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Table 2

Comparison between the observed and CLOUDY model-predicted line fluxes.

HeH+ lines Rest wavelength Upper state Observed line flux CLOUDY model predicted Line flux ratio
(v′, J′) → (v, J) (μm) energy / kB (K) (10−18 W m−2) line flux(†) optical depth (Observed / Predicted)
(10−18 W m−2) (τ) (Fobs/Fpre)
(0, 1) → (0, 0) 149.091 96 163 ± 32(a) 49.14 4.92 × 10−2 3.32 ± 0.651
(1, 0) → (0, 1)[P(1)] 3.51532 4188 1.55 ± 0.16(b) 0.83 7.26 × 10−5 1.87 ± 0.193
(1, 1) → (0, 2)[P(2)] 3.60677 4277 2.08 ± 0.31(b) 0.93 4.50 × 10−6 2.25 ± 0.335
Recombination lines Rest wavelength Upper state Observed line flux(b) CLOUDY model predicted Line flux ratio
(μm) energy / kB (K) (10−18 W m−2) line flux(†) optical depth (Observed / Predicted)
(10−18 W m−2) (τ) (Fobs/Fpre)
H I 19 − 6 3.64493 − 23.9 ± 0.22 20.52 − 1.16 ± 0.011
He II 13 − 9 3.54328 − 53.7 ± 0.21 44.17 − 1.22 ± 0.005
He I 53D − 43P0 3.70256 − 8.44 ± 0.48 11.39 − 0.74 ± 0.042
CH+ rotational lines Rest Upper state Observed line flux CLOUDY model predicted Line flux ratio
(v′, J′) → (v, J) frequency / wavelength energy / kB (K) (10−19 W cm−2) line flux(*) optical depth (Predicted / Observed)
(GHz / μm) (10−19 W cm−2) (τ) (Fpre/Fobs)
(0, 1) → (0, 0) 835.1375 / 358.9738 40 0.47 ± 0.01(c) 1.21 9.19 2.57 ± 0.055
(0, 2) → (0, 1) 1669.2820 / 179.5937 120 1.51 ± 0.05(d) 4.54 10.69 3.01 ± 0.100
(0, 3) → (0, 2) 2501.4430 / 119.8478 240 2.18 ± 0.17(d) 3.67 1.44 1.69 ± 0.131
(0, 4) → (0, 3) 3330.6350 / 90.0106 400 2.00 ± 0.22(d) 2.70 8.14 × 10−2 1.35 ± 0.149
(0, 5) → (0, 4) 4155.8795 / 72.1369 600 2.50 ± 0.41(d) 1.88 9.86 × 10−3 0.75 ± 0.123
(0, 6) → (0, 5) 4976.2080 / 60.2452 838 2.41 ± 0.33(d) 1.53 2.27 × 10−3 0.63 ± 0.087
exp (μ) = 1.43(‡)
CH+ ro-vibrational lines Rest wavelength Upper state Observed line flux(e) CLOUDY 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 2.44 1.35 × 10−3 1.04 ± 0.040
(1, 2) → (0, 1)[R(1)] 3.5811 4058 2.18 ± 0.06 2.87 7.67 × 10−4 1.32 ± 0.036
(1, 3) → (0, 2)[R(2)] 3.5496 4174 1.47 ± 0.31 1.59 6.80 × 10−5 1.08 ± 0.228
(1, 4) → (0, 3)[R(3)] 3.5199 4328 1.09 ± 0.06 1.02 2.61 × 10−6 0.93 ± 0.051
(1, 0) → (0, 1)[P(1)] 3.6876 3942 3.97 ± 0.17 6.01 8.83 × 10−4 1.51 ± 0.065
(1, 1) → (0, 2)[P(2)] 3.7272 3980 7.38 ± 0.11 8.99 1.88 × 10−4 1.22 ± 0.018
(1, 2) → (0, 3)[P(3)] 3.7689 4058 8.33 ± 0.11 12.21 1.57 × 10−5 1.47 ± 0.019
(1, 3) → (0, 4)[P(4)] 3.8129 4174 7.67 ± 0.15 9.65 2.77 × 10−6 1.26 ± 0.025
(1, 4) → (0, 5)[P(5)] 3.8591 4328 7.21 ± 0.07 9.96 9.06 × 10−7 1.38 ± 0.013
(1, 5) → (0, 6)[P(6)] 3.9078 4520 6.45 ± 0.21 8.98 4.17 × 10−7 1.39 ± 0.045
(1, 6) → (0, 7)[P(7)] 3.9589 4751 6.52 ± 0.08 7.87 2.02 × 10−7 1.21 ± 0.015
(1, 7) → (0, 8)[P(8)] 4.0125 5019 5.04 ± 0.09 6.54 1.03 × 10−7 1.30 ± 0.023
(1, 8) → (0, 9)[P(9)] 4.0688 5324 4.20 ± 0.13 4.78 5.57 × 10−8 1.14 ± 0.035
(1, 9) → (0, 10)[P(10)] 4.1278 5667 3.46 ± 0.19 3.43 3.12 × 10−8 0.99 ± 0.054
exp (μ) = 1.22(‡)
H2 lines Rest wavelength Upper state Observed line flux(e) CLOUDY 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)
(0, 10) → (0, 8)[S(8)] 5.05174 8677 11.60 ± 0.23 71.16 3.52 × 10−7 6.13 ± 0.122
(0, 11) → (0, 9)[S(9)] 4.69333 10 261 19.04 ± 0.16 125.38 4.37 × 10−7 6.59 ± 0.055
(0, 15) → (0, 13)[S(13)] 3.84506 17 443 3.27 ± 0.10 15.28 1.33 × 10−8 4.67 ± 0.143
(0, 17) → (0, 15)[S(15)] 3.62518 21 411 1.32 ± 0.08 12.48 2.18 × 10−9 9.46 ± 0.573
(1, 2) → (0, 4)[O(4)] 3.00305 6471 23.91 ± 0.16 134.35 1.06 × 10−6 5.62 ± 0.038
(1, 3) → (0, 5)[O(5)] 3.23411 6951 41.78 ± 0.05 256.00 1.60 × 10−6 6.13 ± 0.007
(1, 4) → (0, 6)[O(6)] 3.49985 7584 9.79 ± 0.17 43.98 2.28 × 10−7 4.49 ± 0.078
(1, 5) → (0, 7)[O(7)] 3.80638 8365 11.70 ± 0.11 58.24 2.53 × 10−7 4.98 ± 0.047
(2, 3) → (1, 5)[O(5)] 3.43693 12 550 2.09 ± 0.11 9.08 1.35 × 10−8 4.35 ± 0.229
exp (μ) = 5.66(‡)

Notes. (a) Güsten et al. (2019), (b) Neufeld et al. (2020), (c) Wesson et al. (2010), (d) Cernicharo et al. (1997), (e) Neufeld et al. (2021). (†) See the footnote of Table 3 of Paper I. (*) The line fluxes in CLOUDY are given in units of erg s−1 cm−2. We converted them into beam-integrated fluxes by scaling to the observed angular sizes for a direct comparison with the observations. The conversion formulas we used are the predicted flux (W cm−2) for CH+ v = 0 lines = CLOUDY flux (ergs−1cm−2)×10−7×14π×π×(5.5×π180×3600)2Mathematical equation: $\[(\left.\mathrm{erg} ~\mathrm{s}^{-1} \mathrm{~cm}^{-2}\right) \times 10^{-7} \times \frac{1}{4 \pi} \times \pi \times\left(5.5 \times \frac{\pi}{180 {\times} 3600}\right)^{2}\]$ [where π × (5.5″)2 is the sky-plane area subtended by a spherical nebula equivalent to that of the elliptical nebula]. The predicted flux (W m−2) for CH+ v = 1 → 0 and H2 lines = CLOUDY flux (ergs−1cm−2)×10−3×14π×(0.375×15)×(π180×3600)2Mathematical equation: $\[\left(\mathrm{erg} ~\mathrm{s}^{-1} \mathrm{~cm}^{-2}\right) \times 10^{-3} \times \frac{1}{4 \pi} \times(0.375 \times 15) \times\left(\frac{\pi}{180 \times 3600}\right)^{2}\]$ [where 0.375″ × 15″ is the area covered by the IRTF/iSHELL slit]. (‡) 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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