Introduction of isotopically light barium from the Rainbow hydrothermal system into the deep Atlantic Ocean

The marine barium (Ba) cycle is closely connected to the short-timescale carbon cycle, and Ba serves as a valuable paleo proxy for export production, ocean alkalinity, and terrestrial inputs. However, the marine Ba budget is poorly constrained, particularly regarding the fluxes of hydrothermally sourced Ba, which hinders our understanding of the Ba cycle and use of Ba-based proxies. Recent studies have suggested a modern source-sink imbalance of Ba isotopes in the global ocean, with sources being overall isotopically heavier than the sinks, and the hydrothermal Ba inputs were considered isotopically heavy sources. In this study, we present the first investigation of Ba and its isotopes in a non-buoyant hydrothermal plume based on dissolved and particulate samples collected from the Rainbow hydrothermal vent field on the Mid-Atlantic Ridge. Our data reveal strong hydrothermal signals at near-field stations, as evidenced by helium isotopes, accompanied by elevated concentrations of dissolved and particulate Ba. Dissolved Ba isotope compositions ( δ 138 Ba) in hydrothermally influenced deep waters (~0.3 % 0 ) are lighter than at similar depths of far-field stations (~0.45 % 0 ) in the Atlantic Ocean. The concentrations and isotopic compositions of dissolved and labile particulate Ba in the non-buoyant hydrothermal plume can be explained by conservative mixing between a Ba-enriched hydrothermal component and North Atlantic Deep Water. By extrapolating the correlations to the vent fluid endmember, our results suggest that there is negligible removal of Ba, and insignificant modification of Ba isotopic signatures, from the vent fluid endmember to the non-buoyant hydrothermal plume. This indicates that the Rainbow hydrothermal system introduces isotopically light Ba ( (cid:0) 0.17 ± 0.05 % 0 ) to the deep Atlantic Ocean. We estimate that global hydrothermal inputs of Ba are 4.6 ± 2.2 Gmol/yr. These observations highlight the potential of hydrothermal Ba to be an isotopically light source component of the marine Ba isotope budget.


Introduction
The marine barium (Ba) cycle is linked to primary productivity and marine biogeochemistry in the modern ocean (Horner and Crockford, 2021).Barium-based proxies extracted form marine archives provide important information on past productivity (Dymond et al., 1992), alkalinity (Lea, 1993), and river runoff (Weldeab et al., 2007).However, our knowledge of the marine Ba budget is incomplete (Horner and Crockford, 2021), which hampers our understanding of Ba biogeochemistry and limits the reliable use of Ba-based paleo proxies.The global marine Ba cycle is governed by inputs from terrestrial sources and hydrothermal vents, with outputs primarily occurring through Ba sedimentation and burial in the form of barite and in association with iron and manganese oxyhydroxides (Carter et al., 2020;Rahman et al., 2022).High-temperature hydrothermal vent fluids exhibit a marked enrichment of Ba with concentrations ranging from 1 to 119 µmol/kg (Diehl and Bach, 2020), which is up to three orders of magnitude higher than seawater (0.03-0.2 µmol/kg).This enrichment results from the leaching of Ba during the hydrothermal alteration of basaltic host rocks.
Despite the potential contribution of hydrothermal systems to the global Ba budget, the ultimate hydrothermal inputs of Ba into the oceans remain poorly constrained (Carter et al., 2020;Rahman et al., 2022).To date, several estimates of the hydrothermal inputs of Ba have been proposed (Dickens et al., 2003;Paytan and Kastner, 1996), all originating from an initial estimate of 1.1-2.3Gmol/yr based on Ba concentrations in vent fluids at the East Pacific Rise (Von Damm et al., 1985).In comparison, recent estimates suggest a much lower hydrothermal flux of dissolved Ba (<0.006Gmol/yr in Bridgestock et al., 2021;<<2.3 Gmol/yr in Hsieh et al., 2021).
The considerable uncertainty associated with determining the net hydrothermal inputs of Ba primarily arises from two challenges.First, the Ba concentrations in vent fluids are difficult to measure accurately (Jamieson et al., 2016;Seyfried et al., 2003).Due to the saturation of barite in sulfate-bearing fluids, barite tends to precipitate rapidly in the vent fluids in response to cooling, along with other highly reactive components (Gartman et al., 2019;Hsieh et al., 2021;Seyfried et al., 2022).These precipitates, commonly referred to as ``dregs'', have often been overlooked and less routinely measured than dissolved fractions (Evans et al., 2020), resulting in a significant underestimation of vent fluid Ba concentrations (Charlou et al., 2000;Jamieson et al., 2016).Some studies separate and dissolve the dregs in aqua regia (Seyfried et al., 2022(Seyfried et al., , 2003) ) or nitric acid (Konn et al., 2022), and combine their metal contents with those in solution to reconstruct the initial metal contents of the vent fluid before collection.However, this approach may not fully recover all the Ba, as aqua regia or nitric acid cannot completely dissolve barite (Al-kaabi et al., 2023).Consequently, direct sampling and analyses of seafloor vent fluids tend to systematically underestimate the true Ba concentrations of hydrothermal endmembers.
Second, the overall contribution of dBa from hydrothermal systems to the oceans is thought to be significantly diminished following venting due to the removal of Ba through barite precipitation during the mixing of vent fluids with sulfate-rich seawater (Jamieson et al., 2016), resulting in a considerably reduced net flux of Ba to the ocean (Carter et al., 2020;Hsieh et al., 2021).Recent studies have documented a non-conservative loss of the total Ba concentration of sampled vent fluids, including the dissolved fractions and the dregs, coinciding with an increase in sulfate concentrations (Hsieh et al., 2021;Seyfried et al., 2022).This has been attributed to the precipitation of barite within the chimney environment during or after mixing with seawater.However, such observations could, in some cases, also be attributed to the incomplete recovery of Ba from the dregs or a combination of these two processes.Therefore, accurately determining the amount of Ba that is removed following venting remains challenging.
Stable barium isotopes (δ 138 Ba) have recently emerged as a valuable tool for understanding the marine Ba cycle (Bridgestock et al., 2021a;Horner et al., 2015;Yu et al., 2022b;Zhang et al., 2023).A recent review suggested a modern source-sink imbalance of Ba isotopes in the ocean, with terrestrial sources (0.1-0.2 % 0 ) being overall isotopically heavier than the sedimentary sinks (0.0-0.1 % 0 ) (Horner and Crockford, 2021 and references therein).This suggests that either the marine Ba isotope budget is currently not in a steady state, or isotopically light sources or isotopically heavy sinks are missing.As this budget estimation did not account for the potential hydrothermal source of Ba, it is important to properly constrain the Ba isotopic contribution of hydrothermal inputs into the ocean to complete the budget.
To date, the main assessment of the isotopic composition of hydrothermal inputs to the deep ocean is from Hsieh et al. (2021).They measured δ 138 Ba in vent fluids from multiple hydrothermal vent sites located in the Pacific and Atlantic Oceans, and estimated that the effective hydrothermal inputs of Ba, after mixing with seawater, are isotopically heavy (1.7 ± 0.7 % 0 ).Their assessment assumed near-complete removal of Ba as a consequence of barite precipitation during the mixing of vent fluids and seawater, and consequential modification of the isotopic signature of the original fluid.These assumptions have, however, not been verified via measurements in the hydrothermal plumes.Therefore, it is crucial to verify the actual isotopic composition of hydrothermal Ba inputs from hydrothermal plumes.Furthermore, it is useful to examine Ba isotope fractionation between seawater and plume particles within the plume.
We conducted a comprehensive investigation of the non-buoyant hydrothermal plume at the Rainbow hydrothermal vent field to explore its dissolved and particulate components.Sampling was carried out during the GEOTRACES-compliant cruise (M176/2) onboard the German R/V Meteor from September to October 2021.The Rainbow hydrothermal vent field, located at 36 • 13.8′N-33 • 54.15′W and a depth of 2300 m on the Mid-Atlantic Ridge (MAR) (Douville et al., 2002), provided an ideal setting for our study due to its well-studied stable hydrothermal activity, and well-characterized vent fluid chemistry (German et al., 1996;Konn et al., 2022).This ultramafic-hosted hydrothermal system exhibits high metal concentrations in its hydrothermal fluids, leading to a distinct plume in the deep Atlantic Ocean (Douville et al., 2002;German et al., 1996), making it conducive for capturing the hydrothermal signal.Our investigation encompassed a high spatial resolution, extending from a distance of 200 m to 60 km away from the Rainbow hydrothermal vent field (Fig. 1).

Rainbow vent field and non-buoyant hydrothermal plume
The Rainbow hydrothermal vent field is characterized by at least black smokers that discharge high-temperature fluids (up to 370 • C) covering an area of approximately 100 by 300 m (Edmonds and German, 2004).Serpentinization and hydrothermal leaching during the circulation of the hydrothermal fluid in the peridotite basement rocks enrich the Rainbow hydrothermal plume in transition metals and rare earth elements (Douville et al., 2002).During the M176/2 cruise, the dissipating Rainbow hydrothermal plume was mapped through cross-sectional CTD surveys based on turbidity signal, extending from the vent field to a station approximately 60 km downstream (Fig. 1).The non-buoyant plume initially moved northward, subsequently shifting southward around the Rainbow Ridge, and then flowed northward along the southern and eastern side of the Azores -MAR rift valley (Achterberg and Steiner, 2021).Turbidity exhibited an exponential decrease with increasing distance from the Rainbow vent field, with the most pronounced decline observed within the first 10 km from the vent site (Fig. S1a).The core of the non-buoyant plume was situated at a depth of 2000-2200 m, with a thickness ranging from 200 to 400 m, as indicated by the peak turbidity signal observed in the vertical CTD casts (Fig. S1b).The main deep-water mass encountered by the plume was the North Atlantic Deep Water (NADW), characterized by a salinity of ~35.00 and a potential temperature of ~3.8 • C, which directly mixed with the hydrothermal plume.

Sampling and analyses
Trace metal clean collection of seawater samples (dissolved and particulate phases) was conducted using a titanium rosette frame equipped with trace metal clean Niskin bottles (Ocean Test Equipment) and sensors for conductivity, temperature, and depth (CTD), turbidity and oxygen (Seabird Electronics).The bottles were closed in duplicate at each sampling depth in the vicinity of the plume, one bottle was taken to a clean lab for trace metal sampling, and the other was sampled for dissolved gases on deck.Seawater samples for helium (He) isotope analyses were collected using a copper tube connected to the Niskin bottles.Sampling depths (1700-2400 m) were based on the turbidity signal, which defined the depth range and intensity of the hydrothermal plume.Details on sampling can be found in Supplementary information (Text S1).
The helium 3 He/ 4 He isotope ratio (R), is expressed relative to the atmospheric ratio (R a = 1.38 × 10 − 6 ), using the delta notation δ 3 He (%) = (R/R a − 1) × 100.Helium isotope samples were analyzed at the University of Bremen using the methods described by Sültenfuß et al. (2009).The background 3 He concentration (~2.38 fM) in the deep ocean was calculated from the background δ 3 He (~− 1.7 %) and equilibrium He concentrations (~1.75 nM) at the observed in situ salinity (~35 PSU) and temperature (~3.5 • C).The excess of 3 He ( 3 He xs ) was then calculated by subtracting the background 3 He and 3 H level from the measured 3 He concentrations.
The dBa concentrations in seawater were analyzed using an isotope dilution technique with an Agilent 7500ce inductively coupled plasma mass spectrometer (ICP-MS) at GEOMAR (Yu et al., 2022a) with a precision of ±2 % (2 standard deviations (2 SD) of repeated sample measurements).Particulate samples were leached (labile components) and digested (refractory components) following a reported protocol (Al-Hashem et al., 2022).Briefly, labile particles were leached with a mixture of 0.02 M hydroxylamine hydrochloride and 25 % acetic acid for a total of 2 h.Refractory particles were digested at 150 • C for 15 h using a mixture of 50 % nitric acid and 10 % hydrofluoric acid.The particulate Ba (pBa) and trace metal concentrations (labile particulate trace metal: pTM L ; refractory particulate trace metal: pTM R ) in the leachates and digestion solution were analyzed by High-Resolution ICP-MS (Thermo Fisher Element XR™) at GEOMAR.Procedural blanks obtained following ship-board filtration of deionized water with polyethersulfone filters showed a pBa L blank of 0.26 ± 0.39 pM and a pBa R blank of 0.29 ± 0.09 pM.Details of the particulate analyses and calibration can be found in supplementary information (Text S2).In this study, we report the dBa and pBa concentrations in units of nM and pM, respectively.The dBa of the vent fluid endmember is presented with the unit of µmol/kg due to the unknown density of the vent fluid discharged during our sampling campaign.
We selected four stations to determine the δ 138 Ba including three near-field stations (Fig. 1, stations 4, 5, 7) and one far-field background station (Fig. 1, station 23).Dissolved and particulate (labile and refractory) δ 138 Ba samples were measured using a double spike technique on a Multi-Collector ICP-MS (Thermo Scientific Neptune Plus) at GEO-MAR, applying methods detailed in Yu et al. (2020).δ 138 Ba values are reported in % 0 deviations from the international Ba standard NIST SRM 3104a (Ba(NO 3 ) 2 , Lot: 070222; δ 138 Ba(% 0 ) = [( 138 Ba/ 134 Ba) sample /( 138 Ba/ 134 Ba) standard − 1] × 1000)).Long-term repeated measurements of seawater reference materials suggested an external reproducibility of 0.04 % 0 (Yu et al., 2022b;Zhang et al., 2023).Samples were measured repeatedly 3-5 times and errors reported in this study are the 2 SD of repeated sample measurements.Details of the isotope analyses and results for reference materials can be found in supplementary text S3.

Tracking the dissipating hydrothermal plume using He isotopes
The reported 3 He xs value of the Rainbow vent fluid endmember was 25 ± 5 pM (Jean-Baptiste et al., 2004).In our survey, the distribution of 3 He xs in the non-buoyant hydrothermal plume reflects contributions of the Rainbow hydrothermal fluid with 3 He xs ranging between − 0.07 and 3.24 fM (fM = 10 − 3 pM), corresponding to an admixture of 0 % to 0.014 % hydrothermal fluid endmember.The highest 3 He xs levels (up to 3.24 fM), indicating the strongest hydrothermal signal, are observed at around 2000 m water depth at stations 5, 7, and 4, and gradually decrease with distance from the Rainbow field (Fig. 2a and Fig. S2a).

The Ba composition in plume samples
Total particulate Ba (pBa T ) account for only 0.03-0.38 % (mean: 0.18 ± 0.05 %) of total Ba (dBa plus pBa T ), with dBa thus being the dominant component (>99 %).Consequently, variations in pBa in the plume are unlikely to significantly influence the dBa concentrations.Labile particulate Ba (pBa L ) and refractory particulate Ba (pBa R ) are determined in this study by chemical leaching and digestion analysis (Section 2.2; Fig. S3).The labile particulate fraction comprises trace metals readily exchangeable or potentially soluble, including reducible, surface-bound (adsorbed/scavenged), and intra-cellular trace elements associated with biogenic and authigenic particulates such as Fe and Mn oxy-hydroxides (Al-Hashem et al., 2022).The pBa L therefore primarily represents the Ba pool adsorbed/scavenged onto particles or partitioned into easily dissolvable minerals or incorporated into acantharia.The pBa R represents the remaining refractory particulate Ba pool, which includes both lithogenic Ba and authigenic barite.However, given that acantharia primarily inhabit the upper 400 m of the water column, acantharia-hosted Ba is unlikely to be present in our samples due to efficient dissolution of most acantharian skeletons at water depths above 900 m (Bernstein et al., 1987).The pBa T pool can also be subdivided into excess particulate Ba (pBa XS ) and lithogenic Ba, with the latter estimated from particulate aluminum concentrations (Supplementary Text S4; Fig. S3).pBa XS is the non-lithogenic Ba consisting of authigenic barite and the pBa L fraction, with barite being the major refractory component of pBa XS .The pBa XS fraction accounts for 93.6 ± 3.8 % of pBa T in all samples collected in this study (n = 182), indicating a minor proportion of lithogenic Ba.The pBa L fraction accounts for 27.5 ± 9.3 % of pBa XS , with most pBa XS being refractory (72.5 ± 9.3 %; mainly authigenic barite).Hence authigenic barite is calculated to range from 14.5 to 125.1 pM (mean = 68.2± 16.2 pM, n = 182), consistent with background NADW pBa XS values (0-100 pM) observed during the GEOTRACES cruise GA03 (Rahman et al., 2022).

Changes of Ba signatures along the dissipating hydrothermal plume
Both dBa and pBa show a pattern similar to 3 He xs along the dissipating hydrothermal plume, displaying a decreasing trend from the near-field to the far-field region (Figs.2, S2).Stations 4, 5, and 7 exhibit a pronounced enrichment in dBa and pBa accompanied by lighter dissolved δ 138 Ba signatures (δ 138 Ba_d) corresponding to depths with high turbidity and enhanced δ 3 He signals (Fig. 3).The highest Ba enrichment is observed at station 5 (1990-2092 m), where dBa, pBa L , and pBa T reach concentrations of 65-70 nM, 150 pM, 250 pM, respectively.These values are markedly higher than the concentrations above and below the plume, as well as the concentrations at a similar depth in the far-field region (e.g., station 23, 50-55 nM, 25 pM, 100 pM).Correspondingly, δ 138 Ba_d values are lower (~0.30% 0 ) within the plume at station 5 compared to station 23 (~0.45 % 0 ).The δ 138 Ba values of particles range from 0.1 to 0.2 % 0 , overall lower than that of the dissolved phase (~0.30-0.48% 0 ).At station 5, the values of labile particulate δ 138 Ba (δ 138 Ba_Lp) and refractory particulate δ 138 Ba (δ 138 Ba_Rp) only show small variations (0.15-0.19 % 0 ) across all depths.This suggests a smaller hydrothermal influence on particulate δ 138 Ba compared to δ 138 Ba_d.

Conservative mixing of dissolved Ba from the vent fluid endmember to the non-buoyant hydrothermal plume
Excess 3 He is a conservative tracer in dispersing hydrothermal plumes (Jean-Baptiste et al., 2004;Lupton and Craig, 1981).If dBa in the non-buoyant plume is controlled only by two-endmember conservative mixing between the hydrothermal component and surrounding deep water, a linear relationship should be observed between dBa and 3 He xs , and a rational function regression should be observed between δ 138 Ba and 3 He xs (formula derivation can be found in supplementary Text S5).Indeed, the dBa and 3 He xs in all samples exhibit a strong positive linear relationship (Fig. 4a Hsieh et al., 2017).The δ 138 Ba_d value of the NADW endmember can also be estimated based on the relationship between δ 138 Ba_d and inverse dBa (µM − 1 ), which exhibits a strong linear relationship (Fig. 4c): (r 2 = 0.87, p < 0.001).Based on our estimated value of the NADW endmember dBa (dBa NADW = 52.7 ± 0.2 nM), δ 138 Ba_d is calculated to be ~0.44 % 0 .Both estimations lead to similar δ 138 Ba_d values of the NADW endmember, supporting the reliability of the endmember estimation and our conclusion of the dominant conservative mixing of dBa in the Rainbow non-buoyant hydrothermal plume.
3 He xs of the Rainbow vent fluid endmember was reported to be 25 ± 5 pmol/kg (Jean-Baptiste et al., 2004).The dBa and δ 138 Ba_d of the Rainbow vent fluid endmember after dreg-correction were determined to be 92 ± 7 µmol/kg and − 0.17 ± 0.07 % 0 , respectively (Hsieh et al., 2021).Notably, extrapolating the linear relationship between dBa and  2021) exhibited highly limited seawater admixture, as indicated by its high temperature (354 • C) and low Mg (2.8 mmol/kg) and SO 4 (0.66 mmol/kg) concentrations, suggesting that it closely represents the true endmember value.In addition, the vent fluid chemistry within the Rainbow vent field has been shown to be remarkably stable over the past several decades (Konn et al., 2022).This suggests that there is negligible Ba removal and insignificant Ba isotopic modification from the vent fluid endmember to the non-buoyant hydrothermal plume.More importantly, when compiling previously published data of the Atlantic deep waters below 1000 m (Bates et al., 2017;Bridgestock et al., 2018;Horner et al., 2015;Hsieh and Henderson, 2017), our observations in the Rainbow non-buoyant hydrothermal plume demonstrate an addition of isotopically light Ba from the Rainbow hydrothermal system into the deep Atlantic Ocean (Fig. 5b).
The Ba isotopic composition of hydrothermal inputs from the Rainbow vent field is thus − 0.17 ± 0.05 % 0 .This result differs strongly from the previous estimates for the Rainbow field (2.0 ± 0.6 % 0 ;Hsieh et al., 2021).Hsieh et al. (2021) proposed that following the initial venting phase, Rainbow vent fluids (~100 µM, − 0.17 ± 0.07 % 0 ) experience substantial barite precipitation, hence almost complete Ba removal and continued Ba isotopic modification, until the mixing point where barite becomes undersaturated and ceases to precipitate (dBa < 0.2 µM).The authors calculated the isotopic composition of Ba at this point as the 'effective' hydrothermal Ba component (2.0 ± 0.6 % 0 ), based on a Rayleigh isotope fractionation model.Our observations, in contrast, suggest that Ba behaves essentially conservatively from the vent fluid endmember to the non-buoyant hydrothermal plume.Even considering the uncertainty in our estimated endmember dBa (SD = 24 µmol/kg), which accounts for 20 % of the mean (118 µmol/kg), a 20 % removal of dBa from the vent fluid endmember would only result in a small modification of the isotopic composition (0.08 % 0 increase).Therefore, the estimation of the global isotopic composition of the 'effective' hydrothermal Ba component (1.7 ± 0.7 % 0 ) by Hsieh et al. (2021), derived using the same assumption as for the Rainbow hydrothermal system, requires a re-evaluation.This is discussed in Section 4.4.

Controls on particulate Ba in the non-buoyant hydrothermal plume
In the Rainbow non-buoyant hydrothermal plume, labile particulate  Z. Zhang et al. iron (pFe L ) dominates the Fe phase, accounting for over 99 % of the total Fe.This component is primarily derived from hydrothermal sources and consists mainly of Fe(III) oxyhydroxides, which is consistent with previous observations (Edmonds and German, 2004).While pBa T shows weak linear relationships with dBa (r 2 = 0.34), 3 He xs (r 2 = 0.47) and pFe L (r 2 = 0.54), pBa L exhibits stronger linear relationships with dBa (r 2 = 0.66), 3 He xs (r 2 = 0.87), and pFe L (r 2 = 0.91) (Fig. 6), indicating that pBa L is primarily associated with hydrothermal inputs.Two potential mechanisms may explain the formation of pBa L : it is either hydrothermally-derived at the initial stage of the plume (i.e.buoyant plume) or adsorbed onto hydrothermally derived Fe(III) oxyhydroxides within the non-buoyant plume.Prior studies have shown that in non-buoyant plumes, the ongoing adsorption of particle-reactive elements from seawater onto circulating and settling oxyhydroxide particles results in a progressive increase in their concentrations relative to Fe in the particles (Edmonds and German, 2004;German et al., 1990).However, we observe a linear relationship between pBa L and pFe L (r 2 = 0.91), suggesting that pBa L within the non-buoyant hydrothermal plume is controlled by conservative mixing between the hydrothermal component and deep seawater.Therefore, the formation of pBa L likely occurs immediately upon entering seawater, such as through adsorption onto Fe (oxyhydr)oxides or partitioning into easily dissolvable minerals at the initial stage of the plume.Evidence has been presented that dBa does not adsorb to common Fe-oxyhydroxides minerals found in near-field non-buoyant plumes, such as ferrihydrite (Hoffman et al., 2018), at low pH (<6) (Sajih et al., 2014), characteristic of the Rainbow vent fluids (Douville et al., 2002).However, dBa adsorption onto Fe oxyhydroxides may occur during the transition to more seawater-like pH.
Based on the linear relationship between pBa L and 3 He xs : pBa the pBa L concentrations of the vent fluid and NADW endmembers are estimated to be 0.8 ± 0.2 µM and 17.9 ± 0.5 pM, respectively.The pBa L concentration of the vent fluid endmember is more than two orders of magnitude lower than the estimated dBa value (118 ± 24 µmol/kg), suggesting that, similar to the non-buoyant hydrothermal plume, dissolved Ba is the predominant Ba phase at the initial stage of the plume.Any isotopic fractionation of Ba that may have occurred during the formation of pBa L will thus have a minor influence on the isotope composition of the dissolved Ba.
Unlike the observed strong linear relationships between pBa L and 3 He xs or pFe L , the correlations between pBa XS and 3 He xs or pFe L are weaker (r 2 = 0.47 or 0.52, respectively, Fig. S4).As mentioned, pBa XS consists of 27.5 ± 9.3 % of pBa L and 72.5 ± 9.3 % of authigenic barite (Section 3.2).This suggests that authigenic barite in the plume particles is not associated with hydrothermal inputs, which likely represents the background barite pool in NADW.
The δ 138 Ba_Rp values (Fig. 7a) are uniform at all stations, with an average of 0.16 ± 0.03 (2SD, n = 20).The δ 138 Ba_Lp values (Fig. 7b) slightly increase from the far-field station 23 (0.10-0.15 % 0 ) to the nearfield stations 5 and 7 (0.15-0.20 % 0 ).The variations in δ 138 Ba_Lp predominantly fall within the range of measurement errors, hence should be interpreted with caution.Even when considering the small variation, δ 138 Ba_Lp values overall follow the conservative mixing between station 23 (0.14 ± 0.02 % 0 ) and station 5 (0.19 ± 0.04 % 0 ) (Fig. 7c).This observation is consistent with the linear relationship between pBa L and 3 He xs (Fig. 6; Eq. ( 4)), which further supports the notion of conservative mixing between hydrothermal inputs with higher pBa L and NADW with lower pBa L .As both δ 138 Ba_d (Section 4.1) and δ 138 Ba_Lp are primarily controlled by conservative mixing, no significant exchange or isotopic fractionation between the dissolved phase and the labile particulate phase is observed within the non-buoyant plume.

Negligible Ba removal in the Rainbow hydrothermal system
The precipitation of sulfate minerals, primarily anhydrite (CaSO 4 ) and barite (BaSO 4 ) in hydrothermal systems has been widely reported (Chavagnac et al., 2018;Eickmann et al., 2014;Feely et al., 1987;Jamieson et al., 2016;Shikazono, 1994).This precipitation process is driven by the direct interaction between vent fluids, with high concentrations of Ca and Ba, and seawater containing high sulfate concentrations.Barite is often found abundant in deposits of hydrothermal fields associated with enriched mid-ocean ridge basalts (E-MORB), such as Menez Gwen, Lucky Strike (Fouquet et al., 2010), the northern Cleft Z. Zhang et al.Segment (Koski et al., 1994) and the Endeavour Segment (Coogan et al., 2017;Jamieson et al., 2016) at the Juan de Fuca Ridge.This is likely attributable to the high Ba content in the underlying E-MORB crust, which is enriched in incompatible trace elements such as K, Ba, La, and Rb compared to normal MORBs.Additionally, barite is found in hydrothermal systems associated with felsic rocks typical of arc settings (andesites and dacites), such as the Mariana backarc spreading axis (Kusakabe et al., 1990;Shikazono, 1994), the JADE hydrothermal field in the Okinawa Trough (Lüders et al., 2001), and the Loki's Castle vent field (Eickmann et al., 2014).Felsic rocks have abundant feldspars, whose destruction can lead to high Ba contents.However, barite is absent in most of the East Pacific Rise (Hannington et al., 1995) and Mid-Atlantic Ridge (Fouquet et al., 2010) deposits.
While barite precipitation in hydrothermal systems appears to be linked to endmember vent fluid Ba contents influenced by the composition of the basement rock, the Rainbow hydrothermal system presents a unique complexity.The Ba contents in fluids from Rainbow field are amongst the highest vent fluid Ba concentrations globally, which may be associated with a deep, Ba-enriched gabbroic intrusion.However, barite is rarely observed in the Rainbow field (Fouquet et al., 2010).Our observations further demonstrate minimal removal of Ba within the Rainbow hydrothermal system (Section 4.1).Saturation indexes (S.I.) of barite and anhydrite in the Rainbow hydrothermal system are calculated using a geochemical model (Dick, 2019) assuming conservative mixing between Rainbow vent fluids (Ba = 117 μM, Ca = 73.2mM (Konn et al., 2022), SO 4 = 0, T = 364 • C) and NADW (Ba = 0.05 μM, Ca = 10.5 mM, SO 4 = 28 mM, T = 2 • C) (Fig. S5).According to the modeling results, the mixing processes in the Rainbow hydrothermal system are expected to lead to the precipitation of both anhydrite and barite.This intriguing finding raises the question of the potential mechanisms that could explain the negligible Ba removal.
The higher S.I. of anhydrite compared to barite at temperatures above 200 • C (Fig. S5) suggests the possibility of a preferential precipitation of anhydrite over barite at high temperatures (Jamieson et al., 2016).The hydrothermal vent fluid endmembers typically exhibit much higher Ca concentrations (29.4 ± 18.6 mmol/kg) than Ba concentrations (32.3 ± 29.1 µmol/kg) globally (Diehl and Bach, 2020).Within the chimneys, anhydrite precipitation leads to the removal of most of the seawater sulfate from the solution, inhibiting the precipitation of barite (Jamieson et al., 2016).Notably, the Ca concentration in the Rainbow vent fluid endmember (73.2 mmol/kg) is relatively high compared to other hydrothermal systems (Diehl and Bach, 2020;Konn et al., 2022), which may further enhance the near-complete consumption of seawater sulfate through anhydrite precipitation at high temperatures and prevent precipitation of barite.This is supported by the presence of abundant anhydrite in hydrothermal particles collected in sediment traps deployed at the Rainbow vent field (Khripounoff et al., 2001).
Our geochemical model indicates that anhydrite becomes unstable and undersaturated at temperatures below 60 • C, but barite remains oversaturated at lower temperatures within the plume (Fig. S5).Hydrothermal barite typically precipitates on the seafloor in the temperature range of ~100-300 • C (Halbach et al., 1989;Hannington et al., 1995;Jamieson et al., 2016).This suggests that Ba remains stabilized at low temperatures in the hydrothermal plume.The geochemical model we employed (Dick, 2019) is a strong electrolyte model.However, ion pairs can form in weak electrolytes where the complete dissociation hypothesis is no longer valid.Factors such as BaSO 4 (aq) ion pair formation are not considered in the model.Ion pair formation can significantly reduce the number of free ions and consequently the saturation index of barite (Monnin, 1999).In the Rainbow hydrothermal system, calculated BaSO 4 (aq) ion pair formation can potentially stabilize all Ba ions at temperature below ~160 • C (Text S6, Fig. S5).Additionally, impurities in the barite (Church and Wolgemuth, 1972;Falkner et al., 1993) may also play a role.For example, the presence of Sr increases the solubility product of Sr-bearing barite, consequently leading to a decrease in the S.I. of barite (Text S6, Fig. S5).
In summary, we have discussed the possibility of anhydrite precipitation at high temperatures in conjunction with Ba stabilization at lower temperatures, as plausible mechanisms to explain the negligible removal of Ba in the Rainbow hydrothermal system.Nonetheless, we can not rule out alternative mechanisms, nor can we conclude that our proposed mechanism is the sole explanation.While the exact mechanism remains uncertain, our suggestions highlight the complexity of barite precipitation and Ba removal in hydrothermal systems.Further studies are warranted to investigate the specific processes and conditions influencing and controlling barite precipitation in hydrothermal environments.

The global net hydrothermal inputs of Ba and the marine Ba isotope budget
Using the observed linear relationship between dBa and 3 He xs in the Rainbow non-buoyant hydrothermal plume (Eq.( 1); slope = ΔdBa/ Δ 3 He xs = 4.7 ± 0.3 × 10 6 mol/mol), and the hydrothermal flux of 3 He from the Rainbow field (12.3 ± 3 nmol/s; Jean-Baptiste et al., 2004), the net hydrothermal input of Ba from the Rainbow hydrothermal system into the deep Atlantic is calculated to be 1.8 ± 0.5 × 10 − 3 Gmol/yr.
The global mean concentrations of Ba and 3 He in the vent fluid endmembers, compiled in MARHYS database (Diehl and Bach, 2020), are 32.3 ± 29.1 µmol/kg (n = 99) and 7.01 ± 3.38 pmol/kg (n = 8), respectively.Consequently, the global endmember Ba to 3 He ratio is calculated to be 4.6 ± 2.2 × 10 6 mol/mol (error calculation in Text S7).The global hydrothermal flux of 3 He, predominantly sourced from high temperature axial hydrothermal vents, has been estimated to be 1 × 10 3 mol/yr (Farley et al., 1995;Von Damm et al., 1985).Accordingly, the global hydrothermal Ba flux is calculated to be 4.6 ± 2.2 Gmol/yr.This estimate, however, comes with significant uncertainty, largely stemming from two aspects: 1) Accurately constraining the global mean hydrothermal endmember Ba concentrations proves challenging.The precipitation of barite during fluid sampling leads to non-linear behavior when determining zero-Mg endmember values of Ba (Fig. S6).As a result, endmember Ba concentrations are rarely reported (Seyfried et al., 2003).
2) The unknown extent of Ba removal in different hydrothermal systems.The degree to which hydrothermal Ba is removed in systems where barite precipitation is evident, has never been constrained.In addition, it is unknown whether the conservative Ba behavior observed in the Rainbow field also occurs in other hydrothermal systems.To better constrain the global hydrothermal Ba inputs, more observations in hydrothermal plumes are required.
Our findings also have implications for the modern source-sink imbalance of Ba isotopes in the ocean, as previously assessed by Horner and Crockford (2021).The estimated isotopic compositions of the global sources of Ba to the ocean, including riverine inputs (+0.2 % 0 ) and terrestrial submarine groundwater discharge (SGD; +0.1 % 0 ), are isotopically heavier than the Ba sinks (sedimentary barite; 0-0.1 % 0 ).Studies in estuaries have reported that the desorption of particulate Ba during estuarine mixing does contribute isotopically light Ba, resulting in an effective dissolved endmember that is lighter than the dissolved river endmember (Bridgestock et al., 2021b;Cao et al., 2021).However, further constraints on the effective riverine inputs (10-20 Gmol/yr) still fall within a range of relatively heavy isotopic compositions, from 0 to 0.1 % 0 for the Amazon, Rio de la Plata, Fly and Johor river systems (Bridgestock et al., 2021b) and the Congo river system (Zhang et al., 2023), and 0.1-0.2% 0 for the Yangtzi and Pearl river systems (Cao et al., 2021), to 0.2-0.3% 0 for the Eurasian river systems (Bridgestock et al., 2021a).Recent global budget estimates have suggested a significant, overlooked marine SGD or sedimentary source (up to 17 Gmol/yr; Rahman et al., 2022), but its isotopic composition has rarely been constrained.Recent studies in coastal regions have revealed large variability in δ 138 Ba values in pore waters of surface sediments, ranging from 0.1 to 0.3 % 0 in Baltic Sea sediments (Scholz et al., 2023) to 0.4-0.7 % 0 in Pearl River Estuary sediments (Cao et al., 2023), implying the likelihood of a marine SGD or sedimentary flux as another isotopically heavy source with respect to the marine budget.
Alternatively, our findings highlight the potential of hydrothermal Ba to be an isotopically light source.The extrapolated isotopic composition of Rainbow vent fluid (− 0.17 ± 0.05 % 0 ) is considerably lighter than the aforementioned Ba sources.Notably, δ 138 Ba in endmember vent fluids have been estimated to be isotopically light (− 0.17 to 0.09 % 0 ) across different vents (Hsieh et al., 2021).It then depends on the extent to which post-venting modification of δ 138 Ba in endmember vent fluids occur.In hydrothermal systems resembling Rainbow, where no significant modifications occur, isotopically light Ba is expected to be introduced into the deep ocean interior.Previous budget estimations have considered the hydrothermal inputs as isotopically heavy sources (Bridgestock et al., 2021b;Hsieh et al., 2021), which warrants careful re-evaluation.

Conclusion
Our study demonstrates that the Rainbow hydrothermal system exhibits negligible removal of Ba and insignificant modification of Ba isotopes from the vent fluid endmember to the non-buoyant hydrothermal plume.Consequently, the Ba isotopic composition of hydrothermal inputs from the Rainbow vent field is significantly lighter (− 0.17 ± 0.05 % 0 ) than the deep-water δ 138 Ba signatures in the Atlantic Ocean.In addition, we estimate the global hydrothermal Ba inputs to be 4.6 ± 2.2 Gmol/yr.Our findings confirm the complexity of Ba removal in hydrothermal systems and suggest that hydrothermal Ba is likely an isotopically light component of the marine Ba isotope budget.Further investigations in diverse hydrothermal systems, especially in hydrothermal plumes, are necessary to improve our understanding of the behavior of Ba and to better constrain the flux and isotopic composition of hydrothermal Ba inputs into the ocean interior.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.Map showing the bathymetry and sampling stations.The white triangle denotes the Rainbow vent field and white circles denote the sampling stations.Stations marked in red are selected for barium isotope analyses.The purple arrow visualizes the dissipating path of the Rainbow hydrothermal plume.This figure is modified from figures 3.1 and 5.4 in Achterberg and Steiner (2021).(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2 .
Fig. 2. Distribution of (a) 3 He xs (fM), (b) dBa (nM), (c) pBa L (pM), and (d) pBa T (pM) along the transect following the dissipating hydrothermal plume.This figure focuses on the region within 10 km distance from the Rainbow vent field.The complete distribution along the transect can be found in Fig. S2.The figure is generated using ODV (Schlitzer, 2023) with the DIVA (Data-Interpolating Variational Analysis) gridding interpolation method.Notably, the x-axis is significantly stretched on the left side.

Fig. 3 .
Fig. 3. Left panels: δ 3 He (green star), dBa (red circle); middle panels: turbidity (grey dashed line), pBa L (blue triangle up), pBa T (black triangle down); right panels: δ 138 Ba_d (red circle), δ 138 Ba_Lp (blue triangle up), δ 138 Ba_Rp (dark yellow triangle down) at four selected stations including three stations close to the vent field (stations 4, 5, 7) and one far-field background station (station 23).(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4 .
Fig. 4. Cross plots of (a) dBa versus 3 He xs , (b) δ 138 Ba_d versus 3 He xs , and (c) δ 138 Ba_d versus inverse dBa in the Rainbow non-buoyant plume.The dashed lines in panels a and c represent linear regressions.The dashed line in panel b represents the rational function regression curve.Dotted lines in all panels represent 95 % confidence intervals.

Fig. 5 .
Fig. 5. Extrapolation of the linear regression of (a) dBa versus 3 He xs and (b) δ 138 Ba_d versus inverse dBa in the non-buoyant hydrothermal plume to the Rainbow vent fluid endmember (red star).The 3 He xs value for the vent fluid endmember was obtained from Jean-Baptiste et al. (2004), while the values of dBa and δ 138 Ba_d for the vent fluid endmember were adopted from Hsieh et al. (2021).In panel b, the Atlantic dataset below 1000 m is compiled from previously published δ 138 Ba data from the Atlantic Ocean and the Atlantic Section of the Southern Ocean, including Horner et al. (2015), Bates et al. (2017), Hsieh et al. (2017), and Bridgestock et al. (2018).

Fig. 7 .
Fig. 7. Changes of particulate Ba isotopes at stations 5 (red diamond), 7 (green triangle), and 23 (blue square), including (a) δ 138 Ba_Rp versus pBa R , (b) δ 138 Ba_Lp versus pBa L , and (c) δ 138 Ba_Lp versus 3 He XS .The grey dashed line in (c) represents the conservative mixing line between the hydrothermally influenced water mass at station 5 and background water mass at similar depths at station 23.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)