Issue 
A&A
Volume 575, March 2015



Article Number  A94  
Number of page(s)  19  
Section  Interstellar and circumstellar matter  
DOI  https://doi.org/10.1051/00046361/201425009  
Published online  03 March 2015 
Online material
Appendix A: Online figures
Fig. A.1
Adopted mass opacities for large vs. small ISM grains. The extinction opacity (absorption+scattering) is shown. 

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Fig. A.2
Rotational diagrams of the models given in Table 2 with G/D = 1000 and constant or jump abundance. Only lines above the detection limit of MIRI within 10 000 s (~10^{20} W m^{2}) are shown. The xaxis shows the upper level energy E_{u} (K) and the yaxis the number of molecules, N_{u} = 4πd^{2}F/ (A_{ul}hν_{ul}g_{u}), where d is the distance, F flux, A_{ul} EinsteinA coefficient, ν_{ul} transition frequency, and g_{u} the upper level degeneracy. 

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Fig. A.3
Predictions for ALMA. The J = 4–3 line within the 01^{1}0_{+} band is shown for the models given in Table 2 with G/D = 1000 and constant or jump abundance. The ALMA 3σ detection limit (5 km s^{1} bin) within 3 h is shown by the gray region. Gray lines represent the constant abundance and jump (T_{jump} = 200 K) model with noise added. 

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Fig. A.4
Spectrum of the a) R(6) 10^{0}0–00^{0}0 line at 3 μm and b) Q(6) 01^{1}0–00^{0}0 line at 14 μm of the AS 205 (N) model convolved to the spectral resolution of EELT METIS. The models given in Table 2 with G/D = 1000 and constant or jump abundance are shown. 

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Appendix B: HCN rovibrational collision rates
The vibrational H_{2}HCN collisional deexcitation rate coefficients at room temperature (297 K) of three transitions have been measured by Smith & Warr (1991). They find for the total vibrational deexcitation rate coefficients between an excited state and the ground state^{7}Thus, the excitation of the stretching modes is much slower than the bending mode. Hence, we will assume that \vspace{16.55cm}
The temperature dependence of the rate coefficients is not know, but comparison with a triatomic system with similar vibrational energy and reduced mass (CO_{2}H_{2}, Boonman et al. 2003 or H_{2}OH_{2}; Faure & Josselin 2008) suggest, that the rate coefficients do not change by more than a factor of a few from 300 to 1000 K. This may be different for low temperatures T ≪ 300 K, but such cold regions do not affect the results presented in this work.
Fig. B.1
Visualization of the collisional deexcitation rate coefficients at 500 K. Each of the blocks shows a vibrational level with its rotational ladders. The vibrational levels are arranged following their rotational ground state energy. 

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Even though strictly applicable only for stretching modes of diatomic molecules, we will approximate the rate coefficients of other transitions which only change either ν_{i} = ν_{1}, ν_{2} or ν_{3} using the LandauTeller relationship for transitions between neighboring states (Procaccia & Levine 1975 and Eqs. (6) and (8) in Chandra & Sharma 2001), Here, ω_{i} is the vibrational constant (cm^{1}). In case a transition changes combinations of ν_{1}, ν_{2}, and ν_{3}, it is assumed that the rate coefficient is the maximum of the above rate coefficient changing one mode at the time.
Table B.1 shows the vibrational deexcitation rate coefficients calculated in this way for a temperature of 300 and 500 K.
Vibrational deexcitation rate coefficients k(v → v′) in cm^{3} s^{1}.
To obtain a full set of rovibrational collisional rate coefficients, we employ the method suggested by Faure & Josselin (2008): assuming a decoupling of the rotational and vibrational levels, we can write (B.6)where (B.7)with the statistical weights g_{i} of the levels. This procedure ensures that the detailed balance is fulfilled. As Faure & Josselin (2008) we assume that pure rotational rate coefficients within one vibrational level are equal to the ground state rate coefficients.
The rate coefficients for the pure rotational transitions k(0,J → 0,J′;T) are taken from Dumouchel et al. (2010). The HeHCN have been scaled by the reduced weight of the H_{2}HCN system and levels with J> 26 are extrapolated using the Infinite Order Sudden (IOS) approximation as described in Sect. 6 of Schöier et al. (2005). The full set of derived deexciatation rate coefficients is visualized in Fig. B.1 for a temperature of 500 K.
Appendix C: Linetocontinuum ratio
The linetocontinuum ratio can be the limiting factor to detect lines. For example the CRIRES detections by Mandell et al. (2012) with linetocontinuum ratios of ~1% in the 3 μm lines required a signaltonoise in the continuum of several 100. Figure C.1 illustrates the linetocontinuum ratio for the nonLTE models with a constant abundance and different gastodust ratios. The peak linetocontinuum ratio for different spectral resolving power (R = λ/ Δλ) is shown for the R(6) 10^{0}0–00^{0}0 line at 3 μm, the Q(6) 01^{1}0–00^{0}0 line at 14 μm, and between 13.7 to 14.1 μm (mostly Qbranch of the 01^{1}0–00^{0}0 band). The required signaltonoise ratio in the continuum to detect a line at a 5σ level is shown in the figure.
Fig. C.1
Peak linetocontinuum ratio of the a)–c) R(6) 10^{0}0–00^{0}0 line at 3 μm, d)–f) Q(6) 01^{1}0–00^{0}0 line at 14 μm, and g)–i) between 13.7 and 14.1 μm. The nonLTE models with a constant abundance and a gastodust (G/D) ratio of 100, 1000 and 100 000 are shown (Fig. 6), convolved to a spectral resolving power R = λ/ Δλ between 100 and 10^{5}. Horizontal red dashed lines show the required signaltonoise (S/N) in the continuum to detect a line at a 5σ level. 

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The linetocontinuum ratio increases with the spectral resolution. The increase is strongest at low spectral resolution in the single lines. The 13.7–14.1 μm range, where several lines contribute to the peak linetocontinuum ratio, has a higher peak linetocontinuum ratio at low R. To detect the 3 μm lines, high resolution spectroscopy (R = 10^{5}) should be used, since these lines have lower linetocontinuum ratios compared to the 14 μm lines. Peak linetocontinuum ratios and line fluxes show the same degeneracy between the abundance and gastodust ratio (Sect. 3.3). A factor of ten higher abundance, but by the same factor lower gastodust ratio yields approximately the same linetocontinuum ratio. For MIRI with a spectral resolving
power of R = 3000, a gastodust ratio of 1000 and an abundance of 3 × 10^{8} (Table 2), a signaltonoise of 1000 in the continuum will allow detecting lines down to 5% of the peak of the Qbranch, i.e., P and Rbranch lines from highJ levels.
© ESO, 2015
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