Interstellar Detection of O-protonated Carbonyl Sulfide, HOCS+

We present the first detection in space of O-protonated carbonyl sulfide (HOCS+), in the midst of an ultradeep molecular line survey toward the G+0.693-0.027 molecular cloud. From the observation of all K a = 0 transitions ranging from J lo = 2 to J lo = 13 of HOCS+ covered by our survey, we derive a column density of N = (9 ± 2) × 1012 cm−2, translating into a fractional abundance relative to H2 of ∼7 × 10−11. Conversely, the S-protonated HSCO+ isomer remains undetected, and we derive an upper limit to its abundance with respect to H2 of ≤3 × 10−11, a factor of ≥2.3 less abundant than HOCS+. We obtain an HOCS+/OCS ratio of ∼2.5 × 10−3, in good agreement with the prediction of astrochemical models. These models show that one of the main chemical routes to the interstellar formation of HOCS+ is likely the protonation of OCS, which appears to be more efficient at the oxygen end. Also, we find that high values of cosmic-ray ionization rates (10−15–10−14 s−1) are needed to reproduce the observed abundance of HOCS+. In addition, we compare the O/S ratio across different interstellar environments. G+0.693-0.027 appears as the source with the lowest O/S ratio. We find an HOCO+/HOCS+ ratio of ∼31, in accordance with other O/S molecular pairs detected toward this region and also close to the O/S solar value (∼37). This fact indicates that S is not significantly depleted within this cloud due to the action of large-scale shocks, unlike in other sources where S-bearing species remain trapped on icy dust grains.


INTRODUCTION
The pursuit of understanding the chemical reservoir of the interstellar medium (ISM) is a cornerstone of modern astrochemistry.At the heart of this quest is the investigation of molecules harboring sulfur (S), which play a key role in diverse aspects, from stellar nucleosynthesis and chemical evolution of galaxies (Perdigon et al. 2021) to atmospheric chemistry in planets (Krasnopolsky 2012; Gómez Martín et al. 2017;Chang et al. 2023), or biological processes (April 1986), and they are consid-ered essential ingredients for life on Earth (Richardson et al. 2013;Todd 2022).
Starting with the discovery of carbon monosulfide (CS; Penzias et al. 1971), the first S-bearing molecule observed in space, and followed by the detection of carbonyl sulfide (OCS; Jefferts et al. 1971), more than thirty interstellar S-bearing molecules have been identified to date, which corresponds to ∼10 % of the overall chemical inventory found in the ISM (see McGuire 2022 for a recent molecular census).In this context, recent detections of new S-bearing molecules (e.g., HC 2 S + , Cabezas et al. 2022; HC 2 S, H 2 C 2 S, H 2 C 3 S, and C 4 S, Cernicharo et al. 2021b; HC 3 S + , Cernicharo et al. 2021a; CH 3 CH 2 SH, HC(O)SH, Kolesniková et al. 2014;Rodríguez-Almeida et al. 2021a;and HSO, Marcelino et al. 2023), strongly encourage the astronomical community to hunt for new sulfurated candidates.However, in the case of S-containing species, additional factors need to be considered: i) despite being one of the most abundant elements in the Universe, its abundance is low compared to that of C and O ([S/O]∼2.7×10−2 , [S/C]∼4.9×10−2 ; Asplund et al. 2009); ii) S has a tendency to deplete rapidly onto the surface of interstellar dust grains (Jiménez-Escobar et al. 2014;Vidal et al. 2017;Vidal & Wakelam 2018;Laas & Caselli 2019;Shingledecker et al. 2020), which dramatically decreases the abundances of S-bearing molecules in the gas phase (Vidal et al. 2017;Marcelino et al. 2023;Fuente et al. 2023).
In this work, we report the first interstellar detection of HOCS + toward the Galactic Center molecular cloud G+0.693-0.027.We also search for the lower-inenergy isomer HSCO + and derive an upper limit to its column density.Their relative abundance is presented and, by using gas-grain astrochemical models, we discuss the possible formation pathways of HOCS + , that favor the production of this molecule over its isomer HSCO + .Finally, we explore a sample of well-known S-and Ocontaining species detected toward several astronomical environments to shed light on the O/S ratio across the ISM.

OBSERVATIONS
We searched for both HOCS + and HSCO + isomers toward the molecular cloud G+0.693-0.027(hereafter G+0.693), located in the Central Molecular Zone (CMZ) of the Milky Way.This astronomical source has been established as one of the prime targets to unravel new interstellar complex organic molecules (or COMs, defined as carbon-based molecules comprised of 6 or more atoms, Herbst et al. 2020), based on the first detection of a deluge of C-, O-and N-and also S-bearing species (see, e.g., Rivilla et al. 2019Rivilla et al. , 2020Rivilla et al. , 2021aRivilla et al. ,b, 2022aRivilla et al. ,b, 2023;;Bizzocchi et al. 2020;Rodríguez-Almeida et al. 2021a,b;Jiménez-Serra et al. 2022;Zeng et al. 2021Zeng et al. , 2023;;Sanz-Novo et al. 2023;Fatima et al. 2023).

Rotational spectroscopy considerations
The [H,C,S,O] + isomeric family comprises two structural isomers1 of remarkable stability, the S-protonated carbonyl sulfide isomer, HSCO + , and the O-protonated form, HOCS + , which was predicted to lie at 4.9 kcal    .The result of the best LTE fit of HOCS + is shown with a red line, the green line plots the predicted emission of HNC 34 S, and the blue line plots the emission from all the molecules identified to date in our survey (including the latter two).The observed spectra are plotted as gray histograms.The structure of HOCS + , taken from Fortenberry et al. (2012), is also shown (carbon atoms in gray; oxygen atoms are in red, sulfur atoms in yellow and hydrogen atoms in white).Note that HNC 34 S is blended with HOCS + because of their similarity of B + C but its contribution can be well constrained based on the HNC 32 S/HNC 34 S isotopic ratio (see text).
According to previous theoretical structural studies (Wheeler et al. 2006;Fortenberry et al. 2012) both isomers are asymmetric tops near the prolate limit (see e.g., Figure 1 for HOCS + ).HOCS + presents a slightly bent heavy atom skeleton, with ∠(O-C-S) = 174.4• (Fortenberry et al. 2012), while the H atom is located at ∠(H-O-C) = 117.9• in the ab plane, which implies that b-type lines are also allowed, in principle, by dipole moment selection rules, even though there is no spectroscopic evidence for them in previous experiments (due to the large value of the A rotational constant, A = 782696 MHz).Therefore, the b-type spectrum of HOCS + remains unknown.Ohshima & Endo (1996) identified the three lowest-J R-branch a-type rotational transitions belonging to the K a = 0 ladder of HOCS + , which were re-measured later on by Gottlieb et al. (2000).Therefore, these single series of lines will be the main target of our astronomical search.Note that this progres-  1. Spectroscopic information of the selected transitions of HOCS + detected toward G+0.693−0.027(shown in Figure 1).
Frequency Transition (a)  log  (a) The rotational energy levels are labelled using the conventional notation for asymmetric tops: JK a ,Kc , where J denotes the angular momentum quantum number, and the Ka and Kc labels are projections of J along the a and c principal axes.Lines that have been observed for the first time in the present astronomical dataset are marked with a * symbol.
sion can be easily extrapolated to higher frequencies, although larger uncertainties will be found once reaching the millimeter-wave region (e.g.0.3 MHz at 100 GHz and 0.6 MHz at 130 GHz, which translates into 1.1 and 1.8 km s −1 , respectively).Nevertheless, even at these frequencies, the uncertainties in the extrapolation are considerably smaller than the standard line widths of the molecular line emission measured toward G+0.693 (FWHM ∼ 15−20 km s −1 ; Requena-Torres et al. 2006a, 2008;Zeng et al. 2018).Consequently, they will not have an impact on the present analysis.

Detection of HOCS + and search for HSCO +
We used the Cologne Database for Molecular Spectroscopy (CDMS) entry 061510 (Müller et al. 2005;Endres et al. 2016) and performed the astronomical line identification of HOCS + using the Spectral Line Identification and Modeling (SLIM) tool (version from 2023 November 15) within the Madcuba package (Martín et al. 2019).This tool works assuming a Local Thermodynamic Equilibrium (LTE) excitation and enable us to generate the LTE synthetic spectra.In Figure 1 we depict all the transitions of HOCS + that fall within the current astronomical dataset, which are detected toward G+0.693.Their spectroscopic information is listed in Table 1.The fitted line profiles of HOCS + are depicted with a red solid line overlaid with the observed spectra (in gray).HOCS + appears to be the dominant carrier of the spectral features, despite the observed partial blend with mainly transitions of HNC 34 S, which will be thoroughly explained below.Also, we stress that we have identified the full progression of K a = 0 lines spanning from J lo = 2 (measured in the Q-band) to J lo = 13 (in the 2mm atmospheric window), with the exception of the J = 4,5 lines which are not observable due to atmo-spheric opacity.Interestingly, apart from the 3 0,3 -2 0,2 transition, the rest of the lines have been observed for the first time in the spectral survey of G+0.693 and still remain undetected in the laboratory (see Table 1).
In order to confirm that the spectral features we observe arise mainly from HOCS + and to thoroughly assess potential line contamination from other molecules, we have taken into account the emission profiles of the more than 130 molecules previously identified toward G+0.693 (Rivilla et al. 2023 and references therein).We found that most of the lines of HOCS + are partially blended with the emission from the 34 S isotopologue of HNCS (HNC 34 S), which to our best knowledge has not been detected yet in the ISM.By coincidence, the B and C rotational constants of both species are extremely similar (B+C = 11453.3MHz for HOCS + versus 11453.6MHz for HNC 34 S; Yamada et al. 1980) and, therefore, their a-type spectra will be governed by nearly identical patterns.To accurately model their expected emission, we can benefit from two different facts: i) the 32 S/ 34 S isotopic ratio for HNC 32 S/HNC 34 S, which will provide information on the expected molecular column density (N ) of HNC 34 S; ii) the different intensities of the rotational lines of both molecules, which will also appear as a fingerprint for each species.
Following this approach, to estimate the contribution of HNC 34 S we have used the 32 S/ 34 S isotopic ratio derived for a variety of molecules (CS, OCS, CCS, SO and H 2 S) and using multiple isotopologues (Colzi et al. in prep.).These values are always ≥20 toward G+0.693, in good accordance with the Solar System 32 S/ 34 S ratio of ∼22 derived by Wilson (1999).They are also close to the value obtained toward the envelope of the neighbouring region Sgr B2(N) by Humire et al. (2020) (∼18), and that reported recently by Li et al. (2023) (17 ± 1).
We then choose the lowest 32 S/ 34 S ratio (∼20), which corresponds to the ratio obtained for the possible precursor of HOCS + , OCS (see Sect. 3.3 and Appendix A), and also to that derived for CS (20 ± 2; Colzi et al in prep.).This is the most conservative or worst case scenario, which is the one employed to produce Figure 1.Larger values (i.e.30-40) will imply a lower column density for HNC 34 S and, therefore, a lower contribution of HNC 34 S to the observed profiles and more "available" emission to be fit by HOCS + , which will be less contaminated (see below).After considering the column density of the parent species, HNCS (analyzed in the Appendix B), we produced the LTE synthetic spectra of HNC 34 S adopting the same physical parameters as derived for the 32 S isotopologue (i.e., excitation temperature of T ex = 20.4K, radial velocity of v LSR = 66.7 km s −1 and line width of FWHM = 21.0 km s −1 ) and a N (HNC 34 S) = 3.1 ×10 12 cm −2 .The possibility that HNC 34 S alone is the molecular carrier of the observed lines was rapidly ruled out, since a significantly larger N (HNC 34 S), which implies a HNC 32 S/HNC 34 S ratio ∼7, almost a factor of ∼3 lower than the value derived for other molecules, was needed to properly explain all the observed emission.
Regarding the LTE analysis of HOCS + , we initially used the same parameters of T ex = 22.9 K, v LSR = 66.8 km s −1 and FWHM = 21.8 km s −1 derived from its proposed precursor, OCS, listed in Table 2 (see Sect. 3.3 and Appendix A).We then performed a population or rotational diagram analysis (Goldsmith & Langer 1999), as implemented in Madcuba, using all the transitions listed in Table 1 and the velocity-integrated intensity over the line width (Rivilla et al. 2021a).The latest version of SLIM also offers the possibility of considering the emission from other identified species to further remove it from the observed data.The results are shown in Figure 2. Following this approach, we derived the following physical parameters for HOCS + : N = (8.2± 0.3) ×10 12 cm −2 and T ex = 28 ± 5 K. Afterward, we carried out the LTE fit to the HOCS + emission using the Autofit tool within SLIM (Martín et al. 2019), which performs a nonlinear least-squares LTE fit to the observed spectra, with the column density left as a free parameter and fixing the T ex to the value obtained with the rotational diagram (28 K).We employed again all the transitions listed in Table 1 and accounted for the expected emission from every molecule detected within the same frequency interval.The results of the best LTE fit are presented in Table 2.We derived a molecular column density of N = (9 ± 2) ×10 12 cm −2 , which yields a fractional abundance with respect to molecular hydrogen of (7 ± 2) × 10 −11 , using a N (H 2 ) = 1.35×10 23 cm −2 from Martín et al. (2008).Moreover, we stress that if we consider a larger 32 S/ 34 S ratio, such as 40 instead of 20 to estimate the contribution of HNC 34 S, the fit would yield a N (HOCS + ) = (1.1 ± 2) ×10 13 cm −2 , just a factor of ∼1.2 higher.Alternatively, if we adopt the T ex of OCS (23 K) to perform the Autofit, it only yields a change in the molecular abundance of ∼10 %, which is within the errors of the derived N , but slightly overestimates the emission of the 3 0,3 -2 0,2 and 4 0,4 -3 0,3 transitions.
During the analysis, we have also tried to include the newly observed astronomical lines of HOCS + in a global fit to a semirigid rotor Hamiltonian along with the previously measured laboratory lines.However, the typical broad line widths of G+0.693, together with the observed partial blends detailed above, did not enable us to determine further centrifugal distortion parameters and improve the set of spectroscopic constants of the molecule (as was done successfully for carbonic acid, HOCOOH; Sanz-Novo et al. 2023).We also inspected the observational data searching for new K a = 1 transitions, but these attempts were unfruitful due to the lack of reliable laboratory measurements for higher K a ladders.Thus, we encourage the laboratory spectroscopic community to perform additional high-resolution rotational measurements and extend the frequency coverage for HOCS + up to the millimeter and submillimeter-wave region.In particular, the detection of higher K a ladders will aid to constrain more accurately both B and C rotational constants as well as centrifugal distortion parameters, thereby enabling us to further disentangle the emission of HOCS + and HNC 34 S.
Figure 3. LTE simulation of the HSCO + emission at the 3σ upper limit column density derived toward G+0.693 using the physical parameters shown in Table 2 (in green) together with the expected molecular emission from all the molecular species identified to date in our survey (in blue), both overlaid on the observations (black line and in gray histogram).The structure of HSCO + is also shown.
scopic study of Lattanzi et al. (2018) together with the previous laboratory data from McCarthy & Thaddeus (2007), which corresponds to the 061509 entry of the CDMS catalog (Müller et al. 2005).In this case, extensive millimeter and submillimeter data were reported by Lattanzi et al. (2018), which allow us to extend the reliability of the predictions for the S-protonated HSCO + to transitions with higher K a values.This isomer remains undetected in the present observational data (only two almost unblended transitions are found, as shown in Figure 3), so we derived an upper limit to its column density.We employed the same physical parameters obtained for the O-protonated form (see Table 2) and selected the brightest a-type R-branch K a = 0,1 transition that appears clean from the emission from other molecules, which correspond to the 3 0,3 -4 0,4 (located at 45.094116 GHz) rotational transition.We derived a line-integrated 3σ upper limit to its column density of N ≤ 4×10 12 cm −2 , which translates into an upper limit to the molecular abundance relative to H 2 of ≤3×10 −11 .Consequently, it is at least a factor of ≥2.3 less abundant than HOCS + .

Analysis of OCS and OC 34 S
For completeness, we also modeled the emission of the related carbonyl sulfide (OCS, v = 0), which appears as a promising precursor of HOCS + , and its 34 S monosubstituted isotopologue OC 34 S. We employed the entries 060503 and 062505, respectively, of the CDMS catalog.The details of the analysis are reported in the Appendix A (see Tables A1 and A2, and Figures A1 and A2).In Table 2, we present the results for the best-fitted LTE model for both species using the Autofit tool within SLIM.We obtained a OC 32 S/OC 34 S ratio of 20 ± 1 and a HOCS + /OCS ratio of ∼2.5×10 −3 toward G+0.693.

Analysis of HOCO +
In order to compare these results with the structurally similar O-bearing molecules, we also report the detection of the ground state of HOCO + , the O-analogue of HOCS + , toward G+0.693.To carry out its interstellar search, we used the rotational data reported in Bizzocchi et al. 2017 (entry 045522 of the CDMS catalog).The LTE analysis is tackled in detail in the Appendix C (see Table C4 and Figure C4), while the results of the Autofit are presented in Table 2 along with the physical parameters of HOCS + and HSCO + .We derived a HOCO + /HOCS + ratio of 31 ± 6 toward this source, which will be discussed in Sect.4.4 4. DISCUSSION 4.1.HOCS + /HSCO + isomeric ratio The identification of the higher-energy O-protonated isomer, HOCS + , and the nondetection of the Sprotonated form, HSCO + (global minimum in energy), toward G+0.693 raises an interesting question: Why is the most stable isomer not being detected?Experimentally, it is found that HOCS + is less abundant than HSCO + , obtaining a ratio of ∼1:3 in the microwave spectrum (McCarthy & Thaddeus 2007).This result approximately correlates with the theoretically computed energy difference between both isomers (Wheeler et al. 2006).Note that the population observed in the supersonic jet during the experiment (McCarthy & Thaddeus 2007) is related to that in an equilibrium situation prior to the adiabatic expansion (at relatively high temperatures of ∼300 K).However, our observational findings points to an opposite trend, showing a lower limit to the HOCS + /HSCO + ratio of ≥2.3.The relative population must then depend on kinetic factors rather than the relative thermodynamic stability of the S-and O-protonated isomers, which will be discussed in Sect.4.2.Hence, these results are an additional example against the minimum energy principle (MEP; Lattelais et al. 2011), which proposes that the thermody-  (1990).The main formation route (see discussion in the text) is highlighted with dark blue bloxes.We depict in blue the molecules that have been identified toward the G+0.693 molecular cloud, in green those species that have been searched for but not detected toward G+0.693, and in gray the molecules that have not been searched for toward G+0.693 because spectroscopy is not available (H 2 CS + ) or no transitions fall in the spectral survey (S and HS).Surface reactions are shown in black dashed arrows, gas-phase reactions are indicated in black solid lines and gas-phase protonation reactions are shown with blue arrows.
namically favored (most stable) isomer is expected to be predominant in the ISM.This fact is not striking, since the MEP has been proven to fail to predict the relative abundances of a plethora of structural isomers (e.g., the Shingledecker et al. 2019;Mininni et al. 2020;Rivilla et al. 2023).Thus, the identification of HOCS + provides clear observational evidence to argue that the MEP does not apply to the interestellar [H,C,S,O] + isomeric family either.

Interstellar formation of HOCS +
Several reactions have already been proposed to produce at least one protonated carbonyl sulfide isomer (Turner et al. 1990;Liu et al. 2002;Vidal et al. 2017;Tinacci et al. 2021).Owing to the ubiquitous nature of OCS and its relatively large abundance in the ISM, chemical intuition suggests that a direct ion-molecule reaction, using protons from diverse sources, may be the dominant formation route.For example, they can form through: OCS + HCO + → HOCS + + CO (2) which will be the most promising routes to form these isomers (the complete reaction scheme is shown in Figure 4).Regarding OCS, it can be formed efficiently on the grains via CO + S (Shingledecker et al. 2020), being then released into the gas phase.Also, it is worth noting that the reaction rate coefficients of 1 and 2 are 1.9 × 10 −9 and 1.1 × 10 −9 cm −3 s −1 , respectively (Rakshit 1982;Adams et al. 1978), which are within the typical values of fast protonation reactions of neutral species.Note that in this study, based on mass spectrometry, there is no differentiation between the two O-and Sprotonated isomers.Alternatively, other protonation reactions, which exhibit slightly slower rate coefficients (k(3) = 0.8 × 10 −10 cm −3 , k(4) = 8.5 × 10 −10 cm −3 and k(5)= 9.5 × 10 −10 cm −3 ; Smith & Adams 1978), may take place as well: Once HOCS + is formed, it can further recombine electronically to yield either CS and OCS (Vidal et al. 2017).Furthermore, the large barrier to the isomerization of HSCO + to HOCS + (located at ∼70 kcal mol −1 above HSCO + , Wheeler et al. 2006) will hamper any interconversion process.Hence, the observed isomeric ratio (HOCS + /HSCO + ≥2.3) can be rationalized in terms of the kinetics of the protonation pathways.A reasonable explanation was already put forward by McCarthy & Thaddeus (2007), who suggested that the arrangement of OCS with respect to the protonating agent, H + 3 , shall play a crucial role in the protonation process.If this reaction is sensitive to the spatial orientation between the reactants, HOCS + may prevail over HSCO + in the ISM, because O is more electronegative than S and it will be the preferred binding site (McCarthy & Thaddeus 2007).Likewise, in G+0.693 the observations suggest that O-protonation process is more efficient, which appears among the main chemical routes to the formation of HOCS + .
In addition, most of the suggested precursors included in Figure 4 (e.g., OCS, HCS + and SO) are simple molecules that are present at relatively high abundances toward the G+0.693 molecular cloud (see e.g., SO with a column density of (30.06 ± 0.07) ×10 14 cm −2 and an abundance of (2.2 ± 0.2) ×10 −8 with respect to H 2 ; Rivilla et al. 2022b).We can thus compare the relative abundance of both protonated isomers (HOCS + and HSCO + ) with respect to the parent carbonyl sulfide, OCS.This ratio appears as an excellent test for ionmolecule formation models since it relies significantly upon the fast protonation rates of the neutral molecules and upon fast dissociative electron recombination rates of the corresponding ion (i.e., HOCS + ; Turner et al. 1990).We find a HOCS + /OCS ratio of ∼2.5×10 −3 , while the HSCO + /OCS upper limit ratio is ≤10 −3 (see Table 2).Our results are in accordance with earlier observations toward warm star-forming regions, where upper limits of a few times 10 −3 were obtained for the HOCS + /OCS ratio (Turner et al. 1990).
We explored other feasible formation routes of HOCS + , following what has been proposed for the formation of the isovalent HOCO + , including the analogue protonation of desorbed CO 2 and also the gas-phase route HCO + + OH → HOCO + + H (see e.g., Fontani et al. 2018;Majumdar et al. 2018;Harada et al. 2022).Thus, if we assume a similar formation for the S-bearing species, we can propose the following ion-molecule reactions: Regarding the gas-phase route starting from HCS + and OH (reaction 6), we find a molecular column density for HCS + of (5.3 ± 2) × 10 13 (using entry 045506 of the CDMS catalog; Margulès et al. 2003), which is ∼5 times more abundant than HOCS + , and appears as another plausible precursor (the complete LTE analysis is shown in Appendix D).Meanwhile, HS remains undetected toward G+0.693 due to the absence of spectroscopic features within the frequency ranged covered by our dataset.

Chemical modeling of HOCS +
Initial models of the HOCS + formation were carried out by Turner et al. (1990) for typical molecular dark clouds conditions.For instance, we find a good agreement with the "low-metal" gas-phase model estimates of HOCS + /OCS gathered in Table 7 of Turner et al. (1990) (e.g., for their model (3) the ratio is 3.3×10 −3 ).However, these conditions are very different from the physical conditions of the molecular clouds located in the Galactic Center.Hence, to rationalize the observed abundances of HOCS + toward G+0.693, we have also employed the chemical code UCLCHEM (Holdship et al. 2017), as previously done for PO + (Rivilla et al. 2022b).The model has been run in three different phases: Phase 0 simulates the chemistry of a translucent cloud exhibiting a n(H) = 10 3 cm −3 and a T kin = 20 K for a period of 10 6 years.In Phase 1 we simulate the collapse of a molecular cloud from n(H) = 10 3 cm −3 to n(H) = 2×10 4 cm −3 (T kin is set constant at 10 K).We then simulate in Phase 2 the passage of a lowvelocity C-type shock with v s =20 km s −1 and pre-shock gas density of n(H) = 2×10 4 cm −3 using the C-type shock parametric approximation by Jiménez-Serra et al. (2008).We adopt a shock velocity of v s =20 km s −1 , consistent with the observed line widths of the molecular line emission (Requena-Torres et al. 2006a;Zeng et al. 2018), and with the gas densities measured toward G+0.693 (Zeng et al. 2020).The initial elemental abundances are those used in Jiménez-Serra et al. ( 2018), adopting the solar value reported for S in Asplund et al. (2009) (1.32×10 −5 ; depletion factor of 1).This value falls within the range of (0.7-3.5)×10 −5 reported for several GC sources (Rodríguez-Fernández & Martín-Pintado 2005), as well as the S abundance found for other sources in the inner Galaxy of (0.7-1.6)×10 −5 (e.g., (0.7±0.1)×10 −5 for SgrC; Martín-Hernández et al. 2002).We also carried out models using larger depletion factors for S of about 4 (a total abundance of 3.51×10 −6 from Jenkins 2009) and 10, respectively, which fail to reproduce the observed abundances of different S-bearing molecules, including HOCS + and OCS, even when considering an enhanced cosmic-ray ionization rate by several orders of magnitude (see below).
Moreover, we employed the default dust-grain network of UCLCHEM, based on Quénard et al. (2018), and the UMIST12 database (McElroy et al. 2013).We have also introduced the gas phase reaction (6), which to our knowledge has not been measured experimentally, assuming a rate constant of 10 −9 cm −3 , which is the typical value for ion-neutral reactions (Puzzarini 2022).
To mimic the extreme physical conditions of G+0.693, which is thought to be affected by a strong ultraviolet field of secondary UV photons induced by cosmic rays, we have explored three distinct values for the cosmicray ionisation rate: the standard Galactic disk value of ζ = 1.3×10 −17 s −1 , and two enhanced values of ζ×100 and ×1000 times higher than the canonical one.In Figure 5 we show the model results for Phase 2, including the modelled fractional abundances of HOCS + , OCS, HCS + , HCO + , SO and OH (solid coloured lines) along with the observed values for HOCS + and OCS, which is suggested as the main precursor (depicted with green and blue thick lines, respectively).The following results are derived from the models: 1. We observe a release of OCS into the gas phase, which is ejected from the grains due to shocks, at time-scales of ∼40 yr once the sputtering of the icy mantles of dust grains is completed (see Jiménez-Serra et al. 2008).
2. It is clear that a high cosmic-ray ionisation rate (at least a factor of 100 higher than the standard value, left panel of Figure 5) is required to yield HOCS + abundances close to the observed value, in line with the results derived for PO + toward G+0.693 (Rivilla et al. 2022b).
3. Although the gas phase reaction (6) slightly increases the overall production of HOCS + , the direct protonation of OCS stands as the dominant formation route of HOCS + , specially for typical time-scales of Galactic center clouds (i.e., G+0.693) of about 10 5 yr (Requena-Torres et al.  we would need to increase its reaction rate by one order of magnitude (k = 10 −8 cm −3 ).
4. We also observed chemical relaxation oscillations for the highest ζ case (right panel of Figure 5).These oscillations are thought to occur due to the existence of bistable solutions (Dufour & Charnley 2019), related to autocatalytic processes in the gas phase.Moreover, they can lead to limit cycles and chemical relaxation oscillation solutions when coupled with the gas-grain exchange of key species (Dufour et al. 2023), and they usually take place at time-scales of interest for comparing models and observations.

Relative O/S ratio in different astronomical sources
Understanding the S depletion problem has been an open subject of debate for astrochemical models (Vidal et al. 2017;Laas & Caselli 2019;Shingledecker et al. 2020).In low-density (n(H) ≤ 10 3 -10 4 cm −3 ; Ruffle et al. 1999) and diffuse molecular clouds, the observed abundance of S with respect to that of O is close to the solar value (O/S∼37; Asplund et al. 2009;Neufeld et al. 2015;Goicoechea & Cuadrado 2021).On the contrary, in dense clouds (n(H) ≥ 10 5 cm −3 ; Tieftrunk et al. 1994) and protostars, the sulfur abundance found for the gasphase chemical content is severely reduced up to several orders of magnitude, leading to the so-called "missing sulfur" issue (e.g., Jiménez-Escobar & Muñoz Caro 2011; Martín-Doménech et al. 2016;Marcelino et al. 2023;Fuente et al. 2023).Thus, it is interesting to study the relative O/S ratio across different stages of star formation to establish general trends.
Hence, we present a compilation of the O/S ratio for a variety of well-known interstellar molecules, ranging from the CO/CS pair to the much more complex species like C 2 H 5 OH/C 2 H 5 SH toward various interstellar sources.We have included shock-dominated regions (L1157-B1, Holdship et al. 2019, andG+0.693 Zeng et al. 2018;Rodríguez-Almeida et al. 2021a  In this work, we obtained a HOCO + /HOCS + ratio of 31 ± 6, which agrees within a factor of 2-3 with the aforementioned pattern and also draws closer to the O/S solar ratio (∼37; Asplund et al. 2009).Only the CO/CS ratio is several orders of magnitude above the solar value, which may be due to the fact that CO traces a significative larger volume of gas than CS due to its lower critical den-sity, or, alternatively, it suggests that the formation of CO is significantly more efficient than the production of CS toward G+0.693.These results can be rationalized in terms of the singular chemistry governing the cloud, which is subjected to large-scale shocks (Requena-Torres et al. 2006b;Zeng et al. 2020).This translates into an enhanced sputtering erosion of the dust particles and a boost in the gas-phase abundance of diverse organics, including S-bearing molecules, rather than remaining anchored in the grains.Therefore, S appears to be relatively less depleted toward G+0.693 compared to other astronomical sources, further suggesting that the "missing sulfur" problem is mitigated by the action of shocks, in agreement with the results presented in Sect.4.2.
Finally, based on the derived O/S ratios toward G+0.693, we can expect that the abundance of new Sbearing species will be at least an order of magnitude lower than the abundance of their O-bearing analogues (e.g., CH 3 OH and C 2 H 5 OH), in agreement with the lower limit ratio of ≥0.8-5.3 derived for the more complex NH 2 CH 2 CH 2 OH/NH 2 CH 2 CH 2 SH pair (Song et al. 2022) and also close to the solar ratio.Therefore, the recognition of O-bearing COMs with enough abundance will be an excellent guide for the selection of new Sbearing astronomical candidates of increasing complexity, fact that is intrinsically related to the cosmic availability of both elements.

SUMMARY AND CONCLUSIONS
We report the first detection of HOCS + , the Oprotonated form of carbonyl sulfide (OCS), in space based on an ultradeep spectral survey conducted toward the G+0.693-0.027molecular cloud.We derived a molecular column density for HOCS + of N = (9 ± 2) × 10 12 cm −2 , which yields a fractional abundance with respect to H 2 of ∼7 × 10 −11 .It is worth noticing that almost the entire set of transitions has been observed for the first time directly in the ISM and are still uncharted in the laboratory.Interestingly, we found that most of the lines of HOCS + are partially blended with the emission from the 34 S isotopologue of HNCS (HNC 34 S), which, to the best of our knowledge, has been observed for the first time in the ISM in this work.Meanwhile, the S-protonated isomer, HSCO + remains undetected, with an upper limit to its molecular abundance with respect to H 2 of ≤ 3 ×10 −11 , at least 2.3 times less abundant than the O-protonated form.We have carried out new chemical models that account for the passage of a Ctype shock, highlighting that high values of the cosmicray ionization rate (ζ = 10 −15 -10 −14 s −1 ) are required to explain the presence of HOCS + in the G+0.693 molecular cloud.We also propose the protonation of OCS at the oxygen end to be one of the main chemical pathways to the formation of HOCS + in the ISM.
We performed a comparison of the O/S ratio across different interstellar environments.In G+0.693, we obtained O/S values that are similar to the solar ratio (e.g., HOCO + /HOCS + ∼31, CH 3 OH/CH 3 SH∼23 and C 2 H 5 OH/C 2 H 5 SH∼15) which suggested that S is not significantly depleted.This is consistent with the idea that large-scale shocks in G+0.693 have released the ices of dust grains, boosting the abundance of diverse S-bearing species in the gas phase, instead of remaining trapped in the grains.Moreover, our results show that the exchange of the O atom by a S atom entails a drop of at least one order of magnitude in abundance.This fact can be used to guide the search for new S-bearing COMs of increasing complexity.
Finally, the detection of a new S-bearing cation provides valuable insights to disclose the role of ionmolecule processes in the formation of more complex interstellar systems, and will also aid theoretical chemists to update and verify both gas and gas-grain astrochemical networks targeting sulfur.Moreover, the discovery of HOCS + reinforces the idea that the G+0.693 molecular cloud as a warehouse of not only N-and O-interstellar molecules but also of new S-bearing species.To conduct the LTE analysis of OCS we selected all the lines that are completely unblended with the emission from other species already identified toward G+0.693 (see Table A1).In this case, since OCS is a linear molecule, we were able to identify harmonic patterns attributed to 13 unblended transitions.The result of the best LTE fit using Autofit tool within SLIM is shown in Figure A1 and the derived physical parameter are reported in the first row of Table 2.Then, we carried out the LTE analysis of its 34 S monosubstituted isotopologue (see Figure A2 and Table A2).For OC 34 S we obtained the following physical parameters in the LTE fit: N = (1.80 ± 0.05) ×10 14 cm −2 , T ex = (23.5 ± 0.6) K, v LSR = (66.7 ± 0.3) km s −1 and FWHM = (23.9± 0.7) km s −1 , in good agreement with the parameters derived for the parent OCS.Thus, we derived a OC 32 S/OC 34 S ratio of 20 ± 1 toward G+0.693, which is very similar to the 32 S/ 34 S obtained in the Galactic center by Wilson (1999) (∼22).Hence, the emission of OCS toward G+0.693 appears to be optically thin, as further corroborated by the 16 OCS/ 18 OCS ratio derived toward this cloud (∼290, Colzi et al. in prep), which is in accordance with the 16 OCS/ 18 OCS ∼250 found in Armijos-Abendaño et al. (2015).The derived value is also similar to the CH 3 OH/CH 3 18 OH ratios of 210 ± 40 and ∼180 reported in Gardner et al. (1989) and Müller et al. (2016a) toward Sgr B2 and Sgr B2(N), respectively, as well as the 16 O/ 18 O ratio presented in Wilson & Rood (1994) toward the Galactic center ISM.

B. ANALYSIS OF HNCS
To carry out the analysis of HNCS under LTE conditions, we used entry 059503 of the CDMS catalog (corresponding to the a-type spectra).Then, we chose transitions that are unblended or slightly blended with the emission from other molecules to perform the fit using the SLIM Autofit tool (Martín et al. 2019), which are collected in Table B3.The result of the best LTE fit is shown in Figure B3 and the derived physical parameter are: N = (6.2± 0.1) ×10 13 cm −2 , which yields a fractional abundance with respect to molecular hydrogen of ∼4.6 × 10 −10 (adopting N (H 2 ) = 1.35×10 23 cm −2 from Martín et al. 2008), T ex = (20.4± 0.5) K and v LSR = (66.7 ± 0.3) km s −1 .The FWHM was fixed to 21.0 km s −1 in the fit.These physical parameters are also collected in Table 2.

C. ANALYSIS OF HOCO +
To properly model the emission of HOCO + under LTE conditions, we needed first to split the K a = 0, 1 rotational ladders.The selected transitions are listed in Table C4 while in Figure C4a (K a = 0) and C4b (K a = 1) we show the results of the best LTE fit using the Autofit tool within SLIM for each ladder.The derived physical parameters for the K a = 0 ladder are reported in Table 2.As it can be seen, two K a = 1 transitions (panels 2 and 3 of Figure C4b) are still overestimated.This fact may be due to plausible non-LTE effects that are currently out of the scope of this work.

D. ANALYSIS OF HCS + AND UPPER LIMIT OF THE NON-DETECTED HCS
To perform the LTE analysis of HCS + , a possible precursor of HOCS + , we have employed entry 045506 of the CDMS catalog, whose spectroscopic information was taken from Margulès et al. (2003).We depict in Figure D5 the result of the best LTE fit using the Autofit tool within SLIM, including the five detected lines (a complete progression ranging from J up = 1 to J up = 5) listed in Table D5.We derived a molecular abundance of N = (5.3± 2) × 10 13 cm −2 , which implies that HCS + is ∼5 times more abundant than HOCS + .Regarding the rest of physical parameters, these are: T ex = (6.9± 0.2) K and v LSR = (68.5 ± 0.2) km s −1 and FWHM = (20.0± 0.6) km s −1 .Note that both the fundamental transition, J = 1 -0, and the J = 5 -4 are most likely unblended features affected by non-LTE effects, whose analysis is beyond the scope of this work.
We have also searched for the HCS radical (CDMS entry 045507; Habara et al. 2002), which is not clearly detected.Therefore, we have derived the 3σ upper limit to its molecular abundance (σ is the rms noise of the spectra) using the 2 0,2 -1 0,1 transition, in particular the J = 5/2 -3/2 F = 3 -2 hyperfine component, which is the brightest transition predicted in the LTE model (see Figure D6) that is fully unblended.We obtain a N ≤ 9.8 × 10 13 cm −2 using the physical parameters reported above for HCS + (e.g., T ex = 6.9 K).As seen in Figure D6 some hyperfine components of the 2 0,2 -1 0,1 and 4 0,4 -3 0,3 transitions are tentatively detected, but there are not enough clear spectroscopic features to achieve a conclusive detection.We find that HCS is ≤11 times more abundant than HOCS + and ≤1.8 times more abundant than its cationic form, HCS + .A1).The result of the best LTE fit is shown with a red solid line, while the blue line shows the expected molecular emission from all the molecular species identified to date in our survey.The observed spectra are plotted as gray histograms.A2).B3).The result of the best LTE fit is shown with a red solid line, the blue line shows the expected molecular emission from all the molecular species identified to date in our survey and the observed spectra are plotted as gray histograms.
Table D5.Spectroscopic information of the transitions of HCS + detected toward G+0.693 (shown in Figure D5).
Frequency Transition (a)  log  (a) The rotational energy levels are labelled using the quantum number J.  C4).The result of the best LTE fit is shown with a red solid line, while the blue line shows the expected molecular emission from all the molecular species identified to date in our survey.The observed spectra are plotted as gray histograms.D5).

Figure 1 .
Figure 1.Transitions of HOCS + identified toward the G+0.693-0.027molecular cloud (listed inTable1).The result of the best LTE fit of HOCS + is shown with a red line, the green line plots the predicted emission of HNC 34 S, and the blue line plots the emission from all the molecules identified to date in our survey (including the latter two).The observed spectra are plotted as gray histograms.The structure of HOCS + , taken fromFortenberry et al. (2012), is also shown (carbon atoms in gray; oxygen atoms are in red, sulfur atoms in yellow and hydrogen atoms in white).Note that HNC 34 S is blended with HOCS + because of their similarity of B + C but its contribution can be well constrained based on the HNC 32 S/HNC 34 S isotopic ratio (see text).

Figure 2 .
Figure 2. Population diagram of HOCS + toward G+0.693 (depicted in blue dots).The gray dotted line corresponds to the best linear fit to the data points.The derived values for the molecular column density, N and the excitation temperature, Tex, are shown in blue.Note that the contamination by all other identified species has been removed from the observed data.

Figure 4 .
Figure 4. Summary of the main chemical routes for the formation of HOCS + in the ISM, adapted and completed fromTurner et al. (1990).The main formation route (see discussion in the text) is highlighted with dark blue bloxes.We depict in blue the molecules that have been identified toward the G+0.693 molecular cloud, in green those species that have been searched for but not detected toward G+0.693, and in gray the molecules that have not been searched for toward G+0.693 because spectroscopy is not available (H 2 CS + ) or no transitions fall in the spectral survey (S and HS).Surface reactions are shown in black dashed arrows, gas-phase reactions are indicated in black solid lines and gas-phase protonation reactions are shown with blue arrows.

Figure 5 .
Figure5.Chemical model results (Phase 2): evolution of the fractional abundances of HOCS + (green), OCS (blue) HCS + (purple), HCO + (brown), OH (red), and SO (orange) as a function of time.We consider for this phase a C-type shock with a shock speed of vs=20 km s −1 and an initial gas density of n(H) = 2×10 4 cm −3 .We also explore three different values for the cosmic-ray ionisation rate: the standard Galactic value of ζ = 1.3×10 −17 (left panel), and two enhanced values of ζ×100 (middle panel) and ×1000 (right panel) times higher than the standard one.The observed abundances of HOCS + and OCS, suggested as the main precursor, are highlighted using green and blue thick lines, respectively, adopting n(H)= 2 × n(H2).
2006b), marked by red dashed vertical lines in Figure 5.Note that to make the contribution of the reaction (6) as relevant as the protonation process,
OF OCS AND ITS 34 S ISOTOPOLOGUE

Figure A1 .
Figure A1.Selected transitions of OCS identified toward G+0.693 molecular cloud (listed in TableA1).The result of the best LTE fit is shown with a red solid line, while the blue line shows the expected molecular emission from all the molecular species identified to date in our survey.The observed spectra are plotted as gray histograms.

Figure B3 .
Figure B3.Selected transitions of HNCS identified toward G+0.693 (listed in TableB3).The result of the best LTE fit is shown with a red solid line, the blue line shows the expected molecular emission from all the molecular species identified to date in our survey and the observed spectra are plotted as gray histograms.

Figure C4 .
Figure C4.Selected Ka = 0 (a) and Ka = 1 (b) transitions of HOCO + identified toward G+0.693 (listed in TableC4).The result of the best LTE fit is shown with a red solid line, while the blue line shows the expected molecular emission from all the molecular species identified to date in our survey.The observed spectra are plotted as gray histograms.

Figure D6 .
Figure D6.LTE simulation of the HCS emission at the 3σ upper limit column density derived toward G+0.693 (in green) together with the expected molecular emission from all the molecular species identified to date in our survey.The observed spectrum is shown as a gray histogram.