Volume 577, May 2015
|Number of page(s)||29|
|Section||Interstellar and circumstellar matter|
|Published online||29 April 2015|
Molecular column densities along the sight-line to W49N. Black histograms show the data and blue curves show a multi-Gaussian fit to the data. In the case of the SH data, the red curve indicates a convolution of the multi-Gaussian 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 1012 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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H3S+ (green) and H2S (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 H3S+ is shown in blue.
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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 TCMB = 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 JN = 32−21 (lower panel) transitions that we observed. Results are presented as a function of H2 density for four different temperatures. The left panels show the results on a log-log plot, while the right panels show the same data on a log-linear plot for a narrower range of n(H2). 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 T2 provided kT ≫ the transition energy, ΔE; this result arises because the difference between the absorption and stimulated emission rates is proportional to where Nu and Nl 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 optically-thin 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 low-density 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 fully-ionized. 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 × 102 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 H2S, 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 H2S transition is larger than those for CS and SO, and because the H2S absorption takes place out of thelowest rotational state of the ortho spin-species.
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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Principal components obtained for W49N, from a joint analysis of the W31C and W49N absorption spectra.
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The chemical network for sulphur-containing molecules adopted in the Meudon PDR code version 1.4.4 – a slightly-updated 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
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