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Volume 574, February 2015
Article Number A107
Number of page(s) 13
Section Interstellar and circumstellar matter
Published online 03 February 2015

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Appendix A: Hyperfine excitation of HCl by H

Rate coefficients for rotational excitation of HCl() by collisions with H2 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 HCl-H2 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 (I1 = 3 / 2) of the chlorine atom and the molecular rotation results in a weak splitting of each rotational level j1 into 4 hyperfine levels (except for the j1 = 0 level which is split into only 1 level and for the j1 = 1 level which is split into only 3 levels). Each hyperfine level is designated by a quantum number F1 (F1 = I1 + j1) varying between | I1j1 | and I1 + j1. In the following, j2 designates the rotational momentum of the H2 molecule.

In order to get HCl–H2 hyperfine resolved rate coefficients, we extend the Infinite Order Sudden (IOS) approach for diatom-atom collisions (Faure & Lique 2012) to the case of diatom-diatom collisions.

Within the IOS approximation, inelastic rotational rate coefficients can be calculated from the “fundamental” rates (those out of the lowest j1 = 0,j2 = 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.

thumbnail Fig. A.1

Temperature dependence of the hyperfine resolved HCl–para-H2 (upper panel) and HCl–ortho-H2 (lower panel) rate coefficients for HCl() transitions.

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Table A.1

A comparison between present hyperfine rate coefficients for ortho- and para-H2, 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 de-excitation 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–H2 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 para-H2(j2 = 0) and ortho-H2(j2 = 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 on-line from the LAMDA6 (Schöier et al. 2005) and BASECOL7 (Dubernet et al. 2013) websites. For illustration, Fig. A.1 depicts the evolution of para- and ortho-H2 rate coefficients as a function of temperature for HCl(j = 2,Fj′ = 1,F) transitions.

First of all and as already discussed in Lanza et al. (2014a), para- and ortho-H2 rate coefficients differ significantly, the rate coefficients being larger for ortho-H2 collisions. One can also clearly see that there is a strong propensity in favour of Δj1 = ΔF1 transitions for both collisions with para- and ortho-H2. This trend is the usual trend for such a molecule (Roueff & Lique 2013).

Finally, we compare in Table A.1 our new hyperfine HCl–H2 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 para-H2. It is generally assumed that rate coefficients with para-H2(j2 = 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 para-H2 (j2 = 0) and ortho-H2 (j2 = 1) could not be obtained from He rate coefficients. HCl molecular emission analysis performed with HCl-He rate coefficients result in large inaccuracies in the HCl abundance determination.

Appendix B: CASSIS fitting of H2Cl+

In Fig. B.1, we show the H2Cl+ lines used in the LTE fitting with the CASSIS software and the best-fit model resulting from the χ2 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).

thumbnail Fig. B.1

The four H2Cl+ lines (black) used in the LTE model fitting with CASSIS, and the best-fit 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 H2Cl+ transitions, while dashed blue lines in the top right panel indicate the native frequencies of C2H transitions. The other H2Cl+ 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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