Guillaume Barré
email: guillaume.barre@univ-lorraine.fr

Laurent Truche

Elena F Bazarkina

Raymond Michels

Jean Dubessy

First evidence of the trisulfur radical ion S 3 -and other sulfur polymers in natural fluid inclusions

Keywords: S3 -, Fluid inclusion, Raman spectroscopy, Sulfur speciation, Thermochemical Sulfate Reduction

Sulfur plays a key role in numerous processes occurring in the Earth's crust. However, its speciation in deep and hot geological fluids remains poorly constrained. Here, we used quantitative in-situ Raman spectroscopy on natural fluid inclusions from deep sedimentary environments where thermochemical sulfate reduction (TSR) occurred to determine the sulfur speciation at temperatures representative of their entrapment conditions (100-300°C). Results unambiguously demonstrate the presence of the trisulfur ion S3 -and other polymeric S species (Sn 2-±Sn 0 ) at temperature (T) > 100°C, whereas only sulfide and sulfate were detected at 25°C.

From 200 to 300°C, sulfate and sulfide, the two dominant S species, contribute to 41 ± 9 % and 59 ± 9 % of the mean total dissolved S concentration ([Stot] = 0.25 mol/kgH2O = 0.8 wt%), respectively. The S3 -concentration accounts for 0.2 to 3 % of Stot in this T range, with a maximum recorded concentration of 2.9×10 -2 mol/kgH2O (2780 ppm) at 300°C. This observation implies that the TSR process occurs under physico-chemical conditions that enhanced the stability of S3 -and other polymeric S species. This conclusion has important consequences for the genesis of base metal sulfide deposits and sour gas fields where reduced sulfur originates from TSR.

Introduction

Sulfur speciation and concentration in deep basinal brines play a crucial role in the formation of sour (H2S-bearing) gas field [START_REF] Orr | Changes in sulfur content and isotopic-ratios of sulfur during petroleum maturationstudy of Big Horn Basin Paleozoic oils[END_REF][START_REF] Worden | H2S-producing reactions in deep carbonate gas reservoirs: Khuff Formation, Abu Dhabi[END_REF][START_REF] Machel | Bacterial and thermochemical sulfate reduction in diagenetic settingsold and new insights[END_REF][START_REF] Walters | Petroleum alteration by thermochemical sulfate reduction -A comprehensive molecular study of aromatic hydrocarbons and polar compounds[END_REF][START_REF] Cai | Sulfur isotopic compositions of individual organosulfur compounds and their genetic links in the Lower Paleozoic petroleum pools of the Tarim Basin, NW China[END_REF] and the genesis of many sedimentary-hosted ore deposits [START_REF] Heydari | Burial diagenesis and thermochemical sulfate reduction, Smackover Formation, southeastern Mississippi salt basin[END_REF][START_REF] Basuki | Sulfur isotope evidence for thermochemical reduction of dissolved sulfate in Mississippi Valley-Type zinc-lead mineralization, Bongara Area, Northern Peru[END_REF][START_REF] Thom | The role of thermochemical sulfate reduction in the origin of Mississippi Valley-Type deposits. I. Experiemental results[END_REF]. One of the most important reactions controlling the sulfur behavior in deep sedimentary environments is the abiogenic reduction of sulfate to sulfide coupled with the oxidation of hydrocarbons, which is termed thermochemical sulfate reduction (TSR). This reaction occurs at temperature above 100-140°C and is under strong kinetic control [START_REF] Kiyosu | Thermochemical reduction and sulphur isotopic behavior of sulfate by acetic-acid in the presence of native sulphur[END_REF][START_REF] Goldhaber | Kinetic controls on thermochemical sulphate reduction as a source of sedimentary H2S[END_REF][START_REF] Cross | Thermochemical sulphate reduction (TSR): experimental determination of reactions kinetics and implications of the observed reaction rates for petroleum reservoirs[END_REF][START_REF] Thom | The role of thermochemical sulfate reduction in the origin of Mississippi Valley-Type deposits. I. Experiemental results[END_REF][START_REF] Zhang | Experimental investigation on thermochemical sulphate reduction by H2S initiation[END_REF][START_REF] Truche | Experimental reduction of aqueous sulphate by hydrogen under hydrothermal conditions: implication for the nuclear waste storage[END_REF][START_REF] Yuan | Disproportionation and thermochemical sulfate reduction reactions in S-H2O-CH4 and S-D2O-CH4 systems from 200 to 340 °C at elevated pressures[END_REF].

The sulfur speciation has also a major impact on the rate and extent of TSR, because both the reactivity of dissolved sulfate compounds (e.g. SO4 2-, HSO4 -, CaSO4 0 , MgSO4 0 ) and the relative stability of intermediate valence sulfur species (e.g. thiosulfate, polysulfides, labile organic sulfur compounds) drive the electron transfer from S +6 to S 2- [START_REF] Goldstein | Thermochemical sulfate reduction: A review[END_REF][START_REF] Cai | Thermochemical sulphate reduction and the generation of hydrogen sulphide and thiols (mercaptans) in Triassic carbonate reservoirs from the Sichuan Basin, China[END_REF][START_REF] Amrani | The role of labile Sulphur compounds in thermal sulphate reduction[END_REF][START_REF] Ma | Theoretical study on the reactivity of sulfates species with hydrocarbons[END_REF][START_REF] Gvirtzman | Compound-specific sulfur isotope analysis of thiadiamondoids of oils from the Smackover Formation, USA[END_REF]. Most of our knowledge of sulfur speciation in saline brines from deep burial diagenetic environments relies on measurements made on quenched fluids from surface springs, water/oil production wells, and fluid inclusions entrapped in minerals. Sulfate and sulfide are the dominant dissolved sulfur species in these environments, with concentrations up to 0.5 mol/kgH2O [START_REF] Boiron | Detailed determination of palaeofluid chemistry: an integrated study of sulphate-volatile rich brines and aquo-carbonic fluids in quartz veins from Ouro Fino (Brazil)[END_REF][START_REF] Horita | Chemical evolution of seawater during the Phanerozoic: Implications from the record of marine evaporites[END_REF][START_REF] Worden | H2S and diagenetic pyrite in North Sea sandstones: due to TSR or organic sulphur compound cracking?[END_REF]. Other intermediate valence sulfur species such as sulfite (SO3 -), thiosulfate (S2O3 2-), polythionates (SnO6 2-), polysulfides (Sn 2-) or dissolved elemental sulfur (S 0 ) have been found in surface hydrothermal springs, and sulfide rich water well [START_REF] Boulègue | Metastable sulfur species and trace metals (Mn, Fe, Cu, Zn, Cd, Pb) in hot brines from the French Dogger[END_REF][START_REF] Takano | Correlation of volcanic activity with sulfur oxyanion speciation in a crater lake[END_REF][START_REF] Webster | Thiosulfate in surficial geothermal waters, North Island, New Zealand[END_REF][START_REF] Veldeman | Sulfur species and associated trace elements in south-west Bulgarian thermal waters[END_REF][START_REF] Takano | Surveillance of Ruapehu Crater, New Zealand, by aqueous polythionates[END_REF][START_REF] Xu | Sulfur geochemistry of hydrothermal waters in Yellowstone National Park, Wyoming, USA: I. Origin of thiosulfate in selected hot spring waters[END_REF][START_REF] Kamyshny | Speciation of polysulfides and zerovalent sulfur in sulfide-rich water wells in Southern and Central Israel[END_REF][START_REF] Nordstrom | Sulfur geochemistry of hydrothermal waters in Yellowstone National Park: IV Acid-sulfate waters[END_REF][START_REF] Kaasalainen | Sulfur speciation in natural hydrothermal waters, Iceland[END_REF].

However, their speciation and concentration may not reflect the true sulfur chemistry in deep geological fluids that is known to be very sensitive to temperature (T), pressure (P), redox, and pH conditions [START_REF] Giggenbach | Equilibrium involving polysulphide ions in aqueous sulphide solutions up to 240°C[END_REF][START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF][START_REF] Barnes | Geochemistry of Hydrothermal Ore Deposits[END_REF].

The recent discovery of the trisulfur ion S3 -in aqueous S-rich fluids from laboratory experiments using in-situ Raman spectroscopy at T > 200°C, acidic-to-neutral pH (2-6), and redox condition enabling coexistence of sulfate and sulfide has challenged our interpretation of sulfur behavior in hydrothermal fluids [START_REF] Pokrovski | The S3ion is stable in geological fluids at elevated temperatures and pressures[END_REF][START_REF] Chivers | Ubiquitous trisulfur radical anion: fundamentals and applications in materials science, electrochemistry, analytical chemistry and geochemistry[END_REF][START_REF] Jacquemet | In situ Raman spectroscopy identification of the S3ion in S-rich hydrothermal fluids from synthetic fluid inclusions[END_REF][START_REF] Truche | The role of S3ion in thermochemical sulphate reduction: Geological and geochemical implications[END_REF]Pokrovski and Dubessy, 2015). Nevertheless, little attention has been given to the sulfur speciation in natural geological fluids, and the concentration of intermediate sulfur species at relevant T-P is unknown. To our knowledge there is no study on sulfur speciation in natural fluid inclusions at elevated T.

Here, we performed quantitative in-situ analysis of sulfur speciation in well-preserved natural fluid inclusions from a geological setting where TSR occurred. We used in-situ Raman spectroscopy coupled to a heating stage to analyze samples under temperatures representative of their entrapment conditions.

Geological setting

For the purpose of this study, rock samples were selected from the Carnian evaporites (upper Triassic), named "gypse nappe" formation, outcropping in the Arc Valley (French Alps), between Modane and Sollières-l'Envers (Fig. 1). This geological formation exposes to the surface a world-class evidence of TSR occurrence in previously deeply buried evaporites, with coexistence of sulfate (anhydrite), sulfide (pyrite), and native sulfur at both macro (Fig. 2) and microscopic scale (not shown). The Carnian evaporites belong to the Triassic formation marking a major Alpine structural discontinuity between the Permian basement and the allochtonous Piedmont unit of Cretaceous age (Fig. 1, see also Debelmas et al., 1989a;Strzerzynski et al., 2012 and reference therein). They are characterized by massive anhydrite embedding dolomite layers and smaller intercalations of micaschist. Elemental sulfur occurs as vugs within the anhydrite or associated to the white well-crystallized dolomite as fracture infillings within the brownish cryptocrystalline dolomite layers. Fluorite and quartz crystals (mm to cm in size) are also found disseminated within the anhydrite or the brownish cryptocrystalline dolomite (Fig. 2b). The Carnian formation is tectonically deformed. Anhydrite shows schistosity and folding while dolomite shows boudinage levels from still recognizable layers to totally isolated blocs.

The formation has been affected by the Modane-Aussois metamorphic event that recorded an isothermal exhumation during the Paleogene. The peak of metamorphism led to maximum temperature and pressure around 350°C and 7.5 kbar [START_REF] Gabalda | Thermal structure of a fossil subduction wedge in the Western Alps[END_REF][START_REF] Lanari | Diachronous evolution of the alpine continental subduction wedge: evidence from P-T estimates in the Brianc¸ onnais Zone houillère (France -Western Alps)[END_REF][START_REF] Strzerzynski | Tectono-metamorphic evolution of the Briançonnais zone (Modane-Aussois and Southern Vanoise units, Lyon Turin transect[END_REF]. The fluid inclusions studied here are preferentially located in the anhydrite ± quartz ± fluorite veins that intersect the dolomitic "boudins", and are distributed in plane, clusters or as isolated inclusions. They do not display any deformation. These textural features strongly suggest that the fluid inclusions were trapped during the retrograde metamorphic pathway under brittle conditions, and not during the prograde pathway.

Samples and methods

Choice of the host mineral

The natural fluid inclusions studied here are hosted in quartz, fluorite or anhydrite. Quartz and fluorite minerals are present as small crystals (100 μm to 1 cm of diameter) embedded in the anhydrite matrix. Fluorite is the best host mineral to study sulfur speciation by Raman spectroscopy, because of the absence of peaks overlap between fluorite and sulfur species.

However, thermal dilatation of fluorite may slightly change the liquid-vapor ratio in the fluid inclusion [START_REF] Bodnar | Systematics of stretching of fluid inclusions I: Fluorite and sphalerite at 1 atmosphere confining pressure[END_REF] and therefore change the sulfur speciation at elevated T.

Having in mind this limitation, and despite the fact that the evolution of sulfate and sulfide concentration in quartz hosted fluid inclusions are identical within errors to those measured in fluorite, we advise the reader that our quantitative concentration measurements of the various sulfur species concentration in fluorite-hosted fluids inclusions at T above 200°C are given for indicative purpose. Quartz has a lower thermal expansion than fluorite, but it has some Raman peaks in the low wavenumber region that may hide the potential presence of polymeric sulfur species. No fluid inclusions hosted in anhydrite were retained for sulfur speciation investigations, owing to numerous peaks overlap between the host mineral and the dissolved sulfur species.

Fluid inclusions analysis

A total of 72 fluid inclusions from 3 different outcrops located in the Arc Valley (Fig. 1 and Supplementary Table S1 andS2) were analyzed by microthermometry, Raman spectrometry, and Fourier Transform Infrared spectrometry (FTIR, specific details in the Supplementary material).

The salinities and homogenization temperatures (Th) of the fluid inclusions were obtained by microthermometry and Raman spectroscopy. Raman analyses were performed at 25-300°C using a heating stage in order to study in-situ the composition of the trapped paleofluids. External standard solutions of HSO4 -, SO4 2-, and H2S(aq) were performed to establish Raman calibration coefficients allowing quantitative analysis of each of these sulfur forms. Calibration coefficients of S3 -were derived from Pokrovski and Dubessy (2015). The complete analytical procedure is described below.

Microthermometric analysis

Microthermometric measurements were performed on a Linkam THMSG600 heating-cooling stage connected to an Olympus BX51 microscope allowing the analysis of fluid inclusions above 5 µm in size. Homogenization temperatures and salinities were deduced from these measurements. The stage was calibrated using natural and synthetic fluid inclusion standards with the following phase transitions: the melting temperature of a CO2 ± Ar mixture at -56.9°C, the ice melting and the critical homogenization temperatures of pure H2O at 0.0 and 374.0°C, respectively. According to the calibration curves, temperatures of phase changes have an accuracy of about ±0.1°C for ice melting and ±1°C for total homogenization.

The composition of fluid inclusions in the H2O-NaCl-CaCl2 system was calculated using the Microsoft Excel-based calculation sheet of [START_REF] Steele-Macinnis | Numerical model to determine the composition of H2O-NaCl-CaCl2 fluid inclusions based on microthermometric and microanalytical data[END_REF]. We used the combination of the measured temperatures of the final dissolution of halite and dissociation of hydrates, hydrohalite (NaCl•2H2O) or antarcticite (CaCl2•6H2O), as input parameters.

All studied fluid inclusions homogenize into the liquid phase. Total homogenization temperatures (Th) were measured in fluid inclusions hosted in quartz. Fluorite and anhydritehosted fluid inclusions are not suitable for Th measurements because of the deformation of the crystal, and change of the internal volume of the inclusion upon heating [START_REF] Bodnar | Systematics of stretching of fluid inclusions I: Fluorite and sphalerite at 1 atmosphere confining pressure[END_REF][START_REF] Vanko | Heating and freezing experiments on aqueous fluid inclusions in anhydrite: recognition and effects of stretching and the low-temperature formation of gypsum[END_REF]. However, their Th are also given in Fig. 3 and Table S1 for indicative purpose.

The fluid inclusions liquid-vapor ratio was estimated on two-dimensional sections by measurements of the greatest area fraction for liquid and vapor phase for each fluid inclusion using ImageJ (free software at http://rsb.info.nih.gov).

Raman spectra acquisition

Raman spectra were recorded at the GeoRessources laboratory (Nancy, France) with a Labram HR spectrometer ( ® Jobin-Yvon, Horiba) coupled with a heating-stage dedicated to fluid inclusion ( ® Linkam, THMS-600) or capillary ( ® Linkam, CAP 500) studies. Raman spectra were mainly obtained using the 514 nm (green) Ar + laser excitation, with a laser power of 200 mW implying a maximal laser power at the sample around 20 mW. Some spectra were also recorded at lower laser power (0.7 to 7 mW at the sample) using filters, and compared with the full power spectra to ensure the absence of laser-induced phenomena such as sample overheating or photochemical reaction. Some spectra were also obtained with the 488 nm (blue) line of the Ar + laser for a better identification of sulfur species exhibiting Raman resonance phenomena such as S3 -, Sn 2-or Sn 0 ions [START_REF] Steudel | Elemental Sulfur and Sulfur-rich Compounds I[END_REF]. As demonstrated by Pokrovski and Dubessy (2015), the use of multiple excitation wavelengths allows more robust identification and quantification of sulfur species that exhibit Raman resonance phenomena, such as S3 -, because their Raman signal is selectively enhanced at specific laser wavelengths, whereas that of non-resonant species such as sulfate and sulfide is little affected.

The spectrometer was calibrated using the Raman stretching vibrations of a Si wafer (520.7 cm -1 at 20°C), and oxygen (1555 cm -1 ) and nitrogen (2331 cm -1 ) gas from the air. The acquisition was performed using a grating of 1800 lines/mm, a slit width of 200 µm and a confocal hole of time of 15 to 60 s per spectral window and 2 to 4 accumulations in the wavenumber interval 100 to 4200 cm -1 . The use of an Olympus 100× objective coupled to the Raman spectrometer, allowed the identification of the different phases (solid, liquid and vapor) present in the fluid inclusions and to analyze them with a 1 μm laser spot size on the sample. In addition, the focus was tuned to optimize the intensity of the water O-H stretching band between 2800 and 3700 cm - 1 . The ratio of the area of a Raman band of an aqueous solute to the OH stretching band of water is proportional to the solute concentration in the molarity scale at each temperature. Raman spectra were processed using the LabSpec 5.64.15 software (®Jobin-Yvon, Horiba). This software allows the baseline-subtraction and peak integration with a combination of Lorentzian and Gaussian functions (pseudo-Voigt function) to determine precisely the frequency position and the integrated peak area.

The samples were further heated step-by-step up to 300°C by steps of 50°C. Each analysis was performed after at least 15 minutes of down time at each step to allow the system to equilibrate. The duration of Raman measurements carried out at 100°C and 300°C was increased to 2 hours to ensure that a steady state was established. Salinities were also determined by Raman spectroscopy according to the technique developed by [START_REF] Dubessy | Determination of chlorinity in aqueous fluids using Raman spectroscopy of the stretching band of water at room temperature: Application to fluid inclusions[END_REF] and [START_REF] Caumon | Fused-silica capillary capsules (FSCCs) as reference synthetic aqueous fluid inclusions to determine chlorinity by Raman spectroscopy[END_REF], which is based on the deformation of the water stretching vibration band.

Raman spectra calibration

Sulfate (SO4 2-), hydrogen sulfate (HSO4 -), and hydrogen sulfide (H2S(aq)) concentration in the liquid phase present in the fluid inclusions was derived using calibration equations established from measurements in standard solutions (see Supplementary material for details on the calibration procedure). Each standard solution was loaded in fused silica capillary capsule (FSCC) purchased from Polymicro Technologies, LLC. This cell enables in-situ Raman measurements up to ~500°C and ~2 kbar [START_REF] Chou | A new method for synthesizing fluid inclusions in fused silica capillaries containing organic and inorganic material[END_REF][START_REF] Truche | The role of S3ion in thermochemical sulphate reduction: Geological and geochemical implications[END_REF]Pokrovski and Dubessy, 2015). It consists of round cross section silica-fused capillary tubing of 360 µm external and 100 µm internal diameters. The capillary is sealed at both ends with a micro-torch under vacuum and with frozen solution inside the capillary. The cell was heated step-by-step up to 300°C on a heating-stage ( ® CAP-500 Linkam) which ensure a very good thermal stability (±1°C) and negligible temperature gradients (<1°C over the cell length of 10-15 mm). To increase the accuracy of concentration determination, the calibration solutions were measured and processed identically to the fluid inclusions to establish calibration relationships allowing quantitative analysis of SO4 2-, HSO4 -, and H2S(aq). In addition, the effect of salinity on the calibration was evaluated at three different NaCl concentrations: 0, 3 and 5 molar. To allow quantitative comparisons of Raman peak areas in the liquid phase at different temperatures, the spectra were normalized to the O-H stretching band of water between 2800 and 3700 cm -1 . We used the linear relationship between the concentration of each species (Ci, mol/L) at given temperature and its H2O-normalized Raman peak area (Ai) given by Pokrovski and Dubessy (2015) to determine calibration coefficients of the major sulfur species:

Ci = ki(T) × Ai (1)
where ki is the calibration coefficient for sulfate, hydrogen sulfate and H2S(aq) at a given T (Fig. 4a and Supplementary Table S6). Equation 2was then applied to convert the corresponding species concentration to molality units:

mi = (Ci/ρfluid) × F (2)
where mi is the molality of sulfate, hydrogen sulfate or H2S(aq) (in mol/kgH2O), Ci, their corresponding volumetric concentration (in mol/L), ρfluid the density (in g/cm 3 ) of aqueous liquid at given T and P, and F, the molinity to molality conversion factor, F = 1000/(1000-W), where W is the mass in grams of total dissolved solutes per 1 kg of liquid fluid.

As there is no standard for S3 -, the kS3 -coefficient was calculated in the 200-300°C temperature range assuming the same temperature dependence as for the corresponding H2S coefficient (see Supplementary material for details) according to:

kS3-(T) = kS3-(500°C) × kH2S (T) / kH2S (500°C) (3)
with kS3 -(500°C) = 0.020 ± 0.002 mol/L and kH2S (500°C) = 15.8 ± 1 mol/L calculated from

Pokrovski and Dubessy (2015) (Fig. 4b; Supplementary Table S7).

The empirical Raman calibrations established on standards measured in the silica capillary are perfectly applicable to our natural fluid inclusions for the following reasons: i) there is no significant difference in refraction index between quartz (n = 1.544) and fused silica glass (n = 1.458), ii) the normalization of the Raman peaks area to the water stretching band avoids any effect of sample geometry on the signal transmission, iii) the standards and the fluid inclusions were processed identically (same configuration of the Raman spectrometer for signal acquisition), iv) our standard solutions have salinity similar to that of the fluid inclusions, so the effect of chlorinity on the shape/area of the water stretching band use to normalize the spectra is accounted for.

The calibration coefficients reported here for sulfate, sulfide and S3 -, combined with the quantification limits for the Raman peak integrated area allow quantitative analysis down to 0.02; 0.01 and 0.0001 mol/kgH2O respectively. The detection limits for these species is about 10 times lower than the quantification limits. The overall uncertainties of the reported concentrations for S-species in the fluid inclusions are between 5 and 30% of the value depending on the calibration coefficient uncertainties and the signal-to-noise ratio, as estimated by fitting multiple spectra acquired at the same T-P at steady state, or using different baseline choices and normalized peak areas.

Results

Fluid inclusions characterization

At 25°C, all studied fluid inclusions contain several phases: aqueous liquid, gas, spherules of native sulfur, and crystals of halite. All fluid inclusions display similar salinities (25 ± 4 wt% eq.

NaCl, with three times more NaCl than CaCl2) and fluid composition (Supplementary Table S1 andS2). Th values ranged from 98 to 355° C, with a quasi-gaussian distribution centered at 176°C (Fig. 3).

Fluid inclusions composition at room temperature (25±2°C) was analyzed by Raman spectroscopy for each phase present: vapor, liquid and solids (Fig. 5). The vapor phase (Fig. 5a,b) is dominated by CO2 and H2S as shown by their intense C-O and S-H stretching vibrations respectively at 1282-1386 cm -1 and 2603 cm -1 . These two gases are the by-products of TSR according to the general reaction:

SO4 2-+ CH4 + 2H + = H2S + CO2 + 2H2O (4)
Minor amount of N2 (υN-N at 2330 cm -1 ), CH4 (υC-H at 2916 cm -1 ) and H2 (υH-H at 4154 cm -1 ) are also detected. The presence of H2 in the vapor phase of the fluid inclusions implies both very limited diffusion of H2 and no or very poor post-entrapment modifications. The diffusion of H2, into and out of fluid inclusion has already been described at temperature above 450°C [START_REF] Mavrogenes | Hydrogen movement into and out of fluid inclusions in quartz: Experimental evidence and geologic implications[END_REF], but such high temperature has never been reached in our geological context. The presence of both CH4 and H2 indicates that the reducing conditions were preserved. The N-N stretching vibration of N2 presents two peaks (at 2330 cm -1 and 2327 cm -1 ).

The first one is due the presence of air along the path of the laser between the sample and the microscope. The second one, more intense and slightly shifted to lower wavenumbers, is a clear indication of the presence of N2 under pressure inside the fluid inclusion [START_REF] Wang | Effect of density on the Raman scattering of molecular fluids. I. A detailed study of the scattering polarization, intensity, frequency shift, and spectral shape in gaseous N2[END_REF].

The aqueous liquid phase is characterized by the broad O-H stretching band of water at 2800-3700 cm -1 . SO4 2-, H2S and HS -are ubiquitous dissolved sulfur species in the aqueous phase of the fluid inclusions (Fig. 5c,d) as indicated by their most intense Raman peaks at ~980 cm -1 , ~2590 cm -1 and ~2570 cm -1 , respectively. Hydrogen sulfate (HSO4 -) characterized by the S-O and S-OH stretching modes at ~1050 cm -1 and ~860 cm -1 , respectively, is not observed in the fluid inclusions at 25°C. Dissolved CO2 and, to a lesser extent, HCO3 -are also identified by their C-O stretching vibrations at 1380 and 1015 cm -1 , respectively. Another important feature observed in the liquid phase is a small peak at 875 cm -1 . This band belongs to the B-O stretching vibrations of boric acid B(OH)3 [START_REF] Servoss | Vibrational spectra of normal and isotopically labeled boric acid[END_REF]. Salinity values measured by Raman spectroscopy (25 ± 2 wt% eq. NaCl) are similar to those derived by microthermometry.

In addition, the fluid inclusions contain spherule of elemental sulfur clearly identified by the characteristic features of the S8 ring molecules at ~150 (S-S bend), ~219 (S-S bend) and ~470 (S-S stretch) cm -1 (Fig. 5e,f). In some rare occasions, tiny crystals of celestine (SrSO4), anhydrite (CaSO4) and calcite (CaCO3) are also observed in fluid inclusions hosted in fluorite only. A comparison with the RRUFF reference (RRUFF database, http://rruff.info/) is shown in Fig. 5e, f, g. The presence of these weakly soluble sulfate minerals together with the high detection limit for dissolved sulfates (0.002 mol/kgH2O; [START_REF] Dubessy | The use of the Raman microprobe mole in the determination of the electrolytes dissolved in the aqueous phase of fluid inclusions[END_REF] explain the fact that SO4 2-is not always detected in fluorite-hosted fluid inclusions.

Fourier Transform Infrared spectroscopy (FTIR) was also performed on some fluid inclusions in order to identify potential organic compounds. The typical vibrations of a CH2 functional group at 2849 and 2920 cm -1 are clearly visible on the spectra displayed in Supplementary Fig. S1. They may indicate the presence of a dissolved organic compound, but the absence of other characteristic vibrations prevents a better identification.

Sulfur speciation at elevated temperatures

Below 100°C, the Raman spectra show no changes with heating, even after 2 hours of continuous heating. At 100°C, native sulfur spherules begin to dissolve according to its disproportionation reaction under hydrothermal conditions yielding mainly sulfate and sulfide:

4S(s) + 4H2O = H + + HSO4 -+ 3H2S(aq) (5)
Simultaneously, a new Raman band appears at 532 cm -1 and increases in intensity upon heating up to 300°C in the liquid phase of fluid inclusions (Fig. 6). This main peak is associated with resonant higher-order overtones 2ν, 3ν and 4ν at 1068, 1608, 2133 cm -1 . These characteristic features correspond without ambiguity to the resonance spectrum of the trisulfur S3 -ion induced by the enhanced symmetric S-S stretching vibration [START_REF] Pokrovski | The S3ion is stable in geological fluids at elevated temperatures and pressures[END_REF]. The trisulfur ion S3 -is unambiguously identified by the main S-S symmetric bending (δ) vibration at ~240 cm -1 and stretching (ν) vibration at ~532 cm -1 , in agreement with previous work [START_REF] Pokrovski | The S3ion is stable in geological fluids at elevated temperatures and pressures[END_REF][START_REF] Chivers | Ubiquitous trisulfur radical anion: fundamentals and applications in materials science, electrochemistry, analytical chemistry and geochemistry[END_REF]Pokrovski and Dubessy, 2015). Because S3 -absorbs at ~600 nm, it exhibits a resonance Raman phenomenon with laser frequencies close to its absorption wavelength (Ar+, 514 nm). The characteristic progression of the overtones δ+ν, 2ν, 3ν, 4ν, 5ν and even 6ν (~780, 1070, 1600, 2130, 2665 and 3198 cm -1 , respectively), is clearly visible in all Raman spectra recorded at T ≥100°C (Fig. 6).

Another important Raman feature clearly visible in the liquid phase is a broad peak at 407 cm - 1 with a shoulder at 440 cm -1 , accompanied by another poorly resolved band at 800-850 cm -1 (Fig. 6a,c), which increases in intensity from 150 to 300°C. These Raman bands belong to S-S stretching vibrations [START_REF] Steudel | Elemental Sulfur and Sulfur-rich Compounds I[END_REF]. All these features are better visible with the blue laser (488 nm) because of the much lower overlapping with the ν1(S3 -) band compared to green-laser spectra and enhanced Raman signal at this laser wavelength (Supplementary Fig. S2). These

Raman features strongly suggest the presence of polysulfide ions (νs, cm -1 : S2 -~590, S2 2-~451, S3 2-~476, S4 -~384 and 439, S4 2-~482, S5 2-~432, S6 2-~373 and 453; [START_REF] Chivers | Raman spectroscopic identification of the S4Nand S3ions in blue solutions of sulfur in liquid ammonia[END_REF].

Polysulfide ions (Sn 2-) are known to promote S3 -formation through their dissociation/disproportionation [START_REF] Chivers | Ubiquitous trisulfur radical anion: fundamentals and applications in materials science, electrochemistry, analytical chemistry and geochemistry[END_REF]. Zero-valent sulfur polymeric molecules, Sn 0 , other than S8 0 (aq) may also display similar Raman characteristics (νs, cm -1 : S2 0 ~717, S3 0 ~583, S4 0 ~352 and 674; [START_REF] Chivers | Raman spectroscopic identification of the S4Nand S3ions in blue solutions of sulfur in liquid ammonia[END_REF]. Sn 0 species were also detected by Pokrovski and Dubessy (2015) in K2S2O3 ± HCl solutions at T above 200°C. However, we believe that S4 2-or S6 2-ions are the major species accounting for the 400-440 cm -1 Raman bands because these polysulfides absorb light at 440-450 nm and therefore have a pronounced Raman resonance of their S-S stretching bands with 488 nm laser excitation [START_REF] Chivers | Raman spectroscopic identification of the S4Nand S3ions in blue solutions of sulfur in liquid ammonia[END_REF].

The characteristic H-S Raman vibrations at 2400-2600 cm -1 of HSn -or H2Sn 0 species [START_REF] Dubessy | Measurements of concentration ratios of polysulfanes in mixtures solvent-sulfur-sulfanes[END_REF] are not detected in our fluid inclusions. The existence of HSn -ions in our fluid inclusions at elevated temperatures cannot be excluded; however we have neither clear spectroscopic evidence nor any thermodynamic data to support their presence. Indeed, the stability constants of HSn -ions are available only at 25°C [START_REF] Boulègue | Constantes de formation des ions polysulfurés S6 2-, S5 2et S4 2en phase aqueuse[END_REF][START_REF] Millero | The thermodynamics and kinetics of the hydrogen sulfide system in natural waters[END_REF][START_REF] Williamson | Correlation between structure and thermodynamic properties of aqueous sulfur species[END_REF]. At 25°C, the maximum concentration of HSn -ions is reached at pH ~ 7, but it remains 3 orders of magnitudes lower than that of Sn 2-ions. Polysulfides concentrations decrease under acidic conditions.

Heating-cooling cycles were performed in order to ensure that the formation of S3 -and polymeric S species was reversible (Supplementary Fig. S3). A fluid inclusion was first heated to 300°C, cooled down to 100°C and heated again to 300°C. The appearance and disappearance of S3 -and Sn 2-(±Sn 0 ) species are clearly visible along this temperature path. On re-heating the fluid inclusion to 300°C (i.e. after cooling), one can observe that the Raman peak area ratio of these species is exactly the same than the one recorded previously at the same temperature (Supplementary Fig. S3). Because the aqueous sulfur speciation is dominated by sulfate and sulfide in our fluid inclusions (see below), the reversible formation of S3 -and Sn 2-(±Sn 0 ) does not affect significantly the concentration of sulfate and sulfide. In addition, the Raman spectra acquired at T up to 300°C show no changes over 2 hours at a constant temperature. The rapid (few tens of minutes) establishment of a steady state concentration of S3 -and polymeric S species, and their reversible formation indicate that chemical equilibrium is likely to be attained for these intermediate valence sulfur species.

Sulfur species concentration in fluid inclusions

The calibration coefficients established above enable estimation of SO4 2-, H2S and S3 - concentration from normalized integrated area of their Raman bands in the fluid inclusions (Eq. 1). These concentrations are then converted in molality using Equation 2. The fluid density needed to convert molarity to molality is estimated to be about 1.19 g/cm 3 at 25°C. This estimation is based on the salinities of the fluid inclusion with the assumption that NaCl is the principal constituent in the system [START_REF] Haas | Physical properties of the coexisting phases and thermochemical properties of the H2O component in boiling NaCl solutions[END_REF][START_REF] Pitzer | Thermodynamics properties of aqueous sodium chloride solutions[END_REF]. Fluid density evolution with T was further calculated using the model provided by [START_REF] Mao | ,χ properties of binary aqueous chloride solutions up to T = 573 K and 100 MPa[END_REF].

The mean total dissolved sulfur concentration (Stot) is 0.14 ± 0.03 mol/kgH2O (i.e. 0.45 wt%) at 25°C, with sulfate and sulfide contributing to 67 ± 2 % and 33 ± 2 % of Stot, respectively in all inclusions. Upon heating above 100°C, both sulfate and sulfide concentrations increase due to elemental sulfur disproportionation. From 200 to 300°C, Stot concentration remain constant around 0.25 ± 0.13 mol/kgH2O (~0.8 wt%), with sulfate and sulfide being the predominant dissolved sulfur species, and contributing to 41 ± 9 % and 59 ± 9 % of Stot respectively. This change in the sulfate/sulfide ratio from 25°C to 200°C is in line with elemental sulfur disproportionation, which produces 3 times more sulfide than sulfate (Equation 5). The temperature behavior of sulfate and sulfide is identical within errors in all studied fluid inclusions. The established calibration coefficients for S3 -allow the calculation of its concentrations from 200 to 300°C and reasonable extrapolation down to 150°C. S3 -accounts for 0.2 to 3 % of Stot in this T range with corresponding mean concentrations increasing from (4.7 ± 2.1) ×10 -4 to (7.3 ± 5.6) ×10 -3 mol/kgH2O (Fig. 7, Table 1). The maximum measured concentration of S3 -is 2.9×10 -2 mol/kgH2O (2780 ppm) at 300°C. Polymeric S species, other than S3 -, are more difficult to quantify because of the absence of standards and important discrepancies associated to mass balance calculations, but a rough estimation can be deduced using some assumptions on the calibration coefficients values. We apply either the calibration coefficient of a resonant species (kS3-) or the mean value of the nonresonant sulfur species (estimated by extrapolation of the kH2S and the kSO4) to the normalized area of the main peaks of Sn 2-(±Sn 0 ) species at 407 cm -1 , according to Equation 1. These two calibration coefficients (Supplementary Fig. S5) provide two extreme boundaries for the Sn 2- (±Sn 0 ) concentration: the upper one is given by the non-resonant calibration coefficients and the lower one is given by S3 -calibration coefficients. This approach provides a wide range of Sn 2- (±Sn 0 ) species concentrations covering two orders of magnitude from 2.2×10 -3 to 1.2×10 -1 mol/kgH2O at 300°C (Fig. 7). Despite important uncertainty, it is noteworthy that the concentration of the polymeric species is far from being negligible.

Discussion

Representativeness and preservation of the fluid inclusions

Here, all the studied fluid inclusions display the same textural and chemical features irrespective of their host minerals: i) same irregular shape, ii) same liquid-vapor ratio (≈8% ± 4%) and chemistry, iii) same salinities, and iv) same sulfur speciation. The fluid inclusions contain H2 and CH4, demonstrating that the reducing conditions have been preserved. This observation does not contradict with the presence of sulfate in the geological fluid because its reduction is under strong kinetic control, and because it is constantly supplied by sulfate minerals dissolution, most notably anhydrite. These characteristics together with the absence of secondary inclusion halo provide strong evidences for very limited post-entrapment modifications [START_REF] Bodnar | Reequilibration of fluid inclusions: Fluid inclusions: Analysis and interpretation[END_REF]. The relatively large range of Th contrasts with the narrow range of measured salinities. It may indicate different entrapment temperature of a single fluid type during the retrograde metamorphism phase with the lowest T as the limit of fluid entrapment and the highest one the peak of metamorphism conditions around 350°C (Strzersynski et al., 2012). We therefore assume that we analyzed the fluid composition trapped during the exhumation of the evaporites in a closed system (no fluid mixing, and degassing). H2S migration from deeper reservoirs is highly improbable in the present case, because the fluid inclusions located in the white quartzite from the lower Trias, which is stratigraphically below the carnian evaporites [START_REF] Strzerzynski | Tectono-metamorphic evolution of the Briançonnais zone (Modane-Aussois and Southern Vanoise units, Lyon Turin transect[END_REF], are free of H2S (Supplementary Table S2).

Sulfur speciation investigated here at T above 100°C after few hours of equilibration time is probably far from sulfate-sulfide equilibrium for the two following reasons: i) the reducing conditions imposed by the presence of both H2 and CH4 in the fluid inclusions imply that H2S is the thermodynamically predicted stable sulfur redox end member, and that the TSR process was not completed, and ii) more than 10 years are required to attain 90% of equilibrium between sulfate and sulfide in aqueous solution at 200°C, neutral pH condition and ΣS = 0.1 mole/kgH2O [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF]. By contrast, a local equilibrium between S-Sn 0 -S3 -and the dominant sulfate and sulfide forms may be achieved rapidly (within minutes) as demonstrated here by the reversible formation (Supplementary Fig. S3) and the steady state concentration of these sulfur species at T > 200°C in our fluid inclusion. In addition, it has been experimentally demonstrated that S3 -is formed upon heating sulfate-sulfide mixtures at T ≥ 100°C within few tens of minutes [START_REF] Truche | The role of S3ion in thermochemical sulphate reduction: Geological and geochemical implications[END_REF], without any elemental sulfur or thiosulfate in the system initially. The same conclusion has been reached by Pokrovski and Dubessy (2015) at T ≥ 300°C. In this study, S3 - has been also observed in some natural fluid inclusions containing only sulfates and sulfides at room temperature and no elemental sulfur (Supplementary Table S1). These independent observations imply that the initial disproportionation of elemental sulfur or thiosulfate is not mandatory for S3 -and polysulfides to appear and, more importantly, that sulfate cannot be considered as a non-reactive species at the time scale of these experiments, even at temperatures as low as 100°C. Thus, these stable intermediate valence sulfur species will form and remain in solution as long as sulfate and sulfide coexist, and their concentrations can be predicted by thermodynamic modeling (see section 5.2. below).

Thermodynamic calculations

Equilibrium concentrations of sulfur species in the fluid phase were modeled using the Phreeqc software [START_REF] Parkhurst | User's guide to PHREEQC (version 2)-A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF] and an updated version of the llnl database [START_REF] Johnson | SUPCRT92: A software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1 to 5000 bar and to 0 to 1000[END_REF]. The stability constants for S3 -, S8 0 and Sn 2-were updated using the HKF equation of state and HKF parameters estimated for these species [START_REF] Johnson | SUPCRT92: A software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1 to 5000 bar and to 0 to 1000[END_REF][START_REF] Kamyshny | Equilibrium distribution of polysulfide ions in aqueous solutions at different temperatures by rapid single phase derivatization[END_REF]Pokrovski and Dubessy, 2015 and updated databases at http://geopig.asu.edu/?q=tools; specific details in the Supplementary materials). In the first round of modeling (Fig. 8a), sulfate-sulfide concentrations correspond to our Raman measurements at room temperature (0.09 mol/kgH2O and 0.05 mol/kgH2O, respectively), and the initial amount of elemental sulfur in the system (0.11 mole S) is proportional to the one calculated in the fluid inclusions based on geometrical considerations. The redox potential is imposed by the sulfatesulfide coexistence. The fluid acidity is buffered by fluid equilibrium with calcite and 10 bars of P(CO2) that imposed a pH around 5 at T >100°C. Such a pH value is in agreement with the speciation of sulfate (only SO4 2-), sulfide (H2S and minor HS -) and carbonate (CO2 and minor HCO3 -) observed in the fluid inclusions at elevated T (Supplementary Fig. S8). We advise the reader that this pH value is close to neutrality at T >100°C, because of the strong decrease of the dissociation constant of water (the neutrality decrease from pH = 6 to pH = 5.5 with temperature increasing from 100 to 250°C). This range of pH is compatible with the very low HSO4 - concentration observed in natural sedimentary formation waters (a typical range of pH is between 6.5 and 8.5 at 25°C; [START_REF] Collins | Geochemistry of oilfield waters[END_REF]. The salinity is fixed at 3.3 mol/kgH2O NaCl and 1.6 mol/kgH2O CaCl2 to mimic the salinity of our fluid inclusions. The extended Debye-Huckel equation for activity coefficients of NaCl-and CaCl2-dominated electrolytes can be applied to such high ionic strengths with reasonable accuracy in the range of temperature explored in this study [START_REF] Helgeson | Theoretical prediction of the thermodynamic behavior of aqueous electolytes at high pressures and temperatures: IV. Calculation of activity coefficients, osmotic coefficients, and apparent molal and standard and relative partial molal properties to 600°C and 5kb[END_REF]. Simulations performed at lower ionic strength (i.e. 1 mol/kgH2O) provide very similar results. Over the entire T range (25-300°C) the dominant species are sulfates and sulfides. At T > 100°C, S3 -is the third most abundant sulfur species predicted in the system with concentrations rising up to 1.37×10 -3 mol/kgH2O at 200-300°C. These thermodynamic predictions are in perfect agreement with our quantitative measurements using in-situ Raman spectroscopy (Table 1 andS10). Concerning other polymeric sulfur species, our preliminary Raman estimations, based on Raman calibration coefficients assumption, give Sn 2- (±Sn 0 ) concentrations (10 -3 -10 -2 m, Fig. 7) far above those predicted thermodynamically (10 -5 -10 -4 m, Fig. 8) and much higher than that of S8(aq). Such conclusions imply that Sn 2-and Sn 0 species must not be ignored in natural fluids and that further studies are needed to determine properly their thermodynamic stability at high T-P.

In a second round of modeling (Fig. 8b,c,d), Stot was fixed at a given value without any specification on the sulfate-sulfide concentrations (elemental sulfur solubility providing the upper limit for Stot concentration in Fig. 8b). The sulfur speciation was then modeled as a function of three different physical-chemical parameters (Stot, f(O2) and pH). The choice of f(O2) value buffered by Hematite-Magnetite (HM) equilibrium is in line with expectation from typical hydrocarbon reservoirs in nature [START_REF] Seewald | Aqueous geochemistry of low molecular weight hydrocarbons at elevated temperatures and pressures: Constraints from mineral buffered laboratory experiments[END_REF]Richard et al., 2005). Note that Hematite-Magnetite-Pyrite assemblage, also relevant in the context of deep sedimentary settings gives the same f(O2) as the HM assemblage, but also control the f(H2S). In our case, the f(H2S) is not buffered, because iron is clearly limiting.

Whatever the chosen conditions in the sedimentary studied domain, sulfate and sulfide are always the dominant S species. However, S3 -may represent a significant contribution to the sulfur budget if the following conditions are satisfied: 1) total sulfur concentration above 0.1 m, 2) T > 150°C, 3) redox potential or f(O2) enabling sulfate-sulfide coexistence, i.e. close to the hematite-magnetite buffer, and 4) slightly acidic to neutral pH. Such a conclusion has also been reached for temperatures higher than 200°C by Pokrovski and Dubessy (2015). Figure 8c andd show that when concentration of sulfates is much higher than that of sulfides, S3 -and other intermediate valence sulfur species have concentrations lower than 10 -6 mol/kgH2O. The same scenario is observed, albeit less pronounced, when sulfides concentration is much higher than that of sulfates. However, in this latter case, S3 -concentration is one or two order of magnitude higher than those of the other intermediate valence sulfur species.

Note that Sn 2-and Sn 0 species probably contribute to the sulfur budget in a similar, or even more important, proportion as S3 -in the range 100-300°C, but their thermodynamic properties are currently poorly constrained at elevated T or unknown and require further studies.

Geochemical implications

The characteristic blue color of the S3 -chromophore ion and its UV-visible and Raman spectral patterns in aqueous solutions has already been noticed in numerous experimental studies involving sulfate and sulfide mixtures at T above 100°C [START_REF] Giggenbach | On the nature of the blue solutions of sulfur[END_REF][START_REF] Uyama | Sulfur isotope exchange reactions in the aqueous system: thiosulfate-sulfide-sulfate at hydrothermal temperature[END_REF][START_REF] Pokrovski | The S3ion is stable in geological fluids at elevated temperatures and pressures[END_REF][START_REF] Jacquemet | In situ Raman spectroscopy identification of the S3ion in S-rich hydrothermal fluids from synthetic fluid inclusions[END_REF]. However, the discovery of both S3 - and other polymeric S species at the millimolar concentration level at T as low as 100°C in natural fluid inclusions associated with a sedimentary formation where TSR occurred is a new finding. These new data from natural samples corroborate the experimental discovery that S3 -is a major stable intermediate valence S species involved in the reaction path of abiogenic sulfate reduction [START_REF] Truche | The role of S3ion in thermochemical sulphate reduction: Geological and geochemical implications[END_REF], and support the fact that disproportionation reaction of sulfur is a key step for TSR [START_REF] Yuan | Disproportionation and thermochemical sulfate reduction reactions in S-H2O-CH4 and S-D2O-CH4 systems from 200 to 340 °C at elevated pressures[END_REF]. The onset temperature of TSR in nature around 100-140°C corresponds remarkably well to the rise of S3 -and Sn 0 concentrations (Fig. 7 and Fig. 8a).

Therefore, S3 -is an important reactive species in the TSR process for the following reasons: i)

the radical nature makes it very reactive, ii) the high concentration compared to the other potential intermediate valence sulfur species taking part in the TSR process increases the contact probability with the reducing agent, and iii) the TSR process itself results from an interaction between S3 -and the electron donor that shift the equilibrium between sulfate and sulfide [START_REF] Truche | The role of S3ion in thermochemical sulphate reduction: Geological and geochemical implications[END_REF].

This study opens up new perspectives on TSR isotopic record [START_REF] Watanabe | Anomalous fractionations of sulfur isotopes during thermochemical sulfate reduction[END_REF][START_REF] Oduro | Evidence of magnetic isotope effects during thermochemical sulfate reduction[END_REF][START_REF] Gvirtzman | Compound-specific sulfur isotope analysis of thiadiamondoids of oils from the Smackover Formation, USA[END_REF][START_REF] Cai | Sulfur isotopic compositions of individual organosulfur compounds and their genetic links in the Lower Paleozoic petroleum pools of the Tarim Basin, NW China[END_REF][START_REF] Meshoulam | Study of thermochemical sulfate reduction mechanism using compound specific sulfur isotope analysis[END_REF]. Indeed, there are numerous similarities between the reaction mechanisms of sulfate-sulfide isotope exchange and the multistep change in oxidative state of sulfur during the TSR process [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF][START_REF] Goldstein | Thermochemical sulfate reduction: A review[END_REF]. The kinetics of both reactions are strongly dependent upon temperature, pH and sulfate-sulfide concentrations, because these parameters play a primary role on the speciation and concentration of the intermediate valence sulfur species, which act as a bridge for electron transfer between sulfate and sulfide. We suggest that the rapid formation of S3 -, Sn 2-and Sn 0 species is a stage allowing TSR and sulfur isotope exchange to occur, and not thiosulfate, or polythionates as believed previously (e.g., [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF]. The rapid decrease of S3 -and Sn 2-concentration at pH above 6 at 200°C (Fig. 8d; [START_REF] Chu | Kinetics of sulfur isotope exchange between aqueous sulfide and thiosulfate involving intra-and intermolecular reactions at hydrothermal conditions[END_REF] reflect well the decrease of the reaction rate of sulfate-sulfide isotope exchange and TSR under alkaline condition. Under strongly acidic condition, it is probable that Sn 0 together with sulfate speciation (dominated by HSO4 -a non-symmetric, so more reactive species) and the abundance of proton (TSR imply a net consumption of H + , see Equation 4) explain the increase of the TSR reaction rate [START_REF] Truche | Experimental reduction of aqueous sulphate by hydrogen under hydrothermal conditions: implication for the nuclear waste storage[END_REF]Pokrovski and Dubessy, 2015). These intermediate valence sulfur species may also facilitate electron transfer between carbon species and enhance the rates of reaction between hydrocarbons, methane and CO2 [START_REF] Seewald | Organic-inorganic interactions in petroleum-producing sedimentary basins[END_REF].

Despite its complexity, TSR is a common reaction in numerous geological settings and represents a key geochemical process in many environments where mass transfer and chemical fractionation are involved. The high concentrations of these intermediate valence S species at T >100°C place significant constraints on the formation of sour gas fields [START_REF] Machel | Bacterial and thermochemical sulfate reduction in diagenetic settingsold and new insights[END_REF][START_REF] Cai | Thermochemical sulphate reduction and the generation of hydrogen sulphide and thiols (mercaptans) in Triassic carbonate reservoirs from the Sichuan Basin, China[END_REF] and sulfide ore deposits (e.g. Mississippi Valley-type deposits, Volcanogenic-Massive Sulfide deposits) where reduced sulfur originates from TSR [START_REF] Huston | Metal leaching and inorganic sulfate reduction in volcanic-hosted massive sulfide minerals systems: Evidence from the paleo-Archean Panorama district[END_REF][START_REF] Thom | The role of thermochemical sulfate reduction in the origin of Mississippi Valley-Type deposits. I. Experiemental results[END_REF]. In geologic conditions, bacterial sulfate reduction at the earliest stage of diagenesis, or the thermal decomposition of sulfur bearing organic compounds, or fluid mixing with sulfide-rich solution, or elemental sulfur disproportionation may provide the necessary reduced sulfur to initiate TSR at T >100°C (Fig. 9; [START_REF] Machel | Bacterial and thermochemical sulfate reduction in diagenetic settingsold and new insights[END_REF]. The TSR process itself may occur under physico-chemical conditions that enhance the stability and concentration of S3 -and Sn -2 (±Sn 0 ) species: high sulfate-sulfide concentration, T >100°C, and circum-neutral pH conditions. The direct effect of S3 -and polymeric S species on base metal solubility (e.g. Pb, Zn, Cu) were only broadly estimated by Pokrovski et al. (2015) but remains to be more evaluated.

The presence of non-negligible concentrations of S3 -and polymeric species in deep sedimentary brines may also have important consequence for petroleum alteration and organosulfur compounds (OSCs) formation during the TSR process [START_REF] Seewald | Aqueous geochemistry of low molecular weight hydrocarbons at elevated temperatures and pressures: Constraints from mineral buffered laboratory experiments[END_REF]2003;[START_REF] Amrani | Organosulfur compounds: molecular and isotopic evolution from biota to oil and gas[END_REF]. There is currently a significant research effort to document the effect of TSR on non-volatile high molecular weight aromatic and polar organic species (e.g. [START_REF] Walters | Petroleum alteration by thermochemical sulfate reduction -A comprehensive molecular study of aromatic hydrocarbons and polar compounds[END_REF][START_REF] Meshoulam | Study of thermochemical sulfate reduction mechanism using compound specific sulfur isotope analysis[END_REF]. It has been suggested that H2S reacts with hydrocarbons to form OSCs (e.g., thiols, sulfides, thiophenes, and condensed thiophenes) that in turn catalyze TSR [START_REF] Amrani | The role of labile Sulphur compounds in thermal sulphate reduction[END_REF][START_REF] Zhang | Experimental investigation on thermochemical sulphate reduction by H2S initiation[END_REF]. Intermediate oxidation-state S species such as elemental S, polysulfides, sulfites or thiosulfates have been also proposed as possible sources for OSCs formation during TSR [START_REF] Goldstein | Thermochemical sulfate reduction: A review[END_REF][START_REF] Lewan | Sulphur-radical control on petroleum formation rates[END_REF]. However, elemental S and thiosulfates are poor nucleophiles and break down into sulfate and sulfide at T >100°C, which make them unfavorable candidate for the reaction with organic matter under deep sedimentary conditions. By contrast, the strong nucleophile character of polysulfides and the S3 - ion [START_REF] Chivers | Ubiquitous trisulfur radical anion: fundamentals and applications in materials science, electrochemistry, analytical chemistry and geochemistry[END_REF], suggests that these species are more prone to react with hydrocarbons than H2S or elemental S. Sulfur isotope fractionation associated with the formation of OSCs is a potential tracer for the occurrence and extent of TSR [START_REF] Amrani | Organosulfur compounds: molecular and isotopic evolution from biota to oil and gas[END_REF][START_REF] Gvirtzman | Compound-specific sulfur isotope analysis of thiadiamondoids of oils from the Smackover Formation, USA[END_REF][START_REF] Cai | Sulfur isotopic compositions of individual organosulfur compounds and their genetic links in the Lower Paleozoic petroleum pools of the Tarim Basin, NW China[END_REF][START_REF] Meshoulam | Study of thermochemical sulfate reduction mechanism using compound specific sulfur isotope analysis[END_REF]. However, important mechanistic details about the overall TSR process are still missing and prevent full explanation of the sulfur isotope records. We suggest that polymeric sulfur species and, in particular, the S3 -ions should be considered in the sulfur isotopic fractionation model to bring back together laboratory and field observations.

Conclusions and perspectives

The main conclusions from this study are:

1. We reveal for the first time the formation of the trisulfur S3 -ion and other polymeric S species (Sn 2-±Sn 0 ) at T >100°C in natural fluids from typical deeply buried sedimentary environment where TSR occurred.

2. The concentration of S3 -ion can reach 2800 ppm at 300°C in fluid inclusions containing sulfate-sulfide concentration above 0.1 mol/kgH2O.

3. This work confirms the previous findings that S3 -is a major stable intermediate valence S species involved in the reaction path of TSR. The onset temperature of TSR in nature around 100-140°C corresponds remarkably well to the rise of S3 -and other polymeric S species concentrations in the fluid inclusions.

4. The TSR process itself occurs under physico-chemical conditions that enhance the stability and concentration of S3 -and Sn 2-(±Sn 0 ) species: high sulfate-sulfide concentration, T ≥100°C, and circum-neutral pH conditions.

5. This study opens up new perspectives on TSR isotopic record and into the S-chain radical reactions involved in organic-inorganic interactions, where sulfur speciation play a key role.

The discovery of the trisulfur S3 -ion and other polymeric S species, in natural geological fluid at T ≥100°C, may also encourage new investigations on sulfur speciation in natural geological fluids associated with metamorphism, mid-oceanic ridge hydrothermal fluid circulation and magmatic/porphyry settings where sulfate and sulfide often coexist. So. 10 t1 25 --0.0020 1.06×10 -1 0.0009 4.80×10 -2 200 0.0057 6.58×10 -4 0.0039 1.55×10 -1 0.0009 7.72×10 -2 250 0.0097 1.05×10 -3 0.0039 1.51×10 -1 0.0013 1.14×10 -1 300 0.0312 2.51×10 -3 0.0053 1.96×10 -1 0.0024 1.55×10 -1 Quartz So. 10 t3 25 --0.0015 7.64×10 -2 0.0007 3.53×10 -2 200 0.0027 3.10×10 -4 0.0019 7.63×10 -2 0.0012 1.06×10 -1 250 0.0125 1.36×10 -3 0.0018 7.04×10 -2 0.0021 1.80×10 -1 300 0.0199 1.61×10 -3 0.0008 2.87×10 -2 0.0021 1.32×10 -1 Quartz So. 10 t4 25 --0.0020 1.01×10 -1 0.0008 4.24×10 -2 200 0.0028 2.91×10 -4 0.0031 1.11×10 -1 0.0015 1.25×10 -1 250 0.0112 1.05×10 -3 0.0038 1.26×10 -1 0.0016 1.18×10 -1 300 0.0068 4.49×10 -4 0.0021 6.53×10 -2 0.0007 3.75×10 -2 Quartz So. 10 t5 25 --0.0013 6.81×10 -2 0.0009 4.67×10 -2 200 --0.0020 8.09×10 -2 0.0027 2.47×10 -1 250 0.0142 1.55×10 -3 0.0011 4.43×10 -2 0.0014 1.20×10 -1 300 0.0068 5.47×10 -4 0.0008 3.01×10 -2 0.0021 1.37×10 -1 Quartz So. 10 t6 25 --0.0020 1.06×10 -1 0.0010 5.11×10 -2 200 0.0030 3.46×10 -4 0.0019 7.79×10 -2 0.0012 1.06×10 -1 250 0.0027 2.94×10 -4 0.0007 2.75×10 -2 0.0015 1.33×10 -1 300 0.0051 4.08×10 -4 0.0020 7.60×10 -2 0.0013 8.37×10 -2 Quartz So. 2.4 t1 200 0.0069 7.12×10 -4 --0.0111 8.98×10 -1 250 0.1047 1.09×10 -2 --0.0110 9.05×10 -1 300 0.3842 2.91×10 -2 --0.0148 9.05×10 -1 Fluorite So. 10.1 t2 25 --0.0025 1.32×10 -1 0.0017 8.40×10 -2 200 --0.0018 7.37×10 -2 0.0019 1.69×10 -1 250 0.0073 7.87×10 -4 0.0029 1.14×10 -1 0.0017 1.48×10 -1 300 0.0391 3.32×10 -3 0.0056 2.58×10 -1 0.0050 3.10×10 -1 Fluorite So. 10.1 t1 25 --0.0018 9.26×10 -2 0.0010 5.09×10 -2 200 0.0043 4.97×10 -4 0.0024 9.74×10 -2 0.0014 1.31×10 -1 200 0.0040 4.63×10 -4 0.0015 6.09×10 -2 0.0026 2.32×10 -1 Fluorite So. 10.1 t3 250 0.0091 9.92×10 -4 0.0013 4.93×10 -2 0.0010 8.68×10 -2 300 0.0311 2.51×10 -3 0.0033 1.22×10 -1 0.0015 9.64×10 -2 Fluorite So. 10.1 t5 25 --0.0021 1.07×10 -1 0.0006 3.30×10 -2 Fluorite So. 10.1 t6 25 --0.0014 7.31×10 -2 0.0007 3.32×10 -2 863

FIGURE CAPTIONS

Fig. 1 .

 1 Fig. 1. Simplified geological map of the Arc Valley (France) with the sampling locations

Fig. 2 .

 2 Fig. 2. (a) Typical outcrops of the sampled Carnian evaporite from the Arc Valley (France)

Fig. 3 .

 3 Fig. 3. Microthermometry results of fluid inclusions from the Arc Valley (France). (a) Histogram

Fig. 4 .

 4 Fig. 4. Raman calibration coefficients (ki) for the 514 nm laser excitation for sulfur species as

Fig. 5 .

 5 Fig. 5. Raman spectra of the several phases in the fluid inclusions at room temperature. (a)

Fig. 6 .

 6 Fig. 6. Raman spectra of the aqueous phase of fluid inclusions hosted in fluorite (a) and quartz (b

Fig. 7 .

 7 Fig. 7. Temperature evolution of sulfur speciation in natural fluid inclusions from the Carnian evaporites formation (French Alps). At high temperature, trisulfur radical ion S3 -(blue circles) and Sn 2-±Sn 0 (estimated in grey shaded area) attain significant concentrations. During cooling,

Fig. 8 .

 8 Fig. 8. Thermodynamic modeling of sulfur speciation as a function of (a) temperature at pH ~ 5

Fig. 9 .

 9 Fig. 9. Conceptual model of TSR and associated processes in deep sedimentary settings

  Figure 1

Table 1 862

 1

	Host mineral	Fluid Inclusion	T (°C)	A S3 -/ A H2O	[S3 -] (mol/kg H2O)	A SO4 2-/ A H2O	[SO4 2-] (mol/kg H2O)	A H2S/ A H2O	[H2S] (mol/kg H2O)
	Quartz

Acknowledgements

This work was funded by LABEX ANR-10-LABX-21-01 Ressources21 (Strategic metal resources of the 21 st Century) and the French Ministry of Higher Education and Research. The authors are extremely grateful to M.C. Jodin-Caumon and P. Robert for technical assistance during Raman spectroscopic analysis and O. Barrès during Infrared spectroscopic analysis. The paper benefited greatly from the review provided by G. Pokrovski, H. Ohmoto and one anonymous reviewer. We thank M. Böttcher for editorial support.

Supplementary information is available in the attached file.