Maria A Kokh

Nelly Assayag

Stephanie Mounic

Pierre Cartigny

Andrey Gurenko

Gleb S Pokrovski
email: gleb.pokrovski@get.omp.eu

Multiple sulfur isotope fractionation in hydrothermal systems in the presence of radical ions and molecular sulfur

Keywords: Trisulfur radical ion, disulfur radical ion, molecular sulfur, hydrothermal fluid, experiment, sulfur isotopes, mass dependent fractionation (MDF), mass independent fractionation (MIF)

This study is aimed to evaluate the role played by the sulfur radical ions (S 3 •-and S 2 •-) and molecular sulfur (S 0 ) on sulfur isotope fractionation and to investigate if these species may leave an isotope fingerprint in hydrothermal systems. For this purpose, we combined i) experiments using a hydrothermal reactor with aqueous S 3 •-(S 2 •-)-S 0 -sulfate-sulfide fluids and pyrite across a wide range of temperatures (300-450°C), pressures (300-800 bar), fluid acidity (4<pH<8) and with elevated total sulfur concentrations (0.1-1.0 mol/kg fluid) favorable for formation of those polymeric sulfur species, ii) precise quadruple S isotope analyses of the different S-bearing aqueous species in sampled fluids and in-situ precipitated pyrite, and iii) thermodynamic modeling of sulfur aqueous speciation and solubility. Our results quantitatively confirm both equilibrium and kinetic SO 4 -H 2 S and pyrite-H 2 S mass dependent fractionation (MDF) factors previously established using extensive experimental and natural data from more dilute fluids in which polymeric sulfur species are negligible. MDF signatures of S 0 measured in the sampled fluids of this study reveal different S 0forming pathways such as i) breakdown on cooling of S 3 •-(and S 2 •-) and other chain-like S 0 polymers only stable at high temperature and being isotopically identical to H 2 S; ii) cyclooctasulfur (S 8 0 , liquid or solid) precipitating by recombination of sulfate and sulfide and/or by exchange with polysulfide dianions (S n 2-) on cooling and being slightly 34 S-enriched compared to H 2 S (by ~2 ‰ of  34 S); and iii) a different type of S 0 resulting from thiosulfate irreversible breakdown and being highly 34 S-depleted (by ~12 ‰) relative to H 2 S.

Our data do not show any significant mass independent fractionation (MIF) of 33 S and 36 S, with  33 S and  36 S values of any S aqueous species and pyrite being within ±0.1 ‰ and ±1.0 ‰, respectively. Therefore, under the investigated experimental conditions, the radical S 3 •-ion is unlikely to generate significant MIF in the hydrothermal fluid phase and in pyrite and native sulfur precipitated therefrom. Our study supports the existing interpretations of small  33 S and  36 S variations between sulfide/sulfate-bearing fluid and pyrite as MDF in terms of reaction kinetics, different reaction pathways, and mass conservation effects such as mixing of S reservoirs or Rayleigh distillation. Our data extend, across a wider range of sulfur concentration and chemical speciation, the existing multiple S isotopes models that exploit such variations as a complement to the traditional  34 S tracer to monitor the approach to equilibrium and evolution of hydrothermal fluids.

Highlights:

 Isotope signatures of sulfur species and pyrite have been studied in hydrothermal fluids.

 MDF equilibrium and kinetic SO 4 -H 2 S and pyrite-H 2 S factors are quantified.

 No MIF anomalies are detected in the presence of sulfur radical ions.

 Isotope signature of molecular sulfur fingerprints the different mechanisms of S 0 formation.  Several environments offer potential for MIF generation in fluid-mineral systems.

INTRODUCTION

Fractionation among the four stable isotopes of sulfur ( 32 S, 33 S, 34 S, and 36 S) has been used for tracing various geological processes since 1960's (e.g., [START_REF] Thode | Sulphur isotope geochemistry[END_REF][START_REF] Hulston | Variations in S 33 , S 34 and S 36 contents and their relation to chemical and nuclear effects[END_REF]. In most chemical and biological reactions, the sulfur isotope ratios obey mass-dependent fractionations (MDF); however, significant mass-independent fractionation (MIF) anomalies ( 33 S >0.2‰) 1 were identified in pyrite and barite from Archean sedimentary rocks likely caused by SO 2 photolysis in the atmosphere (e.g.,  33 S ≈ -4 to +14 ‰; [START_REF] Farquhar | Atmospheric influence of Earth's earliest sulfur cycle[END_REF][START_REF] Johnston | Multiple sulfur isotopes and the evolution of Earth's surface sulfur cycle[END_REF][START_REF] Philippot | Variations in atmosphere sulphur chemistry on early Erath linked to volcanic activity[END_REF], and also in sulfide minerals from a number of younger magmatic, hydrothermal and metamorphic rocks (e.g., [START_REF] Farquhar | Mass-independent sulfur of inclusions in diamond and sulfur recycling on early Earth[END_REF][START_REF] Bekker | Atmospheric sulfur in Archean komatiite-hosted nickel deposits[END_REF][START_REF] Thomassot | Metasomatic diamond growth: A multi-isotope study ( 13 C, 15 N, 33 S, 34 S) of sulphide inclusions and their host diamonds from Jwaneng (Botswana)[END_REF][START_REF] Cabral | Anomalous sulphur isotopes in plume lavas reveal deep mantle storage of Archaean crust[END_REF][START_REF] Young | Reactions of hydrothermal solutions with organic matter in Paleoproterozoic black shales at Talvivaara, Finland: Evidence from multiple sulfur isotopes[END_REF][START_REF] Delavault | Sulfur and lead evidence of relic Archean sediments in the Pitcairn mantle plume[END_REF][START_REF] Ripley | A review of the application of multiple S isotopes to magmatic Ni-Cu-PGE deposits and significance of spatially variable  33 S values[END_REF]LaFlamme et al., 2018a,b;[START_REF] Smit | Sulfur isotopes in diamonds reveal differences in continent construction[END_REF], which were interpreted as the reworking/recycling of Archean supracrustal rocks. These anomalies contrast with very small  33 S values, which are likely generated through MDF processes in low-temperature biological and inorganic sulfur redox reactions in solution or at the mineral surfaces (typically <0.15‰, [START_REF] Farquhar | Multiple sulfur isotopes and the evolution of the atmosphere[END_REF][START_REF] Ono | Mass-dependent fractionation of quadruple stable sulfur isotope system as a new tracer of sulfur biogeochemical cycle[END_REF][START_REF] Ono | S-33 constraints on the seawater sulfate contribution in modern seafloor hydrothermal vent sulfides[END_REF][START_REF] Farquhar | Isotopic evidence for Mesoarchaean anoxia and changing atmospheric sulphur chemistry[END_REF][START_REF] Johnston | Multiple sulfur isotopes and the evolution of Earth's surface sulfur cycle[END_REF]. These MDF processes are quite well understood and result from mass-conservation effects (mostly mixing and Rayleigh distillation). Earlier theoretical work using quantum-chemistry modeling suggested that MIF could be generated by heterogeneous reactions [START_REF] Lasaga | Anomalous fractionation of sulfur isotopes during heterogeneous reactions[END_REF], which was, however, not supported by a subsequent study [START_REF] Balan | Theoretical investigation of the anomalous equilibrium fractionation of multiple sulfur isotopes during adsorption[END_REF].

In most hydrothermal fluids studied so far in nature (e.g., [START_REF] Kamyshny | Multiple sulfur isotopes fractionations associated with abiotic sulfur transformations in Yellowstone National Park geothermal springs[END_REF]Stefansson et al., 2015;[START_REF] Mcdermott | Identification of sulfur sources and isotopic equilibria in submarine hot-springs using multiple sulfur isotopes[END_REF] and laboratory (e.g., [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF][START_REF] Syverson | Multiple sulfur isotope fractionation and mass transfer processes during pyrite precipitation and recrystallization: An experimental study at 300 and 350°C[END_REF][START_REF] Meshoulam | Study of thermochemical sulfate reduction mechanism using compound specific sulfur isotope analysis[END_REF], relevant to active seafloor or surface geothermal systems and different shallowcrust hydrothermal deposits, sulfur isotope fractionation between the different inorganic sulfur species such as sulfate, sulfide, native sulfur, thiosulfate, and some organic thiol species has been interpreted by both equilibrium and kinetic MDF. This type of fractionation can only generate small deviations of 33 S isotope abundance from the classical MDF dependence ( 33 S <0.05 ‰). In contrast, large  33 S anomalies (from -1.1 to +13.0‰) were reported in thermochemical sulfate reduction (TSR) reactions in hydrothermal experiments in the presence of amino-acids [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]. TSR phenomena were also invoked to explain the  33 S record in Paleoproterozoic black shales at Talvivarra, Finland (-0.6< 33 S<1.3%, [START_REF] Young | Reactions of hydrothermal solutions with organic matter in Paleoproterozoic black shales at Talvivaara, Finland: Evidence from multiple sulfur isotopes[END_REF].

In the light of the large variety of sulfur isotope fractionation patterns exemplified above, detailed knowledge of sulfur chemical speciation in the fluid phase is required for understanding sulfur isotope 1 Variations of S isotope ratios (normalized to the most abundant 32 S isotope) are conventionally expressed in the -notation relative to the V-CDT standard (Vienna-Cañon Diablo Troilite meteorite; [START_REF] Ding | Calibrated sulfur isotope abundance ratios of three IAEA sulfur isotope reference materials and V-CDT with a reassessment of the atomic weight of sulfur[END_REF]:  3x S (in ‰) = [( 3x S/ 32 S) sample /( 3x S/ 32 S) V-CDT -1]×1000, where x denotes 3, 4 or 6 for 33 S, 34 S, and 36 S, respectively. MDF means that isotope ratios are proportional to the mass difference between isotopes yielding the relationships:  33 S ≈ (0.515±0.005)× 34 S, and  36 S ≈ (1.89±0.02)× 34 S (e.g., [START_REF] Urey | The thermodynamic properties of isotopic substances[END_REF]. MDF refers to isotope compositions deviating from this mass scaling law (i.e.  33 S ≈  33 S -0.515× 34 S; see section 2.5 for details and rigorous equations). fractionation, both MDF and MIF, in natural processes involving fluids. The major chemical forms of sulfur are known to be sulfate and sulfide (and sulfur dioxide and hydrogen sulfide in gas phase), which have been extensively studied over the last decades. However, recent discoveries of the sulfur radical ions S 3 •-and S 2 •- in geological fluids [START_REF] Pokrovski | The S 3ion is stable in geological fluids at elevated temperatures and pressures[END_REF]Pokrovski and Dubessy, 2015) may lead to reevaluate our vision of a number of geochemical processes in which sulfur is involved. For example, sulfur radicals enhance gold and platinum solubility in hydrothermal fluids involved in porphyry and orogenic deposit genesis (Pokrovski et al., 2015;2019;[START_REF] Laskar | The impact of sulfur on the transfer of platinoïds by geological fluids[END_REF]. These radicals could also contribute to redox changes in the subcontinental lithospheric mantle by slab-liberated S-bearing fluids in subduction zones thereby affecting the sulfur release and metallogenic potential of the arc magmas (e.g., [START_REF] Rielli | Evidence of sub-arc mantle oxidation by sulfur and carbon[END_REF][START_REF] Frimmel | Episodic concentration of gold to ore grade through Earth's history[END_REF][START_REF] Schmidt | In-situ determination of sulfur speciation and partitioning in aqueous fluid-silicate melt systems[END_REF]. At shallow-crust conditions, the S 3 •-ion was hypothesized to be a reaction intermediate controlling the kinetics of TSR processes and associated sulfur isotope fractionations [START_REF] Truche | The role of S 3ion in thermochemical sulfate reduction: Geological and geochemical implications[END_REF]Pokrovski and Dubessy, 2015;[START_REF] Barré | First evidence of the trisulfur radical ion S 3and other sulfur polymers in natural fluid inclusions[END_REF]. The particular properties of S 3 •-make it different from the 'traditional' sulfur species and, therefore, might be responsible for MIF 33 S anomalies found in sulfides from hydrothermal settings and during TSR phenomena evoked above. This is because S 3 •- exhibits a magnetic moment due to a free electron, potentially enabling MIF, contrary to traditional sulfur molecules and ions (Buchachenko, 2001). Furthermore, S 3 •-is a structural and electronic analog of ozone (O 3 ) and its radicals exhibiting large 17 O MIF anomalies due to symmetry effects (e.g., 16 O 16 O 16 O vs 16 O 17 O 18 O), which is a general quantum-level control potentially applicable to other triatomic molecules and radicals [START_REF] Gao | Strange and unconventional isotope effects in ozone formation[END_REF][START_REF] Babikov | Quantum origin of an anomalous isotope effect in ozone formation[END_REF][START_REF] Chakraborty | Sulfur isotopic fractionation in vacuum UV photodissociation of hydrogen sulfide and its potential relevance to meteorite analysis[END_REF][START_REF] Reinhardt | Mass independent isotope fractionation in ozone[END_REF].

The major challenge in studying S 3 •-and S 2 •-is that they are only stable and sufficiently abundant in aqueous solution at elevated temperatures and are not preserved on cooling/quench by very rapidly decomposing into traditional sulfur species such as sulfide, sulfur, polysulfides, and/or sulfate [START_REF] Chivers | Ubiquitous trisulfur radical ion: fundamentals and applications in materials science, electrochemistry, analytical chemistry and geochemistry[END_REF]Pokrovski and Dubessy, 2015 and references therein).

Along with S 3 •-and S 2 •-, another previously disregarded sulfur species in hydrothermal fluids, is a form of polymeric molecular sulfur (S n 0 , where n is undetermined number of uncharged S atoms in chainlike polymers), which has been identified by solubility and in-situ Raman spectroscopy measurements in Srich solutions at >200°C [START_REF] Dadze | Experimental determination of the concentrations of H 2 S, HSO 4 -, SO 2 aq, H 2 S 2 O 3 , S 0 aq, and S total in the aqueous phase in the S-H 2 O system at elevated temperatures[END_REF]Pokrovski and Dubessy, 2015;[START_REF] Barré | First evidence of the trisulfur radical ion S 3and other sulfur polymers in natural fluid inclusions[END_REF], but its effect on both sulfur redox kinetics and isotope fractionation remains unexplored. This form of molecular sulfur is different from the previously recognized aqueous cyclo-octasulfur S 8 0 (e.g., [START_REF] Kamyshny | Solubility of cyclooctasulfur in pure water and sea water at different temperatures[END_REF]Pokrovski and Dubessy, 2015). Similarly to S 3 •-, S n 0 is not preserved on cooling in its original state, by transforming to native sulfur, molten or solid (S (s,l) , composed of S 8 rings), which is a common lowtemperature (<150°C) product of S-bearing fluids both in laboratory and natural hydrothermal-volcanic settings. Therefore, native sulfur may potentially record, through its isotope signature, processes of sulfur species transformation in fluids under elevated T-P conditions inaccessible to direct observation/sampling. Such processes include disproportionation of magmatic SO 2 (e.g., [START_REF] Kusakabe | Sulfur isotopic effects in the disproportionation reaction of sulfur dioxide in hydrothermal fluids: implications for the  34 S variations of dissolved bisulfate and elemental sulfur from active crater lakes[END_REF][START_REF] Kouzmanov | Geology and Genesis of Geology and Genesis of Major Copper Deposits and Districts of the World: A Tribute to[END_REF], TSR reactions [START_REF] Barré | First evidence of the trisulfur radical ion S 3and other sulfur polymers in natural fluid inclusions[END_REF], or S 3 •-and S n 0 transformations on cooling (e.g., Pokrovski and Dubessy, 2015). In this article, these different uncharged polymeric molecular sulfur forms are collectively termed as 'S 0 '.

In an attempt to bring quantitative constraints on the role played by the trisulfur (and disulfur) radical ion and polymeric molecular sulfur on S isotope fractionation in hydrothermal environments, we combined i) experiments in S 3 •-(S 2 •-)-S 0 -sulfate-sulfide hydrothermal fluids, ii) precise analyses of the multiple sulfur isotope ratios in the different sulfur aqueous forms (sulfate, sulfide and S 0 ) and coexisting pyrite, and iii) thermodynamic modeling of sulfur aqueous speciation and solubility. The results contribute to better understanding of complex sulfur isotope fractionation processes in both ancient and modern hydrothermal systems relevant to various types of metal ore deposits formed by S-bearing fluids within the Earth's crust.

MATERIALS AND METHODS

Experimental strategy and conditions

Four experiments were conducted in synthetic aqueous sulfate-sulfide fluids from 300 to 450°C and from ~300 to ~700 bar to investigate both kinetic and equilibrium sulfur isotope fractionation over a wide range of S 3 •-concentrations (from <0.0001 to ~0.1 moles S per kg of fluid (m), Table 1). Aqueous thiosulfate solutions K 2 S 2 O 3 (-HCl-KOH) served as the source of sulfur, following the same approach as recent in-situ Raman spectroscopy studies that identified S 3 •-, S 2 •-and S 0 (Pokrovski and Dubessy, 2015). Potassium was preferred to Na which forms at elevated temperatures a poorly soluble Na 2 SO 4 solid compared to K 2 SO 4 [START_REF] Linke | Solubilities of Inorganic and Metal-Organic Compounds: a Compilation of Solubility Data from the Periodical Literature[END_REF]. Thiosulfate breaks down in aqueous solution on heating above 150°C, producing dominantly sulfate and sulfide

S 2 O 3 2-+ H 2 O = SO 4 2-+ H 2 S
(1)

Adding acid (HCl) or base (KOH) allows enhanced formation of protonated (HSO 4 -) or deprotonated (HS -) species, respectively, enabling acidity buffering

SO 4 2-+ H + = HSO 4 - (2)
H 2 S = HS -+ H + (3)

Alternatively, acidity buffering at slightly acidic pH values may also be achieved by using alkali aluminosilicate mineral assemblages, such as quartz-muscovite-microcline, which was used in one of our experiments (m22, see below). Furthermore, equilibria between sulfate and sulfide at elevated temperatures impose oxygen fugacity (f O2 ), which typically ranges, depending on pH, from HM-2 to HM+2 (where HM denotes the logf O 2 value of the conventional hematite-magnetite mineral buffer):

H 2 S + 2 O 2 = SO 4 2-+ 2 H + (4)
The formation of S 3 •-in such sulfate-sulfide solutions can be formally described by the reaction

19 H 2 S + 5 SO 4 2-+ 2 H + = 8 S 3 •-+ 20 H 2 O (5)
This reaction implies that the abundance of S 3 •-is controlled by total S concentration (S tot , which is proportional to the sum of the dominant sulfate and sulfide), solution pH, and the H 2 S/SO 4 ratio (and therefore oxygen fugacity), with a maximum abundance at a given set of T, S tot and pH at a H 2 S/SO 4 2-ratio of 19/5.

Note that this formal reaction in no way reflects the mechanisms of S 3 •-formation and breakdown, but only illustrates the fundamental thermodynamic controls on the S 3 •-equilibrium concentration in solution. In addition to the above S species produced by reactions (1) to (5), and depending on S and K total content, pH

and T-P conditions, variable amounts of sulfate and sulfide ion pairs with K + , SO 2 , S 8 0 (both aqueous and molten), disulfur ion S 2 •-, and polysulfide dianions S n 2-will also form.

The concentrations of all these species can be estimated using available thermodynamic data (see section 2.6 and Table A2.1 for discussion and data sources). Figure 1 shows the calculated equilibrium distribution of the different sulfur species, using the best up-to-date thermodynamic data (but see section 2.6), in K 2 S 2 O 3 aqueous solutions over the T-P-S tot -pH-redox range of this study, and Table 1 overviews -poor conditions (~0.005 m S) at two contrasting temperatures, 300 and 450°C, followed by an acidification of the fluid at 450°C to increase S 3 •-concentration by a factor of 10 (~0.04 m S). In addition, the S 2 •-may also be present at such elevated temperatures (Fig. 1b; Pokrovski and Dubessy, 2015;[START_REF] Pokrovski | The nature and partitioning of invisible gold in the pyrite-fluid system[END_REF].

The last step of the three experiments above was conducted in the presence of pyrite (plus barite in m22)

whose precipitation was induced by injecting, in-situ into the reactor, an FeCl 2 (plus BaCl 2 in m22) aqueous solution, thus simulating pyrite precipitation in natural hydrothermal fluids. Finally, a fourth experiment (m33) was conducted at 300°C at near-neutral pH (~5.3) by progressively diluting with water the initial K 2 S 2 O 3 -bearing fluid leading to a decrease of S 3 •-concentration by a factor of 10 (from ~0.07 to 0.008 m S), to examine the effect of changing of S 3 •-abundance on sulfur isotope fractionation.

Our experimental systems offer a good analog for natural S-rich fluids in arc-related magmatichydrothermal systems hosting porphyry, skarn and epithermal Cu-Au-Mo deposits, which are characterized by typical temperatures of 250-500°C, pressures of 100-1000 bar, a wide pH (3-8) and redox (HM±2) ranges, typical salinities of 5-15 wt% of NaCl+KCl, the coexistence of sulfate and sulfide in a wide range of concentrations (from ~0.01 to a few wt% S), and the ubiquitous presence of pyrite [START_REF] Einaudi | Sulfidation state of fluids in active and extinct hydrothermal systems: transitions from porphyry to epithermal environments[END_REF][START_REF] Kouzmanov | Geology and Genesis of Geology and Genesis of Major Copper Deposits and Districts of the World: A Tribute to[END_REF]. Furthermore, the isotope fractionation patterns obtained in this study are also relevant to other hydrothermal settings and ore-deposit contexts that are all characterized by the presence of S-bearing fluids and iron sulfide minerals (e.g., seafloor geothermal systems, orogenic and sedimentary basin metal deposits).

Experimental setup

The runs were conducted using a Coretest reactor (Fig. 2) equipped with a flexible gold inner cell with a Ti 2-µm frit filter in its head, i.e. analogous to [START_REF] Seyfried | Rocking autoclaves for hydrothermal experiments II. The flexible reaction-cell system[END_REF] and [START_REF] Rosenbauer | A flexible Au-Ir cell with quick assembly for hydrothermal experiments[END_REF] and recently adapted to multicomponent and S-rich systems as described previously (Pokrovski et al., 2015;[START_REF] Kokh | The role of carbon dioxide in the transport and fractionation of metals by geological fluids[END_REF]. The gold cell (120-180 cm 3 of initial volume) is inserted into a high-pressure vessel (~1000 cm 3 volume, type 316 SS, stainless steel), which is filled with water as a pressure medium controlled by a gasdriven pump, and placed into an electrically heated (±1°C) rocking furnace. An ultrafast sampling device, analogous to that of [START_REF] Seewald | The effect of temperature on metal mobility in subseafloor hydrothermal systems: constraints from basalt alteration experiments[END_REF], consists of a titanium tube attached to two high-pressure titanium valves and a rigid titanium vial (~2.5 cm 3 ) tightly assembled to the second valve. The device enables an almost instantaneous (<1 s) transfer into the vial of a portion of the fluid phase pushed by the internal pressure from the reactor. This design prevents sulfur precipitation or degassing (see [START_REF] Kokh | The role of carbon dioxide in the transport and fractionation of metals by geological fluids[END_REF] for details), which would have inevitably occurred in S-bearing systems using traditional sampling procedures.

Prior to experiments, the gold cell was cleaned with HNO 3 and annealed at 380°C for 1 h to allow for a greater malleability and deformation.

During an experiment, fluids were periodically sampled and processed as described in sections 2.3 and 2.4. In the course of experiments m32 and m33, aqueous HCl or pure water were injected into the cell, initially loaded with a thiosulfate solution, using a calibrated capstan pump (total volume = 12 cm 3 ). This injection allows controlled changes of the fluid pH and S tot concentration and, consequently, the sulfur speciation (in particular, the amount of S 0 and S 3 •-, see Table 1 and Fig. 1). Precipitation of pyrite (together with barite in m22), in the final stage of three experiments (m22, m29 and m32), was induced by injection into the reactor of an FeCl 2 (-BaCl 2 ) aqueous solution in amounts not exceeding those of aqueous sulfide.

Then the fluid composition continued to be monitored by periodic sampling, and the solid was finally recovered upon complete cooling of the reactor.

Chemical analyses of sampled fluids

Because the complex sulfur speciation at elevated T-P strongly evolves upon fluid cooling (Fig. 1d), the original species identity and distribution cannot be adequately recovered in quenched samples. Therefore, special procedures are required for separation and preservation of the different sulfur forms for chemical and isotope analyses. These procedures are based on improved methods developed in our previous studies of Srich fluid systems (e.g., Pokrovski et al., 2008;[START_REF] Kokh | Combined effect of carbon dioxide and sulfur on vapor-liquid partitioning of metals in hydrothermal systems[END_REF]. Each sampling session comprised multiple samples of the fluid phase (usually 5, amounting 0.5 to 1.0 g each), directly taken into specific aqueous reagents (concentrated solutions of I 2 , Cd(CH 3 COO) 2 , Zn(CH 3 COO) 2 , NH 3 ) placed in the sampling vial to allow for quantitative recovery and preservation of the different forms of sulfur, as well as dissolved chloride, potassium, iron and gold (Table A1.1). Total aqueous sulfur (S tot ) was analyzed in samples taken into aqueous ammonia (28 wt% NH 3 ) by inductively coupled plasma -atomic emission spectrometry (ICP-AES) and highperformance liquid chromatography (HPLC) after complete oxidation by hydrogen peroxide (30 wt% aqueous H 2 O 2 ) of all S forms to sulfate. Total aqueous chloride was also analyzed by HPLC in the same NH 3 and H 2 O 2 -treated samples. Total reduced sulfur (S red , comprising H 2 S/HS -/KHS, S n 2-and, eventually, SO 2 and unreacted thiosulfate) was trapped in HCl aqueous solution containing an excess of iodine over sampled sulfur, and quantified by titration of the remaining I 2 by a standard thiosulfate solution, since all these reduced S species react with I 2 (e.g., [START_REF] Charlot | Les Méthodes de la Chimie Analytique: Analyse Quantitative Minérale[END_REF][START_REF] Dadze | Experimental determination of the concentrations of H 2 S, HSO 4 -, SO 2 aq, H 2 S 2 O 3 , S 0 aq, and S total in the aqueous phase in the S-H 2 O system at elevated temperatures[END_REF]. Sulfide-type sulfur (S sulfide , comprising H 2 S, HS -and KHS) was separated from the other sulfur forms by sampling the fluid into a cadmium acetate solution of near-neutral pH (~6), which results in quantitative precipitation of all sulfide species as poorly soluble Cd sulfide (CdS solubility is <mol Cd/kg fluid), followed by iodometric titration in an I 2 -HCl solution. Oxygen gas in the air space of the vial before sampling is less than 0.001 mmol/L, compared to 10s to 100s mmol/L of potentially oxidizable S species in the fluid (e.g., H 2 S), so that oxidation by air is negligible. Sulfate-type aqueous sulfur (S sulfate , comprising SO 4 2-, HSO 4 -, and their K + ion pairs, existing at experimental T-P conditions, Fig. 1) was quantified by HPLC as the SO 4 2-ion in water-diluted near-neutral pH acetate solutions, after removal of sulfide as CdS precipitate by centrifugation. The presence of thiosulfate in the supernatant was also checked by HPLC, but could not be quantified.

Molecular sulfur was separated from other S species as hexane extracts (hereafter S 0 hexane ) collected from samples trapped into Cd acetate solution followed by removal of CdS via centrifugation. The hexane fraction was then analyzed for S 0 by UV spectrometry at a wavelength of 264 nm calibrated using reference solutions prepared by dissolving a given amount of native sulfur in hexane. The analytical uncertainty on the S 0 concentration determination in our systems is typically ±50%, mostly because impurities common in our chemically complex samples (including acetate and its decomposition products that may partition into hexane) absorb in the same UV range. All vials and tubes were also rinsed with hexane after recovery of each sampled solution, and analyzed for S 0 , which has always been found below the detection limit (<0.0001 m S). An independent way for estimating S 0 concentrations in the sampled fluid was using sulfur mass balance between S tot and the sum of sulfate and reduced sulfur (hereafter S 0 balance ), because S 0 does not react with iodine and does not precipitate with Cd or Ba acetate.

Concentrations of potassium, gold and iron were determined by ICP-AES and, selectively, by flame atomic absorption spectrometry (FAAS), after the NH 3 sample treatment with aqua regia. This treatment consists of i) gentle evaporation of the sample on hot plate (60-80°C) in a cleaned Teflon vial (Savilex ®),

ii) reaction of the residue with 2 g of hot aqua regia in the closed vial (at 120°C for 2h), followed by iii) gentle evaporation of solution (at 60-70°C) to 0.2-0.3 g, and iv) dilution of the remaining solution by ultrapure 0.5 wt% HCl -1.5wt% HNO 3 in water. More details on the chemical procedures and associated uncertainties are given in [START_REF] Kokh | Combined effect of carbon dioxide and sulfur on vapor-liquid partitioning of metals in hydrothermal systems[END_REF][START_REF] Kokh | The role of carbon dioxide in the transport and fractionation of metals by geological fluids[END_REF]. The results of fluid analyses are reported in Table 2 and shown as a function of run duration in Fig. 3.

Processing of sampled fluids for sulfur isotope analyses

The sulfur isotope ratios were analyzed (depending on the experiment) in the initial thiosulfate and sampled aqueous sulfate, sulfide and molecular sulfur (if available), and in the precipitated pyrite recovered after the run. Like for the chemical analyses described above, the challenge was to accurately separate the different sulfur forms on sampling to avoid, as much as possible, both chemical recombination and isotope exchange/mixing among these forms in our S-rich systems on cooling. The fluid sample treatment is described as follows and summarized in Table A1.1.

In an exploratory experiment (m22), sulfur samples were taken into an aqueous solution of zinc and barium acetate, resulting in simultaneous precipitation of ZnS and BaSO 4 in the sampling vial. However, difficulties were encountered when converting ZnS to H 2 S from the fine-grained ZnS-BaSO 4 mixture that prevented ZnS, being armored by BaSO 4 , to quantitatively react with the HCl solution, resulting in low yields.

Consequently, the experimental protocol was changed in the subsequent experiments. In runs m29, m32, and m33, aqueous sulfide was trapped as ZnS by placing 1.0-1.5 mL of 1 m zinc acetate solution into the sampling vial. The formed ZnS precipitate was centrifuged (3800 rpm for 15 min) to separate it from the solution, washed with deionized water and dried at 90°C for subsequent isotope analyses. After centrifugation, the supernatant solution was reacted with 1.5 mL of 1 m barium acetate to precipitate BaSO 4 , which was then centrifuged, washed, dried similarly to the ZnS precipitate, and reserved for isotope analyses.

Molecular sulfur S 0 was separated by extraction into hexane after precipitating H 2 S as CdS when sampling the fluid directly into a 1 mL of 1 m cadmium acetate solution. This procedure prevents i) isotope exchange between S 0 and H 2 S/HS -prone to rapid re-equilibration, and ii) possible recombination of sulfate and sulfide to form additional S 0 . Despite all these precautions, native sulfur might still partly precipitate, especially in S-rich acidic solutions, during the fluid passage through the sampling tubes and valves before reaching the vial with the trapping reagent, and thus get transferred into the vial together with the fluid.

Although the different origins and formation mechanisms of S 0 in the sampled fluid cannot be distinguished by bulk S 0 chemical analyses, their isotopic composition is expected to reflect those mechanisms. The supernatant containing sulfate and S 0 was separated from the CdS precipitate by centrifugation (3800 rpm for 15 min), filtered (0.45 µm) and placed into a glass flask with 30 mL of hexane and 10 mL of glycerol (the latter was used to protect the eventually remaining thiosulfate from oxidation that might lead to additional formation of molecular sulfur; [START_REF] Dadze | Experimental determination of the concentrations of H 2 S, HSO 4 -, SO 2 aq, H 2 S 2 O 3 , S 0 aq, and S total in the aqueous phase in the S-H 2 O system at elevated temperatures[END_REF]. The aqueous solution and the hexane phase were allowed to react for at least 48 h to enable the complete extraction of S 0 into the hexane phase, as checked by time-dependent analyses. The S 0 -bearing hexane fraction was then recovered and analyzed for S 0 by UV-Vis spectrometry (section 2.3). After the UV analysis, the hexane was gently evaporated at 50°C and the precipitated sulfur was saved for isotope analyses.

The sulfur isotope composition of the initial thiosulfate was measured separately in its sulfane (S 2-) and sulfonate (S 6+ ) parts according to the slightly modified protocols of [START_REF] Uyama | Sulfur isotope exchange reactions in the aqueous system: thiosulfate-sulfide-sulfate at hydrothermal temperature[END_REF] and [START_REF] Syverson | Multiple sulfur isotope fractionation and mass transfer processes during pyrite precipitation and recrystallization: An experimental study at 300 and 350°C[END_REF]. An aqueous 0.1 m AgNO 3 solution was used to precipitate the sulfane sulfur as Ag 2 S from an aqueous 0.05 m K 2 S 2 O 3 solution. The supernatant was separated from the precipitate by centrifugation and reacted with an excess of barium acetate to precipitate the sulfonate part as BaSO 4 , which was then recovered after centrifugation.

Quadruple sulfur isotope analyses and isotope standardization and notation

Measurements of the four stable sulfur isotope ratios were realized with a gas source Ion Ratio Mass Spectrometer (IRMS) Thermo Finnigan MAT 253 at the Institut de Physique du Globe de Paris (IPGP) as described by [START_REF] Labidi | Determination of multiple sulfur isotopes in glasses: A reappraisal of the MORB δ 34 S[END_REF]. Samples of ZnS, BaSO 4 and S 0 were converted to solid silver sulfide (Ag 2 S) using established techniques [START_REF] Thode | Sulphur isotope geochemistry[END_REF][START_REF] Canfield | The use of chromium reduction in the analysis of reduced inorganic sulfur in sediments and shales[END_REF][START_REF] Labidi | Determination of multiple sulfur isotopes in glasses: A reappraisal of the MORB δ 34 S[END_REF] All  34 S, Δ 33 S and Δ 36 S data obtained in this study are reported relative to the V-CDT standard, which is a virtual S isotope reference adopted instead of the previously used natural Cañon Diablo Troilite (CDT) meteorite, that was found to be slightly isotopically heterogeneous [START_REF] Ding | Calibrated sulfur isotope abundance ratios of three IAEA sulfur isotope reference materials and V-CDT with a reassessment of the atomic weight of sulfur[END_REF]. The V-CDT standard was defined on the base of a homogeneous synthetic standard, IAEA-S-1 (Ag 2 S), with a δ 34 S value of -0.30‰ relative to V-CDT [START_REF] Ding | Calibrated sulfur isotope abundance ratios of three IAEA sulfur isotope reference materials and V-CDT with a reassessment of the atomic weight of sulfur[END_REF]; references therein). Because there is presently no international standard for δ 33 S and δ 36 S, in this study we anchored our 33 S and 36 S data to the V-CDT reference scale, for consistency with the recent studies [START_REF] Ono | S-33 constraints on the seawater sulfate contribution in modern seafloor hydrothermal vent sulfides[END_REF] assuming that δ 33 S V-CDT = -0.055±0.14 ‰, δ 36 S V-CDT = -1.37±0.5 ‰, Δ 33 S V-CDT = 0.100±0.003 ‰, and Δ 36 S V-CDT = -0.8±0.1 ‰ (see also Geng et al., 2019 for a recent intercomparison). Note that this normalization has no consequences on calculations of isotope fractionation factors between different sulfur species. Values of ∆ 33 S and ∆ 36 S were calculated according to [START_REF] Farquhar | Multiple sulfur isotopes and the evolution of the atmosphere[END_REF]:

Δ 33 S V-CDT =  33 S V-CDT -1000 × [(1 +  34 S V-CDT /1000) 33 -1)] (6) Δ 36 S V-CDT =  36 S V-CDT -1000 × [(1 +  34 S V-CDT /1000) 36 -1)] (7)
where 33 and 36 are adopted as 0.515 and 1.889, respectively (note that these values may vary by a few ‰ in different equilibrium and kinetic isotope exchange reactions, Young et al., 2012). Isotope fractionation between the different sulfur forms (here given for  34 S) is expressed relative to aqueous sulfide analyzed as ZnS:

1000×ln i ≈  34 S i - 34 S sulfide (8)
where i denotes sulfate sulfur (collectively termed as SO 4 ), molecular sulfur (S 0 ) or pyrite (Py), and  i is the conventional isotope fractionation factor between i-species and sulfide, ( 34 S/ 32 S) i /( 34 S/ 32 S) sulfide . The results of S isotope analyses obtained in this study are reported in Tables 3 and4 and plotted in Figs 5 to 8.

Chemical equilibrium calculations of aqueous sulfur speciation and solubility

Sulfur speciation and solubility in the fluid phase of the experimental systems were modelled using available thermodynamic data, and the results were compared with the measured S species concentrations.

Calculations were performed using the HCh software package and associated Unitherm database, allowing chemical equilibrium simulations in fluid-mineral systems [START_REF] Shvarov | HCh: new potentialities for the thermodynamic simulation of geochemical systems offered by Windows[END_REF][START_REF] Shvarov | A suite of programs, OptimA, OptimB, OptimC, and OptimS, compatible with the Unitherm database, for deriving the thermodynamic properties of aqueous species from solubility, potentiometry and spectroscopy measurements[END_REF], and accounting for nonideality of the fluid using the extended Debye-Hückel equation [START_REF] Helgeson | Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures: IV. Calculation of activity coefficients, osmotic coefficients and apparent molal and relative partial molal properties to 600° C and 5 kb[END_REF]. The selection of thermodynamic data sources was discussed in detail elsewhere (Pokrovski et al., 2015[START_REF] Pokrovski | The nature and partitioning of invisible gold in the pyrite-fluid system[END_REF][START_REF] Kokh | The role of carbon dioxide in the transport and fractionation of metals by geological fluids[END_REF], and will be only briefly summarized here.

The thermodynamic properties of the minerals, major fluid components, and most aqueous ionic sulfur species were taken from the updated SUPCRT [START_REF] Johnson | SUPCRT92: A software package for calculating the standard modal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1 to 5000 bar and 0 to 1000[END_REF], JANAF [START_REF] Chase | NIST-JANAF Thermochemical Tables, Fourth Edition[END_REF], and USGS [START_REF] Robie | Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (10 5 Pascals) pressure and at higher temperatures[END_REF] databases, complemented by recent data for ionic sulfur forms including S 3 •-(Pokrovski and Dubessy, 2015; references therein) using the revised and extended HKF (Helgeson-Kirkham-Flowers) equation of state [START_REF] Oelkers | Thermodynamic databases for water-rock interaction[END_REF][START_REF] Sverjensky | Water in the deep Earth: the dielectric constant and the solubilities of quartz and corundum to 60 kb and 1200°C[END_REF]references therein). The thermodynamic properties of the aqueous 'gas-like' sulfur nonelectrolytes, H 2 S, SO 2 , as well as H 2 and O 2 , were adopted from [START_REF] Akinfiev | Thermodynamic description of aqueous nonelectrolytes over a wide range of state parameters[END_REF] whose model provides a more accurate description of such species over the T-P range relevant to our study (300-450°C; <1 kbar) than the SUPCRT database, which was based on a more limited experimental dataset for derivation of the HKF model coefficients for those species. The thermodynamic properties of the polysulfide ions (S n 2-, where n is between 2 and 6) and aqueous S 8 0 at 300-450°C were taken from Pokrovski and Dubessy (2015); both types of species were found to be negligible in the fluid at the elevated temperatures of our experiments (<0.001 m S; Fig. 1).

The S 2 •-radical ion, with a stability constant at 450°C and 700 bar from [START_REF] Pokrovski | The nature and partitioning of invisible gold in the pyrite-fluid system[END_REF], was predicted to account for ~0.01 m S in experiment m32, which is comparable to S 3 •-(Fig. 1b). However, the uncertainties on such predictions are large (of an order of magnitude); furthermore, the S 2 •-ion is expected to be negligible in our lower-T experiments since it has not been detected by Raman resonance spectroscopy below 450°C (Pokrovski and Dubessy, 2015). The sources of thermodynamic properties of solid phases and aqueous species used in the modeling are summarized in Table A2.1 and the results of calculations for typical conditions of our experiments are shown in Fig. 1.

The missing species in these calculations are molecular sulfur polymers S n 0 forming around 300°C as detected by in-situ Raman spectroscopy (Pokrovski et Dubessy, 2015;[START_REF] Barré | First evidence of the trisulfur radical ion S 3and other sulfur polymers in natural fluid inclusions[END_REF] and protonated polysulfides (HS n -), for which no thermodynamic data are currently available at elevated temperatures.

Estimations of Pokrovski and Dubessy (2015) suggest that S n 0 equilibrium concentrations in thiosulfate solutions more concentrated than those of our study (S tot ~2 m), attain maximum values of the order of 0.1-0.2 m S around 300°C, and show sharply decreasing amounts with increasing T and/or decreasing S tot concentration. However, considering the large errors of such estimates and possible multiple and likely outof-equilibrium origins of molecular sulfur found in the experiments of this study, quantification of S 0 equilibrium concentrations cannot confidently be made at present. Similarly, the amount of HS n -cannot be quantitatively assessed, but the absence of H-S vibrations in the Raman spectra of Pokrovski and Dubessy (2015) and [START_REF] Barré | First evidence of the trisulfur radical ion S 3and other sulfur polymers in natural fluid inclusions[END_REF] strongly suggests that their concentrations at T-P-pH conditions of our experiments are likely to be too small to affect sulfur mass and isotope balance.

New data obtained in the course of this study allowed estimations of the amount and origin of S 0 at elevated temperatures based of S 0 isotope signatures, and a revision of the stability of the major sulfatebearing species, KSO 4 -(Fig. 1) based on the observation of K 2 SO 4 (s) precipitation in one experiment at 450°C (m32; section 4.1.1 and Appendix A3). The revised calculations, with corrected KSO 4 -stability constants, of equilibrium aqueous sulfate and sulfide concentrations for each experimental step will be compared with their experimental counterparts (Fig. 4) and help to better constrain the interpretation of the S isotope patterns.

RESULTS

Sulfur chemical speciation in the fluid phase

Experiments at 350°C (m22, m29)

Two experiments have been conducted at 350°C and 300-400 bar in acidic (0.5 m K 2 S 2 O 3 -0.14 m HCl, pH 350°C ~4.5, run m22) and less concentrated slightly alkaline (0.2 m K 2 S 2 O 3 -0.09 m KOH, pH 350°C ~7.3, run m29) solutions, corresponding to S 3 •--rich (~0.07 m S) and S 3 •--poor (~0.002 m S) compositions, respectively. The concentrations of S species measured in these experiments are reported in Table 2 and their evolution with time is shown in Fig. 3a,b. In both experiments, before FeCl 2 injection, sulfate and sulfide represent the major fraction of dissolved sulfur. Reduced sulfur (S red ) is slightly higher than sulfide, by 0.01 to 0.04 m S, in the acidic experiment (m22); the difference might be due to the presence of minor quantities of SO 2 which is titrated by iodine together with sulfide. Reduced sulfur concentrations in the alkaline experiment (m29) are identical to those of sulfide. There are no discernable changes of the species concentration with time, suggesting that a chemical steady state is reached at this temperature within less than a few days. Total S concentrations (S tot ) analyzed in the less concentrated alkaline-pH run (m29) match the sum of S sulfate and S red concentrations, implying an insignificant contribution of other S species that might have been omitted by our analytical protocols (<0.03 m S). In contrast, significant imbalance (up to 0.3 m S)

between S tot and the sum of S red and S sulfate is apparent in the more concentrated acidic run (m22). This imbalance (S 0 balance ) is attributed to the presence of molecular sulfur S 0 in the sampled fluid, which can react neither with iodine nor with cadmium or barium acetate. This S 0 balance may have multiple origins that will be discussed in section 4. In the next step of both experiments, after the injection of FeCl 2 (m29) and KCl-FeCl 2 -BaCl 2 (in m22), S tot becomes largely dominated by sulfate given that a major part of reduced sulfur precipitated as pyrite. Concentrations of S tot are similar within errors to S sulfate in m29, and are slightly higher than S sulfate in m22, likely due to the presence of minor amounts of SO 2 favored by acidic pH (Fig. 1).

Experiment at 300 and 450°C (m32)

More complete information about sulfur speciation has been gained in a subsequent experiment conducted at 300 and 450°C (m32), with the development of a protocol for molecular sulfur analysis (see section 2.3). This experiment was started in alkaline solution (0.5 m K 2 S 2 O 3 -0.3 m KOH pH 300°C ~7) at 300°C, 500 bar and run for 13 days (step m32/1); then the temperature was raised to 450°C and kept for 14 days (pH 450°C ~8, m32/2). In a next step lasting 8 days (m32/3), an HCl solution was injected into the reactor resulting in acidification (pH 450°C ~7), allowing a better identification of S 3 •-whose abundance is predicted to increase at more acidic pH (Table 1, Fig. 1). In the final step (m32/4, lasting 8 days), a FeCl 2 solution was injected, resulting in pyrite precipitation and further fluid acidification (pH 450°C ~6). Total K and S concentrations steadily decrease at a molar K/S ratio close to 2 with time during the 300°C step (Fig. 3c andA3.1). This decrease suggests the precipitation of K 2 SO 4 (s), which is known to have a retrograde solubility with temperature (Pokrovski and Dubessy, 2015). Further decrease of S and K concentrations is observed as the temperature was raised to 450°C, following by stabilization for ~1 week, suggesting an attainment of steady state concentrations. The retrograde solubility of K 2 SO 4 (s) was apparent at the 450°C stage during a temporary heating regulation problem before sample #6 (Table 2, Fig. 3c), causing the temperature to decrease to ~260°C, and before sample #7, causing the temperature to increase to ~460°C. The solubility of K 2 SO 4 (s) rapidly responded to these temperature changes by increasing above and then decreasing below the steady-state values obtained in 2 previous samples #4 and #5 (Table 2; Fig. 3c,A3.1).

During the 300°C stage (m32/1), measured concentrations of sulfate and sulfide remained constant over ~1 week, but their sum was inferior to that of S tot by a factor of ~2 (Table 2, Fig. 3c), demonstrating the presence of analytically unreactive molecular sulfur (S 0 balance ). Concentrations of S 0 balance decreased by ~50%

accompanied by an increase in both sulfate and sulfide (in the 2 nd week), reflecting a slow and complex kinetics of thiosulfate transformation. A fourth species contributing to aqueous S is the thiosulfate ion, S 2 O 3 2-, which was detected by HPLC analyses in sample #1 solution after separation of ZnS. The presence of undecomposed S 2 O 3 2-and/or its possible intermediate decomposition products (SO 3 2-) at this stage is also independently confirmed by the systematically higher measured concentrations of S red compared to S sulfide , since both thiosulfate and sulfite are titratable by iodine, but do not precipitate with Cd or Zn.

The T rise to 450°C after that step resulted in a drop of S 0 balance concentrations by a factor of 5 to 10 as compared to the preceding sampling at 300°C (Fig. 3c). It should be noted that the S 0 values exhibit a large scatter due to both analytical difficulties for measuring S 0 in hexane extracts (S 0 hexane ) and the use of massbalance relations (S 0 balance ) for deriving close-to-zero values (~0.01 m S). Yet, despite the scatter, the S 0 hexane concentrations appear, on average, quite similar to the S 0 balance ones (Fig. A4.3), yielding a mean value of 0.04±0.02 m S (1 SD) for S 0 concentration for the whole set of datapoints over the three steps at 450°C (m32/2, 3, 4). Both types of S 0 data do not show any clear tendency as a function of elapsed time (Fig. 3c).

Experiment at 300°C and near-neutral pH (m33)

A fourth experiment was conducted at 300°C and 500 bar in 0.5 to 0.2 m K 2 S 2 O 3 solution at nearneutral pH (pH 300°C ~5.3). This experiment was designed to better explore the effect of dilution resulting in large changes in S 3 •-(and S 0 ) concentrations without much changing the overall solution chemistry and acidity. At the initial stage (~0.5 m K 2 S 2 O 3 , m33/1), sulfate and sulfide account for >60% of S tot (Table 2).

There are no systematic changes within errors of their concentrations with time, suggesting that a chemical steady state is reached. Likewise, there is no systematic difference between measured S red and S sulfide concentrations, suggesting the absence of significant amounts (>0.02 m S) of reduced species other than H 2 S/HS -(e.g., polysulfide ions, SO 2 , or undecomposed thiosulfate). In contrast, there is yet significant imbalance (up to 30% S tot ) between S tot and the sum of S sulfide and S sulfate , due to the presence of molecular sulfur (S 0 balance , Table 2), as was also confirmed by direct analyses of S 0 hexane . After the first injection of water, this imbalance is significantly reduced as a result of dilution (to ~15% S tot ). After the second injection of water, the S 0 fraction further decreased to become <5% S tot after 1 week (Table 2, Fig. 3d). Like in experiment m32, both types of S 0 datapoints (S hexane and S balance ) are quite scattered, but without any systematic trends between them (Fig. A4.3).

Sulfur isotope ratios in the fluid phase and pyrite

In two exploratory experiments (m22 and m29), only a limited dataset could be obtained on S isotope ratios of the different species (Table 3, Fig. A4.1 and A4.2). Most isotope data have been obtained on S sulfide (trapped as ZnS) and S 0 (analyzed by the CRS treatment of the ZnS-BaSO 4 mixture in m22; Appendix A1).

Only few data points could be collected from S sulfate (trapped as BaSO 4 ) due to imperfections in separating ZnS from BaSO 4 . The δ 34 S sulfide and δ 34 S S 0 values are consistently more negative, by 14-21 ‰, than the δ 34 S sulfate values; however, the paucity of the BaSO 4 data does not allow the identification of any systematic trends with time.

A more extensive sulfur isotope data set has been obtained in experiment m32 (Table 3, Fig. 5a and6). The isotope composition of sulfonate (O 3 -S-) and sulfane (-S) sulfur of the initial thiosulfate (which decompose respectively to sulfate and sulfide according to reaction 1), evolves upon heating to 300°C, with sulfate and sulfide becoming through time 34 S-enriched and 34 S-depleted, respectively. In other words, the difference in 1000×ln SO4 (δ 34 S sulfate -δ 34 S sulfide ) at each given moment increases with time, yet without reaching a steady state at 300°C (Fig. 5c). This evolution is mainly controlled by the increase in δ 34 S sulfate , whereas δ 34 S sulfide remains constant within errors (Fig. 5a); this clearly indicates that at least a third S isotope pool is being formed. After the temperature rise to 450°C, δ 34 S sulfide values stay constant while δ 34 S sulfate values increase slightly (by <2‰ over 30 days), yielding a value 1000×ln SO4 of 15.0±1.0 ‰ for the two last data points after pyrite precipitation. Only three isotope compositional data points could be obtained for S 0 hexane in this experiment. One data point from the first sample taken just after T change to 450°C (sample #4, Table 3) has an anomalously light isotope signature relative to sulfide (1000×ln S 0 = -11.6 ‰). Such a low value is unlikely to be an analytical artifact, since it is in good agreement with that calculated using sulfur mass and isotope balance on sulfate and sulfide (Fig. 5a, Appendix A5). The two other S 0 isotope data points, obtained in samples #8 and #9 taken respectively 2 and 5 days after the HCl injection at 450°C (stage m32/3), show 1000×ln S 0 values tending to zero. The isotope composition of the precipitated pyrite in this experiment is similar to that of the aqueous sulfide fraction within 0.4 ‰ of  34 S (Table 4).

Sulfur isotope data obtained in experiment m33 (Table 3, Fig. 5b,d) confirm the major isotope trends for the SO 4 -H 2 S pair observed in m32. The isotope composition of sulfonate (O 3 -S-) and sulfane (-S) sulfur of the initial thiosulfate rapidly evolves upon heating to 300°C, with sulfate and sulfide becoming with time 34 S-enriched and 34 S-depleted, respectively. The resulting 1000×ln SO4 value is almost constant over the run duration, yielding a steady state value of 20.1±1.5 ‰ (Fig. 5d).

In all performed experiments, the values of Δ 33 S for all species vary between -0.02 ‰ and +0.08 ‰, and do not show any systematic trends (Fig. 6, 7, A4.2). The values of Δ 36 S vary between -1‰ and +1‰

without displaying any systematic trends amongst sulfide, sulfate and S 0 , and overlapping with those of the initial thiosulfate. The scatter is mostly due to analytical issues because the analysis of  36 S would commonly be affected by a small contribution of fluorocarbon compounds that shifts measured  36 S towards more positive values [START_REF] Rumble | Analysis of oxygen and sulfur isotope ratios in oxide and sulfide minerals by spot heating with a carbon dioxide laser in a fluorine atmosphere[END_REF]. Nevertheless, these relatively small variations imply that there is no significant sulfur mass independent fractionation on both 33 S and 36 S; however, they do provide additional insight into both equilibrium and kinetic processes affecting mass-dependent fractionation among the sulfur species as will be discussed in section 4.2.4.

DISCUSSION

Solubility and chemical speciation of sulfur

Sulfur solubility and species concentrations measured in this study can be compared with equilibrium thermodynamic calculations. In all experiments, four major types of S chemical forms predicted by the available thermodynamics (Table A2.1) are aqueous sulfate (SO 4 2-, HSO 4 -, KSO 4 -, and KHSO 4 0 ), sulfide (H 2 S, HS -, and KHS 0 ), radical ions (S 3 •-at all T, and S 2 •-at 450°C), and pyrite (FeS 2 ). In addition, in m22 aqueous SO 2 and three other phases, S (s,l) , at step m22/1, and barite (BaSO 4 ) and alunite (KAl 3 (SO 4 ) 2 (OH) 6 ) at step m22/2 after pyrite precipitation were predicted to form (Table 1). All other known solid phases are predicted to be largely undersaturated in our experiments. Other types of aqueous species, such as thiosulfate, S 8 0 , and traditional polysulfide ions, represent a negligibly small amount of S tot at equilibrium (<0.1%).

Comparisons between calculated and measured concentrations of sulfate, sulfide, SO 2 and S 0 / S 3 •-/ S 2 •-are shown in Fig. 4; they reveal several interconnected points of discrepancy regarding the precipitation of the K 2 SO 4 solid (in m32), sulfate-sulfide-pyrite equilibration, and the formation of S 0 , which are discussed below.

K 2 SO 4 (s) precipitation

The precipitation of K 2 SO 4 (s) was inferred in run m32 (0.5 m K 2 S 2 O 3 -KOH-HCl, at 300 and 450°C

with in-situ changes in pH induced by HCl injection), through observation of concomitant decrease of total dissolved potassium and sulfur concentrations through time (Fig. 3c, Appendix A3). The precipitation of K 2 SO 4 (s) is, however, not consistent with equilibrium calculations using the thermodynamic properties of K 2 SO 4 (s), K + and sulfate aqueous species from available data sources (Table A2.1). The calculations predict K 2 SO 4 (s) to be undersaturated in the fluid by a factor of 10. The likely reason for this discrepancy is poor constraints on the thermodynamic parameters of the dominant KSO 4 -ion pair (Fig. 1), which are based on HKF-model extrapolations relying on limited experimental data at low temperatures. To account for K 2 SO 4 (s) formation, a correction to the value of the formation constant of KSO 4 -from K + and SO 4 2-at 450°C

and 700 bar has been made to match the measured solubility of K 2 SO 4 (s) at each 450°C step of experiment m32 (log K 450°C, 700 bar = 3.4±0.5; Appendix A3). This correction does not exceed 1 log unit compared to the SUPCRT original value (log K 450°C, 700 bar = 4.4). The difference is within realistic uncertainties of HKF model predictions for such ion pairs at elevated temperatures (e.g., [START_REF] Pokrovski | Experimental determination of the stability constants of NaSO 4and NaB(OH) 4 0 in hydrothermal solutions using a new sodium selective glass electrode. Implications for boron isotopic fractionation[END_REF][START_REF] Scheuermann | Anhydrite solubility in low-density hydrothermal fluids: Experimental measurements and thermodynamic calculations[END_REF].

The 300°C step of this experiment does not allow direct reliable corrections for KSO 4 -formation constant, because no steady state has been attained (Fig. 3c). Therefore, we have corrected the fluid composition at the 300°C step of m32 by subtracting manually the mass-balance deduced amount of precipitated K 2 SO 4 , but this correction has again a minor effect (Fig. A3.2). Nevertheless, to maintain consistency, in the following discussion both 300°C and 450°C corrections were included when modeling equilibrium S speciation in experiment m32 (Fig. 4c).

Aqueous sulfate and sulfide and pyrite

Before the pyrite precipitation stage, a decent agreement between measured and calculated S sulfide values is observed for the least-concentrated experimental compositions in m29/1 (0.2 m K 2 S 2 O 3 , pH ~7.3, 350°C) and m33/3 (0.2m K 2 S 2 O 3 , pH ~5.3, 300°C). The other experimental compositions show systematically lower measured S sulfide , which is due to the presence of S 0 , as directly confirmed by mass balance calculations and analyses of hexane extracts (discussed in section 4.1.3 below). Another potential cause of the difference between measured and calculated S sulfide in the highest-temperature run (450°C, m32/2,3) might be an underestimation of the thermodynamically predicted amount of S 2 •-forming at the expense of H 2 S. The measured S sulfate concentrations in experiments m22, m29, m33 (and m32 at 450°C, after correction for K 2 SO 4 (s)) agree within errors with the calculated ones, which further confirms that S 0 forms more at the expense of sulfide than sulfate. An exception to this trend is stage m32/1 at 300°C and alkaline pH that still shows significant underestimation of measured S sulfate , which is due to lack of equilibrium and the slowness of thiosulfate decomposition.

In the final stages of experiments m22, m29 and m32 with precipitated pyrite (and barite and alunite in m22), calculations predict almost complete scavenging of the injected Fe (and Ba) amounts by the solid phase, which is in excellent agreement with both low Fe dissolved concentrations (<0.002-0.02 m, Table 2) and the differences in S sulfide concentrations measured before and after the FeCl 2 injection. However, for all three experiments in the presence of pyrite, the measured aqueous S sulfide concentrations are somewhat lower than those predicted using equilibrium thermodynamics (Fig. 4a-c). The difference between measured and predicted S sulfide concentration values in equilibrium with pyrite (0.05-0.1 m S) suggests that pyrite, once precipitated, may not fully chemically re-equilibrate with the solution within the short time frame of these experimental stages (<10 days).

Molecular sulfur formation

Molecular sulfur was clearly identified in three from the four runs conducted in this study. The exception is run m29 at 350°C with the lowest S tot concentration (0.4 m S), which was the simplest from the point of view of aqueous S speciation, with dominant sulfate and sulfide and negligible amounts of S 3 •- (<0.001 m S). The small imbalance between S tot and [S sulfide + S sulfate ] in this experiment before pyrite precipitation (<0.03m S, Table 2) is comparable with the uncertainties of the species concentrations. In contrast, experiment m22, conducted at the same temperature but in a more concentrated and more acid solution, is predicted to contain at equilibrium, along with sulfate and sulfide, significant S 3 •-concentrations (0.067 m S; Table 1, Fig. 4a). The major difference between the analytical data and thermodynamic predictions for this experiment is the presence of large amounts of S 0 (~0.3 m S) as clearly apparent from mass balance between measured S tot and the sum of S sulfate and S sulfide (Table 2). Such elevated S 0 concentrations are not accounted for by thermodynamics, which predicts <0.001 m of S 8 0 (aq) at equilibrium using the thermodynamic data sources from Table A2.1 (Fig. 1). The contribution from breakdown of S 3 •-to molecular sulfur on cooling during sampling can be estimated by the reaction:

2 S 3 •-+ 2 H + = 5 S 0 + H 2 S (9)
Molecular sulfur and H 2 S are the most reactive S species that are known to easily form during rapid cooling of hydrothermal fluids [START_REF] Giggenbach | The origin and evolution of fluids in magmatic-hydrothermal systems[END_REF]Pokrovski and Dubessy, 2015). The formation of sulfate is kinetically too slow to occur during the sampling in our experiments (e.g., [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF]. The formation of polysulfide dianions, such as S 6 2-that is known to form by recombination of two S 3 •-in nonaqueous solvents (e.g., [START_REF] Chivers | Ubiquitous trisulfur radical ion: fundamentals and applications in materials science, electrochemistry, analytical chemistry and geochemistry[END_REF][START_REF] Steudel | The role of polysulfide dianions and radical anions in the chemical, physical and biological sciences, including sulfur-based batteries[END_REF], is negligible at our acidic pH (Fig. 1a). Therefore reaction ( 9) is likely to control the S 3 •-breakdown in this experiment. Yet, the maximum produced amount of S 0 by S 3 •-breakdown in experiment m22, according to reaction (9), is 0.056 m S, which is not enough to account for the difference [S tot -(S sulfate + S sulfide )] in this experiment (~0.3 m S, Fig. 4a). It is thus very likely that the major part of S 0 observed in sampled fluids from this experiment has a different origin. As shown by Pokrovski and Dubessy (2015) by in-situ Raman spectroscopy on similar solutions, another type of S 0 is present at the T-P conditions of this experiment and is likely represented by chain-like polymeric molecules in equilibrium with sulfate, sulfide and S 3 •-ion. Furthermore, part of S 0 found in sampled solutions in this experiment may be produced by a very fast precipitation of the native sulfur phase (S 0 liquid at >115°C and solid at lower T) during the sampling when the fluid is transferred from the hot reactor (350°C) to the cold sampling vial (<100°C). Indeed, thermodynamic predictions suggest that, if solidsolution equilibrium for sulfur is attained at 100°C during sampling, >30% of S tot would precipitate as native sulfur before reaching the trapping iodine or zinc acetate solution in the vial. Even through such rapid attainment of equilibrium at low temperatures within the sampling time frame is unlikely (e.g., [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF], this potential artifact of S precipitation could not be completely excluded, in particular in acidic systems in which sulfur solubility is lower (Fig. 1a,d), and thus may also contribute to the S 0 concentrations found in this experiment.

Further insight into the origin of molecular sulfur is gained from step m32/1 at lower T (300°C) and more alkaline pH (7.2). Under these conditions, sulfur solid/liquid phase precipitation during sampling on cooling is not favorable because of the greater S solubility in alkaline solutions (Fig. 1a) and much slower redox kinetics (e.g., [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF]. Thermodynamic calculations predict negligible amounts of S 8 0 (<0.001 m S) and fairly small amounts of S 3 •-(0.004 m S). These relatively small concentrations cannot account for the major fraction of S 0 observed at this stage (50% of S tot , Table 2, Fig. 3c). This different type of S 0 is likely to originate from irreversible thiosulfate breakdown on heating:

S 2 O 3 2-= S 0 + SO 3 2- ( 10
)
This reaction is the most straightforward and kinetically easiest one, since it requires only breaking the S-S bond of the thiosulfate ion with minimal electron transfer between the two S atoms. With time, both S 0 and SO 3 2-undergo transformation to H 2 S and SO 4 2-, which are thermodynamically stable at these conditions:

4 SO 3 2-+ 2 H + = H 2 S + 3 SO 4 2- (11) 4 S 0 + 4 H 2 O = 3 H 2 S + SO 4 2-+ 2H + (12)
This interpretation is supported by i) systematic positive difference between S red and S sulfide at this stage (Table 2) pointing to the presence of an iodine-titratable S form such as SO 3 2-, in line with reaction (10); ii) decrease of the S 0 balance concentration; and iii) increase of S sulfate and S sulfide with time at 300°C (Table 2, Fig. 3c) in line with reactions ( 11) and ( 12). With the T rise to 450°C, this type of S 0 becomes negligible, since both analyzed and mass-balance derived S 0 (0.045 m S on average, Table 2) is in excellent agreement with the amount that may be produced via collective breakdown of S 3 •-according to reaction (9) and S 2 •-according to an analogous reaction:

2 S 2 •-+ 2 H + = 3 S 0 + H 2 S ( 13
)
In contrast, in experiment m33 at lower T (300°C) and near-neutral pH, S 0 concentration that could be produced by S 3 •-breakdown is ~5 times lower than the concentration obtained using mass balance between measured S tot and sulfate plus sulfide (0.065 vs 0.3-0.5 m S at stage m33/1). This imbalance indicates the presence of far more significant amounts of S 0 , confirmed by direct analyses of hexane extracts (Table 2; Fig. 4d). This additionally formed S 0 observed in the sampled fluids may potentially be due to precipitation of liquid/solid S 0 on cooling via partial recombination of sulfate and sulfide via the reversal of reaction (12), and/or via the breakdown of the polysulfide dianions (S n 2-):

S n 2-+ 2H + = (n-1) S 0 s,l + H 2 S (14) Indeed, S n 2-ions, being negligible at our experimental temperatures of ≥ 300°C (<0.001m S), are predicted to form in increasing amounts upon equilibrium cooling for this experimental composition (up to 0.1m S at <100°C, Fig. 1d). It is impossible, however, to evaluate the exact extent of both reactions ( 12) and ( 14), which are unlikely to attain equilibrium during the fast sampling and cooling of the fluid. Subsequent dilution with water yielded a significant decrease in both S 0 hexane and S 0 balance concentrations, but they are still systematically higher than the S 0 concentrations that may be produced on cooling from thermodynamically predicted S 3 •-amounts (reaction 9). The second dilution with water further decreased the observed S 0 concentrations that became with time almost identical to those predicted from S 3 •-at the end of the last stage of this experiment (~0.01 m S, Table 1).

In summary, molecular sulfur found in our experiments is only significant at rather high S tot concentrations (>0.4-0.5 m) and moderate temperatures (<350°C). It may stem from multiple contributions, as summarized in Fig. 9: i) equilibrium chain-like S 0 forming at elevated temperatures as found by in-situ Raman spectroscopy; ii) S 0 formed by the fast breakdown of S 3 •-(and S 2 •-) during cooling (reactions 9 and 13); iii) liquid or solid S 0 s/l directly precipitated during fluid extraction from the reactor before reaching the sample vial, probably by reverse of reaction ( 12) and/or by reaction ( 14); and iv) S 0 as an intermediate forming at the initial stages of the thiosulfate breakdown (reaction 10). In contrast, at lower S tot concentrations (<0.4 m) and/or higher temperatures (450°C), the S 3 •-(and potentially S 2 •-) is the major source of the measured S 0 in our quenched samples (reactions 9 and 13). These different types of S 0 may be expected to have distinct isotope signatures, which may allow their better identification, as discussed below.

Sulfur isotope fractionation and comparison with literature data

The experimental and modelled data on S speciation in our experiments allow the interpretation of S isotope fractionation between the major aqueous and solid species, and the evaluation of the effect of the radical ions and S 0 on this fractionation.

Sulfate and sulfide

In all experiments, sulfate is systematically enriched in 34 S compared to the coexisting sulfide, in agreement with general concepts of isotope fractionation that more oxidized S atoms such as in SO 4 2-having stronger chemical bonds are enriched in the heavier isotope compared to more reduced and more weekly bonded S atoms such as H 2 S (e.g., [START_REF] Urey | The thermodynamic properties of isotopic substances[END_REF]. Isotope fractionation between sulfate and sulfide, 1000×ln SO 4 = δ 34 S sulfate -δ 34 S sulfide , is 20.3±1.5 ‰ (m33, 300°C), between 14 and 21‰ (m22 and m29, 350°C), and 15.1±0.2‰ (m32/2-4, 450°C). These values are in agreement with literature data at equilibrium from both theory and experiment [START_REF] Ohmoto | Isotopes of sulfur and carbon[END_REF][START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF][START_REF] Ono | S-33 constraints on the seawater sulfate contribution in modern seafloor hydrothermal vent sulfides[END_REF][START_REF] Otake | Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems[END_REF][START_REF] Syverson | Multiple sulfur isotope fractionation and mass transfer processes during pyrite precipitation and recrystallization: An experimental study at 300 and 350°C[END_REF][START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF]references therein), which are in the range 20-24 (300°C), 17-20 (350°C), and 13-16 ‰ (450°C). In contrast, at 300°C and alkaline conditions (m32/1, pH=6.9) after 13 days of reaction, the value of 1000×ln SO 4 is only ~12 ‰, which is much smaller than its equilibrium counterpart of 20-24 ‰. Whereas the  34 S sulfide (ZnS) value becomes constant after 3 days of reaction, the corresponding  34 S sulfate (BaSO 4 ) value continues to steadily increase over the duration of this step (Table 3), causing 1000×ln SO 4 values to increase (Fig. 5a,c). A similar trend is observed at the same T (m33) but more acidic pH (5.3), with a faster reach of a steady state (Fig. 5b,d). The increasing  34 S sulfate values through time while  34 S sulfide remained constant imply another S isotope reservoir in this system that is being depleted in 34 S. Such a reservoir is consistent with the detection of significant amounts of S 0 . The kinetic isotope patterns observed here are in agreement with the generally slow rates of isotopic equilibration of sulfate [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF]; references therein), and attest for much higher chemical and isotope reactivity of H 2 S and the associated reduced S species (S 0 , S 3 •-; Pokrovski and Dubessy, 2015). Using the rate law of [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF], the rate constant log 10 k r (in hour -1 ) for an isotope exchange reaction between sulfide and sulfate at 300°C in these experiments was estimated to be -2.4±0.2 and -1.9±0.3 at pH 6.9 and 5.3, respectively (Fig. 5c,d and Appendix A5). The small difference in the k r values with pH is consistent with faster kinetics of sulfate-sulfide redox exchange rates in more acidic solutions [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF][START_REF] Kusakabe | Sulfur isotopic effects in the disproportionation reaction of sulfur dioxide in hydrothermal fluids: implications for the  34 S variations of dissolved bisulfate and elemental sulfur from active crater lakes[END_REF]. Furthermore, our absolute k r values are similar, within the uncertainties, to those predicted by [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF] based on a large set of compiled experimental data from dilute H 2 S-SO 4 solutions (<0.2 m S tot ) at 300°C and near-neutral pH (pH 300°C ~5 to 7) in which both S 0 and S 3 •-are negligible (log 10 k r ~ -3±1). Despite rather large errors associated with both measured and predicted k r values that depend on the fluid pH, ionic strength, and the presence of alkalis, this comparison does not reveal any significant effect of S 0 and S 3 •-on the sulfate-sulfide chemical and isotope exchange rates.

Molecular sulfur and radical ions

This study reports the first experimental data on the S isotope composition, including both major ( 32 S and 34 S) and minor ( 33 S and 36 S) isotopes, of intermediate-valence aqueous sulfur species, radical sulfur ions and molecular sulfur of different origin in hydrothermal fluids. We will hereafter discuss the S 0 isotope data in terms of S 0 -H 2 S fractionation, which is expected to be much less affected by kinetic constraints than fractionations involving sulfate (e.g., [START_REF] Robinson | Sulphur isotope equilibrium during sulphur hydrolysis at high temperatures[END_REF][START_REF] Kusakabe | Sulfur isotopic effects in the disproportionation reaction of sulfur dioxide in hydrothermal fluids: implications for the  34 S variations of dissolved bisulfate and elemental sulfur from active crater lakes[END_REF]Pokrovski and Dubessy, 2015).

In experiments at acidic to neutral pH (m33/2,3 at 300°C, m22/1 at 350°C, and m32/3,4 at 450°C), the measured  34 S S 0 values are fairly close to those of sulfide (despite some data scatter caused by analytical uncertainties of the measurements of micro quantities of S 0 , Table 3), yielding a mean isotope fractionation factor 1000×ln S 0 of 0±1 ‰ for the most robust data points. The absence of significant fractionation between S 0 and sulfide is confirmed by the few available literature data for both solid/liquid and aqueous S 0 . For example, [START_REF] Robinson | Sulphur isotope equilibrium during sulphur hydrolysis at high temperatures[END_REF] -0.7±0.1‰, [START_REF] Otake | Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems[END_REF], as would be expected considering the small differences in redox state and bonding between the two compounds. Higher-order polysulfide dianions S n 2-with n>4 were reported to be 34 S-enriched compared to HS -in alkaline solutions at ambient T-P (by up to 7‰; [START_REF] Amrani | Sulfur stable isotope distribution of polysulfide anions in an (NH 4 ) 2 S n aqueous solution[END_REF].

However, these anions are very minor at our conditions (Fig. 1) and the amplitude of fractionation is expected to tend closer to zero at the elevated temperatures of our experiments. More recently, the S 3 •-fractionation factor compared to H 2 S ( 34 S S 3 •-- 34 S H 2 S ), has been reported to be about -1.0 ‰ at 450°C from quantumchemical calculations on gas phase [START_REF] Tossell | Calculation of the properties of the S 3radical ion and its complexes with Cu + in aqueous solution[END_REF]. Even though associated with some simplifications, these calculations support the idea that the isotope signatures of S 3 •-, S 0 and H 2 S would be similar within 1 ‰ at hydrothermal conditions. Thus, molecular sulfur produced in the sampled fluids from these experiments is consistent with being derived from S 3 •-(and S 2 •-and chain-like S 0 detected by Raman spectroscopy at high

T).

An exception to this pattern is molecular sulfur produced via slow irreversible thiosulfate breakdown in experiment m32 at 300°C and early stages at 450°C in alkaline solution. This particular type of S 0 exhibits an anomalously low fractionation factor, 1000×ln S 0, of -11.6 ‰ (Table 3, Fig. 5a). Despite the single S 0 isotope compositional value that could directly be measured at the early stages of this experiment, the trend of  34 S S 0 to depletion with time shown in in Fig. 5a is confirmed by sulfur mass and isotope balance (Appendix A5). At present, we do not have a sound physical-chemical explanation of this unique isotope signature, very different from the close-to-zero S 0 -H 2 S isotope equilibrium fractionation value supported so far by the few available experimental and theoretical data. Thus, the anomalously light S 0 observed during thiosulfate breakdown is a new finding that may be related to previously un-recognized kinetic controls operating at far-from-equilibrium conditions and favoring enrichment of S 0 produced by irreversible reaction (10) in the lighter, i.e. generally more reactive, isotope 32 S. We note also that  33 S values show large variations at this step (Fig. 8a) confirming an out-of-equilibrium regime. In contrast, molecular sulfur from later stages of this experiment at more acidic pH (m32/3, samples #8 and #9, Table 3, Fig. 5a) has a  34 S value identical within 1 ‰ to that of the coexisting aqueous sulfide. As it was shown above, the latter type of S 0 fraction is likely to originate from S 3 •-(and S 2 •-) breakdown to S 0 and H 2 S upon fluid quench according to reactions ( 9) and ( 13). Indeed, if no isotope exchange occurs during these fast reactions, the resulting measured S 0 should carry a δ 34 S value similar to that of the radical ions.

Finally, an additional contribution to S 0 might result from direct precipitation of solid/liquid sulfur on cooling via recombination of H 2 S and SO 4 2-according to the reverse of reaction ( 12) and/or via S n 2- breakdown via reaction ( 14), both leading to formation of S 0 s,l . This was likely the case for the early stage of experiment m33 before dilution with water (m33/1, samples #2 and #3, Tables 2 and3, Fig. 5d). The two measured 1000×ln S 0 values are ~2.7 ‰, which may suggest a contribution from the isotopically heavier sulfate to the S 0 formation in this run. Indeed, combining an average value for  34 S H 2 S and  34 S SO 4 of -7 and +15 ‰, respectively, for these samples with the stoichiometry of reaction ( 12), and assuming that no isotope exchange has time to occur during quenching, yields 1000×ln S 0 = +2 ‰, in fair agreement with the measured values (Fig. 5d). Similarly, polysulfide ions that were shown to be 34 S enriched compared to H 2 S and S 0 at ambient conditions (by ~3 ‰, [START_REF] Amrani | Mechanisms of sulfur introduction chemically controlled:  34 S imprint[END_REF][START_REF] Amrani | Sulfur stable isotope distribution of polysulfide anions in an (NH 4 ) 2 S n aqueous solution[END_REF] may partly be responsible for the slightly heavier S 0 isotope signatures, but their exact contribution is impossible to quantify because the extent of reaction ( 14) during the fast fluid sampling is not known. With further dilution by water in this experiment, the degree of supersaturation with respect to S 0 (s,l) in the sampled fluid is significantly reduced, making both reactions ( 12) and ( 14) less favorable. Consequently, the measured 1000×ln S 0 values (for most robust analytical data points) tend to zero at these steps (m33/2,3), since this type of S 0 is mostly produced by decomposition of S 3 •-on cooling, similar to experiment m32 at 450°C discussed above. A schematic summary of S 0 isotope signatures resulting from different formation pathways is shown in Fig. 9. Thus, the isotope signature of S 0 formed in a cooling hydrothermal fluid may directly reflect sulfur chemical speciation at high T-P and the dynamics of speciation changes upon fluid evolution.

Pyrite

Sulfur isotope systematics of the precipitated pyrite exhibits a significant variability among the experiments, which may reflect the differences in aqueous S speciation, fluid acidity, temperature and duration. All these factors potentially affect both equilibrium and kinetic fractionation and pathways of FeS 2 precipitation, even though the interpretation is complicated by the impossibility to sample precipitated pyrite for simultaneous measurement of both aqueous sulfur and pyrite isotope values. Other issues add to this complexity such as i) relatively short durations of the post-precipitation stage (6-14 days), ii) paucity of isotope data for early experiments (m29), and iii) variations of  34 S sulfide in the course of the runs likely due to analytical issues. In the light of these limitations, we have chosen to use the average value of the  34 S sulfide data points analyzed in sampled fluids before and after pyrite precipitation (where available) in the discussion of the pyrite-aqueous sulfide fractionation factors in each experiment, as summarized in Table 4.

The average values of the pyrite-sulfide fractionation factor 1000×ln Py found in the two 350°C experiments, range from -0.5±1.3 ‰ (m22, pH change upon pyrite precipitation from 4.5 to 3.7) to 1.5±0.9 ‰ (m29, pH change upon pyrite precipitation from 7.3 to 5.3), whereas in the 450°C experiment (m32, pH change from 6.8 to 5.9) it is close to zero, 0.3±0.7 ‰ (Table 4). Equilibrium 1000×ln Py values reported in the literature on the basis of theoretical estimations within the range 350-450°C [START_REF] Ohmoto | Isotopes of sulfur and carbon[END_REF][START_REF] Otake | Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems[END_REF][START_REF] Blanchard | Iron isotope fractionation between pyrite (FeS 2 ), hematite (Fe 2 O 3 ) and siderite (FeCO 3 ): A first-principles density functional theory study[END_REF][START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF] are in the range 0.5-1.0 ‰ for the Py-H 2 S pair and 2.4-3.3 ‰ for the pyrite-HS -pair, with aqueous H 2 S being slightly enriched in 34 S compared to HS -, as also confirmed by recent direct experiments at ambient temperatures [START_REF] Sim | Precise determination of equilibrium sulfur isotope effects during volatilization and deprotonation of dissolved H 2 S. Geochim[END_REF]. Thus, our measured 1000×ln Py value of 1.5 ‰ from the higher-pH experiment at 350°C (m29) with comparable fractions of H 2 S and HS -in the fluid before pyrite precipitation, is in reasonable agreement with those predictions. In contrast, for a more acidic (i.e. H 2 S-dominated) and S 0 and S 3 •--richer experiment at the same temperature (m22), the mean 1000×ln Py value of -0.5 ‰ is by ~2 ‰ lower than the theoretical estimations above for the pyrite-H 2 S pair. However, these differences should be interpreted with caution because of the large uncertainty caused by variations of the  34 S sulfide values in the fluid before and after pyrite precipitation (Tables 3 and4).

For the 450°C experiment (m32) at near-neutral pH, our 1000×ln Py value of 0.3 ‰ is identical within analytical errors to the theoretical predictions (0.5±0.5 ‰).

The 1000×ln Py values of -0.5 to 0.3 ‰ for the H 2 S-dominated runs (m22, m32) are only ~1 ‰ higher on average than those reported by [START_REF] Syverson | Multiple sulfur isotope fractionation and mass transfer processes during pyrite precipitation and recrystallization: An experimental study at 300 and 350°C[END_REF] from long-duration (>100 days) fluid-pyrite exchange experiments in more dilute and more acidic (pH<2) H 2 S-HSO 4 -solutions, in which both S 0 and S 3 •-are negligible. Their experimental approach used 3-isotope systematics, convincingly demonstrating attainment of isotope equilibrium between pyrite and H 2 S, with 1000×ln Py of -1.9±0.8 ‰ at 350°C and -1.0±0.5 ‰ at 450°C (the latter value is estimated in this study by extrapolation assuming a T-dependence for 1000×ln Py as in [START_REF] Ohmoto | Isotopes of sulfur and carbon[END_REF]. The 1 ‰ difference between our and [START_REF] Syverson | Multiple sulfur isotope fractionation and mass transfer processes during pyrite precipitation and recrystallization: An experimental study at 300 and 350°C[END_REF] experimental values may be due to multiple factors, such as i) lack of pyrite-fluid isotope equilibrium in our short-duration experiments, and ii) different reaction pathways of pyrite formation caused by differences in S aqueous speciation and fluid pH (this study and [START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF], or degree of solution oversaturation with respect to pyrite that may lead to different crystal morphology (e.g., Murowchick andBarnes, 1986, 1987) and, potentially, S isotope fractionation during crystal growth of different crystallographic faces. All these factors may potentially cause variations of isotope signatures in pyrite compared to the coexisting fluid from which it forms. Unfortunately, our dataset is too meagre to draw more definitive conclusions or to attempt to discriminate amongst the different pyrite formation pathways amply debated in the literature (e.g., [START_REF] Schoonen | Mechanisms of pyrite and marcasite formation from solution: III. Hydrothermal processes[END_REF][START_REF] Butler | Sulfur isotope partitioning during experimental formation of pyrite via polysulfide and hydrogen sulfide pathways: implications for the interpretation of sedimentary and hydrothermal pyrite isotope records[END_REF][START_REF] Ono | S-33 constraints on the seawater sulfate contribution in modern seafloor hydrothermal vent sulfides[END_REF][START_REF] Rouxel | Integrated Fe-and S-isotope study of seafloor hydrothermal vents at East Pacific Rise 9-10[END_REF][START_REF] Saunier | First experimental determination of iron isotope fractionation between hematite and aqueous solution at hydrothermal conditions[END_REF].

Likewise, the existing theoretical estimates of pyrite-aqueous sulfide fractionation factors may be affected by limitations arising from the use of different approaches for calculating -factors of aqueous species from one hand and of solid phases from the other hand (Saunier et al., 2011 and references therein).

An additional limiting factor is imperfections of the theoretical models for estimating hydration energies of ions versus uncharged aqueous species (e.g., HS -versus H 2 S; [START_REF] Syverson | Multiple sulfur isotope fractionation and mass transfer processes during pyrite precipitation and recrystallization: An experimental study at 300 and 350°C[END_REF] and, more generally, by inaccuracies in assessing thermodynamic properties of aqueous non-electrolytes, such as H 2 S, in high T-P fluids (e.g., [START_REF] Oelkers | Thermodynamic databases for water-rock interaction[END_REF][START_REF] Akinfiev | An equation of state for predicting the thermodynamic properties and vapour-liquid partitioning of aqueous Ge(OH) 4 in a wide range of water densities[END_REF]references therein). Nevertheless, despite those experimental and theoretical limitations and the paucity of direct pyrite-fluid isotope exchange data over a wide range of temperature, acidity, and solution compositions, the main conclusion arising from this discussion is that our results do not reveal any detectable effect of S 3 •-and S 0 on pyrite-fluid isotope exchange rates and resulting pyrite isotope signatures.

 33 S and  36 S systematics

The data obtained on the minor S isotopes, 33 S and 36 S, in S-rich hydrothermal fluid-pyrite systems of this study do not provide evidence for significant mass-independent fractionation. First, our  33 S vs  34 S data plot on a commonly reported MDF fractionation line with a slope of 0.515±0.001 (95% confidence level) for all experimental compositions and temperatures (Fig. 6a, 7a, A4.2a). Second, the majority of our  33 S values plot within the area outlining potential variations of the 33 value (Fig. 6b, 7b, A4.2b) predicted among different sulfur aqueous species at equilibrium using Density Functional Theory (DFT) calculations (0.505<33<0.517, [START_REF] Otake | Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems[END_REF][START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF] and those recorded in biological and inorganic reactions among traditional S species both in nature and experiments (0.508<33<0.519; LaFlamme et al., 2018a and references therein). Similarly, the most reliable  36 S values plot within the area of the theoretical 36 slopes for MDF fractionation among S aqueous species (Fig. 6c, 7c, A4.2c; 1.88<33<1.96; Otake et al., 2008;[START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF]. Third, our  36 S- 33 S data do not plot on the MIF Archean array (Fig. 6d,7d and A4.2d).

Thus, within the experimental uncertainties, our data on 33 S and 36 S may be treated in terms of MDF, and therefore may provide additional constraints on both kinetics and equilibrium of sulfur isotope exchange reactions. We followed the approach based on the assumption that the difference of Δ 33 S and Δ 36 S values between the different S species, being initially at disequilibrium, should tend to close-to-zero values when approaching equilibrium [START_REF] Ono | S-33 constraints on the seawater sulfate contribution in modern seafloor hydrothermal vent sulfides[END_REF][START_REF] Syverson | Multiple sulfur isotope fractionation and mass transfer processes during pyrite precipitation and recrystallization: An experimental study at 300 and 350°C[END_REF][START_REF] Dauphas | Mass fractionation laws, mass-independent effects, and isotopic anomalies[END_REF], provided there is no additional MIF contributions. Indeed, the most recent theoretical work of [START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF] predicts equilibrium ∆ 33 S <0.01 ‰ for the SO 4 2--HS -pair at 300°C and even smaller values (<0.001 ‰) for other ionic S species. Our analysis here is limited by consideration of sulfate and sulfide, since no such theoretical predictions exists for S 0 , radical ions or pyrite.

Figure 8 shows the difference in  33 S and  36 S values between aqueous sulfate and sulfide (defined hereafter as Δ 33 S sulfate-sulfide and Δ 36 S sulfate-sulfide ) as a function of time in each stage of experiments m32 and m33. It can be seen that at 300°C during the initial thiosulfate breakdown (m32), the Δ 33 S sulfate-sulfide and Δ 36 S sulfate-sulfide values increase with time, consistent with the absence of equilibrium at this first stage as shown by the temporal changes of both S chemical speciation and 1000×ln SO4 values (Fig. 5). The temperature rise to 450°C (m32) results in a decrease of Δ 33 S sulfate-sulfide and Δ 36 S sulfate-sulfide values, most of which being between 0.00 and 0.02 ‰ (Fig. 8a,b). Even though our first data are not precise enough to fully support those calculated by [START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF], our trend is in line with the tendency for isotope equilibration at higher T shown by the 1000×ln SO4 evolution during the following stages (Fig. 5). Thus, our  33 S data provide additional support for the attainment of sulfate-sulfide (-pyrite) equilibrium in this experiment as independently inferred from the δ 34 S data (Fig. 5a,A4.2). The values of Δ 36 S sulfate-sulfide , which have been obtained for the first time on such S-bearing hydrothermal systems, also indicate a tendency of approaching zero with time in the 450°C stages of experiment m32, in spite of the intrinsically large uncertainties (Fig. 8b).

Values of  33 S in the experiment at 300°C at near-neutral pH (m33) show roughly similar amplitude and pattern as in run m32, by tending towards zero during breakdown of the initial thiosulfate within the first 2 weeks (Fig. 8c). Injection of water results in a 'perturbation' of  33 S values, likely caused by partial decomposition of S 3 •-and S 0 upon dilution. Values of  36 S in this experiment are more scattered, but yet indicate a similar pattern upon water injection. Thus, our study confirms previous experimental and natural findings (e.g., [START_REF] Ono | S-33 constraints on the seawater sulfate contribution in modern seafloor hydrothermal vent sulfides[END_REF][START_REF] Syverson | Multiple sulfur isotope fractionation and mass transfer processes during pyrite precipitation and recrystallization: An experimental study at 300 and 350°C[END_REF][START_REF] Mcdermott | Identification of sulfur sources and isotopic equilibria in submarine hot-springs using multiple sulfur isotopes[END_REF] that  33 S and, potentially,  36 S systematics may reflect the dynamics of sulfur species transformation and exchange in hydrothermal fluids.

GEOCHEMICAL SIGNIFICANCE AND PERSPECTIVES

Implications for tracing hydrothermal processes

The present study is the first experimental investigation of the effect of intermediate-valence polymeric sulfur species on S isotope fractionation involving the four stable S isotopes at conditions typical of hydrothermal S-bearing fluid circulation and metal ore formation in the shallow crust (<2-3 km) leading to various types of deposits. Our findings have several implications for using S isotopes as tracers of hydrothermal processes in the Earth's crust.

First, our data on S-rich fluids in the system pyrite-sulfide-sulfate quantitatively confirm the massdependent equilibrium fractionation amplitudes and kinetic patterns among these major sulfur chemical forms, previously established on the basis of extensive experimental and natural data obtained from more dilute S-poor fluids in which these polymeric sulfur species are negligible. Thus, with the available dataset, our results do not support recent hypotheses that the presence of S 3 •-(and S 0 ) could increase the rates of thermochemical sulfate reduction [START_REF] Truche | The role of S 3ion in thermochemical sulfate reduction: Geological and geochemical implications[END_REF] or control kinetic mechanisms of sulfate-sulfide exchange reactions in hydrothermal solution at acidic and neutral pH (Pokrovski and Dubessy, 2015).

Second, our study highlighted different origins of molecular sulfur in hydrothermal fluids, which may result not only from breakdown of S 3 •-(and S 2 •-), but also from partial recombination of sulfate and sulfide or isotope exchange between polysulfide dianions and H 2 S on cooling out of equilibrium yielding formation of liquid or solid sulfur (S (s,l) ), or by irreversible thermal decomposition of thiosulfate (S 0 thios ). The sulfur radical ions and S 0 have isotopic signatures indistinguishable from aqueous H 2 S. The S (s,l) phase may be slightly 34 S-enriched (by 2-4 ‰) compared to H 2 S thereby reflecting the contribution of SO 4 2-or S n 2-in the reaction of S (s,l) precipitation. In contrast, S 0 thios is strongly 34 S-depleted compared to H 2 S (by as much as equilibrium owing to fast temperature changes, may actually bear information about the evolution of hydrothermal fluids upon their cooling and rise to the surface.

Third, our study confirms the interpretations of small  33 S and  36 S variations (< ±0.1 and < ±1 ‰, respectively) in inorganic sulfur-bearing fluid -mineral (pyrite) systems as MDF in terms of reaction kinetics and mixing of S reservoirs (e.g., [START_REF] Ono | Mass-dependent fractionation of quadruple stable sulfur isotope system as a new tracer of sulfur biogeochemical cycle[END_REF]Stefansson et al., 2015;[START_REF] Syverson | Multiple sulfur isotope fractionation and mass transfer processes during pyrite precipitation and recrystallization: An experimental study at 300 and 350°C[END_REF][START_REF] Mcdermott | Identification of sulfur sources and isotopic equilibria in submarine hot-springs using multiple sulfur isotopes[END_REF][START_REF] Gunnarsson-Robin | Sulfur isotopes in Icelandic thermal waters[END_REF]. These variations are thus an efficient complement to the traditional  34 S tracer to monitor the approach to equilibrium and evolution of hydrothermal fluids and mineralization in a wide range of temperatures and S concentration and chemical speciation.

Finally, our data do not reveal any systematic mass-independent fractionation (MIF) of 33 S in the experimental S-bearing fluid-pyrite systems over a wide range of S concentrations (0.1-1 m), pH (4-8) and temperatures (300-450°C), with  33 S values of any S species being 0.0±0.1 ‰. Such values fall well within the traditionally accepted general MDF threshold of ±0.2 ‰ [START_REF] Farquhar | Multiple sulfur isotopes and the evolution of the atmosphere[END_REF] and the known variations of 33 MDF slope values (e.g., [START_REF] Otake | Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems[END_REF][START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF]LaFlamme et al., 2018a).

Thus, our results do not confirm expectations raised in a number of recent studies (e.g., [START_REF] Truche | The role of S 3ion in thermochemical sulfate reduction: Geological and geochemical implications[END_REF]Pokrovski et Dubessy, 2015;[START_REF] Selvaraja | Atmospheric sulfur in the orogenic gold deposits of the Archean Yilgarn Craton, Australia[END_REF]LaFlamme et al., 2018a,b) that S 3 •-, being a radical, might generate a significant mass-independent fractionation, in addition to the widely recognized processes of SO 2 and other gaseous S species photolysis that shall still be considered as the primary cause of sulfur MIF signatures. Thus, at the current state of our knowledge,  33 S rock record continues to serve as an efficient chemically conservative isotopic tracer of Archean sediment contributions as has been widely used in sedimentary and ore deposit geochemistry over the last 20 years.

Can reactions involving sulfur radical ions generate MIF in fluid-mineral systems?

The data obtained in this study account neither for findings of MIF 33 S signatures in some post-Archean magmatic-metamorphic sulfides (e.g., [START_REF] Farquhar | Mass-independent sulfur of inclusions in diamond and sulfur recycling on early Earth[END_REF][START_REF] Bekker | Atmospheric sulfur in Archean komatiite-hosted nickel deposits[END_REF][START_REF] Cabral | Anomalous sulphur isotopes in plume lavas reveal deep mantle storage of Archaean crust[END_REF][START_REF] Young | Reactions of hydrothermal solutions with organic matter in Paleoproterozoic black shales at Talvivaara, Finland: Evidence from multiple sulfur isotopes[END_REF]LaFlamme et al., 2018b) nor in experiments of sulfate reduction by amino-acids in hydrothermal solution [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] or liquid-phase photolysis of particular organic thiol compounds (e.g., [START_REF] Kopf | Sulfur mass-independent fractionation in liquid phase chemistry: UV photolysis of phenacylphenylsulfone as a case study[END_REF]. Therefore, the question yet remains open as to whether

or not reactions of sulfur radical ions may generate MIF signatures in fluid-mineral systems. Several specific environments in the Earth's crust may offer potential for MIF-generating reactions involving S radical species. The first is TSR processes in sedimentary/metamorphic settings in which S 3 •-is expected to be abundant enough above 150°C (e.g., [START_REF] Truche | The role of S 3ion in thermochemical sulfate reduction: Geological and geochemical implications[END_REF]Pokrovski et Dubessy, 2015;[START_REF] Barré | First evidence of the trisulfur radical ion S 3and other sulfur polymers in natural fluid inclusions[END_REF].

Until now, however, no unambiguous evidence of anomalous S isotope signatures in TSR phenomena other than those in the presence of amino-acids (such as glycine, [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] is available so far. But experimental data at relevant T-P conditions are lacking in the presence of hydrocarbon compounds (C x H y ), a type of organic matter which is the most abundant in sedimentary basins. Such environments may offer a large range of chemical pathways and reaction rates involving, in addition to S 3 •-, different organic S-bearing radical species (e.g., [START_REF] Lewan | Suphur-radical control on petroleum formation rates[END_REF]. The particularly rich chemistry of such settings enlarges the probability to find a subtle favorable interplay of kinetic factors and dynamic parameters of reactions (not too fast and not too slow; e.g., Buchachenko, 2001;2013), and reaction mechanisms involving radical-radical pairs, molecular cages (e.g., [START_REF] Kopf | Sulfur mass-independent fractionation in liquid phase chemistry: UV photolysis of phenacylphenylsulfone as a case study[END_REF]references therein) or specific mineral surfaces (e.g., [START_REF] Lasaga | Anomalous fractionation of sulfur isotopes during heterogeneous reactions[END_REF]. All these factors are expected to favor magnetic isotope effects (MIE) on the nuclear-spin possessing 33 S. Another natural environment that might meet some of the MIE requirements is ultramarine minerals of the zeolite group that host a plethora of S species, from S 2-to SO 4 2-, including S 0 and the radical ions, stabilized in Si/Al network structure cages (e.g., [START_REF] Reinen | The nature of the chalcogen colour centres in ultramarine-type solids[END_REF]Tauson et al., 2011), as well as S 3 •--bearing blue fluorites [START_REF] Müller | La fluorite bleuissante de Tignes, Tarentaise, Savoie. L'origine de sa coloration bleue: mise en évidence de radicaux bleus trisulfurés S 3[END_REF]. Such minerals form in a wide range on hydrothermal-metamorphic conditions and may provide an efficient structural trap for S aqueous species allowing preservation of their anomalous isotope signatures. A third possible environment for MIFgenerating reactions might be in magmatic-hydrothermal settings due to the presence of another radical ion, S 2 •-, which forms at the expense of S 3 •-in S-rich fluids containing sulfate and sulfate at temperatures from 450°C to at least 800°C as demonstrated by in-situ Raman spectroscopy (Pokrovski and Dubessy, 2015;[START_REF] Pokrovski | In situ quantification of the sulfur radical species (S 3 -, S 2 -) in aqueous fluids and silicate melts using a hydrothermal diamond anvil cell (HDAC)[END_REF][START_REF] Schmidt | In-situ determination of sulfur speciation and partitioning in aqueous fluid-silicate melt systems[END_REF][START_REF] Pokrovski | The nature and partitioning of invisible gold in the pyrite-fluid system[END_REF]. Having a magnetic moment similarly to S 3 •-, S 2 •-might potentially be capable of producing, in fluid-magma systems, MIF anomalies at least on 33 S, provided other factors required for MIE have been met. In addition, an improved analytical resolution on the 36 S nonmagnetic isotope may also help discriminating the factors leading to MIF. For example, the  33 S/ 36 S ratio has been used to differentiate the Archean MIF array from the kinetic MDF array (e.g., [START_REF] Johnston | Multiple sulfur isotopes and the evolution of Earth's surface sulfur cycle[END_REF]LaFlamme et al., 2018a). Verifying the hypotheses evoked above, both in nature and laboratory, would require a judicious combination of in-situ time-resolved experiments with highly sensitive analytical methods for different sulfur species and the four S isotopes in the high T-P fluid phase, thus posing a formidable challenge for future research in sulfur isotope geochemistry. 1234 Table 2 Note that two different sources of thiosulfate have been used for experiments m22 plus m29 and m32 plus m33, resulting in different  34 S values relative to V-CDT.

"-"not available or analysis was judged to be unreliable.

a Chemical yield <10%.

b Ag 2 S fraction of the initial K 2 S 2 O 3 corresponding to the isotope composition of the sulfane group.

c BaSO 4 fraction of the initial K 2 S 2 O 3 corresponding to the isotope composition of the sulfonate group.

d Error (1 SD) >0.5‰.

e Micro-volume measurement (<30 g of S).

f Calculated values using mass and isotope balance (see Appendix A5). b δ 34 S sulfide corresponds to the δ 34 S value of the ZnS fraction in the sampled fluid, calculated as the average of the indicated N sulfide number of samples taken before and after FeCl 2 injection for experiments m32 and m22 (3 samples before and 3 after), and before FeCl 2 injection for experiment m29 (2 samples).

c  Py = δ 34 S pyrite -δ 34 S sulfide .

d A different source of thiosulfate has been used in m32 resulting in different  34 S values relative to V-CDT compared to m22 and m29. indicate the pH of the neutrality point of water at the given T and P; vertical dotted lines show approximate compositions of our experiments (see Table 1 and Fig. 4 for calculations at specific compositions of each experimental step; note that experiments m22 and m29 carried out at 350°C are indicated in (A) for the sake of completeness). The oxygen fugacity is indicated relative to the hematite-magnetite buffer (HM, in log units). injection into the reactor of the indicated aqueous solutions (see Table 1 and 2 for the exact fluid compositions). (1982). The fractionation factors 1000×lnα 0 at t=0 for m32 and m33 are 6.0±1.0 and 17.5±1.0 ‰, respectively, as estimated from timeseries fractionation data points regressed to zero. Fitting the 3 data points (m32) and 9 data points (m33, by excluding a single outlier from this trend, 1000×ln SO 4 ~24 ‰, sample #3, which might be due to analytical issues related to a low SF 6 fluorination yield) at 300°C for α yields a log 10 k r value (in hour -1 ) of -2.4±0.2 (pH 6.9, m32) and -1. 9±0.3 (pH 5.3, m33), respectively.

Figure captions

  the composition and different steps of the conducted experiments. In this manuscript, all pH values are thermodynamically calculated at the corresponding T-P-composition. Two exploratory runs (m22 and m29) at 350°C in acidic (pH ~4.5 at experimental T-P) and alkaline (pH ~7.3) solutions were designed to examine S isotope fractionation in a S 3 •--rich (~0.07 m S in the form of S 3 •-) and S 3 •--poor (<0.001 m S) fluids, respectively. A more elaborated experiment (m32) consisted of two succeeding steps in slightly alkaline S 3 •-

a

  Calculated pH of the fluid at each injection step at indicated T-P. b Calculated pH of the neutrality point of water at indicated T-P as a[H + ] = a[OH -] = 0.5×log 10 K w , where K w = 1/(a H+ ×a OH-) is the water dissociation constant, and a is H + or OH -activity. c Quartz-Muscovite-Microcline mineral assemblage. d The pH and S 3 •-concentration values will be slightly refined in the course of this study for experiment m32/1-4 after correction for K 2 SO 4 precipitation (section 4.1.1, Fig. 4c, Appendix A3).

Fig. 1 .

 1 Fig.1. Sulfur species concentrations in aqueous K 2 S 2 O 3 -bearing fluids representative of this study, predicted using thermodynamic modeling with available data sources (TableA2.1), at the indicated compositions as a function of pH (adjusted by adding KOH or HCl) at 300°C, 500 bar (A) and 450°C, 700 bar (B), total sulfur (S tot ) concentration at 300°C, 500 bar (C), and temperature at 700 bar (D). Vertical dashed lines in (A) and (B)

Fig. 2 .

 2 Fig. 2. Sequence of the experimental procedures of this study using the flexible-cell hydrothermal reactor.

Fig. 3 .

 3 Fig. 3. Evolution of sulfur speciation in the fluid with time in experiments performed in this study (m22, m29, m32, and m33). S total , S sulfide , S sulfate and S 0 hexane denote analyzed concentrations whereas S 0 balance is the difference in S concentration between measured S tot and (S red + S sulfate ). Dashed vertical lines show the time of in-situ

Fig. 4 .

 4 Fig. 4. Comparisons between experimentally measured aqueous sulfate and sulfide concentrations and the corresponding thermodynamically predicted values, and between mass-balance derived molecular sulfur (S 0 balance ) and thermodynamically predicted S 3 •-(plus S 2 •-at 450°C), at each sampling point of the four conducted experiments. Calculations for m32 (C) take into account corrections for K 2 SO 4 precipitation and stability constant of KSO 4 -(see Appendix A3).

Fig. 5 .

 5 Fig. 5. Values of δ 34 S (‰) of the indicated aqueous S species and pyrite and the corresponding isotope fractionation factor (, relative to sulfide) of sulfate, S 0 and pyrite as a function of time in experiment m32 (A and C) and m33 (B and D). The dotted curve and 4 cross symbols in (A) show the evolution of S 0 isotope composition calculated using sulfur mass and isotope balance (see Appendix A5). The dotted curves (±1 SD) in (C and D) show a fit of experimental points at 300°C using the rate law from Ohmoto and Lasaga (1982): 2.303×log 10 ((α e -α)/(α e -α 0 )) = -k r ×t×([ΣSO 4 2-]+[ΣS 2-]), where t is the reaction time (in days); α 0 , α and α e are the fractionation factors of sulfate, respectively, at t=0 (initial condition), during the course of reaction, and at equilibrium; and [ΣSO 4 2-]+[ΣS 2-] is the sum of concentrations of sulfate and sulfide species. The equilibrium fractionation factor (1000×lnα e = 20.2 ‰) was taken from[START_REF] Ohmoto | Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems[END_REF]. The fractionation

Fig. 6 .

 6 Fig. 6. Isotope composition of the indicated sulfur species in samples from experiment m32 (K 2 S 2 O 3 -KOH-HCl; 300 and 450°C). Uncertainties of the coefficients of the linear regression equation in (A) are given for 95% confidence level (2 SD). The lower and upper limits of the reported 33 (from 0.505 to 0.519) and 36 (from 1.88 to 1.96) MDF slopes that encompass both equilibrium ab-initio calculated (Otake et al., 2008, for 33 and 36) and experimental and natural equilibrium and kinetic (LaFlamme et al., 2018a; references therein, for 33) variations are shown in (B) and (C) by the blue area within which most of datapoints fall (except only few outliers for sulfate and sulfonate S that are very likely to be related to analytical difficulties of BaSO 4 conversion). The MDF   S vs  33 S array (MDF-S, slope of -9 to -7) and the Archean MIF array (MIF-S, slope of -2 to -1) according to Johnston (2011) are shown in (D).

Fig. 7 .

 7 Fig. 7. Sulfur isotope compositions of the indicated species in samples from experiment m33 (K 2 S 2 O 3 ; 300°C). See Fig. 6 caption for details about the plots.

Fig. 8 .Fig. 9 .

 89 Fig. 8. The difference of  33 S and  36 S values for the sulfate-sulfide pair as a function of time in experiments m32 and m33. Gray symbols at time 0 indicate the difference values for the sulfonate-sulfane pair in the initial thiosulfate.

  Fig. 2

Fig

  Fig. 8.

  did not observe any significant  34 S changes (<0.4‰) during hydrolysis of orthorhombic sulfur (-S 8 ) in water at 200-320°C, with the resulting H 2 S being only slightly enriched in 34 S (by <2‰). Kamishny et al. (2014) investigated multiple sulfur isotope fractionations in Yellowstone hydrothermal springs (<100°C) and found that S 0 had values of  34 S and  33 S identical to or slightly heavier than those of H 2 S (by <1‰). Rare existing theoretical studies and data compilations predict equilibrium values of 1000×ln S 0 close to zero at our high-temperature conditions (-0.3±0.5‰,[START_REF] Ohmoto | Isotopes of sulfur and carbon[END_REF]

Table 1 .

 1 Summary of the experiments conducted in this study.

	Run/step	Experimental system composition at each step	pH T-P a pH 0 T-P	b	T, °C	P range,	Duration,	Injected	Predicted	Solid phases
		(moles of substance/kg fluid)					bar	of step,	aqueous	concentration	precipitated
								days	solution	of S 3 •-,
										mol S/kg fluid
	m22/1	K 2 S 2 O 3 (0.49), HCl(0.14), QMM c	4.5	5.7		350	335-370	10	-	0.067	native sulfur
	m22/2	K 2 S 2 O 3 (0.38), HCl(0.11), KCl(0.10), FeCl 2 (0.18), BaCl 2 (0.09)	3.8	5.7		350	360-380	14	KCl-FeCl 2 -BaCl 2	0.0005	pyrite, barite, alunite
	m29/1	K 2 S 2 O 3 (0.19), KOH(0.091)	7.3	5.7		350	400-405	13	-	0.0004	-
	m29/2	K 2 S 2 O 3 (0.16), KOH(0.075), FeCl2(0.059)	5.3	5.7		350	380-410	6	FeCl 2	0.0002	pyrite
	m32/1 d	K 2 S 2 O 3 (0.50), KOH(0.30)	6.9	5.5		300	430-480	13	-	0.004	-
	m32/2	K 2 S 2 O 3 (0.50), KOH(0.30)	7.9	6.0		450	690-725	14	-	0.007	-
	m32/3	K 2 S 2 O 3 (0.41), KOH(0.20), HCl (0.17)	6.8	6.0		450	705-710	8	HCl	0.037	-
	m32/4	K 2 S 2 O 3 (0.34), KOH(0.17), HCl (0.14), FeCl2(0.051)	5.9	6.0		450	695-720	8	FeCl 2	0.020	pyrite
	m33/1	K 2 S 2 O 3 (0.48)	5.3	5.5		300	410-565	15	-	0.065
	m33/2	K 2 S 2 O 3 (0.32)	5.3	5.5		300	430-550	18	H 2 O	0.024
	m33/3	K 2 S 2 O 3 (0.21)	5.3	5.5		300	380-505	8	H 2 O	0.008

.

  Fluid composition and sulfur speciation measured in sampled fluids from the experiments of this study. red includes S species other than sulfate and molecular sulfur, which all react with iodine (sulfide, radical ions, polysulfide ions, sulfite, thiosulfate). S 0 balance = S tot -(S red + S sulfate ); if S red < S sulfide or not available then S sulfide was used instead of S red . Temperature instability due to heat regulation failure around samples #6 and #7 (see Appendix A3 for details).

	3	13	5	300 44	510 -1.27	1.11	-	0.26	-	0.26	13.85	0.42	15.13	0.61	0.43 0.021	-	1.01	-0.022	--0.33	--	--0.16	76.11
	1235 4		15	300	410	1.15		0.16		0.21		0.38	0.034 c	0.56		1.07	-	-	-	-	64.99
	N Duration, Injection of H 2 O m33: K 2 S 2 O 3 (0.48 m) T, days °C bar P, 5 21 300 545 0 0 5.37 b 6 26 300 490 1 <1 -4.93 m22: K 2 S 2 O 3 (0.49 m)-HCl (0.14 m), Quartz-Muscovite-Microcline mineral assemblage S tot S red S sulfide S sulfate S 0 hexane mol/kg fluid 0.62 0.20 0.21 0.28 0.39 --5.08 a,c -0.64 0.21 0.22 0.27 0.31 --12.93 17.86 1 1 350 1.01 -0.31 0.41 -7 33 300 425 0.60 0.16 0.21 0.26 0.15 2 2 -6.61 -3.87 2.74 11.50 18.11 2 3 350 1.09 -0.31 0.43 -Injection of H 2 O Injection of K 2 S 2 O 3 3 7 350 0.96 0.34 0.30 0.42 -8 35 300 505 0.42 0.15 0.14 0.19 0.14 3 5 -7.51 -4.78 e 2.73 e 16.61 e 24.13 a 4 10 350 0.98 0.33 0.30 0.40 -9 37 300 440 0.42 0.12 0.16 0.19 0.013 4 15 -6.04 -16.46 e 22.50 10 41 300 380 0.38 0.13 0.14 0.22 0.005 Injection of water Injection of KCl-BaCl 2 -FeCl 2 5 14 350 0.27 0.02 <0.01 0.23 -error ±2 ±15 ±10% ±10% ±20% ±15% ±50% 5 21 -6.73 -7.27 -0.54 13.70 20.43 6 17 350 0.28 0.02 <0.01 0.22 -"-" means not analyzed or not applicable. 6 26 -6.32 -3.35 e 2.97 e 12.35 18.67 7 24 350 0.27 0.02 <0.01 0.21 -7 33 -7.10 -6.59 0.51 13.41 20.51 Injection of water m29: K 2 S 2 O 3 (0.19 m) -KOH (0.091 m) 1 7 352 0.37 0.18 0.17 0.17 -8 35 -7.38 --11.44 e 18.82 2 13 352 0.34 0.16 0.14 0.15 -9 37 -7.23 -2.41 e 4.82 e 14.29 21.52 10 41 -8.04 -8.61 -0.57 12.37 20.40 Injection of FeCl 2 3 16 352 0.13 <0.005 <0.01 0.14 -Error, ‰ ±0.05 ±0.05 ±0.10 ±0.05 ±0.10 ±0.010 S 0 balance a 0.13 0.012 b 0.15 0.004 0.29 0.13 0.010 0.35 0.21 0.08 0.022 0.26 0.07 0.025 0.02 <0.03 ±30% 0.035 <0.04 0.013 <0.04 0.031 <0.02 0.041 <0.03 0.025 0.024 <0.01	K 0.60 0.64 1.00 0.63 0.034 --1.02 0.92 0.44 0.080 e 0.97 0.43 -0.39 0.86 ±5% 0.029 0.88 0.023 e 0.86 0.004 0.48 -0.48 0.011 e 0.010 0.39 ±0.020	Cl -0.028 a,c -0.053 0.13 -0.054 0.13 0.13 -0.047 e 0.13 -0.026 e -0.74 ±10% 0.037 0.74 0.045 0.75 0.050 0.02 0.087 e <0.01 0.055 0.027 0.20 ±0.02	Fe -0.45 b -0.04 10 4 -0.61 d 2x10 -5 2x10 -5 -0.28 10 -5 -0.72 d -0.027 ±10% 1.02 d 0.023 -0.25 0.014 -0.38 4x10 -5 -0.26 5x10 -5 0.28 0.13 <0.002 ±0.20	K 2 SO 4 mol -------0.47 ---3.51 e ------0.51 -0.97 e --0.53 ----0.14 e -0.04 -±0.20	Pyrite mol -0.45 a,c -0.11 ---0.07 ---0.24 e --5.01 e -0.028 0.17 0.028 0.09 0.028 0.61 -3.76 d,e -0.66 0.05 0.0039 ±0.20	m fluid 84.60 g 77.73 69.42 150.00 142.72 81.00 136.87 72.71 130.05 64.87 153.19 144.80 136.83 65.62 57.57 59.51
	4		19	352		0.11		<0.005		<0.01		0.10		-	<0.01		0.39	0.19	<0.002	-	0.0039	51.73
	m32: K 2 S 2 O 3 (0.50 m) -KOH (0.30 m)
	1		3	302		0.94		0.28		0.20		0.18		-	0.48		1.15	-	-	0.0083	-	111.23
	2		8	301		0.89		0.31		0.20		0.17		-	0.41		1.11	-	-	0.0095	-	101.69
	3		13	299		0.86		0.28		0.25		0.24		-	0.34		1.06	-	-	0.011	-	96.16
	Temperature rise to 450°C
	4		16	451		0.71		0.31		0.40		0.32	0.062	<0.01		0.79	-	-	0.023	-	90.72
	5		20	451		0.69		0.28		0.35		0.24	0.005	0.10		0.78	-	-	0.022	-	84.36
	6 d		23	453		0.75		0.53		-		-		-	-		0.93	-	-	0.014	-	78.02
	7 d		27	452		0.59		0.33		0.37		0.28	0.006	<0.01		0.60	-	-	0.026	-	75.57
	Injection of HCl
	8		29	452		0.62		0.20		0.20		0.35	0.008	0.07		0.74	0.20	-	0.012	-	84.82
	9		32	451		0.57		0.19		0.19		0.31	0.060	0.07		0.68	0.18	-	0.014	-	79.26
	10		35	452		0.54		0.19		0.25		0.32	0.117	<0.01		0.61	0.22	-	0.015	-	72.16
	Injection of FeCl 2
	11		37	452		0.43		0.09		0.13		0.33	0.023	<0.01		0.68	0.27	-	0.0063	0.0041	79.48
	12		41	452		0.47		0.10		0.11		0.28	0.032	0.08		0.76	0.29	-	0.0027	0.0041	70.14
	13		44	451		0.48		0.03		0.084		0.30		-	0.10		0.75	0.28	-	0.0028	0.0041	63.31
	m33: K 2 S 2 O 3 (0.48 m)
	1		<1	300		0.96		0.20		0.28		0.40	0.87 b	0.28		0.99	-	-	-	-	83.65
	2		2	300		0.98		0.30		0.25		0.44	0.60 b	0.24		1.02	-	-	-	-	70.28
	Injection of K 2 S 2 O 3

S a b Likely overestimated because of the S 0 UV signal contamination by organic impurities from the acetate decomposition. c Underestimated because of insufficient time of reaction with hexane.

d

Table 4 .

 4 Sulfur isotope composition (in ‰) of precipitated pyrite, and pyrite-aqueous sulfide fractionation factors in the experiments of this study. δ 34 S pyrite is the average of N pyrite independent IRMS measurements for the same sample (error is 1SD of the mean).

	Run	T, °C	N pyrite	δ 34 S pyrite a	Δ 33 S pyrite	Δ 36 S pyrite	N sulfide	 34 S sulfide b	Δ 33 S sulfide	Δ 36 S sulfide	1000×	Δ 33 S pyrite -Δ 33 S sulfide	Δ 36 S pyrite -Δ 36 S sulfide
			pts				pts				ln Py c
	m22	350	2	-13.8±0.5	0.036±0.010	-0.22±0.25	6	-13.3±1.2 0.022±0.008 -0.1±0.6	-0.5±1.3	0.014±0.013	-0.13±0.60
	m29	350	4	-13.3±0.5	0.046±0.007	-0.81±0.26	2	-14.8±0.8 0.031±0.004 -0.8±0.1	1.5±0.9	0.014±0.008	-0.05±0.30
	m32 d	450	1	-1.5±0.5	0.010±0.010	-0.30±0.18	6	-1.9±0.6	0.017±0.004 -0.5±0.1	0.3±0.7	-0.006±0.011	0.15±0.30

a

ACKNOWLEDGMENTS

This work was funded by the French National Research Agency (grant RadicalS -ANR-16-CE31-0017), the Institut des Sciences de l'Univers of the Centre National de la Recherche Scientifique (grants S3MIF-PNP and S3MIF2-PNP), the Institut Carnot ISIFoR (grant OrPet), and the French and Icelandic embassies (grant PHC Jules Verne TraceSulf). We thank P. Gisquet, A. Castillo, P. Besson, C. Causserand, F. Candaudap, M. Henry, T. Aigouy, L. Menjot, B.A. Killingsworth, L. Guibourdenche, P. Sans-Jofre, A. Bouyon, D. Yang, and N. Findling for their professional help with the tough hydrothermal experiments and tedious chemical and isotope analyses. We enjoyed fascinating discussions about sulfur isotopes with M. Blanchard, A. Borisova, A. Buchachenko, M. Fiorentini, F. Poitrasson, J. Schott, A. Stefànsson, and L. Truche. Constructive comments of Associate Editor S. Ono, reviewers D. Syverson, H. Ohmoto, C. LaFlamme and two anonymous referees greatly improved this article.