Experimental evaluation of oxygen isotopic exchange between inclusion water and host calcite in speleothems

The oxygen and hydrogen isotopic compositions of water in fluid inclusions in speleothems are important hydroclimate proxies because they provide information on the isotopic compositions of rainwater in the past. Moreover, 15 because isotopic differences between fluid inclusion water and the host calcite provide information on the past isotopic fractionation factor, they are also useful for quantitative estimation of past temperature changes. The oxygen isotope ratio of inclusion water (δOfi), however, may be affected by isotopic exchange between the water and the host carbonate. Thus, it is necessary to estimate the bias caused by this post-depositional effect for precise reconstruction of palaeo-temperatures. Here, we evaluate the isotopic exchange reaction between inclusion water and host calcite based on a laboratory experiment 20 involving a natural stalagmite. Multiple stalagmite samples cut from the same depth interval were heated at 105°C in the laboratory for 0–80 hours. Then, the isotopic compositions of the inclusion water were measured. In the 105°C heating experiments, the δOfi values increased from the initial value by 0.7‰ and then remained stable after ca. 20 hours. The hydrogen isotope ratio of water showed no trend in response to the heating experiments, suggesting that the hydrogen isotopic composition of fluid inclusion water effectively reflects the composition of past dripwater. We then evaluated the 25 process behind the observed isotopic variations using a partial equilibration model. The experimental results are best explained when we assumed that a thin CaCO3 layer surrounding the inclusion reacted with the water. The amount of CaCO3 that reacted with the water is equivalent to 2% of the water inclusions in molar terms. These results suggest that the magnitude of the isotopic exchange effect has a minor influence on palaeo-temperature estimates for the Quaternary climate reconstructions. 30

This indeterminate nature of the δ 18 Oca interpretation is related to the fact that δ 18 Oca values are mainly controlled by two factors: the temperature in the cave and the annual mean δ 18 O value of the rain water. To overcome this ambiguity, the isotopic compositions of water in fluid inclusions in stalagmites have been regarded as important proxies (Schwarcz et al., 40 1976;McDermott, 2004). Cave dripwaters are sealed in micro-scale cavities as fluid inclusions, whose δ 18 O value is usually close to the δ 18 O value of infiltration-weighted mean of local rain (Baker et al., 2019). Generally, stalagmites contain inclusion water, which accounts for 0.05 to 0.5 wt. % of a speleothem (McDermott, 2005). Thus, the isotopic compositions  (Mühlinghaus et al., 2009). The combination of the two isotopic compositions, δ 18 Ofi and δ 18 Oca, provides a direct estimate for the oxygen isotopic fractionation between calcite and water, which is controlled mainly by the formation 50 temperature. Thus, variations in past temperature (i.e., not absolute values but relative changes) can be estimated on the assumption that the kinetic effect is constant during the speleothem formation period.
Early studies analysed the hydrogen isotope ratio of fluid inclusions water (δDfi), and the δ 18 Ofi value was inferred from the modern δD vs δ 18 O relation in meteoric water (Schwarcz et al., 1976;Harmon et al., 1979;Genty et al., 2002;Matthews et al., 2000;McGarry et al., 2004). These studies measured δDfi because of the technical difficulties associated with measuring 55 the small amounts required to estimate δ 18 Ofi values and a fundamental concern about the integrity of the δ 18 Ofi data, namely, oxygen isotopic exchange between inclusion water and host calcite in speleothems.
After being trapped in the host calcite, inclusion water may continue to exchange oxygen isotopes with the surrounding host calcite as follows: This isotopic re-equilibration effect potentially alters the δ 18 Ofi values after the initial trapping of the inclusion water in the stalagmite. Such post-depositional isotopic exchange does not occur for hydrogen because of the small amount of hydrogen in the host calcite. Many studies on geothermal water have shown positive δ 18 O shifts from the global meteoric water line 65 (GMWL) (Clark and Fritz (1999) and references therein). These data suggest an isotopic exchange of oxygen between the geothermal water and the host aquifer rocks. This observation is one of the reasons why the earlier studies mentioned above explored the δD values of fluid inclusions rather than δ 18 Ofi values (Harmon et al., 1979;Matthews et al., 2000;McGarry et al., 2004).
Recently, because of technological developments involving continuous-flow isotope ratio mass spectrometry (Vonhof 70 et al., 2006) and cavity ringdown spectrometry (CRDS) (Uemura et al., 2016;Arienzo et al., 2013;Affolter et al., 2014), isotopic data from fluid inclusion have been accumulating. Interestingly, these studies suggest that post-depositional exchange is not significant. In fact, the fluid inclusions analyses of modern stalagmites have shown that their δ 18 Ofi values are consistent with the δ 18 O values of modern dripwaters (Griffiths et al., 2010;Dennis et al., 2001;Arienzo et al., 2013;Uemura et al., 2016;Labuhn et al., 2015), although a post-depositional alternation induced by recrystallisation has been 75 suggested (Demény et al., 2016). Moreover, several studies successfully quantitatively estimated past temperatures at the time of calcite formation (van Breukelen et al., 2008;Meckler et al., 2015;Uemura et al., 2016). Therefore, these data imply that the oxygen isotopic exchange between inclusion water and stalagmite calcite appears to be limited and/or very slow over natural temperature ranges.
The indirect evidence for the insignificant post-depositional effect cannot provide explanations for the mechanisms 80 behind this phenomenon. Thus, it is essential to investigate the isotopic exchange reaction and evaluate how much the past temperature reconstruction would be biased by this effect. However, to our knowledge, no study has investigated the magnitude of isotopic exchange within natural stalagmites. In addition to this natural process, the isotopic exchange reaction may occur during the drying process of stalagmite samples at high temperatures, which was commonly conducted before fluid inclusion measurement in the laboratory (Affolter et al., 2014;Vonhof et al., 2006;Uemura et al., 2016;Dublyansky and 85 Spötl, 2009).
Here, we evaluate the isotopic exchange reaction between inclusion water and host calcite based on a laboratory heating experiment of natural stalagmite samples. We conducted a heating experiment because a higher temperature induces an increase in the degree of isotopic disequilibrium between water and calcite and increases the rate of isotopic exchange. As a result, an isotopic shift caused by the exchange reaction will be easier to detect. The stalagmite samples and experimental 90 settings are described in Section 2. Section 3 presents the experimental results and discusses them using an isotopic exchange model for inclusion water and host calcite. Concluding remarks are given in Section 4.

Speleothem and dripwater samples
A stalagmite (named HSN1) was collected in Hoshino Cave, Minami-Daito Island, Okinawa, Japan (25˚ 51′ 34″N, 131˚ 95 13′ 29″E). The stalagmite is 246 mm in length, and most parts are milky white with thin transparent layers (Fig. 1). The fabric of milky white layer is open columnar structure. To compare the isotope ratios of fluid inclusions after different heating times, ten layers, A-J, were taken (2.4-3.9 mm in thickness) from a quartered section of the stalagmite (Tables 1 and   2). The position relative to the axis may have an influence on the water content. Thus, to minimize this effect, 3-6 wedgeshaped chipped sub-samples (51-193 mg) were cut from each layer (illustrated in Fig. 1). The sub-samples from the same 100 depth interval were assumed to have the same isotopic compositions.
Dripwater samples were collected in Hoshino cave from March 2011 to May 2016 (1-5 times per a year). At present, there is no dripwater at the sampling point of HSN1, the dripwater samples were collected at a point ca. 50 m away from the sampling point.

Isotope measurements
The oxygen and hydrogen isotopic compositions of the water in the fluid inclusions were measured using a homemade extraction device (Uemura et al., 2016). Briefly, the speleothem sample was crushed under vacuum, and then extracted water vapour was transferred to a CRDS isotope ratio analyser (L2130-I, Picarro Inc.) at the University of the Ryukyus. Compared with the system described in (Uemura et al., 2016), the system has been improved in three ways. (1) The valves were 110 automatically controlled using pneumatic valves. (2) The entire system was heated at 105°C because most parts were easily damaged at 150°C. (3) The water vapour extracted from the stalagmite was immediately trapped cryogenically at the temperature of liquid nitrogen, thereby preventing interaction between CaCO3 and water vapour. The 1σ reproducibility for the inclusion water analysis, based on the replicate analyses, was ±0.3‰ for δ 18 O and ±1.6‰ for δD (Uemura et al., 2016).
The δ 18 O and δD values were measured simultaneously using a cavity ring-down spectrometer (L2130-i, Picarro Inc.) 115 with a vaporizer unit (V1120-i, Picarro Inc.). The 1σ reproducibility, based on repeated analyses of a working water standard water, was ±0.08‰ for δ 18 O and ±0.26‰ for δD.
Stalagmite carbonate sub-samples were measured using an isotope ratio mass spectrometer (Thermo DELTA V Advantage) equipped with a Thermo Gasbench II system at the University of the Ryukyus. Powdered sub-samples of 150-200 μg were reacted with 100% phosphoric acid at 72°C in septa-capped vials before measuring the released CO2. The 1σ (n 120 = 124) reproducibility for the analysis was ±0.04‰ for δ 18 O and ±0.03‰ for δ 13 C based on repeated analyses of a carbonate standard (IAEA CO-1).
The isotopic composition is expressed in units of per mill (‰) using delta notation (δ = Rsample/Rref -1), where R is the isotopic ratio and Rsample and Rref are the isotopic ratios of the sample and reference, respectively. For water samples from fluid inclusions, δ 18 O and δD data are presented relative to Vienna standard mean ocean water (VSMOW) and are 125 normalized to the VSMOW-SLAP scale. For calcite samples, δ 18 O and δ 13 C data are expressed relative to the Vienna Pee Dee Belemnite (VPDB) and/or VSMOW references. For clarity, the δ values of fluid inclusion water and stalagmite calcite are expressed with the subscripts "fi" and "ca", respectively. δ 18 Ofi, for example, indicates the δ 18 O value of the water in fluid inclusions.
Two layers (depths of 75.0 mm and 190.0 mm) of the HSN1 stalagmites were dated using U-Th techniques (Shen et al., 130 2008;Shen et al., 2012). U-Th isotopic compositions and concentrations were measured on a multi-collection inductively coupled plasma mass spectrometer (NEPTUNE, Thermo-Fisher Scientific Inc.) at the High-Precision Mass Spectrometry and Environment Change Laboratory (HISPEC) of the Department of Geosciences at National Taiwan University (Shen et al., 2012). U-Th ages were calculated based on decay constants, half-lives, and 238 U/ 235 U ratios (Jaffey et al., 1971;Cheng et al., 2013;Hiess et al., 2012). Uncertainties in the U-Th isotopic data and 230 Th dates (yr BP, before 1950 AD) are given at the 135 two-sigma (2σ) level or two standard deviations of the mean (2σm) unless otherwise noted.

Heating experiment
To evaluate the effect of isotopic exchange between water and host calcite, a heating experiment was conducted. As a pretreatment process, each stalagmite sample was placed in a small glass tube (o.d. 1/2 inch and 6 cm in length) with an airtight screw cap sealed with two Viton O-rings. Then, the samples were dried in a vacuum line for 17 hours at room 140 temperature using a turbo molecular pump (with a pressure down to 10 -5 Pa).
After this pre-drying process for all samples, the sample tube was subjected to different temperatures of 105°C or 25°C.
For the 105°C heating experiment, the sample tube was heated with a silicone cable heater at 105°C for a defined time period (from 0 to 70 hours) under the same vacuum conditions (i.e., a pressure down to 10 -5 Pa). For comparison, we also performed a non-heating experiment at room temperature (25°C) for the same time periods (from 0 to 70 hours) under the 145 same vacuum conditions. Then, the heated (or non-heated) sample was transferred in the closed sample tube to the fluid inclusion analysis apparatus so that atmospheric exposure when introducing the sample lasted for less than 30 seconds. To evacuate the analytical line, the samples were subjected to an additional 105°C condition for 20 minutes. Then, the sample was crushed, and the isotopic composition of the inclusion water was measured as described in Section 2.2. 150 3 Results and discussion

Isotope composition of inclusion water
The temporal variations in δ 18 Ofi and δDfi values resulting from the 105°C heating and non-heating experiments are shown in Fig. 2. The isotopic compositions of inclusion water are shown as a deviation from the initial value (Δδ 18 Ofi and ΔδDfi). For the 105°C heating experiment, the δ 18 Ofi values gradually increased with the heating time and then reached a 155 constant value after ca. 20 hours (Fig. 2a). The regression curve of the data represents an exponential function (Section 3.5).
The δ 18 Ofi values increased by ca. 0.7‰ with respect to the initial values during ca. 20 hours from the start of heating (Fig.   2a). In contrast, no significant trend was found for ΔδDfi for the 105°C heating experiment (Fig. 3b). For the roomtemperature drying experiment, neither Δδ 18 Ofi nor ΔδDfi values showed any systematic variation ( Fig. 2c and 2d).
Overall, the results suggest that the observed increase in δ 18 Ofi values in the 105°C heating experiment is caused by the 160 oxygen isotopic exchange between inclusion water and the surrounding calcite. The data from the control experiment at room temperature suggest that the oxygen isotopic exchange reaction is too small to detect under 25°C conditions. The δDfi data for the 25°C experiment confirms that there is no systematic isotopic variation caused by subsample cutting and length of drying time. In addition, the ΔδDfi value for the 105°C experiment did not change because there is no significant hydrogen reservoir in calcite. 165 The new calcite precipitation in fluid inclusions did not occur because the δ 18 Ofi is expected to be lower if the new calcite, whose δ 18 O value is higher than that of water, formed inside the inclusions. This is opposite to the result of heating experiment. In the case of internal calcite dissolution, the δ 18 O value of water, will be changed through the isotopic exchange reaction between the bicarbonate in the solution and the water. Thus, if the amount of dissolution is limited, it is not different from the case that the water is re-equilibrated with a limited amount of CaCO3 (will be discussed in section 3.4). 170

Evaporation during heating
Long-term heating may induce leakage from water inclusions through microscopic channels in the calcite caused by decrepitation of the calcite. The measured water content (weight ratio of water in fluid inclusions to carbonate) of the experiments is shown in Fig. 3. Overall, the water content ranged from 0.05 to 0.3 wt. %, which is within the typical observed range of 0.05-0.5% (McDermott, 2005). 175 Although there are large variations in water content among different layers, there is no significant trend between heating time and water content (Fig. 3). This result suggests that the fluid inclusion water does not evaporate/leak even after longterm heating. We should note that larger data sets of various stalagmites are needed to generalize this result because the behaviour of leakage would also be influenced by the fabric and micro-structure of the stalagmite. In addition, this finding suggests that our standard drying procedure (17 hours at room temperature, as described in Methods) is enough to remove 180 the water adsorbed onto the calcite. Therefore, this result confirms that the increase in δ 18 Ofi values (Fig. 3) in the heating experiments is not caused by evaporation due to thermal decrepitation.

Evidence of a post-depositional effect in the D-O plot
The distinct behaviour of δDfi and δ 18 Ofi values is clearly depicted in the δD-δ 18 O plot (Fig. 4). The GMWL, local meteoric water line (LMWL), and the precipitation-weighted annual mean values (2009)(2010)(2011)(2012) of the rain water on Okinawa-185 jima Island are shown in Fig. 4. The LMWLs for summer and winter seasons are calculated based on the rain water data from Okinawa-jima Island (Uemura et al., 2012), ca. 400 km west of Minami-daito Island. The present-day dripwater isotopic data of Hoshino cave are close to the higher ones of annual mean precipitation values on Okinawa-jima (Fig. 4).
Generally, the initial δDfi and δ 18 Ofi values in the 25°C experiment are scattered between the summer and winter LWMLs.
The Thorium-230 dating results of stalagmite HSN1 from Hoshino Cave are shown in Table 3. The ages of layers at 190 depths of 75.0 and 190.0 mm were 6429±55 and 7092± 48 years BP, respectively. Thus, a more detailed comparison between the HSN1 fluid inclusions and the present-day rainwater is not straightforward because the HSN1 speleothem was grown during mid-Holocene and the rainwater isotope ratio is likely different from that of modern rainfall.
The important characteristic of this result is that the δ 18 Ofi values of the heating experiment are systematically shifted in the isotopically enriched direction. The average δ 18 Ofi value of the heating experiments (−5.4±0.4‰) is higher than that of 195 the 25°C experiment (−6.1±0.3‰) by 0.7‰. In contrast, the average value of δD does not differ between these experiments (−34.5±1.9‰ in the heating experiment, −33.9±1.3‰ in the room-temperature experiment).
Such positive δ 18 O shift is opposite to the negative δ 18 O shift of inclusion water in speleothems possibly induced by recrystallisation (Demény et al., 2016). Instead, the positive shift is similar to the δ 18 O shift from GMWL found in observations of geothermal water (Clark and Fritz, 1999). Although the magnitude of the shift is much larger for geothermal 200 water, 5-15‰, the δ 18 Ofi shift found in our experiment is likely caused by the exchange of 18 O between the inclusion water and the host calcite. The possible reasons for the small magnitude of the δ 18 O shift, 0.7‰, in our experiment will be discussed later (Section 3.4 and 3.5).
In fluid inclusion studies, closeness to the LMWL in δD-δ 18 O plots has been used as proof for the validity of analytical methods and the integrity of the sample. Our result calls for caution regarding the δD-δ 18 O plot test. Most of the inclusion 205 data from the heating and room-temperature experiments are distributed between the summer and winter LWMLs. As discussed above, the artificial increase in the δ 18 O value by heating is systematic. However, it is difficult to detect such a shift in the δD-δ 18 O plot because the shift is small in the scattered data points. The data from the heating experiment (more than 10 hours) plot outside the summer LMWL, but a 0.7‰ deviation could be interpreted as resulting from different climate conditions. Because the oxygen isotopic exchange results in higher δ 18 O values without a δD shift, the isotopic exchange 210 results in a lower deuterium excess value (d = δD -8 δ 18 O), -6‰ shift in our experiment. We should note that the d value could become higher if the exchange takes place at lower temperatures than the original precipitation temperature. Therefore, the oxygen isotope exchange under changing temperatures may cause any slight deviation from the LMWL.

Partial isotopic exchange between water and calcite
To interpret the experimental result, we consider two hypotheses: (i) the oxygen isotopic exchange reaction occurred 215 between inclusion water and the entirety of the host calcite (hereafter referred to as the "fully reacted hypothesis") and (ii) the δ 18 Ofi values are equilibrated with a limited amount of CaCO3 (hereafter referred to as the "partially reacted hypothesis").
These hypotheses are schematically explained in Fig. 5.
For the fully reacted hypothesis, the number of oxygen atoms in calcite can be considered infinite compared with that in the water inclusions because the water content of a stalagmite is very small: 0.05-0.5 wt. % (McDermott, 2005). Thus, the 220 δ 18 Ofi is simply controlled by the δ 18 O value of calcite and the equilibrium fractionation factor between CaCO3 and H2O at the ambient temperature (Fig. 5b). At 105°C, the fractionation factor between CaCO3 and water is 1.0167. Because the δ 18 Oca value of HSN1 stalagmite is 25.5‰ vs VSMOW (i.e., −5.3‰ vs VPDB), the δ 18 Ofi value in equilibrium with the calcite should be 8.6‰ vs VSMOW. Thus, δ 18 Ofi value should be enriched by 14 to 15‰. This simple hypothesis, however, is not realistic because the inclusion water likely reacts only with the inner surface of CaCO3 surrounding the inclusions. In fact, 225 the results in Fig. 2a show that the actual change in the δ 18 Ofi value is only 0.7‰.
The small δ 18 Ofi shift observed in the experiment can be interpreted as the result of (i) insufficient reaction time between water and calcite and/or (ii) reaction with a limited amount of CaCO3. The first hypothesis can be rejected because the Δδ 18 Ofi enrichment plateaued within 20 hours (Fig. 2a). Therefore, the experimental results support the latter hypothesis.
A model for this partially reacted hypothesis will be discussed in the following section. 230

Isotopic re-equilibration model
We describe a partial isotopic equilibration model that considers the changes in δ 18 Ofi values from the time when the inclusion water was entrapped in CaCO3 (time 0) to a certain time required to reach a new isotopic equilibrium (time t1; at a certain temperature T1). An example of this re-equilibration scenario is that inclusion waters at room temperature (time = 0, temperature = T0) are heated to 105°C (T1) and reach a new isotope equilibrium at time t1. 235 For the partially reacted hypothesis, we assumed that a limited amount of CaCO3 in the reacted layer exchanged oxygen isotopes with the inclusion water (Fig. 5a). The isotope mass balance between the initial and partially equilibrated conditions at a heating time during a course of reaction at time t can be written as follows: where γ is a molar ratio of CaCO3 involved in the reaction to the inclusion water (i.e., γ = CaCO3 in reacted layer / H2O in inclusion: MCaCO3/MH2O), and ( ) 18 reach an isotopic equilibrium state. This equilibrium state can be written as: where ε T1 18 indicates the oxygen isotopic enrichment factor at the temperature T1. Whereas the rate constant of the isotope 250 exchange reaction only varies with temperature, the number of transferred isotopes varies with the temporal evolution of the isotope ratios of the end members. The reaction can be written as: where (δ ca_ra( ) 18 − δ fi( ) 18 ) is the isotopic difference, T1 18 is the isotopic enrichment factor at the new equilibrium state, and k18 indicates a reaction constant. The integration of Eq. (4) yields: 18 ) represents the oxygen isotopic enrichment factor at the initial temperature of T0.
This equation provides an estimate of γ based on the experimental results.
A regression curve based on Eq. (5), is shown in Fig. 2a. Based on Eq. (7), the value of γ is estimated to be 0.02. This suggests that the amount of CaCO3 reacted with water is equivalent to 2% of the water inclusions in molar terms. The 275 thickness of the reacted layer of CaCO3 can be roughly estimated on the assumption that the fluid inclusions filled with water are cubic with 50 μm edges. With a calcite density of 2.71 g/cm 3 , the thickness of the reacted layer of CaCO3 is estimated to be 0.6 μm.
This result is explained schematically in Fig. 5a and 5c. The δ 18 Ofi value increased by only 0.7‰. Since the equilibrium fractionation factor between CaCO3 and water at 105°C is 1.0167, the δ 18 Oca of the reacted layer should be 11.3‰ vs 280 VSMOW. Thus, in this case, the δ 18 Oca value of the reacted layer changed significantly.

Impact for palaeo-climate reconstruction
In this section, we estimate the impact of the isotopic exchange effect on Quaternary palaeo-climate reconstructions.
First, at 105°C, detectable isotopic exchange occurred within 20 hours. This finding suggests that researchers should be aware of this effect during experimental procedures, such as the heat drying process, before fluid inclusion measurements. 285 Second, we consider a case in which the dripwater enclosed in the fluid inclusions during a glacial period with a temperature of 15°C re-equilibrates at the modern average temperature of 25°C. The isotopic enrichment factors ( T 18 ) for 15°C and 25°C are 30.6‰ and 28.4‰, respectively. Thus, based on Eq. (7) with a γ value of 0.02, the fluid inclusion oxygen isotope ratio δ 18 Ofi would increase by only 0.1‰. With the temperature dependence of the δ 18 O fractionation factor between water and calcite (0.2‰/°C), this isotopic exchange results in a 0.5°C bias in the palaeo-temperature estimate. We should note that we 290 do not know the reaction rate of the isotopic exchange under normal ambient temperatures. Calcite and fluid inclusion water might not reach a new equilibrium state even after thousands of years. Thus, this estimate is an upper limit of the bias.
Because the bias, 0.1‰, is within the typical analytical error for inclusion analyses, the post-depositional effect has little influence on the palaeo-temperature estimates for glacial-interglacial cycles.

Conclusions 295
Our experiment shows that the δ 18 O values of fluid inclusion water in speleothems changes because of isotopic exchange reactions with the host calcite. Unlike the δ 18 O value of inclusion water, the δD value showed no trend even after prolonged heating and thus effectively reflects the original isotopic composition of past dripwater. This study is the first to present experimental data showing that such a post-depositional effect occurs in natural speleothem samples. However, the changes in the δ 18 O values of fluid inclusion were very small, 0.7‰, in the 105°C heating experiment. Based on this result, 300 the inclusion water reacts only with a thin layer of surrounding CaCO3. The amount of CaCO3 that reacted with the water is equivalent to 2% of the water inclusions in molar terms. Thus, the oxygen isotopic exchange results in a minor impact on the estimation of past temperature changes: a maximum bias of 0.5°C for a 10°C climate shift. This study provides a quantitative explanation of the mechanism by which the effect of isotopic exchange appears to be insignificant in previous speleothem studies. The results also suggest that the sample treatment in the laboratory (i.e., heated drying process) should be conducted 305 with caution because isotopic exchange may affect the δ 18 O value of fluid inclusions.

Data availability
The data generated and used in this study are available in Tables 1 and 2 in this article.

Author contributions. 310
RU designed the experiment and study. YK and KO conducted the experiments. C-CS performed U-Th dating. All authors contributed to the discussion. RU analysed the results, generated figures and wrote the paper.

Competing interests.
The authors declare that they have no conflict of interest.      CaCO3. In this case, the sample at room temperature (25°C at time of 0) is heated to 105°C and reaches a new isotopic 495 equilibrium at time t1. (c) The same as (b) but for the partially reacted hypothesis, in which the δ 18 Ofi value changes in response to equilibration with a limited amount of CaCO3. Note that the calcite-water fractionation factor is the same for both hypotheses.