Bottlenecks to interstellar sulfur chemistry: Sulfur-bearing hydrides in UV-illuminated gas and grains
J. R. Goicoechea, A. Aguado, S. Cuadrado, O. Roncero, J. Pety, E. Bron, A. Fuente, D. Riquelme, E. Chapillon, C. Herrera, C. A. Duran
AAstronomy & Astrophysics manuscript no. aa_sulfur_bar_accepted © ESO 2021February 12, 2021
Bottlenecks to interstellar sulfur chemistry
Sulfur-bearing hydrides in UV-illuminated gas and grains
J. R. Goicoechea , A. Aguado , S. Cuadrado , O. Roncero , J. Pety , E. Bron ,A. Fuente , D. Riquelme , E. Chapillon , , C. Herrera , and C. A. Duran , Instituto de Física Fundamental (CSIC). Calle Serrano 121-123, 28006, Madrid, Spain. e-mail: [email protected] Facultad de Ciencias. Universidad Autónoma de Madrid, 28049 Madrid, Spain. Institut de Radioastronomie Millimétrique (IRAM), Grenoble, France. LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 92190 Meudon, France. Observatorio Astronómico Nacional (OAN), Alfonso XII, 3, 28014 Madrid, Spain. Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany. OASU / LAB-UMR5804, CNRS, Université Bordeaux, 33615 Pessac, France. European Southern Observatory, Alonso de Cordova 3107, Vitacura, Santiago, Chile.Received 25 October 2020 / Accepted 23 December 2020
ABSTRACT
Hydride molecules lie at the base of interstellar chemistry, but the synthesis of sulfuretted hydrides is poorly understood and theirabundances often crudely constrained. Motivated by new observations of the Orion Bar photodissociation region (PDR) – 1 (cid:48)(cid:48) resolutionALMA images of SH + ; IRAM 30m detections of bright H S, H
S, and H
S lines; H S + (upper limits); and SOFIA / GREATobservations of SH (upper limits) – we perform a systematic study of the chemistry of sulfur-bearing hydrides. We self-consistentlydetermine their column densities using coupled excitation, radiative transfer as well as chemical formation and destruction models.We revise some of the key gas-phase reactions that lead to their chemical synthesis. This includes ab initio quantum calculations ofthe vibrational-state-dependent reactions SH + + H ( v ) (cid:29) H S + + H and S + H ( v ) (cid:29) SH + H. We find that reactions of UV-pumpedH ( v ≥
2) molecules with S + ions explain the presence of SH + in a high thermal-pressure gas component, P th / k ≈ cm − K, close tothe H dissociation front (at A V < + , H S + , and S atoms with vibrationally excited H , fail to formenough H S + , H S + , and SH to ultimately explain the observed H S column density ( ∼ × cm − , with an ortho-to-para ratio of2.9 ± S (s-H S). The higher adsorption binding energies of Sand SH suggested by recent studies imply that S atoms adsorb on grains (and form s-H S) at warmer dust temperatures ( T d <
50 K) andcloser to the UV-illuminated edges of molecular clouds. We show that everywhere s-H S mantles form(ed), gas-phase H S emissionlines will be detectable. Photodesorption and, to a lesser extent, chemical desorption, produce roughly the same H S column density(a few 10 cm − ) and abundance peak (a few 10 − ) nearly independently of n H and G . This agrees with the observed H S columndensity in the Orion Bar as well as at the edges of dark clouds without invoking substantial depletion of elemental sulfur abundances.
Key words.
Astrochemistry — line: identification — ISM: clouds — (ISM:) photon-dominated region (PDR) — ISM: clouds
1. Introduction
Hydride molecules play a pivotal role in interstellar chemistry(e.g., Gerin et al. 2016), being among the first molecules toform in di ff use interstellar clouds and at the UV-illuminatededges of dense star-forming clouds, so-called photodissociationregions (PDRs; Hollenbach & Tielens 1997). Sulfur is on thetop ten list of most abundant cosmic elements and it is par-ticularly relevant for astrochemistry and star-formation studies.Its low ionization potential (10.4 eV) makes the photoionizationof S atoms a dominant source of electrons in molecular gas atintermediate visual extinctions A V (cid:39) / H], in di ff use clouds (e.g., Howket al. 2006) is very close to the [S / H] measured in the solarphotosphere ([S / H] (cid:12) (cid:39) × − ; Asplund et al. 2009). Still, theobserved abundances of S-bearing molecules in di ff use andtranslucent molecular clouds ( n H (cid:39) − cm − ) make up a very small fraction, < + ; Tieftrunk et al. 1994; Turner 1996; Lucas & Liszt 2002;Neufeld et al. 2015). In colder dark clouds and dense coresshielded from stellar UV radiation, most sulfur is expected inmolecular form. However, the result of adding the abundancesof all detected gas-phase S-bearing molecules is typically afactor of ∼ -10 lower than [S / H] (cid:12) (e.g., Fuente et al. 2019).Hence, it is historically assumed that sulfur species depleteon grain mantles at cold temperatures and high densities (e.g.,Graedel et al. 1982; Millar & Herbst 1990; Agúndez & Wake-lam 2013). However, recent chemical models predict that themajor sulfur reservoir in dark clouds can be either gas-phaseneutral S atoms (Vidal et al. 2017; Navarro-Almaida et al. 2020)or organo-sulfur species trapped on grains (Laas & Caselli 2019).Unfortunately, it is di ffi cult to overcome this dichotomy from anobservational perspective. In particular, no ice carrier of an abun-dant sulfur reservoir other than solid OCS (hereafter s-OCS, withan abundance of ∼ − with respect to H nuclei; Palumbo et al. Article number, page 1 of 25 a r X i v : . [ a s t r o - ph . GA ] F e b & A proofs: manuscript no. aa_sulfur_bar_accepted O) grain mantles in dense molec-ular clouds and cold protostellar envelopes (see reviews by vanDishoeck 2004; Gibb et al. 2004; Dartois 2005), one may also ex-pect hydrogen sulfide (s-H S) to be the dominant sulfur reservoir.Indeed, s-H S is the most abundant S-bearing ice in comets suchas 67P / Churyumov–Gerasimenko (Calmonte et al. 2016). How-ever, only upper limits to the s-H S abundance of (cid:46) S ice abundance ofseveral 10 − with respect to H nuclei. Still, this upper limit couldbe higher if s-H S ices are well mixed with s-H O and s-CO ices(Brittain et al. 2020).The bright rims of molecular clouds illuminated by nearbymassive stars are intermediate environments between di ff use andcold dark clouds. Such environments host the transition fromionized S + to neutral atomic S, as well as the gradual formationof S-bearing molecules (Sternberg & Dalgarno 1995). In oneprototypical low-illumination PDR, the edge of the Horseheadnebula, Goicoechea et al. (2006) inferred very modest gas-phasesulfur depletions. In addition, the detection of narrow sulfur radiorecombination lines in dark clouds (implying the presence of S + ;Pankonin & Walmsley 1978) is an argument against large sulfurdepletions in the mildly illuminated surfaces of these clouds.The presence of new S-bearing molecules such as S H, the first(and so far only) doubly sulfuretted species detected in a PDR(Fuente et al. 2017), suggests that the chemical pathways leadingto the synthesis of sulfuretted species are not well constrained;and that the list of S-bearing molecules is likely not complete.Interstellar sulfur chemistry is unusual compared to thatof other elements in that none of the simplest species,X = S, S + , SH, SH + , or H S + , react exothermically with H ( v = + H → XH + H (so-called hydrogenabstraction reactions). Hence, one would expect a slow sul-fur chemistry and very low abundances of SH + (sulfanylium)and SH (mercapto) radicals in cold interstellar gas. However,H S (Lucas & Liszt 2002), SH + (Menten et al. 2011; Godardet al. 2012), and SH (Neufeld et al. 2012, 2015) have been de-tected in low-density di ff use clouds ( n H (cid:46)
100 cm − ) throughabsorption measurements of their ground-state rotational lines .In UV-illuminated gas, most sulfur atoms are ionized, but thevery high endothermicity of reactionS + ( S ) + H ( Σ + , ν = (cid:29) SH + ( Σ − ) + H ( S ) (1)( E / k = ffi cient unless the gas is heatedto very high temperatures. In di ff use molecular clouds(on average at T k ∼
100 K), the formation of SH + and SH onlyseems possible in the context of local regions of overheated gassubjected to magnetized shocks (Pineau des Forets et al. 1986) orin dissipative vortices of the interstellar turbulent cascade (Godardet al. 2012, 2014). In these tiny pockets ( ∼
100 AU in size), thegas would attain the hot temperatures ( T k (cid:39) / or ion-neutral drift needed to overcome the endothermicities of the abovehydrogen abstraction reactions (see, e.g., Neufeld et al. 2015).Dense PDRs ( n H (cid:39) − cm − ) o ff er a complementaryenvironment to study the first steps of sulfur chemistry. Becauseof their higher densities and more quiescent gas, fast shocks orturbulence dissipation do not contribute to the gas heating. In-stead, the molecular gas is heated to T k (cid:46)
500 K by mechanisms SH was first reported by IR spectroscopy toward the cirumstellarenvelope around the evolved star R Andromedae (Yamamura et al. 2000). that depend on the flux of far-UV photons (FUV; E < ff erent perspective of the H ( v ) reactivity emerges becausecertain endoergic reactions become exoergic and fast when asignificant fraction of the H reagents are radiatively pumped tovibrationally excited states v ≥ ( ν, J ) are needed to make realistic predictions of the abundanceof the product XH (Agúndez et al. 2010; Zanchet et al. 2013b;Faure et al. 2017). The presence of abundant FUV-pumpedH ( v ≥
1) triggers a nonthermal “hot” chemistry. Indeed, CH + and SH + emission lines have been detected in the Orion Bar PDR(Nagy et al. 2013; Goicoechea et al. 2017) where H lines up to v =
10 have been detected as well (Kaplan et al. 2017).In this study we present a systematic (observational andmodeling) study of the chemistry of S-bearing hydrides inFUV-illuminated gas. We try to answer the question of whethergas-phase reactions of S atoms and SH + molecules with vibra-tionally excited H can ultimately explain the presence of abun-dant H S, or if grain surface chemistry has to be invoked.The paper is organized as follows. In Sects. 2 and 3 we reporton new observations of H
S, H
S, H
S, SH + , SH, and H S + emission lines toward the Orion Bar. In Sect. 4 we study theirexcitation and derive their column densities. In Sect. 6 we discusstheir abundances in the context of updated PDR models, withemphasis on the role of hydrogen abstraction reactionsSH + ( Σ − ) + H ( Σ + ) (cid:29) H S + ( A (cid:48) ) + H ( S ) , (2)H S + ( A (cid:48) ) + H ( Σ + ) (cid:29) H S + (X A ) + H ( S ) , (3)S ( P ) + H ( Σ + ) (cid:29) SH (X Π ) + H ( S ) , (4)photoreactions, and grain surface chemistry. In Sect. 5 we sum-marize the ab initio quantum calculations we carried out to deter-mine the state-dependent rates of reactions (2) and (4). Details ofthese calculations are given in Appendices A and B.
2. Observations of S-bearing hydrides
At an adopted distance of ∼
414 pc, the Orion Bar is an interfaceof the Orion molecular cloud and the Huygens H ii region thatsurrounds the Trapezium cluster (Genzel & Stutzki 1989; O’Dell2001; Bally 2008; Goicoechea et al. 2019, 2020; Pabst et al. 2019,2020). The Orion Bar is a prototypical strongly illuminated densePDR. The impinging flux of stellar FUV photons ( G ) is a few10 times the mean interstellar radiation field (Habing 1968). TheBar is seen nearly edge-on with respect to the FUV illuminatingsources, mainly θ Ori C, the most massive star in the Trapezium.This favorable orientation allows observers to spatially resolve theH + -to-H transition (the ionization front or IF; see, e.g., Walmsleyet al. 2000; Pellegrini et al. 2009) from the H-to-H transition(the dissociation front or DF; see, e.g., Allers et al. 2005; vander Werf et al. 1996, 2013; Wyrowski et al. 1997; Cuadrado et al.2019). It also allows one to study the stratification of di ff erentmolecular species as a function of cloud depth (i.e., as the fluxof FUV photons is attenuated; see, e.g., Tielens et al. 1993; vander Wiel et al. 2009; Habart et al. 2010; Goicoechea et al. 2016;Parikka et al. 2017; Andree-Labsch et al. 2017). Article number, page 2 of 25oicoechea et al.: Bottlenecks to interstellar sulfur chemistry A L M A F o V D F U V r a d i a t i o n Fig. 1.
Overview of the Orion Bar. The (0 (cid:48)(cid:48) , 0 (cid:48)(cid:48) ) position corresponds to α = h m . s ; δ = − ◦ (cid:48) . (cid:48)(cid:48) . Left panel : Integrated lineintensity maps in the CO J = -7 emission (gray contours; from 6 to 23.5 K km s − in steps of 2.5 K km s − ) obtainedwith the IRAM 30 m telescope at 8 (cid:48)(cid:48) resolution. The white dotted contours delineate the position of the H dissociation front as traced by the infraredH v = S (1) line (from 1.5 to 4.0 × − erg s − cm − sr − in steps of 0.5 × − erg s − cm − sr − ; from Walmsley et al. 2000). The black-dashedrectangle shows the smaller FoV imaged with ALMA (Fig. 3). The DF position has been observed with SOFIA, IRAM 30 m, and Herschel. Cyancircles represent the ∼ (cid:48)(cid:48) beam at 168 GHz. Right panel : H S lines lines detected toward three positions of the Orion Bar.
Regarding sulfur , several studies previously reported thedetection of S-bearing molecules in the Orion Bar. These includeCS, C S, SO, SO , and H S (Hogerheijde et al. 1995; Jansenet al. 1995), SO + (Fuente et al. 2003), C S, HCS + , H CS, and NS(Leurini et al. 2006), and SH + (Nagy et al. 2013). These detectionsrefer to modest angular resolution pointed observations usingsingle-dish telescopes. Higher-angular-resolution interferometricimaging of SH + , SO, and SO + (Goicoechea et al. 2017) waspossible thanks to the Atacama Compact Array (ACA). S isotopologues and H S + We observed the Orion Bar with the IRAM 30 m telescope atPico Veleta (Spain). We used the EMIR receivers in combinationwith the Fast Fourier Transform Spectrometer (FTS) backends at200 kHz resolution ( ∼ − , ∼ − , and ∼ − at ∼
168 GHz, ∼
217 GHz, and ∼
293 GHz, respectively). These obser-vations are part of a complete line survey covering the frequencyrange 80 −
360 GHz (Cuadrado et al. 2015, 2016, 2017, 2019)and include deep integrations at 168 GHz toward three positionsof the PDR located at a distance of 14 (cid:48)(cid:48) , 40 (cid:48)(cid:48) , and 65 (cid:48)(cid:48) from theIF (see Fig. 1). Their o ff sets with respect to the IF position at α = h m . s , δ = − ◦ (cid:48) . (cid:48)(cid:48) are ( + (cid:48)(cid:48) , -10 (cid:48)(cid:48) ),( + (cid:48)(cid:48) , -30 (cid:48)(cid:48) ’), and ( + (cid:48)(cid:48) , -55 (cid:48)(cid:48) ). The first position is the DF.We carried out these observations in the position switchingmode taking a distant reference position at ( − (cid:48)(cid:48) , 0 (cid:48)(cid:48) ). Thehalf power beam width (HPBW) at ∼
168 GHz, ∼
217 GHz, and ∼
293 GHz is ∼ (cid:48)(cid:48) , ∼ (cid:48)(cid:48) , and ∼ (cid:48)(cid:48) , respectively. The latest obser-vations (those at 168 GHz) were performed in March 2020. Thedata were first calibrated in the antenna temperature scale T ∗ A andthen converted to the main beam temperature scale, T mb , using Sulfur has four stable isotopes, in decreasing order of abundance: S ( I N = S ( I N = S ( I N = / S ( I N = I N is thenuclear spin. The most abundant isotope is here simply referred to as S. T mb = T ∗ A / η mb , where η mb is the antenna e ffi ciency ( η mb = ∼
168 GHz). We reduced and analyzed the data using the GILDASsoftware as described in Cuadrado et al. (2015). The typical rmsnoise of the spectra is ∼ ∼
168 GHz, ∼
217 GHz, and ∼
293 GHz, respectively. Figures 1and 2 show the detection of o -H S 1 , − , (168.7 GHz), p -H S 2 , − , (216.7 GHz), and o -H S 1 , − , lines(167.9 GHz) (see Table E.1 for the line parameters), as well asseveral o -H S 1 , − , hyperfine lines (168.3 GHz).We complemented our dataset with higher frequency H Slines detected by the
Herschel Space Observatory (Nagy et al.2017) toward the “CO + peak” position (Stoerzer et al. 1995),which is located at only ∼ (cid:48)(cid:48) from our DF position (i.e., within theHPBW of these observations). These observations were carriedout with the HIFI receiver (de Graauw et al. 2010) at a spectral-resolution of 1.1 MHz (0.7 km s − at 500 GHz). HIFI’s HPBWrange from ∼ (cid:48)(cid:48) to ∼ (cid:48)(cid:48) in the 500 - 1000 GHz window (Roelf-sema et al. 2012). The list of additional hydrogen sulfide linesdetected by Herschel includes the o -H S 2 , − , (505.5 GHz),2 , − , (736.0 GHz), and 3 , − , (993.1 GHz), as well as the p -H S 2 , − , (687.3 GHz) line. We used the line intensities,in the T mb scale, shown in Table A.1 of Nagy et al. (2017).In order to get a global view of the Orion Bar, we also ob-tained 2.5 (cid:48) × (cid:48) maps of the region observed by us with theIRAM 30 m telescope using the 330 GHz EMIR receiver andthe FTS backend at 200 kHz spectral-resolution ( ∼ − ).On-the-fly (OTF) scans were obtained along and perpendicular tothe Bar. The resulting spectra were gridded to a data cube throughconvolution with a Gaussian kernel providing a final resolution of ∼ (cid:48)(cid:48) . The total integration time was ∼ ∼ CO J = -7 (346.5 GHz)integrated line intensities. Article number, page 3 of 25 & A proofs: manuscript no. aa_sulfur_bar_accepted + emission We carried out mosaics of a small field of the Orion Bar us-ing twenty-seven ALMA 12 m antennas in band 7 (at ∼
346 GHz).These unpublished observations belong to project 2012.1.00352.S(P.I.: J. R. Goicoechea) and consisted of a 27-pointing mosaiccentered at α (2000) = h m s ; δ (2000) = -05 o (cid:48) (cid:48)(cid:48) . Thetotal field-of-view (FoV) is 58 (cid:48)(cid:48) × (cid:48)(cid:48) (shown in Fig. 1). The twohyperfine line components of the SH + N J = − transitionwere observed with correlators providing ∼
500 kHz resolution(0.4 km s − ) over a 937.5 MHz bandwidth. The total observationtime with the ALMA 12 m array was ∼ (cid:48)(cid:48) resolution, as zero- andshort-spacings. Data calibration procedures and image synthesissteps are described in Goicoechea et al. (2016). The synthesizedbeam is ∼ (cid:48)(cid:48) . This is a factor of ∼ + observations (Goicoechea et al. 2017). Figure 3shows the resulting image of the SH + − F = / / o clockwise to bring the FUV illumination in the horizontal di-rection. The typical rms noise of the final cube is ∼
80 mK pervelocity channel and 1 (cid:48)(cid:48) -beam. As expected from their Einsteincoe ffi cients, the other F = / / ∼ / N).We complemented the SH + dataset with the higher fre-quency lines observed by HIFI (Nagy et al. 2013, 2017) at ∼
526 GHz and ∼
683 GHz (upper limit). These pointed observa-tions have HPBWs of ∼ (cid:48)(cid:48) and ∼ (cid:48)(cid:48) respectively, thus theydo not spatially resolve the SH + emission. To determine theirbeam coupling factors ( f b ), we smoothed the bigger 4 (cid:48)(cid:48) -resolutionACA + TP SH + image shown in Goicoechea et al. (2017) to thedi ff erent HIFI’s HPBWs. We obtain f b (cid:39) ∼
526 GHz and f b (cid:39) ∼
683 GHz. The corrected intensities are computed as W corr = W HIFI / f b . These correction factors are only a factor of (cid:46) + emission from a 10 (cid:48)(cid:48) width filament. We finally used the GREAT receiver (Heyminck et al. 2012)on board the
Stratospheric Observatory For Infrared Astron-omy (SOFIA; Young et al. 2012) to search for the lowest-energy rotational lines of SH ( Π / J = / /
2) at 1382.910 and1383.241 GHz (e.g., Klisch et al. 1996; Martin-Drumel et al.2012). These lines lie in a frequency gap that Herschel / HIFIcould not observe from space. These SOFIA observations belongto project 07_0115 (P.I.: J. R. Goicoechea). The SH lines weresearched on the lower side band of 4GREAT band 3. We em-ployed the 4GREAT / HFA frontends and 4GFFT spectrometersas backends. The HPBW of SOFIA at 1.3 THz is ∼ (cid:48)(cid:48) , thuscomparable with IRAM 30 m / EMIR and Herschel / HIFI observa-tions. We also employed the total power mode with a referenceposition at ( − (cid:48)(cid:48) ,0 (cid:48)(cid:48) ). The original plan was to observe duringtwo flights in November 2019 but due to bad weather conditions,only ∼
70 min of observations were carried out in a single flight.After calibration, data reduction included: removal of a firstorder spectral baseline, dropping scans with problematic receiverresponse, rms weighted average of the spectral scans, and cali-bration to T mb intensity scale ( η mb = − has a rms noise of ∼
50 mK (shown in Fig. 4). Two emission peaks are seen at the
Fig. 2.
Detection of H
S (at ∼ CCH. The length of each line is proportionalto the transition line strength (taken from the Cologne Database forMolecular Spectroscopy, CDMS; Endres et al. 2016). frequencies of the Λ -doublet lines. Unfortunately, the achievedrms is not enough to assure the unambiguous detection of eachcomponent of the doublet. Although the stacked spectrum doesdisplay a single line (suggesting a tentative detection) the re-sulting line-width ( ∆ v (cid:39) − ) is a factor of ∼
3. Observational results
S, H
S, and H
S across the PDR
Figure 1 shows an expanded view of the Orion Bar in the CO ( J = v = S (1) line emission (white contours)delineates the position of the H-to-H transition, the DF. Manymolecular species, such as SO, specifically emit from deeperinside the PDR where the flux of FUV photons has consider-ably decreased. In contrast, H S, and even its isotopologue H
S,show bright 1 , -1 , line emission toward the DF (right panelsin Fig. 1; see also Jansen et al. 1995). Rotationally excited H Slines have been also detected toward this position (Nagy et al.2017), implying the presence of warm H S close to the irradiatedcloud surface (i.e., at relatively low extinctions). The presenceof moderately large H S column densities in the PDR is alsodemonstrated by the unexpected detection of the rare isotopo-logue H
S toward the DF (at the correct LSR velocity of thePDR: v
LSR (cid:39) − ). Figure 2 shows the H S 1 , -1 , lineand its hyperfine splittings (produced by the S nuclear spin). Toour knowledge, H
S lines had only been reported toward the hotcores in Sgr B2 and Orion KL before (Crockett et al. 2014).The observed o -H S / o -H S 1 , -1 , line intensity ratiotoward the DF is 15 ±
2, below the solar isotopic ratio of S / S =
23 (e.g., Anders & Grevesse 1989). The observed ratiothus implies optically thick o -H S line emission at ∼
168 GHz.However, the observed o -H S / o -H S 1 , -1 , intensity ratio is6 ±
1, thus compatible with the solar isotopic ratio ( S / S = S and H
S optically thin emission.
Article number, page 4 of 25oicoechea et al.: Bottlenecks to interstellar sulfur chemistry
Fig. 3.
ALMA 1 (cid:48)(cid:48) -resolution images zooming into the edge of the Orion Bar in CO 3-2 ( left panel , Goicoechea et al. 2016) andSH + -0 F = / / middle panel , integrated line intensity). The right panel shows the H v = S (1) line (Walmsley et al. 2000).We rotated these images (all showing the same FoV) with respect to Fig. 1 to bring the FUV illuminating direction in the horizontal direction (fromthe right). The circle shows the DF position targeted with SOFIA in SH (20 (cid:48)(cid:48) beam) and with the IRAM 30m telescope in H S and H S + . + emission from the PDR edge Figure 3 zooms into a small field of the Bar edge. The ALMAimage of the CO J = J = T peak )is a good proxy of the gas temperature ( T k (cid:39) T ex (cid:39) T peak ). The COimage implies small temperature variations around T k (cid:39)
200 K.The middle panel in Fig. 3 shows the ALMA image of the SH + N J = -0 F = / / + emission follows the edge of the molecular PDR,akin to a filament of ∼ (cid:48)(cid:48) width (for the spatial distributionof other molecular ions, see, Goicoechea et al. 2017). The SH + emission shows localized small-scale emission peaks (density orcolumn density enhancements) that match, or are very close to,the vibrationally excited H ( v = ( v = ( v = ( v = Fig. 4.
Search for the SH Π / J = / / ∼ / GREAT. Vertical magenta lines indi-cate the position of hyperfine splittings taken from CDMS. S + , and H S ν = 1 emission We used SOFIA / GREAT to search for SH Π / J = / / n H = cm − , T k =
200 K, and di ff erent SH column densities(see Sect. 4 for more details).Our IRAM 30 m observations toward the DF neither resultedin a detection of H S + , a key gas-phase precursor of H S. The ∼ S + -0 line isshown in Fig. 5. Again, the achieved low rms allows us to providea sensitive upper limit to the H S + column density. This resultsin N (H S + ) = (5.5-7.5) × cm − (5 σ ) assuming an excitationtemperature range T ex = S emission close to the edge of the Orion Bar, and be-cause H S formation at the DF might be driven by very exoergicprocesses, we also searched for the 1 , -1 , line of vibrationallyexcited H S (in the bending mode ν ). The frequency of this linelies at ∼ (cid:39)
16 mK). However, wedo not detect this line either.
Fig. 5.
Search for H S + toward the Orion Bar with the IRAM 30 mtelescope. The blue curve shows the expected position of the line.Article number, page 5 of 25 & A proofs: manuscript no. aa_sulfur_bar_accepted
4. Coupled nonlocal excitation and chemistry
In this section we study the rotational excitation of the observedS-bearing hydrides . We determine the SH + , SH (upper limit),and H S column densities in the Orion Bar, and the “average” gasphysical conditions in the sense that we search for the combina-tion of single T k , n H , and N that better reproduces the observedline intensities (so-called “single-slab” approach). In Sect. 6 weexpand these excitation models to multi-slab calculations thattake into account the expected steep gradients in a PDR.In the ISM, rotationally excited levels are typically populatedby inelastic collisions. However, the lifetime of very reactivemolecules can be so short that the details of their formation anddestruction need to be taken into account when determining howthese levels are actually populated (Black 1998). Reactive col-lisions (collisions that lead to a reaction and thus to moleculedestruction) influence the excitation of these species when theirtimescales become comparable to those of nonreactive collisions.The lifetime of reactive molecular ions observed in PDRs (e.g.,Fuente et al. 2003; Nagy et al. 2013; van der Tak et al. 2013;Goicoechea et al. 2017, 2019) can be so short that they do notget thermalized by nonreactive collisions or by absorption of thebackground radiation field (Black 1998). In these cases, a propertreatment of the molecule excitation requires including chemi-cal formation and destruction rates in the statistical equilibriumequations (d n i / d t =
0) that determine the level populations: (cid:88) j > i n j A ji + (cid:88) j (cid:44) i n i (cid:16) B ji ¯ J ji + C ji (cid:17) + F i = (5) = n i (cid:88) j < i A i j + (cid:88) j (cid:44) i (cid:16) B i j ¯ J i j + C i j (cid:17) + D i , (6)where n i [cm − ] is the population of rotational level i , A i j and B i j are the Einstein coe ffi cients for spontaneous and in-duced emission, C i j [s − ] is the rate of inelastic collisions ( C i j = (cid:80) k γ i j , k n k , where γ i j , k ( T ) [cm s − ] are the collisional ratecoe ffi cients and k stands for H , H, and e − ), and ¯ J i j is themean intensity of the total radiation field over the line profile.In these equations, n i D i is the destruction rate per unit vol-ume of the molecule in level i , and F i its formation rate perunit volume (both in cm − s − ). When state-to-state formationrates are not available, and assuming that the destruction rate isthe same in every level ( D i = D ), one can use the total destruc-tion rate D [s − ] ( = (cid:80) k n k k k ( T ) + photodestruction rate, where k k [cm s − ] is the state-averaged rate of the two-body chemicalreaction with species k ) and consider that the level populationsof the nascent molecule follow a Boltzmann distribution at ane ff ective formation temperature T form : F i = F g i e − E i / kT form / Q ( T form ) . (7)In this formalism, F [cm − s − ] is the state-averaged formationrate per unit volume, g i the degeneracy of level i , and Q ( T form ) isthe partition function at T form (van der Tak et al. 2007). Readers interested only in the chemistry of these species and in depth-dependent PDR models could directly jump to Section 6. We use the following inelastic collision rate coe ffi cients γ ij : • SH + – e − , including hyperfine splittings (Hamilton et al. 2018). • SH + – o -H and p -H , including hyperfine splittings (Dagdigian 2019). • SH + – H, including hyperfine splittings (Lique et al. 2020). • o -H S and p -H S with o -H and p -H (Dagdigian 2020). • SH– He, including fine-structure splittings (Kłos et al. 2009).
This “formation pumping” formalism has been previouslyimplemented in large velocity gradient codes to treat, for example,the local excitation of the very reactive ion CH + (Nagy et al. 2013;Godard & Cernicharo 2013; Zanchet et al. 2013b; Faure et al.2017). However, interstellar clouds are inhomogeneous and gasvelocity gradients are typically modest at small spatial scales.This means that line photons can be absorbed and reemittedseveral times before leaving the cloud. Here we implementedthis formalism in a Monte Carlo code that explicitly models thenonlocal behavior of the excitation and radiative transfer problem(see Appendix of Goicoechea et al. 2006).Although radiative pumping by dust continuum photons doesnot generally dominate in PDRs, for completeness we also in-cluded radiative excitation by a modified blackbody at a dusttemperature of ∼
50 K and a dust opacity τ λ = / λ [ µ m]) . (which reproduces the observed intensity and wavelength depen-dence of the dust emission in the Bar; Arab et al. 2012). Themolecular gas fraction, f (H ) = n (H ) / n H , is set to 2 /
3, where n H = n (H) + n (H ) is the total density of H nuclei. This choiceis appropriate for the dissociation front and implies n (H ) = n (H).As most electrons in the DF come from the ionization of carbonatoms, the electron density n e is set to n e (cid:39) n (C + ) = × − n H (e.g., Cuadrado et al. 2019). For the inelastic collisions with o -H and p -H , we assumed that the H ortho-to-para (OTP) ratio isthermalized to the gas temperature. + excitation and column density We start by assuming that the main destruction pathway ofSH + are reactions with H atoms and recombinations withelectrons (see Sect. 6.1). Hence, the SH + destruction rate is D (cid:39) n e k e ( T ) + n (H) k H ( T ) (see Table 1 for the relevant chemi-cal destruction rates). For T k = T e =
200 K and n H = cm − (e.g., Goicoechea et al. 2016) this implies D (cid:39) − s − (i.e., thelifetime of an SH + molecule in the Bar is less than 3 h). Atthese temperatures and densities, D is about ten times smallerthan the rate of radiative and inelastic collisional transitions thatdepopulate the lowest-energy rotational levels of SH + . Hence,formation pumping does not significantly alter the excitation ofthe observed SH + lines, but it does influence the population ofhigher-energy levels. Formation pumping e ff ects have been read-ily seen in CH + because this species is more reactive and itsrotationally excited levels lie at higher-energy (i.e., their inelasticcollision pumping rates are slower, e.g., Zanchet et al. 2013b)Figure 6 shows results of several models: withoutformation pumping (dotted curves for model “ F = D = + destruction by Hand e − (continuous curves for model “ F , D ”), and usinga factor of ten higher SH + destruction rates (simulating adominant role of SH + photodissociation or destruction byreactions with vibrationally excited H ; dashed curves formodel “ F , D × + is driven byreaction (1) when H molecules are in v ≥
2, here we adopted T form (cid:39) E ( v = J = / k − ≈ N (SH + ) excitation and radiative transfermodels, we used a normalized formation rate F = (cid:80) F i thatassumes steady-state SH + abundances consistent with the varyinggas density in each model. That is, F = (cid:80) F i = x (SH + ) n H D [cm − s − ], where x refers to the abundance with respect to Hnuclei. CH + is more reactive than SH + because CH + does react with H ( v = + at k = × − cm s − (Anicich 2003)and also because reaction of CH + with H is faster, k = × − cm s − .Article number, page 6 of 25oicoechea et al.: Bottlenecks to interstellar sulfur chemistry Fig. 6.
Non-LTE excitation models of SH + . The horizontal lines markthe observed line intensities in the Orion Bar. Dotted curves are for astandard model ( F = D = e − (model F , D ). Dashedlines are for a model in which destruction rates are multiplied by ten(model F , D × The detected SH + rotational lines connect the fine-structurelevels N J = -0 (345 GHz) and 1 -0 (526 GHz). Upper limitsalso exist for the 1 -0 (683 GHz) lines. SH + critical densities( n cr = A i j / γ i j ) for inelastic collisions with H or H are of the sameorder and equal to several 10 cm − . As for many molecular ions(e.g., Desrousseaux et al. 2021), SH + –H (and SH + –H) inelasticcollisional rate coe ffi cients are large ( γ i j (cid:38) − cm s − ). Thus,collisions with H (at low A V ) and H (at higher A V ) generally dom-inate over collisions with electrons ( γ i j of a few 10 − cm s − ). Atlow densities (meaning n H < n cr ) formation pumping increasesthe population of the higher-energy levels (and their T ex ), butthere are only minor e ff ects in the low-energy submillimeterlines. At high densities, n H > cm − , formation pumping with T form = E u / k < T k < T form ) are less populated.The best fit to the observed lines in model F, D isfor N (SH + ) (cid:39) × cm − , n H (cid:39) × cm − , and T k (cid:39)
200 K.This is shown by the vertical dotted line in Fig. 6. Thismodel is consistent with the upper limit intensity of the683 GHz line (Nagy et al. 2013). In this comparison, and fol-lowing the morphology of the SH + emission revealed byALMA (Fig. 3), we corrected the line intensities of the SH + lines detected by Herschel / HIFI with the beam coupling fac-tors discussed in Sec. 2.3, The observed 1 -0 / -0 line ra-tio ( R = W (526.048) / W (345.944) (cid:39)
2) is sensitive to the gas den-sity. In these models, R is 1.1 for n H = cm − and 3.0 for n H = cm − . We note that n H could be lower if SH + forma-tion / destruction rates were faster, as in the F , D ×
10 model. Thiscould happen if SH + photodissociation or destruction reactionswith H ( v ≥
2) were faster than reactions of SH + with H atoms orwith electrons. In Sec. 6 we show that this is not the case. SH is a Π open-shell radical with fine-structure, Λ -doubling, andhyperfine splittings (e.g., Martin-Drumel et al. 2012). However,the frequency separation of the SH Π / J = / / ffi cients forinelastic collisions of SH with helium atoms do not resolve thehyperfine splittings. Hence, we first determined line frequencies,level degeneracies, and Einstein coe ffi cients of an SH moleculewithout hyperfine structure. To do this, we took the complete setof hyperfine levels tabulated in CDMS. Lacking specific inelasticcollision rate coe ffi cients, we scaled the available SH– He ratesof Kłos et al. (2009) by the square root of the reduced mass ratiosand estimated the SH– H and SH– H collisional rates.The scaled rate coe ffi cients are about an order of magni-tude smaller than those of SH + . However, the chemical de-struction rate of SH at the PDR edge (reactions with H, pho-todissociation, and photoionization, see Sect. 6.1) is also slower(we take the rates of SH–H reactive collisions from Zanchetet al. 2019). We determine D (cid:39) × − s − for n H = cm − , T k =
200 K, and A V (cid:39) T form = T k (a lower limit to the unknown forma-tion temperature). Formation pumping enhances the intensity ofthe Π / J = / / + arise from roughly the same gas atsimilar physical conditions ( n H (cid:39) cm − and T k (cid:39)
200 K) thebest model column density is for N (SH) ≤ (0.6-1.6) × cm − .If densities were lower, around n H (cid:39) cm − , the upper limit N (SH) column densities will be a factor ten higher. Fig. 7.
Non-LTE excitation models of SH emission lines targeted withSOFIA / GREAT. Horizontal dashed lines refer to observational limits,assuming extended emission (lower intensities) and for a 10 (cid:48)(cid:48) widthemission filament at the PDR surface (higher intensities).Article number, page 7 of 25 & A proofs: manuscript no. aa_sulfur_bar_accepted
Fig. 8.
Non-LTE excitation models for o -H S and p -H S. Thin horizontal lines show the observed intensities assuming either extended emission(lower limit) or emission that fills the 15 (cid:48)(cid:48) beam at 168.7 GHz. The vertical line marks the best model, resulting in an OTP ratio of 2.9 ± S excitation and column density H S has a X A ground electronic state and two nuclear spinsymmetries that we treat separately, o -H S and p -H S. Pre-vious studies of the H S line excitation have used collisionalrates coe ffi cients scaled from those of the H O – H system.Dagdigian (2020) recently carried out specific calculations ofthe cross sections of o -H S and p -H S inelastic collisions with o –H and p -H at di ff erent temperatures. The behavior of the newand the scaled rates is di ff erent and it depends on the H OTPratio (e.g., on gas temperature) because the collisional cross sec-tions are di ff erent for o -H –H S and p -H –H S systems. At thewarm temperatures of the PDR, collisions with o -H dominate,resulting in rate coe ffi cients for the ∼
168 GHz o -H S line that area factor up to ∼ O–H .H S is not a reactive molecule. At the edge of the PDR itsdestruction is driven by photodissociation. We determine that theradiative and collisional pumping rates are typically a factor of ∼
100 higher than D ≈ × − s − (for n H = cm − , T k =
200 K, G (cid:39) , and A V (cid:39) o -H S and p -H S excitation and radiative transfer models. As H S may haveits abundance peak deeper inside the PDR and display moreextended emission than SH + (e.g., Sternberg & Dalgarno 1995),we show results for T k =
200 and 100 K. When comparing withthe observed line intensities, we considered either emission thatfills all beams, or a correction that assumes that the H S emis-sion only fills the 15 (cid:48)(cid:48) beam of the IRAM 30m telescope at168 GHz. The vertical dotted lines in Fig. 8 show the best model, N (H S) = N ( o -H S) + N ( p -H S) = × cm − , with an OTPratio of 2.9 ± / n H (cid:39) cm − , show worse agreement,and would translate into even higher N (H S) of (cid:38) cm − . Ineither case, these calculations imply large columns of warm H Stoward the PDR. They result in a limit to the SH to H S columndensity ratio of ≤ N (SH) / N (H S) = ff use clouds(Neufeld et al. 2015). This di ff erence suggests an enhanced H Sformation mechanism in FUV-illuminated dense gas.
5. New results on sulfur-hydride reactions
In this section we summarize the ab initio quantum calculationswe carried out to determine the vibrationally-state-dependentrates of gas-phase reactions of H ( v >
0) with several S-bearingspecies. We recall that all hydrogen abstraction reactions,S + + H −−−→ (1) SH + + H −−−→ (2) H S + + H −−−→ (3) H S + , S + H −−−→ (4) SH , are very endoergic for H ( v = T k even in PDRs. Thisis markedly di ff erent to O + chemistry, for which all hydrogenabstraction reactions leading to H O + are exothermic and fast(Gerin et al. 2010; Neufeld et al. 2010; Hollenbach et al. 2012).The endothermicity of reactions involving H n S + ions de-creases as the number of hydrogen atoms increases. The potentialenergy surfaces (PES) of these reactions possess shallow wells atthe entrance and products channels (shown in Fig. 9). In addition,these PESs show saddle points between the energy walls of reac-tants and products whose heights increase with the number of Hatoms. For reaction (2), the saddle point has an energy of 0.6 eV( (cid:39) + .If one considers the state dependent reactivity of vibrationallyexcited H , the formation of SH + through reaction (1) becomesexoergic when v ≥ S emission in the Orion Bar (Figs. 1 and 4) might suggest thatsubsequent hydrogen abstraction reactions with H ( v ≥
2) pro-ceed as well. Motivated by these findings, and before carrying outany PDR model, we studied reaction (2) and the reverse processin detail. This required to build a full dimensional quantum PESof the H S + (X A ) system (see Appendix A).In addition, we studied reaction (4) (and its reverse) throughquantum calculations. Details of these ab initio calculations andof the resulting reactive cross sections are given in Appendix B. If one considers H rovibrational levels, reaction (1) becomes exoergicfor v = J ≥
11 and for v = J ≥ Fig. 9.
Minimum energy paths for reactions (1), (2), and (3). Points cor-respond to RCCSD(T)-F12a calculations and lines to fits (Appendix A).The reaction coordinate, s , is defined independently for each path. Thegeometries of each species at s = ff erent. Table 1 summarizes the updated reaction rate coe ffi cients that wewill include later in our PDR models.The H S + formation rate through reaction (2) with H ( v = ( v = ≈
500 K, corresponding to the opening of the H S + + H thresh-old. For H ( v =
2) and H ( v = Table 1.
Relevant rate coe ffi cients from a fit of the Arrhenius-like form k ( T ) = α ( T /
300 K) β exp( − γ/ T ) to the calculated reaction rates. Reaction α β γ (cm s − ) (K)SH + + H ( v = → H S + + H 4.97e-11 0 1973.4 a SH + + H ( v = → H S + + H 5.31e-10 -0.17 0 a SH + + H ( v = → H S + + H 9.40e-10 -0.16 0 a SH + + H → S + + H b SH + + e − → S + H 2.00e-07 -0.50 c H S + + H → SH + + H a S + H ( v = → SH + H ∼ ∼ ∼ a S + H ( v = → SH + H ∼ ∼ ∼ a SH + H → S + H a , † − a , † S + + H ( v = → SH + + H 2.88e-10 -0.15 42.9 b S + + H ( v = → SH + + H 9.03e-10 -0.11 26.2 b S + + H ( v = → SH + + H 1.30e-09 -0.04 40.8 b S + + H ( v = → SH + + H 1.21e-09 0.09 34.5 b Notes. ( a ) This work. ( b ) From Zanchet et al. (2019). ( c ) From Prasad &Huntress (1980). † Total rate is the sum of the two expressions. tion through reaction (4) (S + H ) are considerably smaller thanfor reactions (1) and (2), and show an energy barrier even forH ( v =
2) and H ( v = S + (SH + ) in reactions with H atomsare a factor of ≥ ≥ T k ≤
200 K) than thosepreviously used in astrochemical models (Millar et al. 1986).Conversely, we find that destruction of SH in reactions with Hatoms (Appendix B) is slower than previously assumed.
6. PDR models of S-bearing hydrides
We now investigate the chemistry of S-bearing hydrides and thee ff ect of the new reaction rates in PDR models adapted to theOrion Bar conditions. In this analysis we used version 1.5.4. ofthe Meudon PDR code (Le Petit et al. 2006; Bron et al. 2014).Following our previous studies, we model the Orion Bar as astationary PDR at constant thermal-pressure (i.e., with densityand temperature gradients). When compared to time-dependenthydrodynamic PDR models (e.g., Hosokawa & Inutsuka 2006;Bron et al. 2018; Kirsanova & Wiebe 2019), stationary iso-baric models seem a good description of the most exposed andcompressed gas layers of the PDR, from A V ≈ ≈ G = × (e.g., Marconi et al. 1998). We adopted anextinction to color-index ratio, R V = A V / E B − V , of 5.5 (Joblinet al. 2018), consistent with the flatter extinction curve ob-served in Orion (Lee 1968; Cardelli et al. 1989). This choiceimplies slightly more penetration of FUV radiation into the cloud(e.g., Goicoechea & Le Bourlot 2007). The main input parame-ters and elemental abundances of these PDR models are sum-marized in Table 2. Figure 10 shows the resulting H , H, andelectron density profiles, as well as the T k and T d gradients. Article number, page 9 of 25 & A proofs: manuscript no. aa_sulfur_bar_accepted
Table 2.
Main parameters used in the PDR models of the Orion Bar.
Model parameter Value NoteFUV illumination, G × Habing ( a )Total depth A V
10 magThermal pressure P th / k × cm − KDensity n H = n (H) + n (H ) n H = P th / kT k VaryingCosmic Ray ζ CR − H s − ( b ) R V = A V / E B − V c M gas / M dust
100 Local ISMAbundance O / H 3.2 × − Abundance C / H 1.4 × − Orion d Abundance S / H 1.4 × − Solar e Notes. a Marconi et al. (1998). b Indriolo et al. (2015). c Cardelli et al.(1989). d Sofia et al. (2004). e Asplund et al. (2009).
Fig. 10.
Structure of an isobaric PDR representing the most FUV-irradiated gas layers of the Orion Bar (see Table 2 for the adoptedparameters). This plot shows the H , H, and electron density profiles(left axis scale), and the gas and dust temperatures (right axis scale). Our chemical network is that of the Meudon code updatedwith the new reaction rates listed in Table 1. This network includesupdated photoreaction rates from Heays et al. (2017). To increasethe accuracy of our abundance predictions, we included the ex-plicit integration of wavelength-dependent SH, SH + , and H Sphotodissociation cross sections ( σ diss ), as well as SH and H Sphotoionization cross sections ( σ ion ). These cross sections areshown in Fig C.1 of the Appendix. The integration is performedover the specific FUV radiation field at each position of the PDR.In particular, we took σ ion (SH) from Hrodmarsson et al. (2019)and σ diss (H S) from Zhou et al. (2020), both determined in labo-ratory experiments. Figure 11 summarizes the relevant chemicalnetwork that leads to the formation of S-bearing hydrides andthat we discuss in the following sections.
Figure 12 shows results of the “new gas-phase” model usingthe reaction rates in Table 1. The continuous curves display thepredicted fractional abundance profiles as a function of clouddepth in magnitudes of visual extinction ( A V ). The dashed curvesare for a model that uses the standard thermal rates previouslyadopted in the literature (see, e.g., Neufeld et al. 2015). As notedby Zanchet et al. (2013a, 2019), the inclusion of H ( v ≥
2) state- s-S s-SH s-H SS SH H SS + SH + H S + H S + G r a i n s u r f a c e G a s - ph a s e s-H s-H !!! ! e - e - e - e - H H H H !! H (9860 K) H (6380 K) H (2900 K) H (10500 K) H (6860 K) H (700 K) H (455 K) adsorption H H s-H photodesorption chemical desorption H ! ! e - S Fig. 11.
Main gas and grain reactions leading to the formation of sulfurhydrides. Red arrows represent endoergic reactions (endothermicitygiven in units of K). Dashed arrows are uncertain radiative associations(see Sect. A.3), γ stands for a FUV photon, and “s-” for solid. dependent quantum rates for reaction (1) enhances the formationof SH + in a narrow layer at the edge of the PDR ( A V (cid:39) + emission revealedby ALMA images (Fig. 3). For H ( v = ∆ k = k ( T ) / k ( T )(see discussion by Agúndez et al. 2010) is about 4 × at T k =
500 K (Millar et al. 1986). Indeed, when the fractionalabundance of H ( v =
2) with respect to H ( v = f = n (H v = / n (H v = − , meaning ∆ k · f >
1, reaction (1) with H ( v ≥
2) dominates SH + forma-tion. This reaction enhancement takes place only at the edge ofthe PDR, where FUV-pumped H ( v ≥
2) molecules are abundantenough (gray dashed curves in Fig. 12) and drive the formationof SH + . The resulting SH + column density increases by an orderof magnitude compared to models that use the thermal rate.In this isobaric model, the SH + abundance peak occursat A V (cid:39) n H (cid:39) × cm − at the PDR edge (the IF) to ∼ × cm − (atthe DF). At this point, SH + destruction is dominated by recom-bination with electrons and by reactive collisions with H atoms.This implies D (SH + ) [s − ] ∼ n e k e (cid:39) n H k H (cid:29) n (H v ≥ k , as weassumed in the single-slab SH + excitation models (Sec. 4.1).Therefore, only a small fraction of SH + molecules further re-act with H ( v ≥
2) to form H S + . The resulting low H S + abun-dances limit the formation of abundant SH from dissociativerecombinations of H S + (recall that we estimated that reactionS + H ( v ≥ → SH + H is very slow). The SH abundance peak isshifted deeper inside the cloud, at about A V (cid:39) S + and it is destroyedby FUV photons and reactions with H atoms. In these gas-phasemodels the H S abundance peaks even deeper inside the PDR, atA V (cid:39) S + and H S + with electrons as well as by charge exchange S + H S + . How-ever, the new rate of reaction H S + + H is higher than assumedin the past, so the new models predict lower H S + abundances atintermediate PDR depths (thus, less H S + and H S; see Fig. 12).The SH column density predicted by the new gas-phasemodel is below the upper limit determined from SOFIA. However,the predicted H S column density is much lower than the valuewe derive from observations (Table 3) and the predicted H S lineintensities are too faint (see Sect. 6.4).Because the cross sections of the di ff erent H S photodissocia-tion channels have di ff erent wavelength dependences (Zhou et al.2020), the H S and SH abundances between A V ≈ Article number, page 10 of 25oicoechea et al.: Bottlenecks to interstellar sulfur chemistry
Table 3.
Column density predictions from di ff erent PDR models (up to A V =
10 mag) and estimated values from observations (single-slab approach). log N (cm − ) Type of PDR model a SH + SH H S H S + H S + Standard gas-phase 11.0 a –12.2 b a –12.5 b a –12.4 b a –11.1 b a –9.0 b New gas-phase (Table 1) 12.1 a –13.2 b a –12.5 b a –11.7 b a –11.0 b a –8.9 b Gas-grain (low E b , (cid:15) = a –13.2 b a –14.4 b a –14.1 b a –10.7 b a –11.2 b Gas-grain (high E b , (cid:15) = a –13.1 b a –14.8 b b –14.8 b b –11.0 b b –12.0 b Estimated from observations ∼ < ∼ < Notes. a Column densities for a face-on PDR. b Edge-on PDR with a tilt angle α = o , leading to the maximum expected geometrical enhancement. Standard ratesNew rates
Fig. 12.
Pure gas-phase PDR models of the Orion Bar. Continuous curvesshow fractional abundances as a function of cloud depth, in logarithmscale to better display the irradiated edge of the PDR, using the newreaction rates listed in Table 1. The gray dotted curve shows f , thefraction of H that is in vibrationally excited levels v ≥ are sensitive to the specific shape of the FUV radiation field (de-termined by line blanketing, dust absorption, and grain scattering;e.g., Goicoechea & Le Bourlot 2007). Still, we checked thatusing steeper extinction curves does not increase H S columndensity any closer to the observed levels. This disagreement be-tween the observationally inferred N (H S) column density andthe predictions of gas-phase PDR models is even worse if oneconsiders the uncertain rates of radiative association reactionsS + + H → H S + + h ν and SH + + H → H S + + h ν included in thenew gas-phase model. For the latter reaction, the main prob-lem is that the electronic states of the reactants do not correlatewith the A ground electronic state of the activated complexH S + ∗ (denoted by ∗ ). Instead, H S + ∗ forms in an excited tripletstate ( A ). Herbst et al. (1989) proposed that a spin-flip followedby a radiative association can occur in interstellar conditions Older gas-phase PDR models previously predicted low H Scolumn densities (Jansen et al. 1995; Sternberg & Dalgarno 1995). and form H S + ∗ ( X A ) (Millar & Herbst 1990). In Appendix A.3,we give arguments against this mechanism. For similar reasons,Prasad & Huntress (1982) avoided to include the S + + H radia-tive association in their models. Removing these reactions in puregas-phase models drastically decreases the H S + and H S + abun-dances, and thus those of SH and H S (by a factor of ∼
100 in thesemodels). The alternative H S + formation route through reactionSH + + H ( v =
2) is only e ffi cient at the PDR surface ( A V < ( v =
2) fractional abundances, f > − at T k >
500 K, required to enhance the H S + production. There-fore, and contrary to S + destruction, reaction of SH + with H is not the dominant destruction pathway for SH + . Only deeperinside the PDR, reactions of S with H + produce small abundancesof SH + and H S + , but the hydrogenation of H n S + ions is note ffi cient and limits the gas-phase production H S. S Similarly to the formation of water ice (s-H O) on grains(e.g., Hollenbach et al. 2009, 2012), the formation of H S maybe dominated by grain surface reactions followed by desorp-tion back to the gas (e.g., Charnley 1997). Indeed, water vapor isrelatively abundant in the Bar ( N (H O) ≈ cm − ; Choi et al.2014; Putaud et al. 2019) and large-scale maps show that the H Oabundance peaks close to cloud surfaces (Melnick et al. 2020).To investigate the s-H S formation on grains, we updated thechemical model by allowing S atoms to deplete onto grains asthe gas temperature drops inside the molecular cloud (for thebasic grain chemistry formalism, see, Hollenbach et al. 2009).The timescale of this process ( τ gr , S ) goes as x (S) − n − T − / ,where x (S) is the abundance of neutral sulfur atoms with respectto H nuclei. In a PDR, the abundance of H atoms is typicallyhigher than that of S atoms and H atoms stick on grains morefrequently than S atoms unless x (H) < x (S) · ff use through-out the grain surface until it finds an adsorbed S atom (s-S). Ifthe timescale for a grain to be hit by a H atom ( τ gr , H ) is shorterthat the timescale for a s-S atom to photodesorb ( τ photdes , S ) orsublimate ( τ subl , S ) then reaction of s-H with s-S will proceedand form a s-SH radical roughly upon “collision” and with-out energy barriers (e.g., Tielens & Hagen 1982; Tielens 2010).Likewise, if τ gr , H < τ photdes , SH and τ gr , H < τ subl , SH , a newly ad-sorbed s-H atom can di ff use, find a grain site with an s-SH radicaland react without barriers to form s-H S. In these surface pro-cesses, a significant amount of S is ultimately transferred to s-H S We only consider the depletion of neutral S atoms. S + ions are ex-pected to be more abundant than S atoms at the edge of the Orion Bar( A V (cid:46) T k and T d are too high, and the FUV radiation fieldtoo strong, to allow the formation of abundant grain mantles.Article number, page 11 of 25 & A proofs: manuscript no. aa_sulfur_bar_accepted
Fig. 13.
Representative timescales relevant to the formation of s-H S ands-H O as well as their freeze-out depths.
Upper panel : The continuousblack curve is the timescale for a grain to be hit by an H atom. Once inthe grain surface, the H atom di ff uses and can react with an adsorbedS atom to form s-SH. The dashed magenta curves show the timescalefor thermal desorption of an s-S atom ( E b / k (S) = E b / k (O) = G values where the continuous line is below the dashed and dotted lines,s-O and s-S atoms remain on grain surfaces su ffi ciently long to combinewith an adsorbed H atom and form s-OH and s-SH (and then s-H O ands-H S). These timescales are for n H = cm − and n (H) =
100 cm − . Bottom panel : Freeze-out depth at which most O and S are incorporatedas s-H O and s-H S (assuming no chemical desorption and T k = T d ). (e.g., Vidal et al. 2017), which can subsequently desorb: thermally,by FUV photons, or by cosmic rays. In addition, laboratory ex-periments show that the excess energy of certain exothermicsurface reactions can promote the direct desorption of the product(Minissale et al. 2016). In particular, reaction s-H + s-SH directlydesorbs H S with a maximum e ffi ciency of ∼
60 % (as observedin experiments, Oba et al. 2018). Due to the high flux of FUVphotons in PDRs, chemical desorption may not always competewith photodesorption. However, it can be a dominant process in-side molecular clouds (Garrod et al. 2007; Esplugues et al. 2016;Vidal et al. 2017; Navarro-Almaida et al. 2020).The photodesorption timescale of an ice mantle is propor-tional to Y − G − exp ( + b A V ), where Y is the photodesorptionyield (the number of desorbed atoms or molecules per incidentphoton) and b is a dust-related FUV field absorption factor. Thetimescale for mantle sublimation (thermal desorption) goes as ν − exp ( + E b / k T d ), where ν ice is the characteristic vibrationalfrequency of the solid lattice, T d is the dust grain temperature,and E b / k is the adsorption binding energy of the species (in K).Binding energies play a crucial role in model predictions be-cause they determine the freezing temperatures and sublimationtimescales. Table 4 lists the E b / k and Y values considered here. Table 4.
Adopted binding energies and photodesorption yields.
Species E b / k Yield(K) (FUV photon) − S 1100 a / b − SH 1500 a / b − H S 2700 b , c × − g (as H S)CO 1300 d × − h O 1800 e − h O d − h OH 4600 a − h H O 4800 f − h (as H O)2 × − h (as OH) Notes. a Hasegawa & Herbst (1993). b Wakelam et al. (2017). c Collingset al. (2004). d Minissale et al. (2016). e He et al. (2015). f Sandford &Allamandola (1988). g Fuente et al. (2017) h See, Hollenbach et al. (2009).
Representative timescales of the basic grain processes de-scribed above are summarized in the upper panel of Fig. 13.In this plot, T d is a characteristic dust temperature inside thePDR, T d = (3 · + · G . ) . , taken from Hollenbach et al.(2009). In the upper panel, the continuous black curve is thetimescale for a grain to be hit by an H atom ( τ gr , H ). The dashedmagenta curves show the timescale for thermal desorption ofan s-S atom ( τ subl , S ) (left curve for E b / k (S) = E b / k (S) = τ photodes , S ) at A V = G strengths where thecontinuous line is below the dashed and dotted lines, an adsorbeds-S atom remains on the grain surface su ffi ciently long to reactwith a di ff using s-H atom, form s-SH, and ultimately s-H S.Figure 13 shows that, if one takes E b / k (S) = S is possible inside clouds illuminated bymodest FUV fields, when grains are su ffi ciently cold ( T d <
22 K).However, recent calculations of s-S atoms adsorbed on water icesurfaces suggest higher binding energies ( ∼ T d ( (cid:46)
50 K) and that s-H S mantles form in more strongly illumi-nated PDRs (the observed T d at the edge of the Bar is (cid:39)
50 K anddecreases to (cid:39)
35 K behind the PDR; see, Arab et al. 2012).The freeze-out depth for sulfur in a PDR, the A V at whichmost sulfur is incorporated as S-bearing solids (s-H S in our sim-ple model) can be estimated by equating τ gr , S and τ photdes , H S .This implicitly assumes the H S chemical desorption does notdominate in FUV-irradiated regions, which is in line with the par-ticularly large FUV absorption cross section of s-H S measuredin laboratory experiments (Cruz-Diaz et al. 2014). With these as-sumptions, the lower panel of Fig. 13 shows the predicted s-H Sand s-H O freeze-out depths. Owing to the lower abundance andhigher atomic mass of sulfur atoms (i.e., grains are hit slowerby S atoms than by O atoms), the H S freeze-out depth appearsslightly deeper than that of water ice. For the FUV-illuminationconditions in the Bar, the freeze-out depth of sulfur is expectedat A V (cid:38) S canproduce enhanced abundances of gaseous H S at A V < S ice mantleshave been studied in the laboratory (e.g., Cruz-Diaz et al. 2014;Jiménez-Escobar & Muñoz Caro 2011). These experiments showthat pure s-H S ices thermally desorb around 82 K, and at higher
Article number, page 12 of 25oicoechea et al.: Bottlenecks to interstellar sulfur chemistry ! = 1 % Grain, high E b Grain, low E b ! = 0 % ! = 1 % Fig. 14.
Gas-grain PDR models leading to the formation of s-H S (shown as black curves). Continuous colored curves show gas-phase fractionalabundances as a function of depth into the cloud. (cid:15) refers to the e ffi ciency of the chemical desorption reaction s-H + s-H S → SH + H (see text). Left panel : Gas-grain high E b model (high adsorption binding energies for S and SH, see Table 4). Right panel : Low E b model. temperatures for H S–H O ice mixtures. These experimentsdetermine a photodesorption yield of Y H S ∼ × − moleculesper FUV photon (see also Fuente et al. 2017). Regardingsurface grain chemistry, experiments show that reactions-H + s-SH → s-H S is exothermic (Oba et al. 2018), whereasreaction s-H + s-H S, although it has an activation energybarrier of ∼ + s-SH → s-H S may trigger the formation ofdoubly sulfuretted species, but it requires mobile s-SH radicals(e.g., Jiménez-Escobar & Muñoz Caro 2011; Fuente et al. 2017).Here we will only consider surface reactions with mobile s-H. Here we show PDR model results in which we add a simple net-work of gas-grain reactions for a small number of S-bearing(S, SH, and H S) and O-bearing (O, OH, H O, O , and CO)species. These species can adsorb on grains as temperatures drop,photodesorb by FUV photons (stellar and secondary), desorbby direct impact of cosmic-rays, or sublimate at a given PDRdepth (depending on T d and on their E b ). Grain size distributions( n gr ∝ a − . , where a is the grain radius) and gas-grain reactionsare treated within the Meudon code formalism (see, Le Petit et al.2006; Goicoechea & Le Bourlot 2007; Le Bourlot et al. 2012;Bron et al. 2014). As grain surface chemistry reactions we includes-H + s-X → s-XH and s-H + s-XH → s-H X, where s-X refers tos-S and s-O. In addition, we add the direct chemical desorption re-action s-H + s-SH → H S with an e ffi ciency of 50 % per reactiveevent, and also tested di ff erent e ffi ciencies ( (cid:15) ) for the chemicaldesorption process s-H + s-H S → SH + H .In our models we compute the relevant gas-grain timescalesand atomic abundances at every depth A V of the PDR. If thetimescale for a grain to be struck by an H atom ( τ gr , H ) is shorterthan the timescales to sublimate or to photodesorb an s-X atom ora s-XH molecule; and if H atoms stick on grains more frequentlythan X atoms, we simply assume these surface reactions proceedinstantaneously. At large A V , larger than the freeze-out depth, thisgrain chemistry builds abundant s-H O and s-H S ice mantles.Figure 14 shows results of two types of gas-grain models. Theonly di ff erence between them is the adopted adsorption binding energies for s-S and s-SH. Left panel is for a “high E b ” modeland right panel is for a “low E b ” model (see Table 4). We notethat these models do not include the gas-phase radiative associa-tion reactions S + + H → H S + + h ν and SH + + H → H S + + h ν ;although their e ff ect is smaller than in pure gas-phase models.The chemistry of the most exposed PDR surface layers( A V (cid:46) drive the chemistry. The re-sulting SH + abundance profile is nearly identical and there is noneed to invoke depletion of elemental sulfur from the gas-phaseto explain the observed SH + emission (see Fig. 15). Beyond thesefirst PDR irradiated layers, the chemistry does change becausethe formation of s-H S on grains and subsequent desorption altersthe chemistry of the other S-bearing hydrides.In model high E b , S atoms start to freeze out closer to thePDR edge ( T d <
50 K). Because of the increasing densities anddecreasing temperatures, the s-H S abundance with respect to Hnuclei reaches ∼ − at A V (cid:39) E b , this levelof s-H S abundance is only reached beyond an A V of 7 mag. Atlower A V , the formation of s-H S on bare grains and subsequentphotodesorption produces more H S than pure-gas phase modelsindependently of whether H S chemical desorption is includedor not. In these intermediate PDR layers, at A V (cid:39) S abundance peaks at A V (cid:39) S abundance in these “photodesorption peaks” depends onthe amount of s-H S mantles formed on grains and on the bal-ance between s-H S photodesorption and H S photodissociation(which now becomes the major source of SH). The enhanced H Sabundance modifies the chemistry of H S + and H S + as well:H S photoionization (with a threshold at ∼ S + at A V (cid:39) ( v ≥ S with abundant molecular ions such as HCO + ,H + , and H O + dominate the H S + production. Article number, page 13 of 25 & A proofs: manuscript no. aa_sulfur_bar_accepted
Fig. 15.
Line intensity predictions for di ff erent isobaric PDR models. Calculations were carried out in a multi-slab Monte Carlo code (Sect. 4)that uses the output of the PDR model. Blue stars show the line intensities observed toward the Bar (corrected by beam dilution). Left panel : SH + emission models for PDRs of di ff erent P th values and α = o . Right panel : SH and H S (adopting an OTP ratio of 3) emission from: high E b (magentasquares), low E b (gray triangles), and gas-phase (cyan circles) PDR models, all with P th / k = × K cm − . Upper limit intensity predictions are fora PDR with an inclination angle of α = o with respect to a edge-on geometry. Lower limit intensities refer to a face-on PDR model. Our gas-grain models predict that other S-bearing molecules,such as SO and SO, can be the major sulfur reservoirs at theseintermediate PDR depths. However, their abundances strongly de-pend on those of O and OH through reactions S + O → SO + Oand SO + OH → SO + H (see e.g., Sternberg & Dalgarno 1995;Fuente et al. 2016, 2019). These reactions link the chemistry of S-and O-bearing neutral molecules (Prasad & Huntress 1982) andare an important sink of S atoms at A V (cid:38) (cid:38) cm − ; Goicoechea et al. 2011), O remains undetecteddespite deep searches (Melnick et al. 2012). Furthermore, theinferred upper limit N (O ) columns are below the expectations ofPDR models (Hollenbach et al. 2009). This discrepancy likely im-plies that these gas-grain models miss details of the grain surfacechemistry leading to O (for other environments and modelingapproaches see, e.g., Ioppolo et al. 2008; Taquet et al. 2016). Herewe will not discuss SO , SO, or O further.At large cloud depths, A V (cid:38) S abundance is con-trolled by the chemical desorption reaction s-H + s-SH → H S.This process keeps a floor of detectable H S abundances ( > − )in regions shielded from stellar FUV radiation. In addition, andalthough not energetically favorable, the chemical desorptions-H + s-H S → SH + H enhances the SH production at large A V (the enhancement depends on the desorption e ffi ciency (cid:15) ), whichin turn boosts the abundances of other S-bearing species, includ-ing that of neutral S atoms.The H S abundances predicted by the high E b model repro-duce the H S line intensities observed in the Bar (Sect. 6.4). Inthis model s-H S becomes the main sulfur reservoir. However,we stress that here we do not consider the formation of morecomplex S-bearing ices such as s-OCS, s-H S , s-S n , s-SO ors-HSO (Jiménez-Escobar & Muñoz Caro 2011; Vidal et al. 2017;Laas & Caselli 2019). Together with our steady-state solution ofthe chemistry, this implies that our predictions are not precisedeep inside the PDR. However, we recall that our observations refer to the edge of the Bar, so it is not plausible that the modelconditions at A V (cid:38) E b produces less H S in the PDR layers below A V (cid:46) E b predicts that the majorsulfur reservoir deep inside the cloud are gas-phase S atoms.This agrees with recent chemical models of cold dark clouds(Vidal et al. 2017; Navarro-Almaida et al. 2020). S ortho-to-para ratio
We now specifically compare the SH + , SH, and H S line inten-sities implied by the di ff erent PDR models with the intensitiesobserved toward the DF position of the Bar. We used the outputof the PDR models – T k , T d , n (H ), n (H), n e , n (SH + ), n (SH), and n (H S) profiles from A V = α ) with respect to a pureedge-on PDR. Di ff erent studies suggest α of ≈ o (e.g., Jansenet al. 1995; Melnick et al. 2012; Andree-Labsch et al. 2017). Thisinclination implies an increase in line-of-sight column density,compared to a face-on PDR, by a geometrical factor (sin α ) − . Italso means that optically thin lines are limb-brightened.The left panel of Fig. 15 shows SH + line intensity predic-tions for isobaric PDR models of di ff erent P th values (leadingto di ff erent T k and n H profiles). Since the bulk of the SH + emis-sion arises from the PDR edge ( A V (cid:39) P th (cid:39) (1–2) × cm − K and α (cid:39) o . These high pressures, at leastclose to the DF, agree with those inferred from ALMA images ofHCO + ( J = J CO lines (Joblin et al. 2018), and IRAM 30 mdetections of carbon recombination lines (Cuadrado et al. 2019).
Article number, page 14 of 25oicoechea et al.: Bottlenecks to interstellar sulfur chemistry
Fig. 16.
Constant density gas-grain PDR models using the high E b chemical network and undepleted sulfur elemental abundances. Left panel : E ff ects of changing the FUV radiation field. Right panel : E ff ects of varying the gas density. Right panel of Fig. 15 shows SH and H S line emissionpredictions for the high E b gas-grain model (magenta squares),low E b gas-grain model (gray triangles), and a pure gas-phasemodel (cyan circles). For each model, the upper limit intensitiesrefer to radiative transfer calculations with an inclination angle α = o . The lower intensity limits refer to a face-on PDR. Gas-phase models largely underestimate the observed H S intensities.Model low E b produces higher H S columns and brighter H Slines, but still below the observed levels (by up to a factor of ten).Model high E b provides a good agreement with observations; thetwo possible inclinations bracket the observed intensities, and itshould be considered as the reference model of the Bar. It is alsoconsistent with the observational SH upper limits.Our observations and models provide a (line-of-sight) N ( o -H S) / N ( p -H S) OTP ratio of 2.9 ± T spin (cid:28) T k ; seedefinition in eq. D.1) implied by the low water vapor OTP ratiosobserved in some sources ( < O molecules might haveformed (i.e., T spin (cid:39) T d ; Mumma et al. 1987; Lis et al. 2013). Inthe case of H S, our derived OTP ratio toward the DF positionimplies any T spin above 30 ±
10 K (see Fig. D.1). Hence, this tem-perature might be also compatible with s-H S formation in warmgrains if T spin (cid:39) T d upon formation is preserved in the gas-phaseafter photodesorption (e.g., Guzmán et al. 2013). Interestingly,the H O OTP ratio derived from observations of the Orion Bar is2.8 ± T spin (H O) = ± T spin (H S) and might reflect thesimilar T d of the PDR layers where most s-H O and s-H S formand photodesorb. Nevertheless, laboratory experiments have chal- Crockett et al. (2014) inferred N ( o -H S) / N ( p -H S) = ± ± T spin (H S) (cid:39)
12 K (Fig. D.1), perhaps related to muchcolder dust grains than in PDRs or to colder gas conditions just before thehot core phase; so that reactive collisions did not have time to establishthe statistical equilibrium value. We note that the observed OTP ratios ofH CO, H CS, and H CCO in the Bar are also ∼ lenged this T spin (cid:39) T d association, at least for s-H O: cold waterice surfaces, at 10 K, photodesorb H O molecules with an OTPratio of ∼ p -H Slines across the Bar will allow us to study possible variations ofthe OTP ratio as G diminishes and grains get colder. and n H conditions In this section we generalize our results to a broader range ofgas densities and FUV illumination conditions (i.e., to cloudswith di ff erent G / n H ratios). We run several PDR models us-ing the high E b gas-grain chemistry. The main di ff erence com-pared to the Orion Bar models is that here we model con-stant density clouds with standard interstellar grain properties( R V = n H = cm − and varying FUV radiation fields, whileFig. 16 (right panel) show models of constant FUV illumina-tion ( G = . The main result ofthis study is the similar gas-phase H S column density (a few10 cm − up to A V =
10) and H S abundance peak (a few 10 − close to the FUV-irradiated cloud edge) predicted by these mod-els nearly irrespective of G and n H . A similar conclusion wasreached previously for water vapor in FUV-illuminated clouds(Hollenbach et al. 2009, 2012). Increasing G shifts the positionof the H S abundance peak to larger A V until the rate of S atomssticking on grains balances the H S photodissociation rate (thedominant H S destruction mechanism except in shielded gas;see also Fig.13). Since s-H S photodesorption and H S photodis-sociation rates depend on G , the peak H S abundance in thePDR is roughly the same independently of G . On the otherhand, the formation rate of s-H S mantles depends on the prod-uct n (S) n gr ∝ n , whereas the H S photodesorption rate dependson n gr ∝ n H . Hence, the H S abundance peak moves toward thecloud surface for denser PDRs (like the Orion Bar). The exactabundance value depends on the adopted grain-size distributionand on the H S photodesorption yield (which is well constrainedby experiments; see, Cruz-Diaz et al. 2014; Fuente et al. 2017). In these models we consider undepleted [S / H] abundances and onlythe chemical desorption s-H + s-SH → H S (with a 50 % e ffi ciency).Article number, page 15 of 25 & A proofs: manuscript no. aa_sulfur_bar_accepted
The role of chemical desorption increases and can dominatebeyond the photodesorption peak as the flux of stellar FUV pho-tons is attenuated. Here we do not carry out an exhaustive studyof this mechanism, which is hard to model in full detail becauseits e ffi ciency decreases considerably with the properties of grainsurfaces (bare vs. icy; see e.g., Minissale & Dulieu 2014). In ourmodels, and depending on ζ CR , photodesorption by secondaryFUV photons can also be important in cloud interiors. Theseprocesses limit the conversion of most of the sulfur reservoir intoS-bearing ices and increase the abundance of other gas-phasespecies deep inside clouds, notably S atoms and H S molecules.The H S abundance in shielded gas depends on thedestruction rate by gas-phase reactions di ff erent than photodisso-ciation, in particular H S reactions with H + . The H + abundanceincreases with ζ CR and decreases with the electron density. Fig-ure 16 ( right ) shows models of constant G and constant ζ CR in which the H S abundance at large depths increases with de-creasing density (more penetration of FUV photons, more ion-ization, more electrons, less H + ). The lowest gas density model, n H = cm − , shows the highest H S abundance at large A V .Because S freeze-out is less e ffi cient at low densities, the low-density model shows higher gas-phase S abundances at largedepths, making atomic S a dominant gas-phase sulfur reservoir.Unfortunately, direct observation of atomic S in cold gas is com-plicated, which makes it di ffi cult to benchmark this prediction.In warm PDRs, in addition to S radio recombination lines(e.g., Smirnov et al. 1995), the P fine-structure lines of atomicsulfur, the [S i ] 25, 56 µ m lines, can be interesting diagnostics ofgas physical conditions and of [S / H] abundances. Unfortunately,the low sensitivity of previous infrared telescopes was not suf-ficient to detect the [S i ] 25 µ m line ( ∆ E =
570 K) in the OrionBar (Rosenthal et al. 2000); although it is detected in protostellaroutflows (e.g., Neufeld et al. 2009; Goicoechea et al. 2012). More-over, the P - D forbidden line of atomic sulfur at 1.082 µ m canbe an interesting tracer of the ionization and dissociation frontsin PDRs. Some of these lines will be accesible to high-angular-resolution and high sensitivity observations with JWST . S emission in other environments
Irrespective of n H and G , grain surface formation of s-H S andphotodesorption back to the gas-phase lead to H S column densi-ties of a few 10 cm − in PDRs. This is in agrement with the ob-served column in the Bar ( G ≈ ) as well as at the mildly illumi-nated rims of TMC-1 and Barnard 1b clouds ( G ≈
10; Navarro-Almaida et al. 2020). The inferred H S abundance in the shieldedinterior of these dark clouds ( A V >
10 mag) drops to a few 10 − ,but the species clearly does not disappear from the gas ( N (H S)of a few 10 cm − ; Navarro-Almaida et al. 2020). Interestingly,neither in the Bar the H S line emission at ∼
168 GHz decreasesmuch behind the PDR (Fig. 1) even if the flux of FUV photons islargely attenuated compared to the irradiated PDR edge.Despite oxygen is ∼
25 times more abundant than sulfur, theH O to H S column density ratio in the Orion Bar PDR is onlyabout ∼
5. This similarity must also reflect the higher abundancesof CO compared to CS. Furthermore, the H S column densityin cold cores is strikingly similar to that of water vapor (Caselliet al. 2010, 2012). This coincidence points to a more e ffi cient des-orption mechanism of s-H S compared to s-H O in gas shieldedfrom stellar FUV photons. Navarro-Almaida et al. (2020) arguesthat chemical desorption is able to reproduce the observed H Sabundance floor if the e ffi ciency of this process diminishes as icegrain mantles get thicker inside cold dense cores. Turning back to warmer star-forming environments, our pre-dicted H S abundance in FUV-illuminated gas is comparableto that observed toward many hot cores ( ∼ − -10 − ; van derTak et al. 2003; Herpin et al. 2009). In these massive protostel-lar environments, thermal desorption of icy mantles, suddenlyheated to T d (cid:38)
100 K by the luminosity of the embedded massiveprotostar, drives the H S production. Early in their evolution,young hot cores ( (cid:46) yr) can show even higher abundancesof recently desorbed H S (before further chemical processingtakes place in the gas-phase; e.g., Charnley 1997; Hatchell et al.1998; Jiménez-Serra et al. 2012; Esplugues et al. 2014). Indeed,Crockett et al. (2014) reports a gas-phase H S abundance of sev-eral 10 − toward the hot core in Orion KL. This high value likelyreflects the minimum s-H S abundance locked as s-H S mantlesjust before thermal desorption. In addition, the H S abundance inthe Orion Bar is only slightly lower than that inferred in protostel-lar outflows (several 10 − ). In these regions, fast shocks erode andsputter the grain mantles, releasing a large fraction of their molec-ular content and activating a high-temperature gas-phase chem-istry that quickly reprocesses the gas (e.g., Holdship et al. 2019).All in all, it seems reasonable to conclude that everywhere s-H Sgrain mantles form, or already formed in a previous evolutionarystage, emission lines from gas-phase H S will be detectable.In terms of its detectability with single-dish telescopes, H Srotational lines are bright in hot cores ( T peak ,
168 GHz (cid:39)
30 K inOrion KL but (cid:39) (cid:39) (cid:39) Semission is fainter toward cold dark clouds ( (cid:39) (cid:39) ff erencesare mostly produced by di ff erent gas physical conditions and notby enormous changes of the H S abundance.Finally, H S is also detected outside the Milky Way (firstly byHeikkilä et al. 1999). Lacking enough spatial-resolution it is moredi ffi cult to determine the origin of the extragalactic H S emission.The derived abundances in starburst galaxies such as NGC 253( ∼ − ; Martín et al. 2006) might be interpreted as arising from acollection of spatially unresolved hot cores (Martín et al. 2011).However, hot cores have low filling factors at star-forming cloudscales. Our study suggests that much of this emission can arisefrom (the most common) extended molecular gas illuminated bystellar FUV radiation (e.g., Goicoechea et al. 2019).
7. Summary and conclusions
We carried out a self-consistent observational and modeling studyof the chemistry of S-bearing hydrides in FUV-illuminated gas.We obtained the following results:– ALMA images of the Orion Bar show that SH + is confined tonarrow gas layers of the PDR edge, close to the H dissociationfront. Pointed observations carried out with the IRAM 30mtelescope show bright H S, H
S, H
S emission toward thePDR (but no H S + , a key gas precursor of H S) as well as behindthe Bar, where the flux of FUV photons is largely attenuated.SOFIA observations provide tight limits to the SH emission.– The SH + line emission arises from a high-pressure gas com-ponent, P th (cid:39) (1–2) × cm − K, where SH + ions are destroyedby reactive collisions with H atoms and electrons (as most H n S + ions do). We derive N (SH + ) (cid:39) cm − and an abundance peakof several ∼ − . H S shows larger column densities towardthe PDR, N (H S) = N ( o -H S) + N ( p -H S) (cid:39) × cm − .Our tentative detection of SH translates into an upper limit Article number, page 16 of 25oicoechea et al.: Bottlenecks to interstellar sulfur chemistry column density ratio N (SH) / N (H S) of < ff usemolecular clouds (Neufeld et al. 2015). This implies an enhancedH S production mechanism in FUV-illuminated dense gas.– All gas-phase reactions X + H ( v = → XH + H (with X = S + ,S, SH + , or H S + ) are highly endoergic. While reaction ofFUV-pumped H ( v ≥
2) molecules with S + ions becomesexoergic and explains the observed levels of SH + , furtherreactions of H ( v ≥
2) with SH + or with neutral S atoms, bothreactions studied here through ab initio quantum calculations, donot form enough H S + or H S + to ultimately produce abundantH S. In particular, pure gas-phase models underestimate theH S column density observed in the Orion Bar by more thantwo orders of magnitude. This implies that these models missthe main H S formation route. The disagreement is even worseas we favor, after considering the potential energy surfaces ofthe H S + ∗ and H S + ∗ complexes, that the radiative associationsS + + H → H S + + h ν and SH + + H → H S + + h ν may actuallynot occur or possess slower rates than considered in the literature.– To overcome these bottlenecks, we built PDR models thatinclude a simple network of gas-grain and grain surface reactions.The higher binding energies of S and SH suggested by recentstudies imply that bare grains start to grow s-H S mantles notfar from the illuminated edges of molecular clouds. Indeed, theobserved N (H S) in the Orion Bar can only be explained by thefreeze-out of S atoms, grain surface formation of s-H S mantles,and subsequent photodesorption back to the gas phase. Theinferred H S OTP ratio of 2.9 ± T spin ≥
30 K)is compatible with the high-temperature statistical ratio as wellas with warm grain surface formation if T spin (cid:39) T d and if T spin ispreserved in the gas-phase after desorption.– Comparing observations with chemical and excitation models,we conclude that the SH + -emitting layers at the edge of theOrion Bar ( A V < A V < S column densities do notrequire depletion of elemental (cosmic) sulfur abundances either.– We conclude that everywhere s-H S grain mantles form (orformed) gas-phase H S will be present in detectable amounts.Independently of n H and G , FUV-illuminated clouds produceroughly the same H S column density (a few 10 cm − ) andH S peak abundances (a few 10 − ). This agrees with the H Scolumn densities derived in the Orion Bar and at the edgesof mildly illuminated clouds. Deep inside molecular clouds( A V > S still forms by direct chemical desorption andphotodesorption by secondary FUV photons. These processesalter the abundances of other S-bearing species and makesdi ffi cult to predict the dominant sulfur reservoir in cloud interiors.In this study we focused on S-bearing hydrides. Still, manysubtle details remain to be fully understood: radiative as-sociations, electron recombinations, and formation of multi-ply sulfuretted molecules. For example, the low-temperature(T k < + used in PDR models may still be not accurateenough (Badnell 1991). In addition, the main ice-mantle sul-fur reservoirs are not fully constrained observationally. Thus,some of the narrative may be subject to speculation. Similarly,reactions of S + with abundant organic molecules desorbed fromgrains (such as s-H CO, not considered in our study) may con-tribute to enhance the H S + abundance through gas-phase reac-tions (e.g., S + + H CO → H S + + CO; Prasad & Huntress 1982).Future observations of the abundance and freeze out depths ofthe key ice carriers with
JWST will clearly help in these fronts.
Acknowledgements.
We warmly thank Prof. György Lendvay for interestingdiscussions and for sharing the codes related to their S( P ) + H ( Σ + g ,v)PES. We thank Paul Dagdigian, François Lique, and Alexandre Faure forsharing their H S–H , SH + –H, and SH + –e − inelastic collisional rate coe ffi -cients and for interesting discussions in Grenoble and Salamanca. We thankHelgi Hrodmarsson for sending his experimental SH photoionization crosssection in tabulated format. We finally thank our referee, John H. Black,for encouraging and insightful suggestions. This paper makes use of theALMA data ADS / JAO.ALMA / NRAO, and NAOJ. It also includes IRAM 30 m telescope obser-vations. IRAM is supported by INSU / CNRS (France), MPG (Germany), andIGN (Spain). We thank the sta ff at the IRAM 30m telescope and the work ofthe USRA and NASA sta ff of the Armstrong Flight Research Center in Palm-dale and of the Ames Research Center in Mountain View (California), and theDeutsches SOFIA Institut. We thank the Spanish MICIU for funding supportunder grants AYA2016-75066-C2-2-P, AYA2017-85111-P, FIS2017-83473-C2PID2019-106110GB-I00, and PID2019-106235GB-I00 and the French-Spanishcollaborative project PICS (PIC2017FR). We finally acknowledge computingtime at Finisterrae (CESGA) under RES grant ACCT-2019-3-0004. References
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Appendix A: H S + formation and destruction In this Appendix we give details about how we calculated the H vibrational-state-dependent rates of reaction (2) and of the reversereaction, the destruction of H S + ( A (cid:48) ) by reactive collisons withH ( S ) atoms (summarized in Fig. A.1).We first built a full dimensional potential energy surface (PES)of the triplet H S + ( A ) system by fitting more than 150,000 ab initio points, including the long range interactions in the reac-tants and products channels. The main topological features of thePES are summarized in the minimum energy path between reac-tants and products (see middle panel of Fig. 9). These ab initio points were calculated with an explicitly correlated restrictedcoupled cluster including a single, double, and (perturbatively)triple excitations (RCCSD(T)-F12a) method (Knizia et al. 2009).The analytical fit has a overall rms error of (cid:39) + SH + entrancechannel (named W a and W b , with a depth of (cid:39) + H S + products (named W , with adepth of 0.08 eV). Between the reactants and products wells thereis a saddle point, with an energy of 0.601 eV. This saddle point,slightly below the products, has a geometry similar to W inwhich the H–H distance is strongly elongated compared to that ofH . These features are also present in the maximum multiplicityPES of reactions H + S + ( S ) and H + H S + ( A ) (see Fig. 9).We determine the state-dependent rates of reaction (2) and of thereverse reaction using a quasi-classical trajectory (QCT) methodon our ground triplet PES. We provide more details on how thereactive cross sections for fixed collision energies were calculatedin Appendix. A.2.The formation rate of H S + from H ( v =
0) is very slow. ForH ( v = ≈
500 K,corresponding with the opening of the H S + + H threshold. Atthis point, it is important to consider the zero-point energy (ZPE)of the products (see next section for details). For H ( v =
2) andH ( v = S + destruction rate constant is very similar to thatof its formation from H ( v = n S + ions throughradiative association and spin flip mechanisms. Appendix A.1: Ab initio calculations and PES
Dagdigian (2019) presented a PES for the SH + -H system thatincludes 4-dimensions and is based on RCCSD(T)-F12a ab initio calculations. This PES was used to study SH + –H inelastic col-lisions using a rigid rotor approach in which the two diatomicmolecules are kept fixed at their equilibrium distances. However,in order to study the reactivity of the collision, the two diatomicdistances have to be included to account for the breaking andformation of new bonds.Reaction (2) corresponds to a triplet state H S + ( A ). TheH S + ( A (cid:48) ) + H ( S ) products can form a triplet and a singletstate. The triplet state can lead to the destruction of H S + throughreaction with H atoms. The singlet state, however, produces veryexcited states of the reactants. Thus, it only leads to inelasticcollisions but not not to the destruction of H S + ( A (cid:48) ). In con-sequence, here we only consider the ground triplet electronicstate of the system. In addition, the H + + S ( P ) channel is about2.4 eV above the H + SH + asymptote, and will not be includedin the present study. -12 -11 -10 -9
100 500 900 1300H (v=2) + SH + H (v=1) + SH + H (v=3) + SH + H (v=0) H S + + H R a t e c on s t an t ( c m / s ) Temperature (K)
Fig. A.1.
Calculated rate constants as a function of temperature (for trans-lation and rotation) for SH + ( v = j = + H ( v =
1, 2, 3, j =
0) andH S + ( v = j = + H reactions (lavender) using ZPE corrected QCTmethod. Dotted curves are fits of the form k ( T ) = α ( T / β exp( − γ/ T ).Rate coe ffi cients are listed in Table 1. + (X Σ - ) + H (X Σ g+ )TS H S + ( A) H + S( P)H S + ( A") + H( S) W r m s ( e V ) N u m be r o f geo m e t r i e s Energy (eV)rms (eV)number of geometries
Fig. A.2.
Rms error as a function of total energy, showing the number of ab initio points used to evaluate the error in the PES calculation. Arrowsindicate selected critical points in the PES and provide an estimate ofthe error in each region. TS means transition state.
In order to study the regions where several electronic statesintersect, we performed a explicitly correlated internally con-tracted multireference configuration interaction (ic-MRCI-F12)calculation (Shiozaki & Werner 2013; Werner & Knowles1988a,b) including the Davidson correction (icMRCI-F12 + Q;Davidson 1975). The ic-MRCI-F12 calculations were carried outusing state-averaged complete active space self-consistent field(SA-CASSCF) orbitals with all the CAS configurations as thereference configuration state functions. We used a triple zeta corre-lation consistent basis set for explicitly correlated wave functions(cc-pVTZ-F12; Peterson et al. 2008). In order to avoid orbitalflipping between core and valence orbitals. SA-CASSCF calcula-
Article number, page 20 of 25oicoechea et al.: Bottlenecks to interstellar sulfur chemistry tions with three lowest triplet states were carried out includingthe core and valence orbitals as active space (18 electrons in 11orbitals). For the ic-MRCI-F12 calculation, the core orbitals waskept doubly occupied, resulting in about 2 . × (9 × ) con-tracted (uncontracted) configurations. All ab initio calculationswere performed with MOLPRO (Werner et al. 2012).Our ic-MRCI-F12 calculations show that the crossings withelectronic excited states are 2 eV above the energy of the re-actants. The energy interval below 2 eV is enough to studyreaction 2. In these low-energy regions, RCCSD(T)-F12a cal-culations were also performed. They are in good agreement withthe ic-MRCI-F12 results and the t diagnostic is always below0.03. This allows us to conclude that for energies below 2 eV, theRCCSD(T)-F12a method performs well, presents a simple con-vergence, and being size consistent, is well adapted to the presentcase. This method is the same one employed in the inelasticcollision calculations by Dagdigian (2019).We performed extensive RCCSD(T)-F12a calculations in allaccessible regions to properly describe the six-dimensional phasespace. 150000 ab initio points were fitted to a multidimensionalanalytic function, that generates the six-dimensional PES repre-sented as H = H diab + H MB (A.1)(Aguado et al. 2010; Sanz-Sanz et al. 2013; Zanchet et al. 2018;Roncero et al. 2018), where H diab is an electronic diabatic matrixin which each diagonal matrix element describes a rearrangementchannel – six in this case, three equivalent for SH + + H channels,and three equivalent for H S + + H fragments (we omitted theH + + S channel) – as an extension of the reactive force fieldapproach (Farah et al. 2012). In each diagonal term, the molecularfragments (SH + , H and H S + ) are described by 2 or 3 body fits(Aguado & Paniagua 1992), and the interaction among themis described by a sum of atom-atom terms plus the long rangeinteraction. The non diagonal terms of H diab are described aspreviously (Zanchet et al. 2018; Roncero et al. 2018) and theparameters are fitted to approximately describe the saddle pointsalong the minimum energy path in the right geometry.In the reactants channel, the leading long range interactionSH + ( X Σ − ) + H ( X Σ + g ) corresponds to charge-quadrupole andcharge-induced dipole interactions (Buckinghan 1967): V charge( r HH , R ) = Θ ( r HH ) P (cos θ ) R − − (cid:34) α ( r HH ) + (cid:0) α (cid:107) ( r HH ) − α ⊥ ( r HH ) (cid:1) P (cos θ ) (cid:35) R − (A.2)and the dipole-quadrupole interactions (Buckinghan 1967): V dipole( r S H , r HH , R ) = µ ( r S H ) Θ ( r HH ) × (cid:2) cos θ P (cos θ ) + sin θ sin θ cos θ cos φ (cid:3) R − , (A.3)where Θ ( r HH ) is the cuadrupole moment of H ( X Σ + g ), α ( r HH ), α (cid:107) ( r HH ), and α ⊥ ( r HH ) are the average, parallel, and perpendicu-lar polarizabilities of H ( X Σ + g ), respectively, and µ ( r S H ) is thedipole moment of SH + ( X Σ − ). P (cos θ ) represents the Legen-dre polynomial of degree 2. The dependence of the molecularproperties of H with the interatomic distance r HH is obtainedfrom Velilla et al. (2008). The dipole moment of SH + dependson the origin of coordinates. Since SH + ( X Σ − ) dissociates inS + ( S ) + H( S ), we select the origin of coordinates in the S atom,so that the dipole moment tends to zero when R goes to infinity.In the products channel, the long range interactionH S + ( X A (cid:48)(cid:48) ) + H ( S ) corresponds to the isotropic charge- Table A.1.
RCCSD(T)-F12a and fit stationary points on the PES.
Stationary point Geometry Energy / cm − Energy / eVReactants SH + + H + − H − − + ·· H − − + − H − − + ·· H ·· H 4843.9 0.6006Minimum 3 H S + − H 4766.5 0.5910Products H S + + H 5422.3 0.6723
Table A.2. E v of reactants and products, and adiabatic switching energiesfor the QCT initial conditions. System(vibration) Exact E v (eV) AS energy (eV)H ( v =
0) 0.270 0.269H ( v =
1) 0.786 0.785H ( v =
2) 1.272 1.272H ( v =
3) 1.735 1.730SH + ( v =
0) 0.157 0.157H S + ( v =
0) 0.389 0.388induced dipole and charge-induced quadrupole dispersion terms V disp( R ) = − R − − R − . These long range terms diverge at R =
0. To avoid this behavior,we replace R by R : R = R + R e − ( R − R e ) with R =
10 bohr . In Eq. (A.1), H MB is the many-body term, which is describedby permutationaly invariant polynomials following the methodof Aguado an collaborators (Aguado & Paniagua 1992; Tableroet al. 2001; Aguado et al. 2001). This many-body term improvesthe accuracy of the PES, especially in the region of the reactionbarriers (as shown in Fig. 9). Features of the stationary points arelisted in Table A.1. Appendix A.2: Determination of reactive collision rates
We studied the reaction dynamics using a quasi-classical trajec-tory (QCT) method with the code miQCT (Zanchet et al. 2018;Roncero et al. 2018). In this method, the initial vibrational en-ergy of the reactants is included using the adiabatic switchingmethod (AS) (Grozdanov & Solov’ev 1982; Johnson 1987; Qu& Bowman 2016; Nagy & Lendvay 2017). Energies are listedin Table A.2. The initial distance between the center-of-massof the reactants (H + SH + or H S + + H) is set to 85 bohr, andthe initial impact parameter is set randomly within a disk, theradius of which is set according to a capture model (Levine &Bernstein 1987) using the corresponding long-range interaction.The orientation among the two reactants is set randomly.A first exploration of the reaction dynamics is done atfixed collision energy, for H ( v =
0, 1, 2 , 3) + SH + ( v =
0) andH + H S + ( v = σ v j ( E ) = π b max P r ( E ) with P r ( E ) = N r N tot , (A.4) Article number, page 21 of 25 & A proofs: manuscript no. aa_sulfur_bar_accepted R ea c t i on c r o ss s e c t i on ( boh r ) Collision energy (meV)H (v=3) + SH + H (v=2) + SH + H (v=1) + SH + H (v=0) + SH + H S + (0,0,0)+H Fig. A.3.
Reaction cross section (in bohr ) as a function of collisionenergy (in meV) for the SH + ( v = j = + H ( v =
1, 2, 3, j =
0) andH S + ( v = j = + H collisions. Filled symbols are obtained countingall trajectories leading to products, while open symbols correspond tothe ZPE corrected ones. where N t is the maximum number of trajectories with initial im-pact parameter lower than b max , the maximum impact parameterfor which the reaction takes place, and N r is the number of trajec-tories leading to products. Fig. A.2 shows results for N t > + ( v = j = + H ( v , j =
0) reaction there is astrong dependence on the initial vibrational state. For H ( v = ( v = b max ,consistent with the variation of the cross section.Reaction SH + ( v = j = + H ( v = j =
0) shows an unex-pected behavior that deserves some discussion. At energies below40 meV, the cross section is large and decreases with increasingenergy. In the 40-200 meV range, the reactive cross section dropsto zero, showing a threshold at 200 meV that is consistent withthe endothermicity of the reaction.In order to analyze the reaction mechanism for H ( v = and SH + reactants are attracted to each other by long rangeinteractions, until they get trapped in the W wells, as it is shownby the evolution of R , the distance between center-of-mass of thetwo molecules. The trapping lasts for 8 ps, thus allowing severalcollisions between H and SH + and permitting the energy transferbetween them. The H molecule ultimately breaks, and leavesSH + with less vibrational energy. This can be inferred from thedecrease in the amplitudes of the SH + distance. The energy of theH S + product is below the ZPE (see Table A.2). This is a clearindication of ZPE leakage in the QCT method, due to the energytransfer promoted by the long-lived collision complex.Several methods exist that correct the ZPE leakage. One isthe gaussian binning (Bonnet & Rayez 1997, 2004; Bañares et al.2003, 2004). Here we have applied a simplification of this method, d i s t an c e ( boh r) time (ps)RHS + H Fig. A.4.
H-H, SH + and R distances (in bohr) versus time (in ps), fora typical reactive trajectory for the SH + ( v = j = + H ( v = j = which assigns a weight ( w ) for each trajectory as w = (cid:40) E v ib > ZPEe − γ ( E v ib − ZPE ) for E v ib < ZPE , (A.5)where E v ib is the vibrational energy of reactants (adding thoseof H and SH + ) or H S + products at the end of each trajectory.These new weights are used to calculate N r and N tot in Eq. A.4.ZPE-corrected results are shown in Fig. A.3 with open symbols.This plot shows that all values are nearly the same as those calcu-lated simply by counting trajectories as an integer (as done in thenormal binning method; see filled symbols in Fig. A.3). The onlyexception is the case of SH + + H ( v =
1) below 400 meV, whichbecomes zero when considering the ZPE of fragments at the endof the trajectories.The reaction thermal rate in specific initial vibrational state ofreactants are calculated running a minimum of 10 trajectories pertemperature, with fixed vibrational states of reactants, assuming aBoltzmann distribution over translational and rotational degreesof freedom, and following the ZPE-corrected method as: k v ( T ) = (cid:115) k B T πµ π b max ( T ) P r ( T ) . (A.6)The results of these calculations are shown in Fig. A.1. Appendix A.3: On the radiative associations of H n S + Herbst et al. (1989) and Millar & Herbst (1990) proposed that theradiative association H n S + + H → H n + S + + h ν is viable pro-cess at low gas temperatures. Although this chemical route iswidely used in astrochemical models, here we question the viabil-ity of this process. The lower multiplicity (L) PESs of H S + ( A (cid:48)(cid:48) )and H S + ( A ) are L = / S + (bottom panel). This state does not have a deep well orany higher multiplicity state that could connect to higher statesof reactants and products.For of H S + formation through radiative association, this pro-cess assumes that a H S + ( A ) ∗ complex forms in a triplet state, the Article number, page 22 of 25oicoechea et al.: Bottlenecks to interstellar sulfur chemistry high spin state H considered here. According to our calculations,such a complex is formed after low-energy H ( v =
0, 1) + SH + reactions (below 40 meV). The complex is formed in the W well, corresponding to geometries very far from those of the lowspin well, the W well. Therefore, a radiative spin flip and decaythrough phosphorescence is not possible. Herbst et al. (1989)proposed a second step, in which the spin flips from the tripletto the singlet state, followed by a radiative association, finallyleading to the H S + ( A ) product.The origin of the spin flip must be the spin-orbit couplings,very relevant for S-bearing species, that favor the spin transitionwhen singlet and triplet states are close in energy. Using the PESscalculated here, the lowest crossing region is at (cid:39) ( v = S + ( A ) ∗ complex formed by H ( v = + SH + reactions might allow atransition between the two electronic states with di ff erent spin.However, the spin flip probability is proportional to the square ofthe overlap |(cid:104) H S + ( A ) ∗ | H S + ( A ) ∗ (cid:105)| . This probability is verysmall because the two wells, W and W , correspond to verydi ff erent geometries. In consequence, we conclude that this ra-diative association mechanism must be negligible, especially atthe high gas temperatures of PDR edges where the H S + ( A ) ∗ complex is not formed.As an alternative, a spin flip in a direct collision (not form-ing a H S + ( A ) ∗ complex) may be more e ffi cient and should befurther investigated. Indeed, experimental measurements of theS + ( S ) + H ( v =
0) cross section show a maximum at about 1 eVof collisional energy attributed to spin-orbit transitions leading tospin flip (Stowe et al. 1990).
Appendix B: Reaction
S ( P) + H ( v ) (cid:29) SH + H This reaction involves open shell reactants, S ( P ), and products,SH ( Π ). Neglecting spin flipping, there are three states that corre-late to S( P ), two of them connect to the SH ( Π ). These two elec-tronic states are of A (cid:48) and A (cid:48)(cid:48) symmetry, and have been studiedin detail by Maiti et al. (2004). Here we use the adiabatic PES cal-culated by Maiti et al. (2004). Reaction S + H → SH + H is en-dothermic by (cid:39) + + H → SH + + H(Zanchet et al. 2013a, 2019). The main di ff erence is the presenceof a barrier, of (cid:39)
78 meV ( (cid:39)
905 K) with respect to the SH + Hasymptote.We performed quantum wave packet calculations for the re-actions S + H ( v =
2, 3, j =
0) and SH ( v = j = + H. We usedMADWAVE3 (Gómez-Carrasco & Roncero 2006; Zanchet et al.2009) to calculate the reaction probabilities for the initial vibra-tional state of the diatomic reactant (in the ground state rotationalstate, j = J =
0, 10 and 20. Theother J needed in the partial wave expansion were obtained usingthe J -shifting-interpolation method (see Zanchet et al. 2013a).The initial-state-specific rate constants are obtained by numericalintegration of the cross section using a Boltzmann distribution(Zanchet et al. 2013a). The resulting reaction rate constants areshown in Figs. B.1 and B.2. The numerical values of the rate con-stants are fitted to the usual analytical Arrhenius-like expresion(shown as dotted curves). We note that the shoulder in the rateconstants of reaction SH ( v = + H requires two functions in thetemperature range of 200-800 K. Rate coe ffi cients are tabulatedin Table 1. -13 -12 -11
100 500 900 1300H (v=2) + SH (v=3) + S R a t e c on s t an t ( c m / s ) Temperature (K)
Fig. B.1.
Calculated rate constants as a function of temperature forreaction S( P ) + H ( v ) → SH + H. Dotted curves are fits of the form k ( T ) = α ( T / β exp( − γ/ T ). Rate coe ffi cients are listed in Table 1. -13 -12 -11
100 500 900 1300SH(v=0)+H R a t e c on s t an t ( c m / s ) Temperature (K)
Fig. B.2.
Calculated rate constants as a function of temperature for reac-tion SH ( v = + H → S + H . The best fit to the calculated rate requirestwo Arrhenius-like expressions (one for low temperatures and one forhigh temperatures). Rate coe ffi cients of these fits are listed in Table 1.Article number, page 23 of 25 & A proofs: manuscript no. aa_sulfur_bar_accepted
Appendix C: SH and H S photoionization andphotodissociation cross sections
Figure C.1 shows the experimental SH and H S photoionizationand photodissociation cross sections (cm − ) used in our PDRmodels. We integrate these cross sections over the specific FUVradiation field at each A V depth of the PDR to obtain the specificphotoionization and photodissociation rates (s − ). Fig. C.1.
Photoionization and photodissociation cross sections.
Top panel : σ ion (SH) (blue curve from laboratory experiments by Hrod-marsson et al. 2019). The pink curve is σ diss (SH) (Heays et al. 2017, andreferences therein). Bottom panel : σ ion (H S) (blue curve) and σ diss (H S)(gray and pink curves; from Zhou et al. 2020).
Appendix D: H S ortho-to-para ratio and T spin The OTP ratio is sometimes related to a nuclear-spin-temperature( T spin , e.g., Mumma et al. 1987) defined, for H O or H S, as:OTP = (cid:80) (2 J +
1) exp( − E o ( J ) / T spin ) (cid:80) (2 J +
1) exp( − E p ( J ) / T spin ) . (D.1)Here, E o ( J ) and E p ( J ) are the energies (in Kelvin) of o -H S and p -H S rotational levels (with the two ground rotational statesseparated by ∆ E = S nuclear spin isomers as a function of T spin . The OTP ratiowe infer toward the DF position of the Bar, 2.9 ± /
1, and implies T spin ≥ ±
10 K.
Appendix E: Line parameters of IRAM 30m, ALMA,and SOFIA observations
Fig. D.1.
OTP ratio of H S as a function of spin temperature (eq. D.1).Article number, page 24 of 25oicoechea et al.: Bottlenecks to interstellar sulfur chemistry
Table E.1.
Parameters of H S and H
S lines detected with the IRAM 30 m telescope toward three positions of the Orion Bar.
Position Species Transition Frequency E u / k A ul S ul g u (cid:90) T mb dv v LSR ∆ v T mb J K a , K c [GHz] [K] [s − ] [K km s − ] [km s − ] [km s − ] [K]( + − o -H S 1 , – 1 , × − o -H S 1 , – 1 , × − p -H S 2 , – 2 , × − + − o -H S 1 , – 1 , × − o -H S 1 , – 1 , × − + − o -H S 1 , – 1 , × − o -H S 1 , – 1 , × − Notes.
Parentheses indicate the uncertainty obtained by the Gaussian fitting programme.
Table E.2.
Parameters of SH + targeted with ALMA toward the DF position. Position Species Transition Frequency E u / k A ul (cid:90) T mb dv v LSR ∆ v T mb [GHz] [K] [s − ] [K km s − ] [km s − ] [km s − ] [K]( + −
10) SH + N J = -0 F = / / × − a (0.03) 10.7 (0.2) 2.7 (0.3) 0.12SH + N J = -0 F = / / b × − a (0.03) 10.4 (0.1) 2.5 (0.1) 0.26 Notes. a Integrated over a 5 (cid:48)(cid:48) aperture to increase the S / N of the line profiles. b Line integrated intensity map shown in Fig. 3.
Table E.3.
Parameters of SH lines (neglecting HFS) targeted with SOFIA toward the DF position.
Position Species Transition Frequency E u / k A ul (cid:90) T mb dv v LSR ∆ v T mb [GHz] [K] [s − ] [K km s − ] [km s − ] [km s − ] [K]( + −
10) SH Π / J = / + –3 / − × − < a (0.20) 12.1 a (0.8) 7.9 a (1.3) 0.16SH Π / J = / − –3 / + × − < Notes. aa