The Sulphur depletion problem in molecular clouds: the H 2 S case.

Sulphur is one of the most abundant elements in the Universe [1] and plays a crucial role in biological systems. However, sulphuretted molecules are not as abundant as expected in the ISM – the Sulphur depletion problem – and there is no clear answer of where the missing Sulphur is yet. To shed light onto this open question, we focus our attention on the chemistry of H 2 S in dark clouds. This molecule is thought to be an important reservoir of Sulphur [2], mainly in solid state, locked in grain ices. Using a subset of the GEMS IRAM Large Program data, including IRAM 30m telescope millimeter observations of CS, SO and H 2 S, in this work [3] we have determined the physical conditions and modeled the H 2 S chemistry in the TMC 1-C, TMC 1-CP and Barnard 1b cores. The N AUTILUS chemical code is used to model the sulfur chemistry and explore the impact of chemical desorption on the H 2 S abundance. Our results confirm H 2 S as the main reservoir of S in icy mantles, mainly formed by chemical desorption with a decreasing efficiency towards higher densities. This is expected as the chemical composition of the grains change by the presence of ice coverings [4]. This transition occurs precisely when the abundance of H 2 O and CO ices achieves their maximum value. Therefore, H 2 S might be tracing the snowline of dark clouds. Our model also yields an elemental abundance of S/H of around the cosmic value within a factor of ten. Aiming at a better understanding of the chemical desorption process, its efficiency, and ice coverings, we complement these results with additional methanol data observed with the IRAM 30m telescope. Recent results [5] indeed show the high sensitivity of the gas-phase abundance of this molecule to the physical properties of the environment. We look for correlations


Introduction
Despite being one of the most abundant elements in the Universe, with an elemental solar abundance of S/H ∼ 1.35 × 10 −5 , sulphur-bearing molecules are not as abundant as expected. While in diffuse clouds and PDRs the sulphur abundance is found to be close to the cosmic value [1], sulphur is thought to be depleted inside molecular clouds by a factor of 1000 compared to its estimated cosmic abundance [2]. Due to the high hydrogen mobility in the ice matrix, the sulphur atoms depleted in interstellar ice mantles are expected to form H 2 S preferentially. Therefore, H 2 S is a candidate for the main sulphur reservoir in dark cores [3]. In [4], we found H 2 S to be the main sulphur reservoir in TMC 1 and Barnard 1b, released into the gas phase by chemical desorption. The chemical modeling of this molecule allowed us to conclude that it is a tracer of the snow-line in these regions, as the gas-phase abundance at higher extinctions is reduced due to the lower chemical desorption efficiencies. The observed abundances are reproduced with the models using a cosmic elemental Sulphur abundance and allowing an order of magnitude of uncertainty. This work is a follow-up of [4] where we used a subset of the GEMS database [5] and complementary CO and methanol observations to investigate the H 2 S and methanol abundances, the interplay of CO, methanol, and the snowline, and the mechanisms and efficiencies of formation of methanol and H 2 S in Barnard 1b.

Observations: Barnard 1b
Barnard 1 is a young, intermediate-mass star forming cloud, embedded in the western sector of the molecular cloud complex Perseus (see Fig. 1). It hosts several dense cores in different   Table  1. Additionally, CH 3 OH A + 1 0,1 → 0 0,0 data from the Yebes 40m telescope was observed at the lowest extinctions.

Analysis and results
For a better understanding of the depletion of species, the presence of the snow-line, and the formation of H 2 S and CH 3 OH, we derived the column densities of the species listed in Table 1, and the physical properties at every position. First, we obtained the hydrogen nuclei number density and the methanol column density using the methanol lines shown in Table 1. To do so, we used the radiative transfer code Radex with the most up-to-date collisional coefficients for e-methanol and a-methanol [6]. Assuming the gas temperature profile obtained in [4], the intensity ratio W(E2 2 1,2 → 1 1,1 )/W(E1 2 0,2 → 1 0,1 ) provides an estimation of the hydrogen nuclei number density that is then used to compute the column density of both methanol species. In positions where at least one of these lines were not detected, we performed additional observations with the Yebes 40m telescope to obtain the density from the W(A + 1 0,1 → 0 0,0 )/W(A + 2 0,2 → 1 0,1 ) intensity ratio. The column density of the rest of the species are derived fitting the integrated intensity of the lines. The resulting abundances are shown in Fig. 2. We first notice the presence of H 2 S in the gas phase at the most external positions where CH 3 OH is not detected. This is compatible with an early depletion of Sulphur atoms onto grain surfaces [7], before significant depletion of CO. Since reactions with CO are the main destruction path of N 2 H + [8], when CO depletion occurs, N 2 H + starts increasing its abundance. At the same time, CH 3 OH also starts increasing, slightly, its abundance, as it is mainly formed by hydrogenation of depleted CO. The depletion of CO is linked to ice growth which, in turn, reduces the desorption efficiency of molecules formed via grain-phase reactions. This is the case of H 2 S, whose abundance decreases as 13 CO starts depleting and methanol and N 2 H + increase their abundances.
Methanol, like H 2 S, is also produced more efficiently through grain-phase reactions in cold core conditions. However, the gas abundance of methanol does not seem to be affected

Analysis and results
For a better understanding of the depletion of species, the presence of the snow-line, and the formation of H 2 S and CH 3 OH, we derived the column densities of the species listed in Table 1, and the physical properties at every position. First, we obtained the hydrogen nuclei number density and the methanol column density using the methanol lines shown in Table 1. To do so, we used the radiative transfer code Radex with the most up-to-date collisional coefficients for e-methanol and a-methanol [6]. Assuming the gas temperature profile obtained in [4], the intensity ratio W(E2 2 1,2 → 1 1,1 )/W(E1 2 0,2 → 1 0,1 ) provides an estimation of the hydrogen nuclei number density that is then used to compute the column density of both methanol species. In positions where at least one of these lines were not detected, we performed additional observations with the Yebes 40m telescope to obtain the density from the W(A + 1 0,1 → 0 0,0 )/W(A + 2 0,2 → 1 0,1 ) intensity ratio. The column density of the rest of the species are derived fitting the integrated intensity of the lines. The resulting abundances are shown in Fig. 2. We first notice the presence of H 2 S in the gas phase at the most external positions where CH 3 OH is not detected. This is compatible with an early depletion of Sulphur atoms onto grain surfaces [7], before significant depletion of CO. Since reactions with CO are the main destruction path of N 2 H + [8], when CO depletion occurs, N 2 H + starts increasing its abundance. At the same time, CH 3 OH also starts increasing, slightly, its abundance, as it is mainly formed by hydrogenation of depleted CO. The depletion of CO is linked to ice growth which, in turn, reduces the desorption efficiency of molecules formed via grain-phase reactions. This is the case of H 2 S, whose abundance decreases as 13 CO starts depleting and methanol and N 2 H + increase their abundances.
Methanol, like H 2 S, is also produced more efficiently through grain-phase reactions in cold core conditions. However, the gas abundance of methanol does not seem to be affected by the decreasing desorption efficiency expected by grain growth. The desorption of COMs like methanol in grains covered by CO ice has been discussed in several works [9]. Current chemical models do not consider a detailed chemical composition of the outermost layers of ices. It is likely that these layers, containing mainly depleted CO, could enhance the chemical desorption of COMs [9] while also reducing the desorption efficiencies of other molecules like H 2 S. Surface-dependent parameters like the diffusion rate of hydrogen through the ice matrix have also been found to have a great impact in the methanol production [10]. Now we explore the role of ices in the production of H 2 S and methanol. The chemical code Nautilus [11], using the densities obtained here and the parameters described in [4], yields the abundances shown in Fig. 3. This model adjusts the desorption efficiency with the ice growth, being at its highest when no ice is present. The efficiency of desorption is reduced as ice grows at higher extinctions. The desorption schemes used in the model are described in [4]. The model results for H 2 S (Fig. 3) are in good agreement with the observations, with high desorption efficiencies and low desorption efficiencies best describing low and high extinction areas, respectively, as a consequence of the build-up of ices towards the interior of the core. The model does not however reproduce the observations of methanol, even in a scenario of early chemistry at 10 5 yr (Fig. 3), since it underestimates its gas-phase abundance. In the following section we discuss several ideas that may be behind this disagreement.

Discussion and summary
The chemistry of sulphur and COMs are tightly related to grain-phase reactions. The chemical desorption process is crucial for the incorporation of these species into the gas-phase. Even thought H 2 S and methanol are mainly formed via chemical desorption, we have revealed great differences between the distribution of their gas-phase abundances.
• Gas-phase abundance of H 2 S is anti-correlated with the ice growth expected when CO is being depleted. Our model, which takes into account different desorption schemes as ice grows, shows a good agreement with the observations, thus suggesting that the H 2 S gas-phase abundance traces the CO snowline. Other possibility that may help explain the observed abundance profile is that H 2 S, in presence of depleted CO, reacts with it forming other compounds such as OCS and therefore no H 2 S is released to the gas phase [12]. • Methanol gas-phase abundance is correlated with CO depletion, in agreement with the formation of methanol by hydrogenation of depleted CO. The measured abundances of methanol and H 2 S follow different behaviors despite having similar formation pathways. As discussed previously, CO-ices could enhance the desorption of COMs, although this is yet to be confirmed. Recent results also suggest alternative routes of methanol formation that need to be incorporated into chemical networks [13]. • Finally, uncertainties in the physical structure, grain sizes, and the dynamical behavior may explain the striking differences in methanol and H 2 S gas-phase abundances.