 1.990(–1) | 3.313(–2) | 2.015(–3) | –5.636 | –1.402 |
| C18O/CF+ | –3.824(0) | 8.235(0) | –1.565(1) | 1.360(1) | –6.064(0) | 1.263(0) | –9.831(–2) | 0.93 | 0.19 | (1.53) | 0.74 | (5.52) | 5.740(–3) | –1.372(–3) | –2.414(–3) | 2.222(–2) | –1.045(–2) | 1.273(–3) | 0.310 | 4.291 |
| HCN/CF+ | –3.151(0) | –4.520(–1) | –7.391(–1) | –3.476(–1) | 5.622(–2) | 3.622(–2) | –6.675(–3) | 0.92 | 0.20 | (1.58) | 0.79 | (6.20) | –1.630(–2) | 3.703(–2) | 6.947(–2) | –1.994(–2) | –1.537(–2) | 4.409(–3) | 1.454 | 2.698 |
| C2H/C18O | –4.104(0) | 2.499(0) | 1.619(0) | –6.992(–1) | –4.739(–1) | –8.592(–2) | –4.882(–3) | 0.91 | 0.22 | (1.65) | 1.07 | (11.85) | 4.621(–2) | –2.457(–2) | 4.130(–2) | 5.330(–2) | 1.611(–2) | 1.478(–3) | –4.625 | –0.938 |
| HCN/CN | –3.948(0) | –1.851(0) | 3.336(–1) | –4.178(–1) | –1.094(1) | –1.086(1) | –3.002(0) | 0.88 | 0.25 | (1.78) | 1.82 | (65.92) | 1.486(–1) | 1.234(–1) | 2.341(–1) | 5.713(–1) | 4.508(–1) | 1.090(–1) | –2.119 | 0.092 |
| 13CO/CF+ | –3.861(0) | 9.452(1) | –1.327(2) | 7.579(1) | –2.152(1) | 2.990(0) | –1.622(–1) | 0.88 | 0.25 | (1.77) | 1.18 | (15.10) | –2.722(–1) | 1.420(0) | –1.649(0) | 7.481(–1) | –1.448(–1) | 1.003(–2) | 1.733 | 5.037 |
| SO/HCS+ | –3.937(0) | 7.348(0) | –1.481(1) | 1.225(1) | –4.821(0) | 8.667(–1) | –5.790(–2) | 0.85 | 0.28 | (1.91) | 1.10 | (12.67) | –7.201(–3) | –5.729(–2) | 8.149(–2) | 1.230(–2) | –1.518(–2) | 1.998(–3) | –0.588 | 4.940 |
| C2H/HNC | –3.525(0) | –1.265(0) | 9.225(–1) | –4.240(–2) | –1.323(–1) | 1.760(–2) | 1.387(–2) | 0.82 | 0.31 | (2.03) | 1.61 | (40.76) | 1.435(–1) | 7.221(–2) | –5.232(–2) | –3.427(–2) | 4.612(–3) | 3.616(–3) | –2.749 | 2.001 |
| HCO+/CF+ | –4.062(0) | 1.013(–1) | –1.493(0) | –5.710(–1) | 4.317(–1) | 2.263(–1) | –1.113(–1) | 0.82 | 0.30 | (2.01) | 1.15 | (14.13) | 1.473(–1) | 3.230(–2) | –6.171(–2) | –3.840(–2) | 6.062(–3) | 6.361(–3) | –2.187 | 2.343 |
| C2H/CN | –4.085(0) | 2.350(0) | 6.570(–1) | –5.369(0) | –4.544(0) | –1.383(0) | –1.455(–1) | 0.81 | 0.31 | (2.05) | 1.12 | (13.27) | –1.678(–1) | –8.364(–1) | –5.548(–1) | 3.671(–2) | 9.602(–2) | 1.703(–2) | –3.045 | –2.004 |
| 13CO/C18O | –4.413(0) | –1.376(3) | 4.285(3) | –3.801(3) | –4.142(2) | 1.950(3) | –6.427(2) | 0.81 | 0.31 | (2.05) | 1.06 | (11.53) | –2.662(1) | 9.190(1) | –1.232(2) | 8.077(1) | –2.599(1) | 3.294(0) | 1.537 | 1.746 |
| C2H/HCO+ | –4.040(0) | –7.828(–1) | 8.847(–1) | 6.397(–2) | –8.373(–2) | 1.195(–3) | 6.546(–3) | 0.77 | 0.35 | (2.22) | 1.29 | (19.71) | 2.277(–1) | 4.613(–2) | –7.111(–2) | –2.400(–3) | 5.612(–3) | –3.318(–4) | –2.675 | 2.561 |
| SO/C2H | –3.726(0) | –1.373(0) | –5.037(–1) | 2.892(–2) | 2.025(–2) | –2.726(–4) | –5.281(–4) | 0.77 | 0.34 | (2.21) | 1.27 | (18.66) | 1.601(–1) | –5.940(–2) | –1.611(–2) | 3.737(–3) | 4.482(–4) | –4.508(–5) | –4.428 | 3.991 |
| HNC/CF+ | –3.953(0) | 3.128(–1) | –3.844(–1) | –5.504(–1) | –7.870(–1) | 7.526(–1) | –1.539(–1) | 0.76 | 0.35 | (2.25) | 1.31 | (20.28) | 1.545(–1) | 1.244(–1) | –5.586(–2) | –4.392(–2) | 5.847(–3) | 3.900(–3) | –3.233 | 2.420 |
| H2CS/C2H | –3.932(0) | –2.060(0) | –4.396(–2) | –3.645(–2) | –8.939(–2) | –1.980(–2) | –1.291(–3) | 0.75 | 0.36 | (2.30) | 1.20 | (15.91) | –6.965(–2) | 3.752(–2) | 1.385(–1) | 4.521(–2) | 5.197(–3) | 2.020(–4) | –7.441 | –0.375 |
| SO/CF+ | –3.911(0) | –6.385(–1) | –6.249(–1) | –4.971(–2) | 3.138(–2) | 5.788(–3) | –1.529(–3) | 0.74 | 0.37 | (2.33) | 1.27 | (18.42) | 2.277(–1) | –1.366(–2) | –3.289(–2) | –8.874(–4) | 1.036(–3) | 7.759(–5) | –3.604 | 3.682 |
| CN/CF+ | –3.930(0) | 1.246(2) | –3.004(2) | 2.888(2) | –1.369(2) | 3.170(1) | –2.863(0) | 0.73 | 0.37 | (2.36) | 1.58 | (37.65) | 2.958(–1) | –4.309(–1) | –1.273(0) | 2.041(0) | –8.987(–1) | 1.239(–1) | 1.265 | 2.891 |
| CS/SO | –4.138(0) | 1.013(–2) | 1.554(0) | –1.174(0) | –9.575(–1) | 4.480(–1) | 3.229(–1) | 0.69 | 0.40 | (2.52) | 1.77 | (59.26) | 3.102(–1) | –1.434(–1) | –2.798(–1) | 1.635(–1) | 5.832(–2) | –3.287(–2) | –1.316 | 2.510 |
| C18O/CN | –4.120(–1) | –4.024(0) | –1.043(0) | –5.355(–1) | –1.223(–1) | 5.611(–1) | –1.755(–1) | 0.68 | 0.41 | (2.56) | 1.24 | (17.32) | 1.645(–1) | 6.466(–1) | –4.403(–1) | –1.157(0) | 1.123(0) | –2.616(–1) | –0.673 | 1.823 |
| HCO+/CN | 8.833(0) | –1.516(1) | 7.408(–1) | 3.082(0) | 1.917(0) | 4.716(–1) | 4.116(–2) | 0.66 | 0.42 | (2.64) | 2.14 | (136.69) | –2.239(–2) | 8.260(–1) | 2.605(0) | 1.973(0) | 5.569(–1) | 5.327(–2) | –4.482 | 0.377 |
| SO/CN | –3.978(0) | –1.821(0) | –4.141(–1) | 2.051(–1) | 2.088(–2) | –1.389(–2) | –2.321(–3) | 0.65 | 0.43 | (2.68) | 1.44 | (27.28) | 8.152(–2) | –1.765(–1) | –1.356(–3) | 2.063(–2) | 2.697(–3) | 1.888(–5) | –4.865 | 0.783 |
| HNC/CN | –4.201(0) | –1.808(0) | –8.136(–1) | –1.069(1) | –2.839(1) | –2.231(1) | –5.527(0) | 0.61 | 0.45 | (2.83) | 1.27 | (18.44) | –1.931(–2) | 1.551(0) | 5.046(0) | 4.541(0) | 1.585(0) | 1.917(–1) | –3.301 | –0.490 |
| CS/C2H | –3.770(0) | –1.192(0) | –7.400(–1) | 7.328(–3) | 5.782(–2) | 1.405(–3) | –2.178(–3) | 0.63 | 0.44 | (2.75) | 1.33 | (21.20) | 2.706(–1) | –9.081(–2) | –4.556(–2) | 1.102(–2) | 1.754(–3) | –3.864(–4) | –1.312 | 2.180 |
| CS/HCS+ | –3.648(0) | 2.920(2) | –5.013(2) | 3.417(2) | –1.149(2) | 1.896(1) | –1.228(0) | 0.64 | 0.44 | (2.74) | 1.48 | (30.19) | –3.115(0) | 1.318(1) | –1.535(1) | 7.549(0) | –1.661(0) | 1.350(–1) | 2.258 | 3.604 |
| H2CS/HCS+ | –3.991(0) | –9.394(–1) | –1.776(0) | 1.009(0) | 1.073(0) | –3.221(–1) | –2.743(–1) | 0.62 | 0.45 | (2.80) | 1.57 | (37.31) | 3.064(–1) | 7.900(–2) | –1.855(–1) | –7.805(–2) | –1.412(–3) | 1.601(–3) | –1.386 | 0.693 |
| H2CS/CF+ | –3.881(0) | –1.970(0) | –2.273(–1) | –4.858(–2) | –7.103(–2) | –1.508(–2) | –9.724(–4) | 0.62 | 0.45 | (2.82) | 1.31 | (20.40) | 2.987(–2) | –9.972(–2) | 9.940(–2) | 5.239(–2) | 7.456(–3) | 3.323(–4) | –6.112 | –0.673 |
| HCS+/C2H | –4.110(0) | –1.786(0) | –7.555(–1) | –1.665(0) | –1.042(0) | –2.232(–1) | –1.584(–2) | 0.57 | 0.48 | (2.99) | 1.89 | (77.03) | 1.135(–1) | 1.207(–1) | 1.116(–1) | 9.235(–2) | 2.315(–2) | 1.738(–3) | –5.545 | –1.885 |
| SO/13CO | –4.194(0) | –1.879(0) | –1.026(0) | –1.531(0) | –8.797(–1) | –1.806(–1) | –1.243(–2) | 0.56 | 0.48 | (3.03) | 1.42 | (26.19) | 1.702(–1) | 8.542(–1) | 8.353(–1) | 2.667(–1) | 3.510(–2) | 1.657(–3) | –5.763 | –1.594 |
| C2 H/CF+ | –4.550(0) | –1.147(0) | 4.789(–1) | 2.745(0) | 4.953(0) | –2.355(–1) | –2.466(0) | 0.51 | 0.51 | (3.22) | 2.30 | (201.21) | 2.612(–1) | 7.017(–1) | –4.663(–1) | –6.193(–1) | 3.600(–1) | 1.172(–2) | 0.299 | 1.473 |
| SO/HNC | –4.145(0) | –8.731(–1) | –1.090(0) | 9.796(–2) | 1.584(–1) | –2.686(–3) | –1.105(–2) | 0.51 | 0.51 | (3.22) | 1.41 | (25.80) | 3.250(–1) | –2.133(–1) | –1.030(–1) | 3.483(–2) | 9.133(–3) | –8.541(–4) | –2.371 | 0.647 |
| SO/HCN | –4.004(0) | –1.455(0) | –8.495(–1) | 2.256(–1) | 1.154(–1) | –1.973(–2) | –8.133(–3) | 0.50 | 0.51 | (3.24) | 1.59 | (38.96) | 2.539(–1) | –2.286(–1) | –7.418(–2) | 2.577(–2) | 9.280(–3) | 6.229(–4) | –3.316 | 0.305 |
| CS/CF+ | –3.887(0) | –4.910(–1) | –6.626(–1) | –1.164(–1) | 3.678(–2) | 1.710(–2) | –3.709(–3) | 0.50 | 0.51 | (3.25) | 1.43 | (26.71) | 3.976(–1) | 6.585(–2) | –8.564(–2) | –1.212(–2) | 3.812(–3) | 4.385(–4) | –1.948 | 2.035 |
Notes. We list the fit coefficients for predicting log10(x(e−) (according to the fit formula given in Eq. (3)), 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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