Table 2
Free parameters involved in the fits.
| Parameter | Units | Continuum | High resolution observations | Comments | ||
|---|---|---|---|---|---|---|
| 7.5 μm | 13–14 μm | mm | ||||
| Rph(HCN) | R⋆ | – | – | – | 168 ± 22 | |
| Rph(H13CN) | R⋆ | – | – | – | 155 ± 20 | |
| T⋆ | K | 2910 ± 70 | – | – | – | |
| Td0 | K |  |
– | – | – | |
| ndust(Rii) | ×10−5 cm−3 |  |
– | – | – | |
| ndust(Riii) | ×10−8 cm−3 | 6.2 ± 0.9 | – | – | – | |
| vexp(R⋆) | km s−1 | – |  |
– | ||
| vexp(r ≥ Rii) | km s−1 | – | 8.00 ± 0.11 | – | ||
| Δv(R⋆) | km s−1 | – |  |
– | ||
| Trot(R⋆) | K | – |  |
 |
– | |
| Trot(Rii) | K | – | 900 ± 60 | 700 ± 50 | – | |
| Trot(Riii) | K | – | – | – | 79 ± 11 | |
| Tvib[ν2(π) −GS(σ+)](R⋆) | K | – |  |
– | ||
| Tvib[ν2(π) −GS(σ+)](Rii) | K | – |  |
360.0 ± 1.4 | – | |
| Tvib[ν2(π) −GS(σ+)](Riii) | K | – |  |
70.0 ± 2.1 | – | I |
| Tvib[2ν2(σ+) − ν2(π)](R⋆) | K | – |  |
 |
– | |
| Tvib[2ν2(σ+) − ν2(π)](Rii) | K | – | 330 ± 30 | 400 ± 40 | – | |
| Tvib[2ν2(σ+) − ν2(π)](Riii) | K | – | 30 | 70 | – | I,F |
| Tvib[2ν2(δ) − 2ν2(σ+)](R⋆) | K | – | TK(R⋆) |  |
– | F,S |
| Tvib[2ν2(δ) − 2ν2(σ+)](Rii) | K | – | TK(Rii) |  |
– | F,S |
| Tvib[2ν2(δ) − 2ν2(σ+)](Riii) | K | – | TK(Riii) | 10 | – | I,F,S |
| Tvib[ν3(σ+) − 2ν2(δ)](R⋆) | K | – |  |
 |
– | |
| Tvib[ν3(σ+) − 2ν2(δ)](Rii) | K | – |  |
 |
– | |
| Tvib[ν3(σ+) − 2ν2(δ)](Riii) | K | – | 30 | 70 | – | I,F |
| x(R⋆) | ×10−4 | – |  |
0.35 ± 0.05 | – | |
| x(Rii) | ×10−4 | – |  |
– | ||
| x(r ≥ Riii) | ×10−4 | – | – | – | 1.3 ± 0.7 | |
| 12 C/13 C | – | 2.50 ± 0.15 | 2.5 ± 1.0 | |||
| Other useful derived parameters | ||||||
| τdust (11.3 μm) | × 10−3 |  |
– | – | – | |
| Ncol (HCN) | × 1018 cm−2 | – | 2.1 ± 1.1 | V | ||
| Ncol (H13CN) | × 1017 cm−2 | – | 8 ± 4 | V | ||
Notes. Several initially free parameters were fixed at some point during the line modeling due to the model insensitivity to them (see below). These parameters do not show uncertainties. The uncertainties are 1σ errors. All the molecular parameters are for HCN and are valid for H13CN unless it is indicated. Rph: photodissociation radius; T⋆: stellar effective temperature; Td0: temperature of dust grains at Rii; ndust (r): density of dust grains (∝ r−2); vexp: gas expansion velocity (continuous function with a linear dependence on r in each Region); Δv: line width; Trot: rotational temperature; Tvib: vibrational temperature for consecutive bands and energy differences higher than 100 K (for lower differences Tvib = TK); x: HCN abundance with respect to H2 (continuous function with a linear dependence on r in each region); τdust: dust optical depth along the line of sight; Ncol(HCN) and Ncol(H13CN): column densities of HCN and H13CN; 12C/13C: isotopic ratio. Comments: I: model insensitive to at least one of these parameters; F: at least one of the parameters fixed during the calculations; S: these parameters might be affected by spectroscopic inaccuracies or an incomplete envelope model (see Sect. 5.2.6); V: average of the results derived from the fits to all the molecular lines.
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