Free Access
Volume 575, March 2015
Article Number A94
Number of page(s) 19
Section Interstellar and circumstellar matter
Published online 03 March 2015

Online material

Appendix A: Online figures

thumbnail Fig. A.1

Adopted mass opacities for large vs. small ISM grains. The extinction opacity (absorption+scattering) is shown.

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thumbnail 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 x-axis shows the upper level energy Eu (K) and the y-axis the number of molecules, Nu = 4πd2F/ (Aulhνulgu), where d is the distance, F flux, Aul Einstein-A coefficient, νul transition frequency, and gu the upper level degeneracy.

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thumbnail Fig. A.3

Predictions for ALMA. The J = 4–3 line within the 0110+ 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 (Tjump = 200 K) model with noise added.

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thumbnail Fig. A.4

Spectrum of the a) R(6) 1000–0000 line at 3 μm and b) Q(6) 0110–0000 line at 14 μm of the AS 205 (N) model convolved to the spectral resolution of E-ELT 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 ro-vibrational collision rates

The vibrational H2-HCN collisional de-excitation rate coefficients at room temperature (297 K) of three transitions have been measured by Smith & Warr (1991). They find for the total vibrational de-excitation rate coefficients between an excited state and the ground state7Thus, 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 (CO2-H2, Boonman et al. 2003 or H2O-H2; 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.

thumbnail Fig. B.1

Visualization of the collisional de-excitation 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 νi = ν1, ν2 or ν3 using the Landau-Teller relationship for transitions between neighboring states (Procaccia & Levine 1975 and Eqs. (6) and (8) in Chandra & Sharma 2001), Here, ωi is the vibrational constant (cm-1). In case a transition changes combinations of ν1, ν2, and ν3, 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 de-excitation rate coefficients calculated in this way for a temperature of 300 and 500 K.

Table B.1

Vibrational de-excitation rate coefficients k(vv′) in cm3 s-1.

To obtain a full set of ro-vibrational 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 gi 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 He-HCN have been scaled by the reduced weight of the H2-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 de-exciatation rate coefficients is visualized in Fig. B.1 for a temperature of 500 K.

Appendix C: Line-to-continuum ratio

The line-to-continuum ratio can be the limiting factor to detect lines. For example the CRIRES detections by Mandell et al. (2012) with line-to-continuum ratios of ~1% in the 3 μm lines required a signal-to-noise in the continuum of several 100. Figure C.1 illustrates the line-to-continuum ratio for the non-LTE models with a constant abundance and different gas-to-dust ratios. The peak line-to-continuum ratio for different spectral resolving power (R = λ/ Δλ) is shown for the R(6) 1000–0000 line at 3 μm, the Q(6) 0110–0000 line at 14 μm, and between 13.7 to 14.1 μm (mostly Q-branch of the 0110–0000 band). The required signal-to-noise ratio in the continuum to detect a line at a 5σ level is shown in the figure.

thumbnail Fig. C.1

Peak line-to-continuum ratio of the a)–c) R(6) 1000–0000 line at 3 μm, d)–f) Q(6) 0110–0000 line at 14 μm, and g)–i) between 13.7 and 14.1 μm. The non-LTE models with a constant abundance and a gas-to-dust (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 105. Horizontal red dashed lines show the required signal-to-noise (S/N) in the continuum to detect a line at a 5σ level.

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The line-to-continuum 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 line-to-continuum ratio, has a higher peak line-to-continuum ratio at low R. To detect the 3 μm lines, high resolution spectroscopy (R = 105) should be used, since these lines have lower line-to-continuum ratios compared to the 14 μm lines. Peak line-to-continuum ratios and line fluxes show the same degeneracy between the abundance and gas-to-dust ratio (Sect. 3.3). A factor of ten higher abundance, but by the same factor lower gas-to-dust ratio yields approximately the same line-to-continuum ratio. For MIRI with a spectral resolving

power of R = 3000, a gas-to-dust ratio of 1000 and an abundance of 3 × 10-8 (Table 2), a signal-to-noise of 1000 in the continuum will allow detecting lines down to 5% of the peak of the Q-branch, i.e., P- and R-branch lines from high-J levels.

© ESO, 2015

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