Issue 
A&A
Volume 574, February 2015



Article Number  A107  
Number of page(s)  13  
Section  Interstellar and circumstellar matter  
DOI  https://doi.org/10.1051/00046361/201424737  
Published online  03 February 2015 
Online material
Appendix A: Hyperfine excitation of HCl by H
Rate coefficients for rotational excitation of HCl() by collisions with H_{2} molecules have been computed by Lanza et al. (2014a) for temperatures ranging from 5 to 300 K. The rate coefficients were derived from extensive quantum calculations using a new accurate potential energy surface obtained from highly correlated ab initio approaches (Lanza et al. 2014b).
However, in these calculations, the hyperfine structure of HCl was neglected. To model the spectrally resolved HCl emission from molecular clouds, hyperfine resolved rate coefficients are needed. In this appendix, we present the calculations of HClH_{2} hyperfine resolved rate coefficients from the rotational rate coefficients of Lanza et al. (2014a). Note that, for rotational levels, we use here the lowercase j instead of the astronomical J notation used in the main body of the paper.
Appendix A.1: Methods
In HCl, the coupling between the nuclear spin (I_{1} = 3 / 2) of the chlorine atom and the molecular rotation results in a weak splitting of each rotational level j_{1} into 4 hyperfine levels (except for the j_{1} = 0 level which is split into only 1 level and for the j_{1} = 1 level which is split into only 3 levels). Each hyperfine level is designated by a quantum number F_{1} (F_{1} = I_{1} + j_{1}) varying between  I_{1} − j_{1}  and I_{1} + j_{1}. In the following, j_{2} designates the rotational momentum of the H_{2} molecule.
In order to get HCl–H_{2} hyperfine resolved rate coefficients, we extend the Infinite Order Sudden (IOS) approach for diatomatom collisions (Faure & Lique 2012) to the case of diatomdiatom collisions.
Within the IOS approximation, inelastic rotational rate coefficients can be calculated from the “fundamental” rates (those out of the lowest j_{1} = 0,j_{2} = 0 channel) as follows (e.g. Alexander 1979): (A.1)Similarly, IOS rate coefficients amongst hyperfine structure levels can be obtained from the rate coefficients using the following formula: (A.2)where and { } are respectively the “3 − j” and “6 − j” Wigner symbols.
Fig. A.1
Temperature dependence of the hyperfine resolved HCl–paraH_{2} (upper panel) and HCl–orthoH_{2} (lower panel) rate coefficients for HCl() transitions. 

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A comparison between present hyperfine rate coefficients for ortho and paraH_{2}, and those of LL12 for He.
The IOS approximation is expected to be moderately accurate at low temperature. As suggested by Neufeld & Green (1994), we could improve the accuracy by computing the hyperfine rate coefficients as: (A.3)using the CC rate coefficients of Lanza et al. (2014a) for the IOS “fundamental” rates in Eqs. (A.1)–(A.2). are the rotational rate coefficients also taken from Lanza et al. (2014a). We named the method “SIOS” for scaled IOS.
In addition, fundamental excitation rates were replaced by the deexcitation fundamental rates using the detailed balance relation: (A.4)This procedure is found to significantly improve the results at low temperature due to important threshold effects.
Hence, we have determined hyperfine HCl–H_{2} rate coefficients using the computational scheme described above for temperature ranging from 5 to 300 K. We considered transitions between the 28 first hyperfine levels of HCl (j, j′ ≤ 7) due to collisions with paraH_{2}(j_{2} = 0) and orthoH_{2}(j_{2} = 1). The present approach has been shown to be accurate, even at low temperature, and has also been shown to induce almost no inaccuracies in radiative transfer modeling compared to more exact calculations of the rate coefficients (Faure & Lique 2012).
Appendix A.2: Results
The complete set of (de)excitation rate coefficients is available online from the LAMDA^{6} (Schöier et al. 2005) and BASECOL^{7} (Dubernet et al. 2013) websites. For illustration, Fig. A.1 depicts the evolution of para and orthoH_{2} rate coefficients as a function of temperature for HCl(j = 2,F → j′ = 1,F′) transitions.
First of all and as already discussed in Lanza et al. (2014a), para and orthoH_{2} rate coefficients differ significantly, the rate coefficients being larger for orthoH_{2} collisions. One can also clearly see that there is a strong propensity in favour of Δj_{1} = ΔF_{1} transitions for both collisions with para and orthoH_{2}. This trend is the usual trend for such a molecule (Roueff & Lique 2013).
Finally, we compare in Table A.1 our new hyperfine HCl–H_{2} rate coefficients with the HCl–He ones calculated by Lanza & Lique (2012) which are scaled by a factor 1.38 to account for the mass difference (see Fig. 6 for a visual comparison).
Indeed, collisions with helium are often used to model collisions with paraH_{2}. It is generally assumed that rate coefficients with paraH_{2}(j_{2} = 0) should be larger than He rate coefficients owing to the smaller collisional reduced mass.
As one can see, the scaling factor is clearly different from 1.38. The ratio varies with the transition considered and also with the temperature for a given transition. The ratio may be larger than a factor 10. This comparison indicates that accurate rate coefficients with paraH_{2} (j_{2} = 0) and orthoH_{2} (j_{2} = 1) could not be obtained from He rate coefficients. HCl molecular emission analysis performed with HClHe rate coefficients result in large inaccuracies in the HCl abundance determination.
Appendix B: CASSIS fitting of H_{2}Cl^{+}
In Fig. B.1, we show the H_{2}Cl^{+} lines used in the LTE fitting with the CASSIS software and the bestfit model resulting from the χ^{2} minimization. The hyperfine components and other lines detected nearby are also shown. The data are all from the HIFI spectral survey of FIR 4 (Kama et al. 2013).
Fig. B.1
The four H_{2}Cl^{+} lines (black) used in the LTE model fitting with CASSIS, and the bestfit model (red). All spectra are corrected for the foreground PDR velocity of 9.4 km s^{1}. The dashed red lines show the hyperfine components of H_{2}Cl^{+} transitions, while dashed blue lines in the top right panel indicate the native frequencies of C_{2}H transitions. The other H_{2}Cl^{+} transitions do not have any lines nearby that were listed as detections in the spectral survey of Kama et al. (2013). 

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© ESO, 2015
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