Rapid hydrothermal cooling above the axial melt lens at fast-spreading mid-ocean ridge

Axial melt lenses sandwiched between the lower oceanic crust and the sheeted dike sequences at fast-spreading mid-ocean ridges are assumed to be the major magma source of oceanic crust accretion. According to the widely discussed “gabbro glacier” model, the formation of the lower oceanic crust requires efficient cooling of the axial melt lens, leading to partial crystallization and crystal-melt mush subsiding down to lower crust. These processes are believed to be controlled by periodical magma replenishment and hydrothermal circulation above the melt lens. Here we quantify the cooling rate above melt lens using chemical zoning of plagioclase from hornfelsic recrystallized sheeted dikes drilled from the East Pacific at the Integrated Ocean Drilling Program Hole 1256D. We estimate the cooling rate using a forward modelling approach based on CaAl-NaSi interdiffusion in plagioclase. The results show that cooling from the peak thermal overprint at 1000–1050°C to 600°C are yielded within about 10–30 years as a result of hydrothermal circulation above melt lens during magma starvation. The estimated rapid hydrothermal cooling explains how the effective heat extraction from melt lens is achieved at fast-spreading mid-ocean ridges.

and Fe-Ti oxides assemblages (see Supplementary Information). Four of the hornfelses close to the gabbroic intrusions were investigated in this study for intra-plagioclase zoning. Petrological studies suggest that the granoblastic mineral assemblages were transformed from sheeted dikes which experienced hydrous alteration, following the recrystallization under granulite-facies conditions (refs. 18-20) as a consequence of heating by the underlying magma. This contact metamorphic horizon thus represents an interface between the hydrothermal circulation system in the upper crust and the magmatic regime of the melt reservoir, and might be accompanied by partial melting of former sheeted dikes involving breakdown of hydrous minerals 21 . Cooling in this interface zone from such high temperatures (ca. 1000uC, ref. 19) to low-temperature hydrothermal fluid-dominated conditions (,600uC, ref. 20) plays a fundamental role in extracting heat from the melt lens 3,15 , but the cooling rate is poorly constrained.
Several lines of evidence suggest periodic replenishment of magma into the melt lens (refs. 8,22,23), which would inevitably induce alternating hydrothermal alteration and thermal recrystallization in the overlying sheeted dikes. The root of the sheeted dikes undergoes peak thermal overprint at t 0 when the melt lens reaches its highest position and the hydrothermal circulation is blocked therein (Fig. 3), while later suffers hydrothermal alteration at t 1 when the melt lens retreats as magma replenishment is waning or even stops. It is generally accepted that there are multiple cycles of such processes 22 , and the thermal and hydrothermal overprints formed at an earlier time are largely erased by later cycles. Therefore, the current information represents the last on-ridge cycle which is then followed by off-ridge spreading (Fig. 3).
Thermal modelling of fast-spreading ridges for a static melt lens indicates that the off-ridge cooling rate at the roof of the melt lens decreases with distance from the ridge centre and the largest temperature gradient occurs at the vicinity of melt lens 15 . This implies, for a dynamic melt lens model, that heat loss within the recrystallized sheeted dike overlying a retreating melt lens should be very intense. Combining the results of thermal modelling 15 and Ti-in-amphibole thermometry 19,24 , we consider that the temperature in the roof rocks above the axial melt lens should be about 600uC when the off-ridge regime starts (at t 1 in Fig. 3). The off-ridge cooling then proceeds, from about 600uC to 100uC within a relatively short spreading distance from the ridge centre, being about 6 km for a half fast-spreading rate of 100 mm/yr (Fig. 3).
Cooling rates for the lower oceanic crust of fast-spreading MOR systems were previously calculated based on the Ca-in-olivine diffusion speedometry 25 . Since olivine is absent in the contact metamorphic roof rocks above the axial melt lens, the olivine speedometry cannot work for modelling the cooling rates in this case. However, magmatic plagioclase phenocrysts in the hornfels samples which survived the granoblastic overprint, probably as a result of the sluggish character of high-Ca plagioclase during high-temperature reactions (refs. 26,27), offer another opportunity for applying diffusion speedometry to constrain cooling rate. Many relics of plagioclase phenocrysts in hornfelses show an inherited igneous core and an overgrowth rim equilibrated with the hornfelsic matrix (Fig. 4, see from numerous previous studies, mainly from refs. 2,3,6,7,43-48. The situation shown here is corresponding to a peak magma supply and shallowest position of melt lens, and in this situation, the conductive boundary layer atop of melt lens is nearly totally composed of granoblastic hornfelses (recrystallized sheeted dike). The whole axial magma chamber is composed of a melt zone at the top of upper mantle, a mush zone and an axial melt lens in the upper crust. The mush zone has a much higher fraction of crystals compared to the melt zone and axial melt lens, which are assumed to consist of pure liquid (e.g., ref. 1). The melt ascent zone in the lower crust (yellow arrow) denotes the path along which melts rise up, and it might be numerous small dikelets rather than a single tube as shown here. The white dashed curves in the mush zone are isotherms, and the grey solid curves indicate transport vectors of crystalline phases. A dynamic model for the evolution of melt lens defined by the blue rectangle is shown in Fig. 3.  also Supplementary Information and ref. 19). The cores throughout the recrystallized sheeted dikes show euhedral habits and high An contents (65-75%) similar to the primary plagioclase phenocrysts in fresh lavas and dikes 28 , clearly indicating a magmatic origin of these plagioclase cores. In contrast, the plagioclase rims have much lower An contents (45-55%) like the matrix plagioclases which have grown during the granoblastic overprint. The overgrowth rims usually contain abundant microgranular inclusions of plagioclase, pyroxene and Fe-Ti oxides, which are identical to the matrix in mineralogy. This texture indicates that the overgrowth rims of plagioclase phenocrysts are products of thermal overprint, similar as found in other hornfelsic rocks at the gabbro-dike transition sampled from modern ocean crusts or from ophiolites 18,29 . Comprehensive petrographic studies on the drilled samples from the IODP Hole 1256D revealed a coherent increasing degree of the thermal-overprint recrystallization with depth, from non at shallow sections through low-amphibolite facies to granulite facies (or two-pyroxene hornfelsic facies) at the dike/ gabbro contact 19 . The hornfelsic samples investigated in this study were collected just above the uppermost gabbroic intrusion (see Supplementary Information) and thus should record the highest degree of thermal overprint.
For simplicity, we assume that each overgrowth rim has a homogenous composition and formed very fast at the peak temperature of thermal overprint (at t 0 in Figs. [3][4]. Analyses of magmatic cores of the plagioclase phenocrysts indicate two different cases: (1) the magmatic core is homogeneous and (2) a high-An rim surrounds the magmatic core. In the second case, the high-An rims are interpreted as being generated by an individual crystallization event induced by changing conditions, i.e., mixing with a more primitive or relatively water-rich melt 30,31 .
Subsequent to the peak thermal overprint in the root of the sheeted dikes, the temperature decreases as a combined result of magma starvation in melt lens and hydrothermal circulation. Amphibole crystallization at that stage is ubiquitous, occurring both as individual grains and overgrowth around clinopyroxene cores (Fig. 4), which indicates a wide temperature range of hydrothermal alteration from up to 1000uC to lower than 600uC 19,20 . Analyzed whole-rock d 18 O values of sheeted dikes show gradual decrease with increasing depth towards the dike/gabbro transition zone 32 , also evidencing high-temperature (.600uC) hydrothermal alteration exclusively near the top of the melt lens. Having undergone on-ridge cooling and subsequent off-ridge cooling (Fig. 2), the initial sharp step in plagioclase An content between the magmatic core and granoblastic overgrowth would be broadened to some extent due to thermally induced intraplagioclase diffusion (Fig. 4). In this study we compare the modelled diffusion profiles to the measured ones to reveal the timescales and cooling rates associated with the formation of the intra-plagioclase diffusion profiles. However, as stated previously and illustrated in Fig. 3, multiple cycles of thermal recrystallization and hydrothermal alteration should occur above the melt lens, which might result in complicated pulsing in An profiles at the core-rim boundary of plagioclase phenocrysts rather than the simple zoning depicted in Fig. 4. Because numerical modelling for such unconstrained pulsing is almost unrealistic, we obviate this problem by selecting plagioclase phenocrysts showing simple zoning but negligible pulsing and modelling the timescale for a single cooling process.

Results
Constraining the peak temperature of the hornfelsic overgrowth is a key issue in calculating cooling rate. In this study, we applied the two- . Subsequent to the latest on-ridge heating by the melt lens to the latest peak thermal overprint (from t X to t 0 ), there were two cooling stages: on-ridge cooling from t 0 to t 1 , and off-ridge cooling from t 1 to t 2 . The temperature variation from t 2 to present time is minimal and ignored. The average off-ridge cooling rate from time t 1 to t 2 is estimated to be about 0.01uC/yr for an average half spreading rate of 100 mm/yr. The dashed curve in d shows another hypothetical temperature pattern if considering a sinusoidal melt lens fluctuation 22 and decreasing off-ridge cooling rate outwards 15 . www.nature.com/scientificreports SCIENTIFIC REPORTS | 4 : 6342 | DOI: 10.1038/srep06342 pyroxene thermometry 33 to estimate the peak temperature of thermal overprint in the hornfelses. As shown in Fig. 5, three studied samples, 203R-1-10_14, 205R-1-10_14 and R12-B, indicate an identical upper limit temperature of about 1050uC, and this value is thus used as the peak temperature for modelling cooling rates of these three samples. One sample R12-S has an upper limit temperature of about 1010uC and a wider temperature range down to 850uC, which demonstrates that the peak temperature of granoblastic thermal overprint of R12-S is lower than the other three samples. These temperature estimates are consistent to those made for hornfelses in the dike/gabbro transition zone from other locations at EPR and from ophiolites 29 .
Taking into account the estimated peak temperatures, the boundary condition of an on-ridge regime and an assumption of linear cooling at hydrous conditions, we modelled the An% content profiles applying a forward finite-difference approach for the four granoblastic dike samples using CaAl-NaSi interdiffusion at hydrous conditions determined by Liu and Yund (1992) 34 . As shown in Fig. 6 (also Fig. S6-S9 in Supplementary Information), the modelled on-ridge cooling rates for CaAl-NaSi interdiffusion are about 30 6 15uC/yr for the investigated four samples, corresponding to timescales of 10 to 30 years for the production of the CaAl-NaSi profiles. The small discrepancies from different measured profiles and estimated cooling  analyzing coexisting clinopyroxene and orthopyroxene grains adjacent to relic plagioclase phenocrysts. Note that although sample R12-S has a longer temperature span than other three samples, its upper limit temperature is lower. rates might potentially result from several factors, such as the effect of crystallographic orientation on diffusion rate 35 , small-scale heterogeneous distribution of temperature and/or water activity, and nonlinear temperature changing routes. However, further detailed exploration of the possible causes of the discrepancies from different profiles will not change the range of the modelled timescales and thus is out of the scope of this study. From an overall perspective, the estimates of cooling rate apply to both cases of the magmatic cores, i.e. the magmatic plagioclase cores with or without a high-An rim. It should be noted that the off-ridge cooling below 600uC does not modify the profiles significantly as indicated by our calculations, but low-temperature late-stage hydrothermal activities should have occurred as documented by alteration phase assemblages mainly involving quartz, chlorite, and etc, showing a major temperature range of 250-500uC 20 . The estimated on-ridge cooling timescales are consistent with inferred yearly to decadal variations in the melt lens geometry 36 and the timescales of lava eruption 37,38 and shallow hydrothermal discharge 39 at fast-spreading MORs. This implies that hydrothermal cooling in the hornfelses at the roof of the melt lens and fluctuation of magma replenishment into the melt lens are coupled with each other in time.
Trace diffusion of Mg in plagioclase is another useful speedometry in constraining timescales of high-temperature geological processes 40 . Based on measured Mg concentration profiles, we modelled Mg diffusion in plagioclase which occurred simultaneously with CaAl-NaSi interdiffusion (see detailed modelling methods in Supplementary  Information). The modelled Mg diffusion rates imply very low SiO 2 activity in the hydrothermal fluids during the on-ridge cooling processes down to 600uC (Fig. 7), provided that the experimentally determined dependence of Mg diffusivity on SiO 2 activity 41 can be extrapolated to such low SiO 2 activity. An important support for this hypothesis is given by a study on the saturation temperature of the Figure 6 | Images, concentration-distance profiles and modeled profiles for intra-plagioclase CaAl-NaSi couple interdiffusion. The measured An% contents along boundary-cutting profiles (denoted by arrows on back-scattered electron images) are shown as red dots. The best-fit final profiles at time t 2 (green curves) were calculated involving two cooling steps (see Fig. 3) from the assumed initial profiles at time t 0 (blue dashed curves). T C0 at t 0 is estimated based on two-pyroxene thermometer (see Fig. 5). See more profiles and modelling results in Supplementary Information. fluid inclusions in quartz grains recovered from the IODP Hole 1256D 20 , which shows that all the quartz has crystallized from hydrothermal fluids at temperatures , 450uC and thus implies that the SiO 2 activity should be very low at higher temperatures.

Discussion
In order to examine the validity of the estimated cooling rate above the axial melt lens, we performed a simple heat balance calculation to compare the total heat released from the melt lens and that extracted from the overlying hornfelsic zone during cooling (see Methods for the procedure). The calculation assumes (i) that all the heat originated from cooling and partial crystallization of the melt lens is released into the overlying hornfelsic zone which acts as a conductive boundary layer, and (ii) that the timescales of replenishment and starvation of the melt lens is identical to each other. In order to balance the heat output of a melt lens at a fast-spreading MOR similar to the case of IODP Hole 1256D, the cooling rate above the melt lens is required to be around 30uC/yr (Fig. 8). This independent estimation from heat balance calculation is strikingly consistent with that from the modelling of intra-plagioclase CaAl-NaSi interdiffusion. We conclude that rapid hydrothermal cooling above melt lens is therefore essential for extracting heat during the crustal accretion at fast-spreading MORs. This is in complete accord with the dramatic decrease in cooling rate with depth in the lower crust estimated from Ca-in-olivine speedometry, which indicates that cooling in the plutonic lower crust is driven by hydrothermal circulation from top 25 . The fast energy release above the melt lens might promote enhanced magma cooling and crystallization within the melt lens 42 and is thus important in constraining the geological model for crustal accretion at fast-spreading MORs. The two commonly evoked tectonic models, namely the ''gabbro glacier'' model 3 and the ''sheeted sill'' model 13 , interpret the thermal structure and heat extraction by contrasting ways. Recent estimation of magma crystallization depths at the fast-spreading EPR 5 indicates that most crystallization carried out within the melt lens, although a minor part of crystallization has occurred prior to the magmas reached the melt lens, supporting a hybrid ''gabbro glacier''-dominating model. Furthermore, the primitive layered gabbros recovered from Hess Deep 4 and the strong mush subsidence recorded in the frozen axial magma chamber of the Oman ophiolite 6 also support that a large proportion of magma crystallization occurred within the shallow melt lens and subsequently the crystals sank to form the mush zone (Fig. 1). The rapid cooling rates above the melt lens determined in this study, as well as the coupled timescale of cooling and melt lens fluctuation, indicate that effective heat extraction from the top of the melt lens can be achieved through overlying hydrothermal circulation within the overlying sheeted dikes (Fig. 8). Therefore, our data support a model suggesting that hydrothermal circulation above the melt lens plays a dominant role of heat extraction for solidifying the lower crustal at fast-spreading MORs, in favor of the ''gabbro glacier'' model (for details see review in ref. 16). The melt lens might wax and wane in a yearly to decadal timescale, which can explain the observed variations in melt lens geometry 36 , lava eruptions 37,38 and shallow hydrothermal discharge 39 at fast-spreading MORs.

Methods
Electron microprobe analysis. Mineral spot compositions and intra-plagioclase profiles were measured using a Cameca SX100 electron microprobe analyzer Figure 8 | Heat balance calculation showing the correlation between ridge spreading rate and cooling rate above melt lens. Q tot is total heat originated from melt lens by cooling and partial crystallization; Q extr is heat extracted out of the recrystallized sheeted dikes via hydrothermal circulation after retreat of melt lens. Heat flux is balanced when Q extr /Q tot 5 1, which may be achieved by hydrothermal cooling above melt with a cooling rate of about 30uC/yr for a fast-spreading ridge with an average half spreading rate of about 100-110 mm/yr. equipped with 5 spectrometers and an operation system ''Peak Sight''. Spot analyses of all mineral phases were performed with an acceleration potential of 15 KeV and a beam current of 15 nA. For analyzing Na, Si, Al and Ca of intra-plagioclase profiles, firstly a normal setting of 15 KeV and 15 nA has been used. In order to improve analytical spatial resolution for very short diffusion distances (5 , 15 mm) within plagioclase, that is, to diminish excitation volume of analytical spot, we used a modified setting of 8 KeV and 10 nA for measuring most intra-plagioclase profiles for Na, Si, Al and Ca, but trace Mg, K, Fe and Ti were not analyzed in this case. The spatial resolution of this setting has been tested to be able to fulfill the requirement of the measurement (see Supplementary Information). For analyzing the MgO content of the intra-plagioclase profiles, 15 KeV and 40 nA have been used in order to improve the detection limit, which can analyze Mg . 55 ppm with an uncertainty about 70 ppm.
Diffusion modelling. Initial step-like transitions in An content at the interface were assumed for forward numerical modelling applying a finite-difference approach, similar to the method used in ref. 40. Both on-ridge and off-ridge cooling processes were considered in diffusion modelling by superimposing the latter one on the former output. For both processes simplified linear cooling rates were assumed, which might slightly overestimate the timescale of on-ridge cooling 22 and underestimate the timescale of off-ridge cooling 15  constant, T is temperature in Kelvin, and a SiO2 is silica activity in the system, and the unit of diffusivity is mm 2 s 21 . We chose the diffusivity data based on careful examination of the available diffusion experiments (see details in Supplementary Information).
Heat balance calculation. The calculation method used here follows principally that of ref. 43, and the used physical quantities are listed in Table 1. Within an episode of melt lens fluctuation (b, from t X to t 1 , Fig. 3), the total heat released from half melt lens originates from magma cooling to the solidus and from latent heat of crystallization, which can be expressed as: Q tot 5 ubr m hC m DT m 1 ubr g hL. During the on-ridge cooling process, the heat extracted from the hornfelsic zone by hydrothermal circulation can be expressed for half-ridge width as Q extr 5 ar d kC d DT d . Assuming constant cooling rate r, the average temperature decrease in the hornfelsic zone during the cooling process (h, from t 1 to t 0 , Fig. 3) can be calculated by DT d 5 0.5hR. For an episode of melt lens fluctuation, we assume that the timescales of melt lens waxing and waning are identical to each other. Therefore, we have b 5 2h. Finally we calculate the ratio of Q extr /Q tot as a function of the cooling rate above the melt lens and the half spreading rate, and the results are illustrated in Fig. 8.
Error analysis. Errors of the cooling rates obtained in this study may come from several potential sources, mainly including: (1) uncertainty due to the spatial resolution of the electron beam, (2) nonlinear cooling path, (3) uncertainty in temperature estimation for peak thermal overprint, and (4) uncertainty in experimentally determined diffusion coefficients. Evaluations on these potential factors indicate that our modelled cooling rates using the assumptions are reasonable within a relative error of a factor of 2 (see details in Supplementary Information).