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Appendix A: Absorption features and molecular column densities
Figures A.1−A.5 show the column density per velocity interval for each detected molecule in each observed source. Figure A.6 presents upper limits on H_{3}S^{+}.
Fig. A.1
Molecular column densities along the sightline to W49N. Black histograms show the data and blue curves show a multiGaussian fit to the data. In the case of the SH data, the red curve indicates a convolution of the multiGaussian fit with the hyperfine structure; it is this curve that should be compared with the black histogram (see text). Red boxes indicate the velocity ranges for which results are presented in Tables 1 and 2, with the red numbers at the top showing the integrated column density in units of 10^{12} cm^{2}. Blue symbols above each panel indicate the velocity centroid and full width at half maximum for each Gaussian absorption component. 

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Fig. A.2
Same as Fig. A.1, but for W31C. 

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Fig. A.3
Same as Fig. A.1, but for W51. 

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Fig. A.4
Same as Fig. A.1, but for G34.3+0.1. 

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Fig. A.5
Same as Fig. A.1, but for G29.960.02. 

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Fig. A.6
H_{3}S^{+} (green) and H_{2}S (red, scaled by a factor 0.1) optical depth spectra obtained for the W49N 40 km s^{1} foreground absorption component and the 30 km s^{1} W31C foreground absorption component. The 3σ upper limit on H_{3}S^{+} is shown in blue. 

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Appendix B: Excitation of sulphurbearing molecules in diffuse molecular clouds
In order to determine the equilibrium level populations for CS and SO in diffuse molecular clouds, we have solved the equations of statistical equilibrium as a function of temperature and density. Our excitation model includes radiative pumping by the cosmic microwave background (CMB), at temperature T_{CMB} = 2.73 K, spontaneous radiative decay, and collisional excitation by molecular hydrogen. We adopted the collisional rate coefficients recommended in the LAMDA database (Schöier et al. 2005)^{8}, which were obtained by a simple scaling of the values computed for the excitation of CS (Lique et al. 2006a) and SO (Lique et al. 2006b) by He.
In Fig. B.1, we present results for the ratio of total molecular column density to optical depth, N/τ, for the CS J = 2−1 (upper panel) and SO J_{N} = 3_{2}−2_{1} (lower panel) transitions that we observed. Results are presented as a function of H_{2} density for four different temperatures. The left panels show the results on a loglog plot, while the right panels show the same data on a loglinear plot for a narrower range of n(H_{2}). In the limit of low density, the level populations are in equilibrium with the CMB, at a temperature of 2.73 K, while in the limit of high density the level populations are in local thermodynamic equilibrium (LTE) at the gas temperature, T. In the latter limit, N/τ is proportional to T^{2} provided kT ≫ the transition energy, ΔE; this result arises because the difference between the absorption and stimulated emission rates is proportional to where N_{u} and N_{l} are the column densities in the lower and upper states, and Z is the partition function, proportional to T for diatomic molecules. At intermediate densities and temperatures ≳ 100 K, the populations are inverted.
Two caveats affecting the results shown in B.1 are our neglect of radiative trapping and of electron impact excitation in determining the level populations. While the SO transition is clearly opticallythin in all the absorption components we observed, the optical depth of the CS transition can reach values of order unity at line center; thus, for CS, radiative trapping can lead to a modest reduction in the critical density at which departures from the lowdensity behavior become significant. For polar molecules like CS and SO, electron impact excitation can be of comparable importance to excitation by neutral species in regions where carbon is fullyionized. If the CS and SO absorption is occurring in regions where C is ionized, a further modest reduction in the critical density could result.
Notwithstanding these caveats, for the temperatures (T ≤ 80 K) and densities (≤ few × 10^{2} cm^{3}) typical of the foreground diffuse molecular clouds observed in this study (e.g. Gerin et al. 2015), the N/τ ratio is very comfortably in the low density limit for both CS and SO, justifying the assumption underlying our computation of column densities in Sect. 3 above. In the case of H_{2}S, the effects of collisional excitation upon the N/τ ratio are expected to be even smaller than those for CS and SO, both because the spontaneous radiative rate for the H_{2}S transition is larger than those for CS and SO, and because the H_{2}S absorption takes place out of thelowest rotational state of the ortho spinspecies.
Fig. B.1
Column densities required for an optical depth of unity. 

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Appendix C: Principal component analysis for W49N
Figures C.1 and C.2 show the optical depth spectra for eleven transitions observed towards W49N, and the principal components determined from a simultaneous analysis of the W31C and W49N spectra.
Fig. C.1
Optical depths for eleven transitions observed toward W49N as a function of LSR velocity. Black curve: rebinned observed data (see text). Red histogram: approximate fit using only the first two principal components. Blue histogram: approximate fit using only the first three principal components. 

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Fig. C.2
Principal components obtained for W49N, from a joint analysis of the W31C and W49N absorption spectra. 

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Appendix D: Reaction network for sulphurbearing molecules
The chemical network for sulphurcontaining molecules adopted in the Meudon PDR code version 1.4.4 – a slightlyupdated version of which is used here for TDR and shock modeling – includes 432 reactions. In Table D.1, we present an abbreviated list containing rates for those reactions and protoprocesses that play a dominant role in the formation and destruction of sulfur bearing species (Fig. 12) and/or whose rates have been updated for use in our study.
Abbreviated reaction list.
© ESO, 2015