Table 4
Comparison between the observed and RADEX model-predicted CH+ line fluxes obtained considering the physical parameters at CH+ ro-vibrational emission peak (noted in Table 3) from the CLOUDY modela.
| CH+ rotational lines | Rest frequency / wavelength | Upper state | Observed line flux | RADEX model predicted | Line flux ratio | |
|---|---|---|---|---|---|---|
| (v′, J′) → (v, J) | (GH/z / μm) | energy / kB (K) | (10−19 W cm−2) | line flux* | Optical depth | (Predicted / Observed) |
| (10−19 W cm−2) | (τ) | (Fpre/Fobs) | ||||
| (0, 1) → (0, 0) | 835.1375 / 358.9738 | 40 | 0.47 ± 0.01 | 0.52 | 2.77 | 1.11 ± 0.024 |
| (0, 2) → (0, 1) | 1669.2820 / 179.5937 | 120 | 1.51 ± 0.05 | 1.41 | 1.72 | 0.93 ± 0.031 |
| (0, 3) → (0, 2) | 2501.4430 / 119.8478 | 240 | 2.18 ± 0.17 | 1.05 | 1.63 × 10−1 | 0.48 ± 0.038 |
| (0, 4) → (0, 3) | 3330.6350 / 90.0106 | 400 | 2.00 ± 0.22 | 0.87 | 9.60 × 10−3 | 0.43 ± 0.048 |
| (0, 5) → (0, 4) | 4155.8795 / 72.1369 | 600 | 2.50 ± 0.41 | 0.67 | 1.90 × 10−3 | 0.27 ± 0.044 |
| (0, 6) → (0, 5) | 4976.2080 / 60.2452 | 838 | 2.41 ± 0.33 | 0.61 | 4.91 × 10−4 | 0.25 ± 0.035 |
| exp (μ) = 0.50(‡) | ||||||
| CH+ ro-vibrational lines | Rest wavelength | Upper state | Observed line flux | RADEX model predicted | Line flux ratio | |
| (v′, J′) → (v, J) | (μm) | energy / kB (K) | (10−18 W m−2) | line flux* | Optical depth | (Predicted / Observed) |
| (10−18 W m−2) | (τ) | (Fpre/Fobs) | ||||
| (1, 1) → (0, 0)[R(0)] | 3.6146 | 3980 | 2.35 ± 0.09 | 1.56 | 3.32 × 10−4 | 0.66 ± 0.025 |
| (1, 2) → (0, 1)[R(1)] | 3.5811 | 4058 | 2.18 ± 0.06 | 1.95 | 1.20 × 10−4 | 0.89 ± 0.025 |
| (1, 3) → (0, 2)[R(2)] | 3.5496 | 4174 | 1.47 ± 0.31 | 1.07 | 7.75 × 10−6 | 0.73 ± 0.153 |
| (1, 4) → (0, 3)[R(3)] | 3.5199 | 4328 | 1.09 ± 0.06 | 0.73 | 3.32 × 10−7 | 0.67 ± 0.037 |
| (1, 0) → (0, 1)[P(1)] | 3.6876 | 3942 | 3.97 ± 0.17 | 4.16 | 1.38 × 10−4 | 1.05 ± 0.045 |
| (1, 1) → (0, 2)[P(2)] | 3.7272 | 3980 | 7.38 ± 0.11 | 5.77 | 2.15 × 10−5 | 0.78 ± 0.012 |
| (1, 2) → (0, 3)[P(3)] | 3.7689 | 4058 | 8.33 ± 0.11 | 8.30 | 1.99 × 10−6 | 1.00 ± 0.013 |
| (1, 3) → (0, 4)[P(4)] | 3.8129 | 4174 | 7.67 ± 0.15 | 6.48 | 5.56 × 10−7 | 0.84 ± 0.017 |
| (1, 4) → (0, 5)[P(5)] | 3.8591 | 4328 | 7.21 ± 0.07 | 7.12 | 2.07 × 10−7 | 0.99 ± 0.01 |
| (1, 5) → (0, 6)[P(6)] | 3.9078 | 4520 | 6.45 ± 0.21 | 6.63 | 1.06 × 10−7 | 1.03 ± 0.033 |
| (1, 6) → (0, 7)[P(7)] | 3.9589 | 4751 | 6.52 ± 0.08 | 6.07 | 5.75 × 10−8 | 0.93 ± 0.011 |
| (1, 7) → (0, 8)[P(8)] | 4.0125 | 5019 | 5.04 ± 0.09 | 5.20 | 3.26 × 10−8 | 1.03 ± 0.018 |
| (1, 8) → (0, 9)[P(9)] | 4.0688 | 5324 | 4.20 ± 0.13 | 3.89 | 1.92 × 10−8 | 0.93 ± 0.029 |
| (1, 9) → (0, 10)[P(10)] | 4.1278 | 5667 | 3.46 ± 0.19 | 2.87 | 1.17 × 10−8 | 0.83 ± 0.046 |
| exp (μ) = 0.87(‡) | ||||||
Notes. * RADEX line flux is given erg s−1 cm−2. We converted them into beam-integrated fluxes by scaling to the observed angular sizes (see notes in Table 2) for direct comparison with the observations. a CLOUDY parameters obtained at CH+ ro-vibrational emission peak: Tkin = 1507 K, n(e−) = 5.55 × 102 cm−3, n(H) = 5.16 × 105 cm−3, N[CH+] = 6.09 × 1014 cm−2, line width (FWHM) = 30 km s−1. (‡) The quantity exp (μ) indicates the geometric mean of the factor by which the model reproduces the observations, where μ is the mean logarithmic ratio of model-predicted and observed line fluxes.
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