*3.2. Secondary Ion Mass Spectrometer (SIMS) Analyses of Calcite*

We measured carbonate grains in the core of the serpentine mesh textures using a Secondary Ion Mass Spectrometer Cameca 1280HR. We used a 10 kV Cs<sup>+</sup> primary beam, a ~1.5 nA current, resulting in a ~15 μm beam size. The electron flood gun, with normal incidence, was used to compensate charges.

For oxygen isotope measurements, 16O and 18O were analyzed with a mass resolving power of 2400 and collected in 2 faraday cups (1010 and 10<sup>11</sup> Ω) in multi-collection mode. Each analysis takes ~4 min, including pre-sputtering (30 s) and automated centering of secondary electrons. This setting allowed an average reproducibility of ±0.28% (2 standard deviations (2 SD)) on an in house calcite reference material (UNIL\_C1; <sup>δ</sup> 18OVSMOW <sup>=</sup> 18.29 <sup>±</sup> 0.12% (2 standard error (2 SE))) at the beginning of each session. A set of 4 analyses of the calcite standard were also measured every 12 analyses for monitoring the instrument stability. The variation of the calcite standard over the 24 h session was ±0.52% (2 SD), suggesting a magnetic drift, for which the data were corrected. The error reported for samples reflected the 2 SD bracket between the surrounding set of standard analyses.

12C and 13C, measured in a second SIMS session, were separated using a mass resolving power of 4600, and collected in 2 faraday cups (both 1011 Ω). Each analysis takes ~4–6 min, including pre-sputtering (45 s) and automated centering of secondary electrons. This setting allowed an average reproducibility of <sup>±</sup>0.6% (2 SD) on a calcite in house standard (UNIL\_C1; <sup>δ</sup> 13CVPDB = 0.64 <sup>±</sup> 0.08% (2 SE)) at the beginning of the session. A set of 4 analyses of a calcite standard was also measured every 10 unknowns; the variation of the calcite standard over the entire session (~3 h) was ±0.8% (2 SD), suggesting a slight magnetic drift. The error reported for samples reflected the 2 SD bracket between the surrounding set of standard analyses.

During both sessions, the faraday cups were calibrated at the beginning of the sessions using a calibration routine. Mass calibrations were performed at the beginning of the sessions and again after 12 h for the 18O session.

We converted the measured δ18OVSMOW values from calcite into temperatures using the standard procedure of Kim and O'Neil [43] and assumed that calcite crystallized in equilibrium with seawater with a <sup>δ</sup>18OVSMOW <sup>=</sup> 0% at present-day, and a <sup>δ</sup>18OVSMOW <sup>=</sup> <sup>−</sup>1.2% for an ice-free world [44].

#### *3.3. Thermodynamic Modeling*

Fluid/rock interaction was modelled at the equilibrium with the EQ3/6 software [45]. The evolution of the mineralogy and the fluid chemistry were predicted for oceanic serpentinized peridotite during hydrothermal fluid recharge or discharge. We model hydrothermal circulation in one dimension with a medium discretized in a sequence of 50 to 60 boxes. The temperature was fixed in each box and either linearly increases (recharge) or decreases (discharge) from one box to the other along the flow path (Figure 2). The simulations consisted of 3000 to 7000 iterations subdivided into two steps. First, the composition of the fluid phase in equilibrium with the solid was calculated independently in each box. This induces mass transfer between the solid and the fluid. The aim of this model was to determine the impact on mineralogical composition of fluid-mediated mass transfer from low to high temperatures (recharge) or high to low temperatures (discharge). Therefore, during the second step, the fluid of modified composition was transferred from one box to the next one in flow direction, while seawater with fixed composition was introduced into the first box (Figure 2). This latter step conserves mass. Time is not a parameter of the model since time dependent processes such as fluid flow, diffusion or reaction kinetics were not considered. To determine the extent of fluid-rock interaction, we used the cumulative mass of fluid introduced in the first box of the model ((W/R)d; scaled to 1 kg of solid initially present in this box). This parameter could seem similar to the water to rock ratio commonly used in thermodynamic calculations (e.g., [46]), but it does not correspond to a single calculation at the equilibrium since over the number of iterations it integrates the amount of fluid added in the first box (it is thus a "dynamic" water to rock ratio). This water to rock ratio should ideally be of 2 <sup>×</sup> <sup>10</sup>−<sup>2</sup> to correspond to the porosity of ~ 5% measured in serpentinized peridotites [47]. However, with such a low amount of fluid, the computing time is too long to obtain significant mass transfer leading to carbonates formation. Therefore, at each iteration, we added into the model 38 kg (discharge) or 380 kg (recharge) of fluid (for 1 kg of solid) in the first box. Thermodynamic calculations at the equilibrium were performed with the database of Johnson et al. [48] with additional data for ferrous and ferric serpentine and ferrous brucite from Klein et al. [49] (see [50] for details). No organic components were considered. In the calculations, we suppressed the reduction of carbon by H2 to account for the slow kinetics of methanogenesis reactions [51]. The composition of the reacting serpentine was initially fixed at Mg2.77Fe<sup>2</sup><sup>+</sup>0.13Fe3<sup>+</sup>0.13Si1.94O5(OH)4 based on microprobe analyses. Serpentine composition can then evolve as a result of fluid-rock interactions. Iron oxidation state in serpentine was not determined, therefore, half of the iron was assumed to be trivalent, based on the compilation of serpentine composition by Evans [52], in agreement with the thermodynamic calculations by Klein et al. [48] and the μ-X-ray Absorption Near Edge Structure serpentine analyses on mesh textures by Andreani et al. [53]. The composition of seawater introduced in the first box of the model is given in Table S3. Simulations were run at a constant pressure of 50 MPa for simplicity. This pressure corresponds to the lithostatic pressure expected at drill site 1277, where drilling was performed at 4600 m water-depth up to 180 m below the seafloor. As expected, tests of the respective impacts of temperature and pressure on the thermodynamic equilibrium show that temperature is the primary control of the stable assemblage whereas pressure variations are less important in the pressure and temperature ranges relevant to MORs (4 to 350 ◦C and 20 to 50 MPa).

**Figure 2.** Sketch summarizing the modeling approach. (**a**) The model consists in calculating the equilibrium of a fluid + solid system in a series of boxes in which the fluid is transferred from one box to the next one at each time step. Two flow directions were investigated, either flow from high to low temperatures (discharge model) or from low to high temperatures (recharge model). Seawater was introduced in the first box of the model at 250 ◦C in the discharge model (**b**) and at 4 ◦C in the recharge model (**c**).

We applied equilibrium thermodynamics at low temperature in far from the equilibrium conditions. Reaction kinetics may prevent the achievement of equilibrium in these conditions. Taking into account reaction kinetics is fraught with uncertainty due to the lack of data on reaction rates in hydrothermal conditions and the need for modeling other time-dependent processes such as fluid flow. Several studies investigated the coupling between reaction kinetics and fluid flow in hydrothermal systems [54–56], but they simplified the system to a single chemical reaction and are therefore not able to model the changes in chemical composition investigated here. We therefore chose to calculate the system composition at the equilibrium towards which the system tends [57]. Such calculations were successfully applied to processes occurring at MORs (e.g., [47,48]). The use of equilibrium thermodynamics may be

challenged by the production of metastable phases during reaction. The main minerals formed here are serpentine and carbonates. Metastable serpentine minerals such as chrysotile have similar composition and thermodynamic properties to stable phases (lizardite; [58]). They will thus have a limited effect on the model outputs. However, Mg-carbonates (i.e., magnesite and dolomite) have precipitation kinetics at least 6 orders of magnitude slower than calcite precipitation at ambient conditions [59]. The high activation energy of Mg-carbonate precipitation makes Mg-carbonates formation possible at high temperature. Because of the slow Mg-carbonate kinetic reaction, we run both simulations including and excluding Mg-carbonate precipitation. Finally, we assumed thermodynamic equilibrium in each box of the model. This requires that transport processes (i.e., diffusion and advection) are fast enough compared to the reaction to achieve equilibrium at a scale of several meters.
