Chemistry and ro-vibrational excitation of HeH+ in the Planetary Nebula NGC 7027

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Table 3

Comparison between the observed and CLOUDY model predicted line fluxes.

Lines	Rest wavelength (μm)	Observed line flux (10⁻¹⁸ Wm⁻²)	Predicted line flux (10⁻¹⁸ W m⁻²)		Ratio (Observed / Predicted)
Lines	Rest wavelength (μm)	Observed line flux (10⁻¹⁸ Wm⁻²)	This work^(*)	Neufeld et al. (2020)	This work	Neufeld et al. (2020)
HeH⁺ (υ, J) = (0,1 → 0,0)	149.091	163 ± 32	47.35	56	3.44 ± 0.68	2.86 ± 0.56
HeH⁺ (υ, J) = (1,0 → 0,1) [P(1)]	3.51532	1.55 ± 0.16	0.81	1.68	1.91 ± 0.20	0.92 ± 0.095

HeH⁺ (υ, J) = (1,1 → 0,2) [P(2)]	3.60677	2.08 ± 0.31	0.91	0.89	2.29 ± 0.34	2.33 ± 0.35
H I 19 − 6	3.64493	23.9 ± 0.22	20.44	34.6	1.17 ± 0.011	0.69 ± 0.006
He II 13 − 9	3.54328	53.7 ± 0.21	44.20	108	1 .22 ± 0.005	0.50 ± 0.002
He I 5³ D − 4³P⁰	3.70256	8.44 ± 0.48	11.35	12.8	0.74 ± 0.042	0.66 ± 0.038

Notes. ^(*)The line fluxes in CLOUDY are given in units of erg s⁻¹ cm⁻². To compare with the observations, we converted them to W m⁻², accounting for the observational angular sizes tabulated in Table 4 (see notes) of Neufeld et al. (2020). The conversion formula used are: Predicted flux (W m⁻²) for ${HeH}^{+} (v, J) = (0, 1 \to 0, 0) = CLOUDY flux (erg s^{- 1} {cm}^{- 2}) \times 10^{- 3} \times \frac{1}{4 π} \times π \times {(4.6 \times \frac{π}{180 \times 3600})}^{2}$ ${\rm{He}}{{\rm{H}}^ + }(v,J) = (0,1 \to 0,0) = {\rm{ CLOUDY flux }}\left( {{\rm{erg}}{{\rm{s}}^{ - 1}}{\rm{c}}{{\rm{m}}^{ - 2}}} \right) \times {10^{ - 3}} \times \frac{1}{{4\pi }} \times \pi \times {\left( {4.6 \times \frac{\pi }{{180 \times 3600}}} \right)^2}$ . Predicted flux (W m⁻²) for HeH⁺ υ = 1 → 0 P(1), P(2), H i, He ii, and $He I = CLOUDY flux (erg s^{- 1} {cm}^{- 2}) \times 10^{- 3} \times \frac{1}{4 π} \times (0.375 \times 11) \times {(\frac{π}{180 \times 3600})}^{2}$ ${\text{He I}} = {\text{ CLOUDY flux }}\left( {{\text{erg}}{{\text{s}}^{ - 1}}{\text{c}}{{\text{m}}^{ - 2}}} \right) \times {10^{ - 3}} \times \frac{1} {{4\pi }} \times (0.375 \times 11) \times {\left( {\frac{\pi } {{180 \times 3600}}} \right)^2}$ .

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