Jabrane Labidi

E D Young

T Giunta

I E Kohl

J Seewald

M.D H Tang

G L Lilley

Früh-Green

M D Lilley

G L Früh-Green

Methane thermometry in deep-sea hydrothermal systems: Evidence for re

HAL is

Introduction

Deep-sea hydrothermal fluids host mantle-derived CO2 and various forms of reduced carbon that include methane, C2+ alkanes, formate, and a variety of unsaturated molecules [START_REF] Charlou | Compared geochemical signatures and the evolution of Menez Gwen (37 50ʹ N) and Lucky Strike (37 17ʹ N) hydrothermal fluids, south of the Azores Triple Junction on the Mid-Atlantic Ridge[END_REF][START_REF] Charlou | Geochemistry of high H2 and CH4 vent fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36°14ʹN, MAR)[END_REF][START_REF] Charlou | High production and fluxes of H2 and CH4 and evidence of abiotic hydrocarbon synthesis by serpentinization in ultramafic-hosted hydrothermal systems on the Mid-Atlantic Ridge[END_REF][START_REF] Holm | Initial indications of abiotic formation of hydrocarbons in the Rainbow ultramafic hydrothermal system, Mid-Atlantic Ridge[END_REF][START_REF] Konn | Hydrocarbons and oxidized organic compounds in hydrothermal fluids from Rainbow and Lost City ultramafichosted vents[END_REF][START_REF] Lang | Elevated concentrations of formate, acetate and dissolved organic carbon found at the Lost City hydrothermal field[END_REF][START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF][START_REF] Reeves | The origin of methanethiol in midocean ridge hydrothermal fluids[END_REF][START_REF] Welhan | Origins of methane in hydrothermal systems[END_REF][START_REF] Welhan | Methane and hydrogen in East Pacific Rise hydrothermal fluids[END_REF]. So-called 'black smokers' vent hydrothermal fluid with exit temperatures >300 °C and show significant amounts of molecular hydrogen (Fig. 1), which may allow for the abiotic reduction of CO and/or CO2 to methane [START_REF] Berndt | Reduction of CO2 during serpentinization of olivine at 300 °C and 500 bar[END_REF][START_REF] Horita | Abiogenic methane formation and isotopic fractionation under hydrothermal conditions[END_REF][START_REF] Jones | Carbonate control of H2 and CH4 production in serpentinization systems at elevated P-Ts[END_REF][START_REF] Mccollom | Laboratory simulations of abiotic hydrocarbon formation in Earth's deep subsurface[END_REF][START_REF] Mccollom | Abiotic methane formation during experimental serpentinization of olivine[END_REF][START_REF] Mccollom | The influence of carbon source on abiotic organic synthesis and carbon isotope fractionation under hydrothermal conditions[END_REF][START_REF] Mccollom | A reassessment of the potential for reduction of dissolved CO2 to hydrocarbons during serpentinization of olivine[END_REF][START_REF] Neubeck | Formation of H2 and CH4 by weathering of olivine at temperatures between 30 and 70 C[END_REF][START_REF] Okland | Formation of H2, CH4 and N-species during low-temperature experimental alteration of ultramafic rocks[END_REF][START_REF] Oze | Differentiating biotic from abiotic methane genesis in hydrothermally active planetary surfaces[END_REF][START_REF] Seewald | Experimental investigation of single carbon compounds under hydrothermal conditions[END_REF]. In the laboratory, abiotic methane formation is sluggish [START_REF] Mccollom | Abiotic synthesis of organic compounds in deep-sea hydrothermal environments[END_REF] but may be enhanced by the presence of a catalyst, typically a Fe-Ni alloy, preferably in the presence of H2 vapor [START_REF] Mccollom | Laboratory simulations of abiotic hydrocarbon formation in Earth's deep subsurface[END_REF][START_REF] Mccollom | Abiotic methane formation during experimental serpentinization of olivine[END_REF][START_REF] Mccollom | The influence of carbon source on abiotic organic synthesis and carbon isotope fractionation under hydrothermal conditions[END_REF]. In natural hydrothermal systems, the synthesis of abiotic methane may rather be catalyzed by oxides present in mafic and ultramafic rocks [START_REF] Foustoukos | Hydrocarbons in Hydrothermal Vent Fluids: The Role of Chromium-Bearing Catalysts[END_REF] during serpentinization. However, it is unclear whether natural fluids are saturated in vapor [START_REF] Welhan | Origins of methane in hydrothermal systems[END_REF][START_REF] Charlou | High production and fluxes of H2 and CH4 and evidence of abiotic hydrocarbon synthesis by serpentinization in ultramafic-hosted hydrothermal systems on the Mid-Atlantic Ridge[END_REF]. Whether they offer a set of conditions allowing the rapid conversion of oxidized carbon to methane remains debated. Secondary fluid inclusions may be an alternative source of abiotic methane: worldwide oceanic peridotites and gabbros host vapor H2-and CH4-rich secondary fluid inclusions [START_REF] Grozeva | Chemical and isotopic analyses of hydrocarbon-bearing fluid inclusions in olivine-rich rocks[END_REF][START_REF] Kelley | Abiogenic methane in deep-seated mid-ocean ridge environments: Insights from stable isotope analyses[END_REF][START_REF] Klein | Abiotic methane synthesis and serpentinization in olivine-hosted fluid inclusions[END_REF]. Within the inclusions, a complex interplay of reactions between olivine, oxidized carbon and gaseous H2 can lead to the synthesis of methane. As a result, inclusions contain up to 50 mole percent CH4 [START_REF] Grozeva | Chemical and isotopic analyses of hydrocarbon-bearing fluid inclusions in olivine-rich rocks[END_REF][START_REF] Kelley | Methane-rich fluids in the oceanic crust[END_REF][START_REF] Kelley | Abiogenic methane in deep-seated mid-ocean ridge environments: Insights from stable isotope analyses[END_REF][START_REF] Klein | Abiotic methane synthesis and serpentinization in olivine-hosted fluid inclusions[END_REF] and could be a large reservoir where abiotic methane formation occurs at temperatures below 340 °C by reduction of trapped magmatic CO2 [START_REF] Klein | Abiotic methane synthesis and serpentinization in olivine-hosted fluid inclusions[END_REF][START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF][START_REF] Grozeva | Chemical and isotopic analyses of hydrocarbon-bearing fluid inclusions in olivine-rich rocks[END_REF]. Dissolution or fracturing of the olivine that hosts the inclusions could simply release abiotic methane in hot hydrothermal fluids, like at Von Damm or Rainbow sites [START_REF] Klein | Abiotic methane synthesis and serpentinization in olivine-hosted fluid inclusions[END_REF][START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF]. Regardless of the exact process of abiotic methane synthesis, it appears associated specifically with high temperature fluid-rock interaction in deep-sea hydrothermal systems.

are characterized by considerably lower temperatures. However, Lost City fluids contain relatively high CH4 and H2 concentrations (Fig. 1), with isotopic and chemical signatures that are consistent with alkane abiogenesis [START_REF] Lang | Microbial utilization of abiogenic carbon and hydrogen in a serpentinitehosted system[END_REF][START_REF] Proskurowski | Abiogenic hydrocarbon production at Lost City hydrothermal field[END_REF], similar to observations made in hotter fluids [START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF]. It is unclear whether fluids at Lost City record high-temperature events (Proskurowski et al., 2006) and subsequently underwent conductive cooling, or if low-temperature chemistry allowed the synthesis of abiotic alkanes. A complication is that the coldest vents at Lost City (T < 60°C) host biofilms containing 10 6 -10 9 cells per gram of carbonate, dominated by the Lost City Methanosarcinales [START_REF] Brazelton | Methane-and sulfur-metabolizing microbial communities dominate the Lost City hydrothermal field ecosystem[END_REF][START_REF] Kelley | A serpentinite-hosted ecosystem: the Lost City hydrothermal field[END_REF][START_REF] Schrenk | Low archaeal diversity linked to subseafloor geochemical processes at the Lost City Hydrothermal Field, Mid-Atlantic Ridge[END_REF]. These methanogens may contribute methane to the fluids at those vents [START_REF] Bradley | Multiple origins of methane at the lost City hydrothermal field[END_REF] and the contribution

The concentrations of the mass-18 isotopologues of methane, 13 CH3D and 12 CH2D2 , can elucidate the origins and thermal histories of methane gases in hydrothermal fields. In D 13 CH3D versus D 12 CH2D2 space (Figure 2), 13 CH3D/ 12 CH4 and 12 CH2D2/ 12 CH4 ratios are reported relative to the stochastic distribution of isotopologues. In this diagram, methane in thermodynamic equilibrium with respect to isotopologue abundances falls on an equilibrium curve, where the relative abundances of rare isotopologues yield concordant temperatures (Figure 2). When equilibrium signatures are observed, the assumption that methane isotopologue may constrain CH4 thermometry [START_REF] Stolper | Formation temperatures of thermogenic and biogenic methane[END_REF]) may be valid [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]. In laboratory experiments, both biotic and abiotic methane exhibits disequilibrium deficits of 12 CH2D2 at varying D 13 CH3D values [START_REF] Giunta | Methane sources and sinks in continental sedimentary systems: New insights from paired clumped isotopologues 13CH3D and 12CH2D2[END_REF], Young et al. 2017). In the case of microbial methane, kinetic controls result in anomalously low values for both D 12 CH2D2 and D 13 CH3D relative to formation-temperature estimates [START_REF] Wang | Nonequilibrium clumped isotope signals in microbial methane[END_REF], Young et al. 2017). Such signatures were observed in sedimentary and lacustrine settings [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF][START_REF] Giunta | Methane sources and sinks in continental sedimentary systems: New insights from paired clumped isotopologues 13CH3D and 12CH2D2[END_REF][START_REF] Young | A Two-Dimensional Perspective on CH4 Isotope Clumping: Distinguishing Process from Source[END_REF]. Alternatively, partial reversibility of key enzymatic reactions during microbial methanogenesis [START_REF] Stolper | Distinguishing and understanding thermogenic and biogenic sources of methane using multiply substituted isotopologues[END_REF][START_REF] Wang | Nonequilibrium clumped isotope signals in microbial methane[END_REF] and/or syntrophic microbial mediation [START_REF] Ash | Exchange catalysis during anaerobic methanotrophy revealed by 12CH2D2 and 13CH3D in methane[END_REF][START_REF] Giunta | Methane sources and sinks in continental sedimentary systems: New insights from paired clumped isotopologues 13CH3D and 12CH2D2[END_REF][START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF][START_REF] Young | A Two-Dimensional Perspective on CH4 Isotope Clumping: Distinguishing Process from Source[END_REF] could lead to biogenic methane characterized by equilibrium abundances of CH4 isotopologues. Abiotic methane may exhibit peculiar signatures at high temperatures [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]; the few experimental data suggest D 13 CH3D may preserve CH4 formation temperatures of abiotic methane, while D 12 CH2D2 can exhibit substantial depletions qualitatively similar to those produced by microbial methanogenesis. This pronounced abiotic disequilibrium in D 12 CH2D2 values is well illustrated by methane in ~25°C fluids from the Kidd Creek mine, where CH4 has been suggested to be abiotic in origin [START_REF] Sherwood Lollar | Abiogenic methanogenesis in crystalline rocks[END_REF][START_REF] Sherwood Lollar | Unravelling abiogenic and biogenic sources of methane in the Earth's deep subsurface[END_REF][START_REF] Sherwood Lollar | Abiogenic formation of alkanes in the Earth's crust as a minor source for global hydrocarbon reservoirs[END_REF]. There, D 13 CH3D values are broadly consistent with environmental temperatures in the mine and inferred temperatures of methane formation [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF][START_REF] Sherwood Lollar | Abiogenic formation of alkanes in the Earth's crust as a minor source for global hydrocarbon reservoirs[END_REF] while remarkable D 12 CH2D2 depletions of up to ~25‰ relative to equilibrium are observed [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]. Although the D 12 CH2D2 formation temperatures are lost in this case, the disequilibrium isotopologue signature may be a diagnostic feature of abiotic methanogenesis [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF][START_REF] Young | A Two-Dimensional Perspective on CH4 Isotope Clumping: Distinguishing Process from Source[END_REF]). Based on these burgeoning but still unclear signatures of methane formation pathways, methane isotopologues may provide new constraints on the origin and/or the thermal history of CH4 in hydrothermal vent settings. [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF] published the first D 13 CH3D methane isotopologue data for deep-sea hydrothermal fields.

At Rainbow, Lucky Strike, Von Damm, and Lost City, they measured a homogenous D 13 CH3D values of ~1.6±0.3‰. This value suggests a temperature of 13 CH3D ordering of 310 #', &%$ °C, indicating abiotic methane formed at high-temperatures contributes to all studied hydrothermal fluids, including the fluids at Lost City [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF]. Because the homogeneous D 13 CH3D is observed for fluids with varying exit temperatures (between 370 and 96°C), it was suggested that D 13 CH3D ordering is preserved upon fluid cooling [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF]). An original aspect of the clumped CH4 systematics is that two doubly-substituted isotopologues can be measured independently (Young et al. 2016). Coupling these two species may help constrain the thermal history of methane. A current unknown is the relative behavior of D 12 CH2D2 compared to D 13 CH3D in hydrothermal fluids containing methane. It is unclear whether D 12 CH2D2 may provide new constraints on the origin of CH4 in hot hydrothermal fluids. If so, we predict disequilibrium D 12 CH2D2 signatures will help track abiotic methane in natural samples, similar to signatures observed in the ~25 °C fluids at the Kidd Creek mine [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]. Alternatively, any D 12 CH2D2 abiotic signature may be erased at elevated temperatures, via re-ordering of 12 CH2D2 isotopologue. It is unclear whether D 13 CH3D would also affected by re-ordering at all.

In other words, potential re-ordering processes may cloud the meaning of the CH4 systematics. In the absence of experimental data on the behaviors of D 12 CH2D2 and D 13 CH3D in hot fluids, we present data of D 13 CH3D and D 12 CH2D2 measured in gases from deep-sea hydrothermal fluids sampled at Lucky Strike, Rainbow, Von Damm and Lost City. These fluids experienced variable extents of conductive cooling, allowing a test of whether D 13 CH3D and D 12 CH2D2 may be re-ordered in natural fluids. Ultimately, the data are used to examine how D 13 CH3D and D 12 CH2D2 may constrain the origin and/or the thermal evolution of methane in hydrothermal systems. Some of our samples are the same aliquots of gas analyzed for D 13 CH3D by laser spectroscopy by [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF], to which we add the first D 12 CH2D2 measurements. For Lost City, D 13 CH3D and D 12 CH2D2 measurements are reported for four new samples. Our samples from all of the sites span a large range of measured vent temperatures, from 65 to 370°C. With these samples, we ascertain whether both mass-18 methane isotopologues record concordant temperatures of bond-ordering or if they record distinctive aspects of methane thermal history.

Samples and geological context

Rainbow is a hydrothermal field hosted in ultramafic rocks at 36°14' N on the Mid-Atlantic ridge (MAR), at a water depth of 2300 meters [START_REF] Charlou | Geochemistry of high H2 and CH4 vent fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36°14ʹN, MAR)[END_REF][START_REF] Seyfried | Vent fluid chemistry of the Rainbow hydrothermal system (36 N, MAR): Phase equilibria and in situ pH controls on subseafloor alteration processes[END_REF]. At Rainbow, hydrothermal fluids have temperatures up to 370 °C and are the hottest fluids studied here. Hydrothermal fluids show chloride concentrations significantly higher than seawater, indicative of a brine-vapor phase separation occurring at depth at a minimum temperature of 380 °C [START_REF] Charlou | Geochemistry of high H2 and CH4 vent fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36°14ʹN, MAR)[END_REF]. The hydrothermal endmember contains ~2 mM CH4 (Fig. 1) with a d 13 C of ~-15‰ [START_REF] Charlou | Geochemistry of high H2 and CH4 vent fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36°14ʹN, MAR)[END_REF][START_REF] Seyfried | Vent fluid chemistry of the Rainbow hydrothermal system (36 N, MAR): Phase equilibria and in situ pH controls on subseafloor alteration processes[END_REF].

Lucky Strike is an unsedimented hydrothermal vent field hosted in basaltic rock, at 37°17' N on the MAR, with fluid temperatures up to 324 °C [START_REF] Charlou | Compared geochemical signatures and the evolution of Menez Gwen (37 50ʹ N) and Lucky Strike (37 17ʹ N) hydrothermal fluids, south of the Azores Triple Junction on the Mid-Atlantic Ridge[END_REF][START_REF] Pester | Subseafloor phase equilibria in high-temperature hydrothermal fluids of the Lucky Strike Seamount (Mid-Atlantic Ridge, 37 17ʹ N)[END_REF]. Lucky Strike is a relatively shallow system with a seafloor depth of 1700 meters. There, the vent fluids have low silica, metal and rare earth content and are thought to reflect a rapid upflow of fluids to the surface with short water-rock reaction times [START_REF] Charlou | Compared geochemical signatures and the evolution of Menez Gwen (37 50ʹ N) and Lucky Strike (37 17ʹ N) hydrothermal fluids, south of the Azores Triple Junction on the Mid-Atlantic Ridge[END_REF]. Chloride concentration of hydrothermal fluids at Lucky Strike indicate the circulating seawater experienced brine-vapor phase separation at T>360°C, but at relatively low-pressure [START_REF] Charlou | Compared geochemical signatures and the evolution of Menez Gwen (37 50ʹ N) and Lucky Strike (37 17ʹ N) hydrothermal fluids, south of the Azores Triple Junction on the Mid-Atlantic Ridge[END_REF]. The methane concentration at Lucky Strike is ~1mM (Fig. 1) with a d 13 C of ~-13‰ [START_REF] Charlou | Compared geochemical signatures and the evolution of Menez Gwen (37 50ʹ N) and Lucky Strike (37 17ʹ N) hydrothermal fluids, south of the Azores Triple Junction on the Mid-Atlantic Ridge[END_REF][START_REF] Pester | Subseafloor phase equilibria in high-temperature hydrothermal fluids of the Lucky Strike Seamount (Mid-Atlantic Ridge, 37 17ʹ N)[END_REF].

The Von Damm site at 18°22' N on the Mid-Cayman rise is hosted in ultramafic, gabbroic, and basaltic rocks, at 2350 meters below seafloor [START_REF] Connelly | Hydrothermal vent fields and chemosynthetic biota on the world's deepest seafloor spreading centre[END_REF]. There, hydrothermal fluids emanate at temperatures as high as 226 °C [START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF]. Evidence that fluids experienced phase separation at Von Damm is inconclusive [START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF]. Methane concentration in the hydrothermal endmember is ~ 3mM CH4 (Fig. 1) with a d 13 C of ~-15‰ [START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF]. For all high-temperature hydrothermal fields, dD data for CH4 are scarce. To date, only [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF] published dD values for the studied sites, with all samples yielding values around -110±15‰. These values are consistent with a D/H equilibrium between methane and water established during methane formation, at ~300 °C [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF], based on the experimental data from [START_REF] Horibe | DH fractionation in the system methane-hydrogen-water[END_REF].

Lost City is located ∼15 km west of the Mid-Atlantic Ridge in 1.5 my old lithosphere dominated by ultramafic rocks with minor mafic intrusions that have been exposed through detachment faulting. It is a serpentinitehosted hydrothermal system, venting relatively cool (20-100 °C) fluids. In contrast with other systems studied here that vent acidic fluids, Lost City is the only field venting highly alkaline fluids with pH values > 9 [START_REF] Kelley | An off-axis hydrothermal vent field near the Mid-Atlantic Ridge at 30 N[END_REF][START_REF] Kelley | A serpentinite-hosted ecosystem: the Lost City hydrothermal field[END_REF]. The lower temperatures at LCHF may be due to the location of the site, a few kilometers off the mid-Atlantic ridge axis and thus not directly above a localized heat source. The chlorinity of Lost City fluid is similar to seawater, suggesting no brine separation occurred beneath the Lost City hydrothermal field [START_REF] Allen | Serpentinization and heat generation: constraints from Lost City and Rainbow hydrothermal systems[END_REF]. This is generally consistent with thermodynamic modelling suggesting maximum temperatures of 200±50°C [START_REF] Foustoukos | Chemical and isotopic constraints on water/rock interactions at the Lost City hydrothermal field, 30°N Mid-Atlantic Ridge[END_REF][START_REF] Seyfried | The Lost City hydrothermal system: Constraints imposed by vent fluid chemistry and reaction path models on subseafloor heat and mass transfer processes[END_REF] although in the past mantle rocks in the Lost City basement experienced a higher-temperature alteration history [START_REF] Früh-Green | Magmatism, serpentinization and life: Insights through drilling the Atlantis Massif (IODP Expedition 357)[END_REF][START_REF] Rouméjon | Alteration heterogeneities in peridotites exhumed on the southern wall of the atlantis massif (IODP expedition 357)[END_REF]. Maximum temperatures of 200±50°C for fluids currently circulating in the system appear to be lower than at the other sites, but the much cooler effusion temperatures of < 100°C nonetheless suggest that circulating fluids at Lost City underwent significant conductive cooling prior to venting.

Samples from Rainbow and Lucky Strike were collected by ROV Jason II during cruises to the Mid-Atlantic Ridge in 2008 [START_REF] Pester | Subseafloor phase equilibria in high-temperature hydrothermal fluids of the Lucky Strike Seamount (Mid-Atlantic Ridge, 37 17ʹ N)[END_REF][START_REF] Reeves | The origin of methanethiol in midocean ridge hydrothermal fluids[END_REF][START_REF] Seyfried | Vent fluid chemistry of the Rainbow hydrothermal system (36 N, MAR): Phase equilibria and in situ pH controls on subseafloor alteration processes[END_REF] In contrast, based on Mg concentration reported in the literature, subseafloor seawater mixing before discharge occurred in some of the samples from Von Damm. One of our samples from a central vent (Summit) is devoid of seawater contamination and represents the local hydrothermal endmember, at 226°C, while the other (Ravelin) shows evidence for subseafloor mixing with seawater that is reflected by a lower exit temperature of 145°C [START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF].

Measurement protocol

Methane was extracted from breakseals on a vacuum system at UCLA and purified by gas chromatography using procedures described previously by [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]. Between 40 and 120 micromoles of methane were available for each sample in our study (Table 1). Gases analyzed previously at MIT were subsequently trapped onto silica gel and sealed in quartz tubes for storage and transport to UCLA. At UCLA, the vacuum-line with a resting pressure of 3x10 -5 mbar or lower was used to purify the samples. The gases were transferred from the breakseals into a silica gel-filled stainless-steel u-trap cooled with liquid nitrogen. Helium carrier gas was used to flush the sample to the gas chromatograph. Separation was accomplished with a 3m long, 1/8 in. OD stainless steel column packed with 5 A molecular sieve, followed in series by a 2m long 1/8 in. OD stainless steel column packed with HayeSep D porous polymer. Gas chromatograph peaks were detected with an in-line, passive thermal conductivity detector (TCD). Once methane collection was complete, methane was transferred to a glass vial filled with silica-gel at liquid nitrogen temperature and subsequently connected to the inlet of the Panorama mass spectrometer where it was warmed and expanded into the mass spectrometer.

Isotopologue measurements were made using the Panorama instrument, a Matsuda-type large radius high-resolution mass spectrometer at UCLA with a mass resolving power that allows the simultaneous measurement of ion currents for resolved 12 CH4 + , 13 CH4 + , 12 CH3D + , 13 CH3D + and 12 CH2D2 + ion beams. The measured ratios of these ion currents yield values for both D 13 CH3D and D 12 CH2D2 as well as for bulk 13 C/ 12 C and D/H. The mass spectrometer is set to a mass resolving power equal to or greater than 40,000. Both low abundances of the mass-18 isotopologues, 13 CH3D + , and 12 CH2D2 + , require that measurements are made with an electron multiplier. Isotopologues of masses 16 and 17 are measured on Faraday collectors with amplifier resistors of 10 11 W. The bulk carbon and hydrogen stable isotopic ratios are reported relative to the international standards V-PDB and V-SMOW, respectively, and expressed in permil units using the delta notation:

δ 13 C= [( 13 C/ 12 C)sample/( 13 C/ 12 C)VPDB -1] x 1000 (1)
and

δD= [(D/H)sample/(D/H)VSMOW -1] x 1000 (2).
Mass-18 isotopologue compositions are reported versus a stochastic distribution expressed in permil using the capital delta notation:

Δ 13 CH3D= [( 13 CH3D/ 12 CH4)sample/( 13 CH3D/ 12 CH4)stochastic -1] x 1000

(3) and

Δ 12 CH2D2= [( 12 CH2D2/ 12 CH4)sample/( 12 CH2D2/ 12 CH4)stochastic -1] x 1000 (4).
The relationship between Δ 13 CH3D and Δ 12 CH2D2 and temperature has been predicted through ab initio calculations and can be represented by the following expressions [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]:

Δ 13 CH3D (T)
)
where T is in Kelvin. These equations were verified using methane samples equilibrated over a range of temperatures in the UCLA laboratory [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]) and are consistent with gases equilibrated at low temperatures in other laboratories [START_REF] Eldridge | Comparison of Experimental vs Theoretical Abundances of 13CH3D and 12CH2D2 for Isotopically Equilibrated Systems from 1 to 500[END_REF][START_REF] Wang | Method for calibrating methane clumped isotope measurements via catalytic equilibration of methane isotopologues on γ-alumina[END_REF]. Equations ( 5) and ( 6) show that when methane is formed at thermodynamic equilibrium, D 13 CH3D and D 12 CH2D2 are both positive, and must approach 0‰ at high temperatures (>1000 K).

Variable volume bellows for the sample and reference gases are adjusted after each measurement cycle of approximately 30 seconds so that ion current intensities are always balanced during the analyses. The mass spectrometry integration methods are described in Young et al. (2016). For standards and samples available in quantities > 80 µmol, relative abundances of 13 CH3D + and 12 CH2D2 + are measured for up to 10 and 20 hours, respectively. In these cases, typical propagated internal errors for the calculation of D

Results

Our bulk isotope ratios are in general agreement with previously-published CH4 isotopic data for these localities [START_REF] Charlou | Geochemistry of high H2 and CH4 vent fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36°14ʹN, MAR)[END_REF][START_REF] Seyfried | Vent fluid chemistry of the Rainbow hydrothermal system (36 N, MAR): Phase equilibria and in situ pH controls on subseafloor alteration processes[END_REF], 2015;[START_REF] Pester | Subseafloor phase equilibria in high-temperature hydrothermal fluids of the Lucky Strike Seamount (Mid-Atlantic Ridge, 37 17ʹ N)[END_REF][START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF][START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF][START_REF] Proskurowski | Abiogenic hydrocarbon production at Lost City hydrothermal field[END_REF]. In dD vs d 13 C space the samples plot in the 13 C-and D-enriched extremity of the abiotic methane field (Fig. 3) [START_REF] Etiope | Abiotic methane on Earth[END_REF]. Comparison with the data of [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF] shows good agreement. Disagreement is found for one datum for sample J2-612-IGT2 from Von Damm where there is a discrepancy in dD between the two laboratories, with the UCLA value being lower by ~5‰. The UCLA datum for this sample also exhibit a low d 13 C value relative to the MIT value, consistent with a 1:10 d 13 C -dD fractionation that must have occurred between the moment it was measured at MIT and the moment it was measured at UCLA. We speculate that a fractionation could have occurred during incomplete sample freezing onto the silica gel in the quartz tube at MIT. Nonetheless, we determined a D 13 CH3D value from this gas that is indistinguishable from that reported by [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF], within uncertainties. This suggests that if a fractionation had occurred during the trapping of the sample at MIT, or during gas processing at UCLA, it was not sufficient to affect the apparent bond ordering.

Our methane isotopologues results ( We find no relationships between the isotopologue signatures and host rock (whether hydrothermal fluids are hosted in basaltic versus ultramafic rocks), seafloor depth, or likely maximal pressures reached in the subsurface (Fig. 2). We argue below that the isotopologue signatures result from partial or near-complete reequilibration of doubly-substituted isotopologues at environmental temperatures.

Discussion

Equilibrium signatures for methane isotopologues

The methane isotopologue data for the hydrothermal systems studied here show signatures ranging from equilibrium to disequilibrium, from the hottest to the coldest fluids, respectively (Fig. 2). Samples from Rainbow have average D 13 CH3D and D 12 CH2D2 values that represent thermodynamic equilibrium among the methane isotopologues. The D 13 CH3D values correspond to an apparent temperature of 343 #$% &'( °C, similar to that derived previously [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF]. The temperature indicated by the D 12 CH2D2 values is 334 #%$ &5-°C, indistinguishable from that derived from the more abundant 13 CH3D isotopologue, albeit less precise. This establishes that methane from Rainbow is in isotopic bond-ordering equilibrium.

Equilibrium could result from abiotic methane synthesis. This would be in contrast with deficits in D 12 CH2D2

where abiotic methanogenesis may have occurred at low temperatures at the Kidd Creek mine, where fluids carrying methane show measured temperatures of ~25°C [START_REF] Sherwood Lollar | Abiogenic formation of alkanes in the Earth's crust as a minor source for global hydrocarbon reservoirs[END_REF], Young et al., 2017).

Equilibrium signatures in hot fluids could alternatively represent re-equilibration at high temperatures rather than being the result of the formation mechanism. Re-ordering is also suspected because disequilibrium D 12 CH2D2 signatures seem to be associated with abiotic CH4 formation in laboratory experiments with durations from 12 to 30 days [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]. The few data for abiotic methane synthesized experimentally suggest D 13 CH3D-based temperatures to be roughly consistent with experimental temperatures of abiotic CH4 formation, while D 12 CH2D2 depletions of ~2 to 60‰ relative to equilibrium were observed between 75 and 500 °C. Only experiments where methane was synthesized at 600°C during about 12 days yielded equilibrium for both D 12 CH2D2 and D 13 CH3D values [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]. We emphasize that it is unlikely that the experiments presented in [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF] are an accurate representation of geochemical processes in deep-sea hydrothermal fields. It is interesting, however, that the two sets of experiments explored different formation mechanisms, the Fischer-Tropsch-type Sabatier reaction and silane hydration, and yielded broadly consistent results. In the silane experiments, Si5C12H36 reacts with H2O to produce SiO2, CH4 and H2 [START_REF] Foustoukos | H/D methane isotopologues dissolved in magmatic fluids: Stable hydrogen isotope fractionations in the Earth's interior[END_REF] In the Sabatier processes, CO2 is converted to CH4 catalyzed with ruthenium at temperature < 100 °C [START_REF] Etiope | Low-temperature catalytic CO 2 hydrogenation with geological quantities of ruthenium: a possible abiotic CH 4 source in chromitite-rich serpentinized rocks[END_REF]. In both experiments, the large D 12 CH2D2 depletions may result from a quantum tunneling effect expressed during hydrogenation of methane precursors [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]).

Alternatively, it may result from what is termed a "combinatorial effect" caused by mixing sources of hydrogen with markedly different D/H produced by classical kinetic and equilibrium partitioning of isotopes associated with the various hydrogenation steps during reduction of oxidized carbon [START_REF] Cao | A kinetic model for isotopologue signatures of methane generated by biotic and abiotic CO2 methanation[END_REF][START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF][START_REF] Young | A Two-Dimensional Perspective on CH4 Isotope Clumping: Distinguishing Process from Source[END_REF]. Hydrogen with wide ranging D/H ratios is sourced from different reversible and irreversible steps during methane formation, resulting in deficits in D 12 CH2D2 caused by mixing the various sources of hydrogen [START_REF] Röckmann | Statistical clumped isotope signatures[END_REF][START_REF] Taenzer | Low apparent Δ12CH2D2 in microbialgenic methane result from combinatorial isotope effects[END_REF][START_REF] Yeung | Combinatorial effects on clumped isotopes and their significance in biogeochemistry[END_REF]. The two mechanistic interpretations described here both allow the preliminary experimental results from [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF] to be extrapolated to natural settings, but further experimental work is needed.

In the context of the limited natural and experimental evidence, we tentatively suggest that equilibrium signatures at Rainbow (Fig. 2) might result from re-ordering rather than being inherited directly from abiotic methane synthesis. Secondary fluid-inclusions in gabbroic and ultramafic rocks likely contribute abiotic methane to hydrothermal fields (Kelley and Fruh Green, 1999[START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF][START_REF] Mccollom | Abiotic methane formation during experimental serpentinization of olivine[END_REF][START_REF] Klein | Abiotic methane synthesis and serpentinization in olivine-hosted fluid inclusions[END_REF]. The inclusions may also provide conditions suitable for post-formation re-equilibration, since they contain metal oxides possibly contributing to catalysis [START_REF] Klein | Abiotic methane synthesis and serpentinization in olivine-hosted fluid inclusions[END_REF][START_REF] Grozeva | Chemical and isotopic analyses of hydrocarbon-bearing fluid inclusions in olivine-rich rocks[END_REF] which yields an apparent temperature of 325 #$( &'6 °C. The D 12 CH2D2 values are homogeneous as well but with an average of ~+4.5±1.0‰, corresponding to a lower temperature of 247 #$% &'$ °C, similar to the measured hydrothermal maximum temperature of 226 °C (Fig. 4). We see no correlations between methane isotopologue data and the extent of subseafloor mixing with seawater (Table 1). The methane concentration of seawater is so low that arguably, seawater contamination does not add significant amounts of methane to the bulk vent fluid. We additionally conclude that both D 13 CH3D and D 12 CH2D2 values remain unaffected by the abrupt cooling associated with seawater infiltration.

Based on these results, we suggest that the methane isotopologue data at Rainbow, Lucky Strike and Von Damm are all consistent within 2s with high-temperature methane formed at ~ 330 °C, as recorded by D 13 CH3D.

This thermometry is consistent with methane originating from secondary fluid inclusions, where thermodynamic modeling suggests it was synthesized over geological timescales at temperatures between 300 and 400°C [START_REF] Klein | Abiotic methane synthesis and serpentinization in olivine-hosted fluid inclusions[END_REF]. Our results also imply re-ordering of the original D 12 CH2D2 values in the cooler carrier fluids. However, the D 12 CH2D2 re-ordering is about 2‰ and thus its detection is marginal given the measurement uncertainties of ~1‰. We show below that data obtained on the coldest site studied here, Lost

City, are more dispositive with regard to the origin of discordance between D 13 CH3D and D 12 CH2D2 values. These discordant isotopologue temperatures constitute marked disequilibrium (Fig. 2).

5.2: Substantial

Before discussing the evidence of D 12 CH2D2 re-ordering at Lost City, we consider first whether the disequilibrium seen in the D 13 CH3D and D 12 CH2D2 data could be the result of mixing (e.g., [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]. A relatively constant CH4/ 4 He ratio observed in Lost City vent fluids argues in favor of a unique abiotic source [START_REF] Proskurowski | Abiogenic hydrocarbon production at Lost City hydrothermal field[END_REF][START_REF] Lang | Microbial utilization of abiogenic carbon and hydrogen in a serpentinitehosted system[END_REF]. However, others have suggested a possible contribution from biotic sources (Bradley et al. 2009[START_REF] Bradley | Multiple origins of methane at the lost City hydrothermal field[END_REF]; the coldest vents at Lost City (T < 60°C) host biofilms dominated by the Lost City Methanosarcinales phylotype [START_REF] Brazelton | Methane-and sulfur-metabolizing microbial communities dominate the Lost City hydrothermal field ecosystem[END_REF][START_REF] Kelley | A serpentinite-hosted ecosystem: the Lost City hydrothermal field[END_REF][START_REF] Schrenk | Low archaeal diversity linked to subseafloor geochemical processes at the Lost City Hydrothermal Field, Mid-Atlantic Ridge[END_REF]. The methanogens may contribute significant microbial methane to the fluids at those vents [START_REF] Bradley | Multiple origins of methane at the lost City hydrothermal field[END_REF]. In principle mixing between abiotic and microbial methane could account for the Lost City characteristic excesses in D 12 CH2D2. Our use of two mass-18 isotopologues affords the ability to identify mixing if it occurred at Lost City: mixing trajectories in D 13 CH3D versus D 12 CH2D2 space may trend above the equilibrium curve into positive D 12 CH2D2 deviations from equilibrium when endmembers are similar in d 13 C values but disparate in dD values. Multiple two-component mixing scenarios can satisfy mixing relationships in the isotopologue space. For example, in Figure 5 we show a two-component mixing model between a gas equilibrated at 400°C and a microbial gas with characteristic D 12 CH2D2 deficits. The high-T endmember d 13 C and dD values are taken to be similar to the values observed at Lucky Strike for illustration. Approximately 20 to 25% of a microbial gas mixed with high-temperature gas like that at the other vent sites can explain the methane isotopologue data at Lost City (Figure 5, panel a). However, for the mixing loop to reach the compositions of the Lost City samples, unusually high d 13 C values of between -35‰ and -20‰ must be ascribed to the microbial methane component (Fig. 5, panel b). This is because the bulk isotopes and clumped isotopologue values, by design, do not vary independently. Such high d 13 C values would be considered unreasonable for microbial methane in most systems [START_REF] Whiticar | Carbon and hydrogen isotope systematics of bacterial formation and oxidation of methane[END_REF], but may be conceivable at Lost City, where biomarkers were observed with extraordinarily high d 13 C values (Bradley et al. 2009). This mixing scenario, however, fails to match the data trends where bulk isotope ratios are considered, including d 13 C vs. dD and D 13 CH3D vs. d 13 C (Figure 5, panel b and c respectively). Conversely, when mixing is successful in panels comparing bulk isotopes and clumped isotopes (Fig. 5, panel b and d), it fails at accounting for the data in mass-18 isotopologue space (Figure 5, panel a). For this reason, we conclude that mixing with a microbial methane component is not the main source of the anomalously high D 12 CH2D2 values at Lost City. An alternative mixing scenario involves two gases both at isotopologue thermodynamic equilibrium at two disparate temperatures (Figure 5). A ~50:50 mixing of two gases, one on the equilibrium curve at 400°C, and the other on the equilibrium curve at any temperature < 150°C, could fit the Lost City isotopologue and bulk isotope data as long as the d 13 C and dD of the endmembers are restricted to a tight range of values. An example is shown in Fig. 5, with a gas taken at 100°C for illustration (curve 2). The 100°C gas at Lost City would have to have d 13 C values ≥-8‰, and corresponding dD values of -170‰ and lower. This is at the high-d 13 C and low-dD end of the empirically-defined abiotic field in Figure 2 ( [START_REF] Etiope | Abiotic methane on Earth[END_REF][START_REF] Whiticar | Carbon and hydrogen isotope systematics of bacterial formation and oxidation of methane[END_REF]. The high d 13 C would be consistent with the nearquantitative reduction of magmatic CO2 [START_REF] Horita | Abiogenic methane formation and isotopic fractionation under hydrothermal conditions[END_REF] Mixing involving a microbial endmember seems to be ruled out, and mixing between gases equilibrated at high and low temperatures yields imperfect fits to the methane isotopologue and bulk isotope data taken together. If mixing cannot satisfy the data in Fig. 5, we speculate that this is because D 12 CH2D2 was altered by re-ordering at the temperature of the ambient fluids in the vent system at shallow depths. The near-perfect match between D 12 CH2D2-based temperatures and fluid temperatures (Fig. 4) argues in favor of D 12 CH2D2 reordering. This conclusion is independent of the initial isotopologue composition of the abiotic methane, be it on the equilibrium curve or below the equilibrium curve, as observed with the limited experimental evidence [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]; see discussion above). We also suggest that the evidence for re-equilibration at Lost City (Fig. 4) allows re-equilibration to have occurred at high-temperatures sites like Rainbow (see section 5.1). The mechanism of re-equilibration remains unclear. In the laboratory, methane isotopologues reorder only in the presence of a metal catalyst or alumina [START_REF] Eldridge | Comparison of Experimental vs Theoretical Abundances of 13CH3D and 12CH2D2 for Isotopically Equilibrated Systems from 1 to 500[END_REF][START_REF] Stolper | Formation temperatures of thermogenic and biogenic methane[END_REF][START_REF] Wang | Method for calibrating methane clumped isotope measurements via catalytic equilibration of methane isotopologues on γ-alumina[END_REF]Young et al., 2017) when methane is in a gas phase, but no experiments exist for dissolved methane in water. At Lost City (and in all other deep-sea hydrothermal sites), methane is dissolved in water. Since D 12 CH2D2 is evidently reordered specifically at the exit temperature of the host fluids, the re-equilibration must have occurred in the cooling fluid upon ascent, perhaps facilitated by the metals that occur in underlying serpentinites at Lost City [START_REF] Kelley | A serpentinite-hosted ecosystem: the Lost City hydrothermal field[END_REF], Fruh-Green et al., 2018) or in metal deposits in chimneys observed at other sites (Von Damm, 1990). It is also possible that the re-equilibration of D 12 CH2D2 values is microbially mediated. The Archeal community at Lost City includes anaerobic methane-oxidizing Archaea, ANME-1 (Brazelton et al., 2010). Equilibration of D 12 CH2D2 values has been attributed to anaerobic oxidation of methane (AOM) at several localities, notably in gases from the Baltic Sea and the Western Ontario Basin [START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF][START_REF] Giunta | Methane sources and sinks in continental sedimentary systems: New insights from paired clumped isotopologues 13CH3D and 12CH2D2[END_REF][START_REF] Ash | Exchange catalysis during anaerobic methanotrophy revealed by 12CH2D2 and 13CH3D in methane[END_REF]. However, the evidence for equilibration by AOM has been circumstantial and yet to be demonstrated conclusively in the laboratory, and would not account for the equilibrated D 12 CH2D2 data at Rainbow, Von Damm and Lucky Strike, where temperatures are above 122 °C, often considered the upper limit for life (Takai et al. 2008).

In all cases, the data suggest that bond re-ordering is substantially slower for D 13 CH3D, as if re-ordering was inhibited when the isotopologue includes 13 C rather than 12 C. The mechanism allowing one isotopologue, 12 CH2D2, to be re-ordered to fluid temperature, while 13 CH3D remains seemingly constant deserves experimental attention. The observation that D 12 CH2D2 is prone to re-equilibration at lower temperatures while D 13 CH3D is not suggests that the abundances of 13 CH3D may represent a geochemical indicator that preserves information about temperatures associated with methane formation, even when the methane is transported at low temperatures prior to venting. The latter point is consistent with an earlier suggestion based on D 13 CH3D measurements alone [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF]), but it is verified and underscored by the contrasting behaviors of the two mass-18 isotopologues of methane at the vents studied here. The value of the D 12 CH2D2 values may lie with their sensitivity to subsequent environmental conditions.

A caveat to the basic picture described above arises from the observation of a ~1.5‰ D 13 CH3D variability at Lost City, when the Beehive Marker C and Marker 2 vents are compared. To explain this in the context of just one high-temperature source of methane at Lost City [START_REF] Lang | Microbial utilization of abiogenic carbon and hydrogen in a serpentinitehosted system[END_REF], one must invoke partial re-ordering of D 13 CH3D. The implication is that the cooling that resets D 12 CH2D2 values also partially re-equilibrates [START_REF] Brazelton | Methane-and sulfur-metabolizing microbial communities dominate the Lost City hydrothermal field ecosystem[END_REF]) may be poorly suited to process methane in Lost City (Lang et al. 2018) but if any biological mediation of methane occurred, it might have affected D 13 CH3D at Marker 2, raising the values to 3.0±0.2‰ there. The advantage of the hypothesis for partial D 13 CH3D re-equilibration at Lost City is that it explains why gases with higher D 13 CH3D are only observed in the coldest vents. It also removes the need for multiple methane pools, which is inconsistent with the broadly constant CH4/ 4 He ratio observed in the vents of Lost City [START_REF] Proskurowski | Abiogenic hydrocarbon production at Lost City hydrothermal field[END_REF][START_REF] Lang | Microbial utilization of abiogenic carbon and hydrogen in a serpentinitehosted system[END_REF].

D 13 CH3D

The relative vulnerability of 12 CH2D2 to re-ordering

A process allowing D 12 CH2D2 to be equilibrated at fluid temperature during conductive cooling, while D 13 CH3D remains broadly constant, appears to account for natural data. This process calls for differences in reequilibration rates. Here we explore this possibility with a simple kinetic model for exchange. Sophisticated models, where re-equilibration is driven by D/H exchange between methane and water, could be envisioned.

In this context, water would be a reactive intermediate for re-ordering of methane isotopologues. At Lost City, this approach would be consistent with the overall lower D/H ratio for vented methane compared to other sites, suggesting some (but rather limited) D/H exchange occurred between methane and water during fluid cooling (Proskurowski et al., 2006, Reeves et al., 2012). As a first approximation, we explore the specific case of exchange of H and D between methane molecules. Our result based on molecular symmetry turns out to be the same if we use water as the exchange partner. In either case, the stretched bond permitting the fleeing of a protium or deuterium from a methane molecule is the reaction coordinate. We can describe the transition state formed by this stretching symbolically, in the case of CH4, as CH3-H. The relative magnitudes of rate constants for exchange reactions among isotopologues are dominated by differences in symmetry numbers, as can be deduced from the analysis by [START_REF] Haghnegahdar | A model for 12CH2D2 and 13CH3D as complementary tracers for the budget of atmospheric CH4[END_REF]. Indeed, both kinetic rate constants and equilibrium constants for the mass-18 isotopologues are controlled to first order by differences in symmetry numbers of the molecules. For example, the high-temperature limits for the equilibrium constants shown in Equations ( 5) and ( 6) are 1 and 3/8, respectively, both corresponding to the relevant ratios of reactant and product symmetry numbers.

Consider the reactions One may apply transition state theory and write the reaction in terms of the transition state for one molecule that will control the rate of the reaction, treating the deuterated reactant as rate limiting in a matrix of exchangeable CH4 gas (or, as it turns out, H2O). While the full equation that includes vibrational and rotational partition functions is necessary for capturing isotope ratios in detail at the per mil level of precision, the rate constant ratio can be well approximated for our purposes using the ratio of symmetry numbers for the transition states and the reactants where si are the symmetry numbers. For this purpose, we use the known symmetry numbers for the reactants: s12CH4 = 12, s13CH3D =3, and s12CH2D2 = 2 and recall that the rotational partition functions are proportional to the inverse of the symmetry numbers. We estimate the likely symmetry numbers for the transition states CH2D-D* and 13 CH3-D* based on previous work [START_REF] Haghnegahdar | A model for 12CH2D2 and 13CH3D as complementary tracers for the budget of atmospheric CH4[END_REF]. This result shows that the reaction involving the re-equilibration of 12 CH2D2 can be expected to have a rate constant that is twice that for 13 CH3D. In practice, this means that during conductive cooling of a fluid, simple symmetry effects will lead D 12 CH2D2 to equilibrate twice as fast to environmental temperature than D 13 CH3D.

Because the symmetry number of the exchange partner ( 12 CH4 as written) cancels in Equation ( 9), substituting H2O for 12 CH4, where sH2O =2, gives the same ratio of rate constants. We note, however, that the geometries associated with CH4-H2O exchange are highly uncertain (e.g., [START_REF] Van Mourik | Ab initio calculations on the CH… O hydrogenbonded systems CH4-H2O, CH3NH2-H2O and CH3NH3+-H2O[END_REF][START_REF] Cappelletti | H2O-CH4 and H2S-CH4 complexes: a direct comparison through molecular beam experiments and ab initio calculations[END_REF][START_REF] Richardson | Concerted hydrogen-bond breaking by quantum tunneling in the water hexamer prism[END_REF].

In order to apply these rate constants to the exchange process, we make use of rate equations for kinetic isotope exchange expressed in terms of fractional approaches to equilibrium [START_REF] Criss | Kinetic theory of oxygen isotopic exchange between minerals and water[END_REF] for the reactions in Equations ( 7) and ( 8), respectively:

(10) and

21

(11) where subscript t refers to time, subscript o refers to initial concentrations, and subscript EQ refers to the equilibrium concentrations for the isotopologues.

The re-equilibration mechanism with various rate constant ratios is plotted on figure 2, alongside the data. We explore whether the trajectory of a gas equilibrated at high temperatures undergoing cooling matches the Lost City observation. We take the low-temperature endpoint to be constrained by the measured temperature in the relevant Lost City vents, at 65 °C. Although the rate constant ratio of 2 resulting from Equation ( 9) yields a trajectory in the right direction, it does not fully account for the data. We find that a rate constant ratio kCH2D2/k13CH3D of ~5 is required to explain the data (Fig. 2). Again, our data highlight the need for experimental work to explore whether these re-equilibration patterns are to be expected on a physicochemical basis. The simple theoretical framework explored here may offer a first order guide to how methane isotopologues behave during fluid cooling in natural settings.

Conclusion

We report D 13 CH3D and D 12 CH2D2 data in methane samples from deep-sea hydrothermal systems. We show that in the hottest fluids at the Rainbow site, concordant temperatures are recorded by the two mass-18 isotopologues. Thus, methane is in internal thermodynamic equilibrium. In the other sites, we observe variable D 12 CH2D2 at nearly constant D 13 CH3D. The data exclude mixing with microbial gas; mixing produces imperfect fits to the bulk isotope ratios and isotopologue abundances. With the exception of a sample from Vom Damm, Ravelin, all the samples studied here have Mg concentrations 5 mmol/kg (Data in Reeves et al., 2014, McDermott et al., 2015, andthis study). Ravelin, however, shows a concentration of ~16 mmol/kg, together with a lower temperature than the local fluid endmember [START_REF] Reeves | The origin of methanethiol in midocean ridge hydrothermal fluids[END_REF]. This one gas can be accounted for by seawater infiltration, abruptly lowering temperature venting. equations in section 5.3. Three scenarios are shown with three different ratios for the exchange rate constants for D 12 CH2D2 and D 13 CH3D (see text). Note that the endmember low temperature is picked at 65 °C for illustration. This corresponds to the approximate temperature of the fluid from marker 2, the coldest vent studied here. For the Beehive vent, a temperature of 96 °C would be required for the low-temperature endmember. Although not shown here for the sake of clarity, such an endmember temperature fits the Beehive data if k1~ 5 x k2.

Figure 3: dD and d13C values of methane samples in the "Schoell" plot [START_REF] Schoell | Multiple origins of methane in the Earth[END_REF]. Fields are suggested by those from [START_REF] Etiope | Abiotic methane on Earth[END_REF]. As suggested in previous work [START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF], Microbial Thermogenic Abiotic [START_REF] Proskurowski | Abiogenic hydrocarbon production at Lost City hydrothermal field[END_REF][START_REF] Charlou | High production and fluxes of H2 and CH4 and evidence of abiotic hydrocarbon synthesis by serpentinization in ultramafic-hosted hydrothermal systems on the Mid-Atlantic Ridge[END_REF][START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF], methane in deep-sea hydrothermal field plots defines the extremity of the abiotic field. Data and uncertainties are from Table 1.

(

  115 °C). Six Lost City samples were collected during the 2008 ROV Jason II cruise (J2-361-IGT5), the 2005 Lost City expedition (H06_GT_15/16) and the 2018 cruise to Lost City (J2-1107-GT9, J2-1111-Titan, J2-1110-GT18, J2-1110-Titan). They are from three vents: Beehive (~100°C), Marker C (~85°C), and Marker 2 (~65 °C). Eight of our samples were previously analyzed by laser spectroscopy at MIT[START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF]. Those were from Rainbow (n=3), Von Damm (n=3), Lucky Strike (n=3) and Lost City (Beehive only, n=1). The six remaining samples were not analyzed previously for either methane bulk isotope compositions nor for the rarer mass-18 methane isotopologues.Due to near-zero concentrations of dissolved magnesium (Mg) in endmember hydrothermal vent fluids, measured Mg concentrations in sampled fluids can be used to estimate the extent of seawater entrainment during sampling or subsurface mixing. Concentrations of dissolved CH4 concentrations plotted against dissolved Mg concentration for fluids from all sites studied are shown in Figure1with data from the literature[START_REF] Reeves | The origin of methanethiol in midocean ridge hydrothermal fluids[END_REF][START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF]. Despite the considerable mixing shown in Figure1, we picked samples from Lucky Strike, Lost City, and Rainbow with low Mg concentration that can be considered to have minimal seawater contribution from sampling and thus more representative of the hydrothermal endmember.

  and would likely host methane over long periods of time. Alternatively, the concordant temperatures may reflect a rapid reequilibration of all doubly-substituted isotopologues in the hot carrier fluid: at Rainbow, the D 13 CH3D-based temperature of 343 #$% &'( °C and the D 12 CH2D2 temperature of 334 #%$ &5-°C are both statistically indistinguishable from the temperature of the carrier fluid (360±10°C). Our data are therefore consistent with abiotic methane synthesis or re-equilibration in either the source fluid inclusions or in the carrier fluid at this site. Methane from Lucky Strike and Von Damm show D 13 CH3D values similar to those at Rainbow, but display marginally higher D 12 CH2D2 values. Our one sample from Lucky Strike (from the Isabel vent) is virtually devoid of seawater contamination and is associated with a measured fluid temperature of 292 °C (Pester et al., 2012). The D 13 CH3D values of 1.0±0.2‰ suggest a temperature of 430 #%6 &06 °C. The D 12 CH2D2 value of +2.9±0.7‰ corresponds to an apparent temperature of 320 #$2 &%6 °C. The latter estimate is within uncertainty of the measured fluid temperature (Fig. 4). At Von Damm, fluids are venting at a maximum temperature of 226 °C, but many of the fluids have experienced subseafloor mixing with cold seawater and are thus characterized by vent temperatures <226°C (McDermott et al., 2015). The D 13 CH3D values are homogeneous and average 1.5±0.2‰

  D 12 CH2D2 re-equilibration or mixing in the cold Lost City fluids Unlike at the other sites, at Lost City methane is carried to the seafloor by relatively cool fluids. The three vents examined, Beehive (~100 °C), Marker C (~85°C), and Marker 2 (~65°C), show much lower temperatures than other vents studied here. The D 13 CH3D values are consistent with equilibration temperatures between 265 #,' &,-°C and 158 #(' &(0 °C, far hotter than the measured fluid temperatures. The D 12 CH2D2 values yield temperature estimates of 101 #- &2 °C, 93 #- &2 °C and 69 #' &' °C, showing a near-perfect match with the vent fluid temperatures (Fig. 4). The highest D 13 CH3D and D 12 CH2D2 values are observed in the coldest vent, Marker 2.

  . The required dD value of -170‰ would indicate a methane-water D/H equilibrium established at low temperature compared to Rainbow, Lucky Strike, or Von Damm (Horibe and Craig, 1995), consistent with the bond-ordering inferences. However, again, this type of mixing relationship fails to account for the details of the data trend in panel b of Figure 5. Where the mixing proportions needed in the isotopologue plot (Fig. 5, panel a) are roughly 50-50, they are about 80-20 in the bulk isotope space (Fig. 5 panel c), causing a mismatch in Figure 5, panel b.

  Stretching of the 12 CH2D2 molecule to donate a D to 12 CH4 should result in a highly asymmetric transition state with sCH2D-D* = 1. The transition state for 13 CH3D involves stretching the one 13 C-D bond, forming 13 CH3-D*, and preserving the symmetry of 13 CH3D, yielding sCH3-D* = 3. We therefore have for the rate constant ratio(9)

Figure 1 :

 1 Figure 1: Dissolved methane and hydrogen concentrations in hydrothermal fluids from the five locations studied here plotted against Mg concentrations. Data are from Reeves et al. (2014) and McDermott et al. (2015).

Figure 2 :

 2 Figure 2: Plot of D 12 CH2D2 vs. D 13 CH3D for methane samples from the hydrothermal vent systems that are part

Figure 4 :Figure 5 .

 45 Figure 4: Plot showing the relationship between the two mass-18 isotopologues of methane samples from the hydrothermal systems and the endmember temperatures of the fluid containing the methane. Note the

  13 CH3D and D 12 CH2D2 are generally ±0.1‰ and ±0.5‰, respectively. The external reproducibility is estimated based on repeated measurements of the thermogenic Utica shale gas, done with ~ 80 µmol of CH4. Eight standards were measured over the course of this study (Supplementary table 1), yielding average d 13 C and dD values of -25.81±0.06‰ The internal uncertainties range from 0.2‰ and 0.5‰ for D 13 CH3D, and between 0.5‰ and 2.7‰ for D 12 CH2D2. Note that for all samples except two gases from Von Damm that yielded the smallest CH4 quantities of the sample set, the internal uncertainties remained below 0.3‰ for D 13 CH3D, and 1.0‰ for D 12 CH2D2.

and -154.0±0.1‰, and average D 13 CH3D and D 12 CH2D2 values of 2.8±0.1‰ and 8.8±0.8‰ (all 1 s.d.). In our study, often only 40 to 60 µmol of CH4 were available (Table

1

), and uncertainties are larger, reflecting less favorable counting statistics.

Table 1 ,

 1 Fig.2) yield values of D 13 CH3D between 1.0±0.2 and 3.0±0.2‰, expanding the range of 1.0±0.6 to 1.9±0.3‰ reported by[START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF] for deep-sea hydrothermal vent systems. No direct relationship is observed between the UCLA and MIT values, because of the narrow spread of the eight samples measured in both laboratories, and because of the relative uncertainties. For the first time, abiotic methane from the Kidd Creek mine[START_REF] Young | The relative abundances of resolved 12CH2D2 and 13CH3D and mechanisms controlling isotopic bond ordering in abiotic and biotic methane gases[END_REF]. Within analytical uncertainties, isotopologue abundances in samples from Rainbow are consistent with internal equilibrium with the ambient fluids (Fig.2), with average D 13 CH3D and D 12 CH2D2 values of 1.4±0.2‰ and 2.7±0.9‰ (n=3, both 1 s.d.), respectively. Samples from Lucky Strike and Von Damm show similar signatures, with D 13 CH3D data ranging from 1.0±0.2‰ to 1.7±0.4‰, and D 12 CH2D2 values that are slightly higher than values at Rainbow. At Von Damm, D 12 CH2D2 values are +4.4±1.0‰ and 4.5±1.8‰ for Ravelin and Summit vents, respectively. In contrast, gases from Lost City are characterized by disequilibrium isotopologue signatures (Fig.2). The Lost City samples exhibit D 13 CH3D values between 1.9±0.2‰ and 3.0±0.2‰ extending the range of values previously known for Lost City[START_REF] Wang | Clumped isotopologue constraints on the origin of methane at seafloor hot springs[END_REF]. D 12 CH2D2 values are between 10.7±0.9‰ and 14.5±1.0‰.The highest values are observed in Marker 2, the coolest vent, while Beehive and Marker C show consistent compositions. All methane from Lost City plots far above the equilibrium curve in D 13 CH3D vs. D 12 CH2D2 space.

we report D 12 CH2D2 values for deep-sea hydrothermal methane, and we show the samples have values ranging from 1.7±1.0‰ to 11.6±0.5‰ (Table

1

, Fig.

2

). No D 12 CH2D2 values below zero are observed, in contrast with measurements of putative

  values. High-temperature methane formed at ~330 °C would exhibit D 13 CH3D values of ~1.5‰. At 85 °C, thermodynamic equilibrium drives D 13 CH3D to ~4‰. Beehive, Marker C, and Marker 2 are vented at 96°C, 81 °C and 64 °C, respectively, where the expectation of a D 13 CH3D trending towards ~4‰ because of partial re-equilibration is valid. One may speculate that cooling allowed partial reordering of D 13 CH3D to 1.9±0.2‰ at Beehive and 2.3±0.2‰ at Marker C. The ANME-1 identified at Marker 2

Table 1 :

 1 The variable D 12 CH2D2 values correlate surprisingly well with fluid temperatures and thus we suggest they record rapid 12 CH2D2 re-equilibration in cooling hydrothermal fluids upon ascent. None of the isotopologue signatures resemble those obtained from experimental investigations of abiotic CH4 synthesis in the laboratory, nor do they resemble the isotopologue signatures of abiotic methane formation in natural settings to date. The mechanism of re-equilibration in the case of these deep-sea hydrothermal fluids but not in the case of Kidd Creek cold fluids deserves experimental investigation. The discovery of resetting of D 12 CH2D2 values during transport affords the opportunity to use these values in concert with D 13 CH3D values to obtain a more complete picture of the thermal evolution of 22 methane gases. This is because D 12 CH2D2 appears to be completely reset to fluid temperatures in a wide temperature range, between 360 and 65°C. In contrast, D 13 CH3D shows limited evidence for re-ordering. We suggest that to first order, equilibration of D 12 CH2D2 should be faster than that for D 13 CH3D by a factor of ~ 2, but further investigation on relative rates of reaction is warranted. Because the apparent D 13 CH3D-based temperatures greatly exceed those amenable to microbial life in all sites, and because the isotopologue data rule out mixing with microbial gases, our data indicate that methane formation at all of the sites, including Lost City, is probably dominantly abiotic. Methane isotope data for hydrothermal fluids. bulk 13 C/ 12 C and D/H are reported alongside D 13 CH3D and D 12 CH2D2 . Analytical uncertainties are below 0.1‰ (95% confidence intervals) for d 13 C and dD. Propagated uncertainties are listed for D 13 CH3D and D 12 CH2D2 in 1s. They are variable from a sample to another, depending mostly on counting statistics. Hence the magnitude of the uncertainties for both D 13 CH3D and D 12 CH2D2 are a simple function of the processed CH4 quantity (in µmol). Temperature data are extracted from the literature[START_REF] Mcdermott | Pathways for abiotic organic synthesis at submarine hydrothermal fields[END_REF][START_REF] Reeves | The origin of methanethiol in midocean ridge hydrothermal fluids[END_REF], but see also[START_REF] Pester | Subseafloor phase equilibria in high-temperature hydrothermal fluids of the Lucky Strike Seamount (Mid-Atlantic Ridge, 37 17ʹ N)[END_REF], Charlou et al. 2010, Seyfried et al.,

	2011).

Acknowledgements

We acknowledge support from the Deep Carbon Observatory Deep Energy grants G-2018-11346 and G-2017-9815 to EdY. We acknowledge Susan Lang for leading the 2018 Lost City cruise and for providing the temperature data funded by NSF-OCE-1536702 and a DCO-Deep Life sub-awards. We thank Tamara Baumberger for shipboard assistance with processing the gas samples. We thank Shuhei Ono and David Wang for sharing samples. We thank Orit Sivan and four anonymous reviewers for comments that improved the manuscript.

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