The origin and degassing history of the Earth's atmosphere revealed by Archean xenon

Xenon (Xe) is an exceptional tracer for investigating the origin and fate of volatile elements on Earth. The initial isotopic composition of atmospheric Xe remains unknown, as do the mechanisms involved in its depletion and isotopic fractionation compared with other reservoirs in the solar system. Here we present high precision analyses of noble gases trapped in fluid inclusions of Archean quartz (Barberton, South Africa) that reveal the isotopic composition of the paleo-atmosphere at ≈3.3 Ga. The Archean atmospheric Xe is mass-dependently fractionated by 12.9±2.4 ‰ u−1 (± 2σ, s.d.) relative to the modern atmosphere. The lower than today 129Xe excess requires a degassing rate of radiogenic Xe from the mantle higher than at present. The primordial Xe component delivered to the Earth's atmosphere is distinct from Solar or Chondritic Xe but similar to a theoretical component called U-Xe. Comets may have brought this component to the Earth's atmosphere during the last stages of terrestrial accretion.

T he building blocks of the Earth accreted in regions where temperatures were too high to permit significant retention of volatile elements (for example, H,C,N, noble gases). The Earth probably acquired its volatile components late from more distant sources 1 such as the Main Belt asteroids and/or comets. Simulations suggest that during the final stages of solar system formation, the orbits of asteroids were disturbed by the migration of the giant planets and, for some of them, their trajectories crossed the Earth's orbit 2 . Even if the isotopic composition of cometary water argues against comets being the source of terrestrial water 3 , the high Ar/H 2 O ratio measured in comet 67P/C-G by the Rosetta spacecraft 4 suggests that cometary objects may have contributed noble gases to the terrestrial atmosphere 5 .
At least two distinct cosmochemical sources contributed noble gases to the Earth's mantle: a Solar end-member detected in Ne isotopes 6 and a Chondritic component (that is, asteroidal) apparent in the isotopic compositions of Kr (ref. 7) and Xe (ref. 8). The presence of radiogenic and fissiogenic noble gases in the atmosphere ( 40 Ar, 129,131-136 Xe), produced by the radioactive decays of parent nuclides ( 40 K, 129 I, 244 Pu, 238 U) in the mantle and crust, attests for exchanges between the surface and the silicate Earth. However, the ultimate origin of the Earth's atmosphere remains unknown, especially for xenon. The Xe abundance in the Earth's atmosphere is depleted, the atmospheric Xe/Kr ratio being lower by a factor of B20 relative to the chondritic composition 9,10 . Furthermore, atmospheric Xe is enriched in heavy isotopes by 30-40 % u À 1 relative to Chondritic (Q-Xe) or Solar (SW-Xe) (ref. 11). These two features form the so-called 'xenon paradox' 12 . When corrected for mass-dependent isotope fractionation, atmospheric Xe is depleted in its heavy isotopes ( 134 Xe and 136 Xe) relative to Solar or Chondritic Xe, and cannot be related to any known cosmochemical component 13,14 . These observations led to the definition of a theoretical primordial component labelled 'U-Xe' (ref. 13), which has solar-like composition for the light isotopes 124-130 Xe, and is depleted in heavy Xe isotopes. However, this composition was derived from statistical correlations and its presence has never been observed in any terrestrial or extraterrestrial material. Recently, Meshik et al. 15 proposed an alternative explanation to U-Xe for the origin of atmospheric Xe. Their model is not based on a different primordial component but involves Chemically Fractionated precursors of Fissiogenic Xe producing the so-called CFF-Xe (see ref. 16 and refs therein). Degassing of this component, enriched in 134 Xe and 136 Xe, accompanied by atmospheric escape seems to match the fission spectrum of atmospheric Xe. However, when SW-Xe is taken as a precursor of atmospheric Xe and is mass-fractionated to reproduce, for example, the 128 Xe/ 130 Xe in the modern atmosphere, the result produces anomalous 136 Xe excesses (about 26 ± 6 % (1s) compared with the modern atmosphere) before any fission contribution. Thus, CFF-Xe cannot be the sole explanation for the origin of the isotopic composition of atmospheric Xe since this modified fission component can only increase the 136 Xe budget of the atmosphere.
Recent studies of Archean barite and quartz samples from North Pole, Pilbara (NW Australia) demonstrated that, 3.5 to 3.0 Ga ago, atmospheric Xe had an isotopic composition less isotopically fractionated than the modern atmospheric Xe relative to any of the potential primordial components [17][18][19][20] . These data suggest a progressive long-term evolution of the isotopic composition of atmospheric Xe by mass-dependent isotope fractionation, that may be due to ionization of atmospheric xenon 21 by ancient, ultraviolet-rich, solar radiation and progressive escape of Xe ions to space 22,23 . However, these studies did not elucidate the original composition of atmospheric xenon, which was then tentatively attributed to Solar/ Chondritic 10,19 . Xenon escape processes could have also led to mass-independent isotope fractionation, in addition to the massdependent one, that could account for the unique isotope composition of modern atmospheric Xe. To investigate the ultimate origin of atmospheric xenon, we selected and analysed with unprecedented high precision Archean quartz samples from the Barberton Greenstone Belt (BGB), South Africa.
Here we demonstrate that fluid inclusions in the Barberton quartz samples record the Xe isotope composition of the Archean atmosphere. This 3.3 Ga-old atmospheric Xe is mass-dependently fractionated by E13 % u À 1 . Depletion in radiogenic 129 Xe relative to the modern atmosphere allows us to compute a degassing rate from the Earth's mantle to the atmosphere over the last 3.3 Ga. Furthermore, Archean Xe originates from a primordial component different from all other known reservoirs of Xe in the solar system and similar to the theoretical U-Xe. Comets may have been the source of this noble gas component, added to the Earth's atmosphere during late accretionary events.

Results
Samples characteristics. Samples analysed in this study are from a core (BARB 3) drilled in the BGB, South Africa. The drilling project is part of an ICDP Project ('Peering into the cradle of life', PI: N. Arndt). The BARB 3 core was drilled in rocks of the Kromberg formation (3.33-3.47 Ga) and mainly comprises a succession of white and black cherts and ultramafic rocks 24 . All samples of this study consist of macro-crystalline quartz (Supplementary Fig. 1) with different modes of emplacement in rocks from the BGB and probably linked to early hydrothermal activity 25 . Some of the samples are from well-defined cm-sized bedded veins (Supplementary Fig. 1 26). This excess argon component is correlated with the chlorine (Cl) content (Figs 1 and 2) and probably reflects enrichment of the fluids in crustal-derived radiogenic argon and chlorine during fluid-rock interaction processes before entrapment. Only step-heating steps yielding elevated K/Cl ratios give realistic ages between 3 and 3.5 Ga that are broadly compatible with the age of the formations in which the quartz veins are emplaced (Fig. 2). We correct 40 Ar- 39 Ar data for excess argon using a plane (R 2 ¼ 0.975) to the data in three-dimensional (3D) space (Cl-K-40 Ar) space by applying a Monte Carlo method to propagate errors on measurements (Methods, Fig. 3 and Supplementary Fig. 2). This approach leads to a 40 Ar-39 Ar age of 3.3 ± 0.1 Ga ( ± 2s, s.d.) for Barberton sample BMGA3-9 (Fig. 3). This age is similar within errors to the formation age 24 but may also be consistent with late hydrothermal fluid circulation events 25 linked to the intrusion of adjacent 3.22 Ga-old plutons 27 . The initial 40 Ar/ 36 Ar is 458 ± 4 (±2s, s.d.) for sample BMGA3-9, which is higher than the modern atmospheric ratio of 298.6 (ref. 28), this may be explained by the presence of some 40 Ar excess uncorrelated with the chlorine content.
A different approach (Methods) was used to constrain the age of sample BMGA3-13, which contains relatively lower excess 40 Ar abundances as indicated by a less-well defined correlation between 40 Ar E and Cl (R 2 ¼ 0.95) and lower 40 Ar/ 36 Ar values  Table 1). This method uses the 40 Ar E /Cl derived from crushing data to correct step-heating data for the 40 Ar E component (Methods). This leads to a similar, but less precise, age of 3.5±1.0 Ga (±2s, s.d., mean square weighted deviation (MSWD) ¼ 1.06). The initial atmospheric 40 Ar/ 36 Ar ratios of sample BMGA3-13, computed for ages varying between 3.2 and 3.4 Ga (see above) have values ranging from 178 to 202 with a mean of 190±12 (±2s, s.d.) (Supplementary Fig. 3). This value is a minimum value for the Archean atmospheric 40 Ar/ 36 Ar ratio but is in broad agreement with previous estimates and prediction (143 ± 21, 3.5 Ga ago, (ref. 20)) and models invoking a peak in crustal extraction between 3.8 and 2.5 Ga (refs 20,29).
Xenon isotopic composition. The reproducibility of the crushing experiment results (Supplementary Table 2) on different samples and duplicates (Methods and Supplementary Fig. 4) enables a precise determination of the error-weighted average for the isotopic ratios of xenon trapped in Barberton quartz ( Fig. 4 and Supplementary Table 2). The isotopic spectrum of xenon in Barberton quartz normalized to 130 Xe indicates excesses of the light isotopes ( 124-129 Xe) together with depletions of heavy isotopes ( 131-136 Xe) relative to the modern atmospheric composition (Fig. 4a). The absence of mantle-derived 129 Xe excesses from the decay of now extinct 129 I (T 1/2 ¼ 16 Ma) relative to the atmospheric composition (Fig. 4), together with an isotopic composition of krypton similar to the modern atmosphere ( Fig. 5) argues against the presence of a mantle-derived component trapped within the fluid inclusions. Xenon in Barberton quartz thus has an Archean isotopic composition that differs from the modern atmosphere. The isotopic fractionation of xenon in Barberton quartz relative to the isotopic composition of the modern atmosphere was computed using the light stable, non-fissiogenic, non-radiogenic isotopes of Xe ( 126,128,130 Xe) plus 131 Xe, for which production by the fission of 238 U is small 30 . Error-weighted correlations were obtained using the Isoplot 4.1 software 31 , however, note that correlations involving 124 Xe were excluded for reasons explained in the Supplementary Discussion (Supplementary Information). The results show that Archean atmospheric xenon was isotopically fractionated by 12.9 ± 2.4 % u À 1 ( ± 2s s.e.m., MSWD ¼ 1.4) relative to modern atmospheric Xe (Fig. 6).

Discussion
Our observations provide strong confirmation, with greater precision, of previous observations on samples from different regions and geological settings (Fig. 6) [17][18][19][20]32 that the peculiar Xe isotopic composition during the Archean eon was ubiquitous and not due to local fractionation effects. The results provide confirmation for the specific and long-term evolution of the isotopic composition of atmospheric Xe, since the fractionation determined here is significantly different from 21±6 % u À 1 ( ± 2s, s.d.) Xe in North Pole, Pilbara barite with an age of 3.48±0.18 Ga (±2s, s.d.) 18 (Fig. 6). A mass-dependent isotope fractionation process acted on atmospheric Xe isotopes from at least 3.3 Ga until the present day. However, neither modern atmospheric Xe, nor Archean atmospheric xenon trapped in Barberton quartz can be derived from Q-Xe (Chondritic) or SW-Xe (Solar) by mass-dependent isotope fractionation, because these primordial components carry 134,136 Xe excesses 13 relative to ancient atmospheric Xe (Figs 7 and 8; see also Supplementary  Fig. 5). In the following discussion, we show how the Archaen atmosphere composition is consistent with U-Xe being a primordial component present in the atmosphere Z3.3 Ga ago.
We start by making the reasonable assumption that the primordial component had a solar-like 132 Xe/ 130 Xe ratio of 6.061 ± 0.029 ( ± 2s, s.d.) 33 (Fig. 7a, Supplementary Discussion); this is supported by the following: (1) Barberton 126-132 Xe/ 130 Xe (and not 134-136 Xe/ 130 Xe) ratios can be related to solar Xe by a mass-dependent isotopic fractionation of E25 % u À 1 ; (2) Solar gas represents the major gas reservoir of the solar system and any higher 132 Xe/ 130 Xe ratios as found in Chondritic meteorites are often accompanied by 134 Xe and 136 Xe excesses 34 . Note that this starting assumption is valid for 132 Xe only and does not imply that the whole isotopic spectrum of primordial Xe component Step-heating Crushing

BMGA3-9 BMGA3-3 BMGA3-13
Step Light isotopes excesses in the Barberton Xe isotopic spectrum ( Fig. 4) correspond to an isotopic fractionation (E 12.9 % u À 1 ) that can be propagated towards heavy isotopes to compute a theoretical primordial isotopic composition for the atmosphere, especially for 134 Xe and 136 Xe (Fig. 7c). The resulting range of possibilities for the initial isotopic composition (range at ±2s) corresponds to 136 Supplementary Fig. 5). The mass-dependent isotopic fractionation of this composition, combined with the addition of fissiogenic 132-136 Xe isotopes with known yields 12 , accounts for the Xe isotopic composition measured in Barberton quartz ( Fig. 8 and Supplementary Fig. 5). Hence, our results demonstrate that an initial isotopic composition different from Q-Xe or SW-Xe, and similar to U-Xe, must have existed in the ancient atmosphere, without making use of the isotopic composition of the modern atmosphere as it was done in previous studies 13,14 .
The fidelity of our deconvolution of Archean Xe is revealed by the Xe fission spectra shown in Fig. 9 35) produced by the radioactive decay of extinct 129 I (T 1/2 ¼ 16 Ma). For the Archean atmosphere, the excess of 129 Xe(I), is calculated to be 6.07 ± 0.22% ( ± 1s, s.d.) after correction for isotopic fractionation (Methods). This value is lower than the modern atmospheric excess (Fig. 4b) and probably results from the amount of 129 Xe(I) that has been degassed from the mantle 12 during the last 3.3 Gyr. Thus, by comparing the 129 Xe/ 130 Xe of 3.3 Ga-old atmosphere to that of the modern atmosphere provides insight into mantle degassing, and, therefore, convection, through time. This approach is advantageous compared with atmospheric 40 Ar degassing models because the latter are much more closely related to crustal production than mantle degassing flux (for example, ref. 20), due to 40   Depletions in 134 Xe and 136 Xe for the primordial component similar to U-Xe as recorded by Barberton quartz may reflect either a mass-independent isotope fractionation process, not yet identified, or the presence of a nucleosynthetic anomaly (for example, r-process deficit) in the early atmosphere compared with other major components of the solar system (Chondritic or Solar Xe). This nucleosynthetic anomaly is problematic, as the contribution from meteorites, in particular the carbonaceous chondrites during the final stages of Earth's accretion is usually advocated to explain the abundances of volatile elements on Earth 10 . However, neither carbonaceous chondrites nor any other meteorite group contain U-Xe. Comets are primitive volatile-rich objects in the solar system that potentially may carry such an exotic primordial component, possibly inherited from other planetary systems formed in the vicinity of our Sun 46 . The abundances of the heavy noble gases in comets are not well constrained (only Ar has been measured so far 4 ) and their capacity to transport noble gases will be highly dependent on the physical state of the ice (amorphous ice vs. clathrates). However, a rough estimate of the composition of these objects can be made (Supplementary Tables 4 and 5 Supplementary Fig. 6). If Xe is present as amorphous ices in comets, then a 10% cometary contribution to a mass flux similar in magnitude to the Terrestrial Late Heavy Bombardment (2 Â 10 23 g, see Supplementary Information), added to the Earth following Moon formation, would be sufficient to bring the current budget of atmospheric Xe. For Xe contained in cometary clathrates, a 10% cometary contribution could deliver up to two orders of magnitude higher Xe than the surficial budget of Xe corrected for the loss (Supplementary Fig. 6). Thus, even if the nature of the late accreting events is not well constrained, comets may have contributed significantly to the budget of atmospheric noble gases, and specially Xe, after the Moon formed ( Supplementary Fig. 6) 5 .
The emerging picture for the history of Xe on Earth is schematically depicted in Fig. 10 47 (Fig. 10a). The intense 129 Xe(I) degassing rate of 8 ± 4 (±1s, s.d.) mol a À 1 integrated over 3.3 Ga probably reflects degassing of the whole mantle in the active early Earth. The overall budget and isotopic composition of modern terrestrial xenon (Fig. 10b)     interactions between the different reservoirs on Earth. A precise determination of the time-dependent evolution of the isotopic composition of atmospheric Xe could shed light on major events on Earth such as the timing of the onset of Xe subduction and the mechanisms and cessation of atmospheric escape.
Methods 40 Ar- 39 Ar experiment and determination of ages. Separated quartz fractions of the samples have been analysed following the extended 40 Ar-39 Ar method that enables simultaneous analysis of K, Cl abundances and the isotopic composition of argon 48 . Before irradiation, each sample was wrapped in aluminum foil. Samples were placed in a quartz tube, evacuated and sealed to a maximum length of 6.5 cm using a flame. Hb3gr hornblende samples, used as neutron flux monitors, were positioned at the bottom, and top of the quartz tube. Samples were irradiated (irradiation designated 'MN2014b') in the G-Ring In-Core Irradiation Tube facility of the TRIGA Reactor, Oregon State University. As the halogen-derived noble gas isotopes are produced by low energy thermal neutrons and epithermal neutrons, the irradiation cans were not Cd-shielded. Samples were irradiated for a few hour intervals each day over several weeks (22/4/14-1/7/14) to give a total irradiation time of 205 h for MN2014b.
The irradiation parameter J is determined from the measured 40 Ar/ 39 Ar ratio in the Hb3gr hornblende standards that were irradiated in the same tubes as the samples (equation 1): where t m is the age of Hb3gr of 1074.9 ± 3.5 Ma (ref. 49) and l is the total decay constant (5.531 Â 10 À 10 a À 1 , ref. 50). Values of J are 0.01789±0.00008 and 0.01773 ± 0.00008 for Hb3gr monitors place at the top and bottom of the tube, respectively.
The abundances of Ca and Cl in samples can also be determined from Hb3gr using additional irradiation parameters, a (ref. 51) and b (ref. 52) (equations 2 and 3): The abundances (in wt.%) of K, Ca and Cl in Hb3gr are, respectively, 1.247 ± 0.008, 7. Thus in units of moles cm À 3 STP: Ca Cl Following irradiation, samples were analysed in two successive steps: (1) stepcrushing to release fluids trapped in fluid inclusions; (2) step-heating up to 1,700°C to release K, Cl and Ar trapped in small inclusions, and present in the quartz lattice. Extraction, purification, measurement and correction techniques are already described elsewhere 54 .
Results obtained for samples BMGA3-9, BMGA3-13 and BMGA3-3 are listed in Supplementary Table 1. The 40 Ar/ 36 Ar ratios measured during the crushing and step-heating experiments are high (up to about 8,500) and cannot be solely explained by in situ decay of 40 K even during 4.5 Ga. This 40 Ar excess, referred to as 40 Ar E hereafter, is correlated to the chlorine content (Figs 1 and 2) and probably linked to a hydrothermal fluid circulation through the samples 26 . One of the methods to correct the data for this 40 Ar E contribution is to use the K-Cl- 40 Ar (x-y-z) space where crushing and step-heating data would lie on a plane with the following equation (equation 7) is the initial ratio trapped in the sample, A represents the correlation between 40 Ar E and the chlorine content, and B ( ¼ 40 Ar*/K) reflects the relationship between in situ produced 40 Ar ( 40 Ar*) and the potassium content computed from the abundance of 39 Ar produced by neutron irradiation. The errors on the parameters of the plane defined by the data points were determined by a Monte Carlo propagation method using a Matlab code. First, for each point, coordinates on the x, y and z axes were divided by the mean error of the data set for normalization purpose. This was done to avoid overestimation of residuals resulting from different scale ranges (Supplementary Table 1). For each point a randomly generated cloud of 5,000 points was then created in order to properly represent the error envelop in the 3D space. The function of surface fitting 'sfit' of Matlab was applied to the 80,000 points. 'sfit' is a total least squares regression method through the entire cloud of points, the robust option permitting removal of outliers on an iterative basis based on least absolute residuals. Plots of residuals are shown in Supplementary Fig. 2. The fitting method led to a 40 Ar/K value of 6.63 Â 10 À 5 ( ± 8 Â 10 À 6 , ± 2s, s.e.m.) for B that formally corresponds to an age of 3.3 (±0.1) Ga (2s, s.e.m.). ( 40 Ar/ 36 Ar) 0 , representative of the initial 40 Ar/ 36 Ar trapped in Barberton quartz, is 458 ± 4 (2s, s.e.m.) higher than the present day atmospheric value of 298.6. This higher value is almost certainly due to some 40 Ar excess remaining even after correction for 40 Ar E linked to the chlorine content ( Supplementary Fig. 3) and for radiogenic 40 Ar from in situ decay of 40 K during 3.3 Ga. The Matlab code used in this section is available through requests to G.A. (gavice@caltech.edu).
A second method originally proposed by Pujol et al. 20 has been applied to sample BMGA3-13 for which 40 Ar E is less evidently linked to the Cl content but 40 Ar/ 36 Ar measured during experiments are lower (see Fig. 1, Supplementary Fig. 3 and results in Supplementary Table 1). Crushing and step-heating results show a similar correlation in the 40 Ar-Cl diagram (Fig. 1). A Cl\ 40 Ar E ratio of 6,500±949 was thus obtained from analysis of crushing results. Second, this ratio was used to subtract 40 Ar E using the chlorine content released during each heating step multiplied by Cl\ 40 Ar E . A set of initial 40 Ar/ 36 Ar ratios and times of fluid entrapments for in situ decay of 40 K were then manually tested. A best solution was found for an initial atmospheric 40    not addressed in this section and thus, that the age uncertainty could be underestimated.
Analytical procedure for Xe and Kr measurements. Xenon and krypton isotopic compositions (and abundance of Xe) in fluid inclusions in quartz were determined by stepwise crushing (see results in Supplementary Tables 2 and 3). Before noble gas analyses, selected quartz fragments were gently crushed in a metal mortar to obtain grain-size fractions between 1 and 3 mm. This is the ideal range of sizes that minimizes adsorption of air on the surface of the grains and enables up to 2 g of sample to be loaded in to each crusher for noble gas analysis required to obtain a significant Xe signal in the mass spectrometer. Grains were subsequently cleaned with acetone in an ultrasonic bath, then rinsed with acetone and dried in an oven at 90°C for 30 min. Following cleaning, quartz grains were hand-picked under a binocular microscope to ensure the absence of impurities on the surface of the grains and inside individual crystals. Each sample was then loaded in a stainless steel crusher. It consists of a modified valve where the valve's bellow has been replaced by a stainless tube moving downward when the modified valve is closed. Our samples were rich in fluid inclusions and their crushing released significant amounts of water and other inert or chemical reactive species (including N 2 and hydrocarbons). Ti-sponge getters, usually placed in a heating tube connected to the line and used to remove active species, were unable to remove all the water as indicated by monitoring the pressure in the purification system (up to 10 À 4 mbar).
A new system was thus designed that consisted of an in-line Ti-sponge getter placed just after the crusher and heated at 700°C ensuring that all the gas passed through the Ti-sponge. This new design solved the problem of the water purification, as demonstrated by the low pressure measured before the introduction in the mass spectrometer (for example, 1-5 Â 10 À 8 mbar). Xenon and krypton were condensed over a period of 20 min in a quartz tube held at liquid nitrogen temperature. Adsorption on the walls of the glass tube is unlikely to induce detectable isotopic fractionation 55 . The remaining part of the gas was pumped out. The amounts of 40 Ar released during crushing of samples were so high, that even the minor fraction present in the tube with Xe and Kr prevented efficient ionization of Xe resulting in low sensitivity. Ten dilutions of the volume of the glass tube (20 cm 3 ) into the whole line (1,500 cm 3 ) dramatically decreased, by a factor of 750, the residual Ar partial pressure. Fractions rich in in Xe and Kr were then released and purified on three Ti-sponge getters at 550°C for 5 min and at room temperature for 5 min before expansion into the noble gas multicollector mass spectrometer (Helix MC Plus, Thermo Fisher). Xe was the first gas to be analysed using a peak jumping mode with the magnet field, ion currents were detected using and a compact discrete dynode multiplier and Kr was subsequently analysed using a similar procedure. Procedural Xe blanks were monitored before each crushing experiment and were very low, on the order of 10 À 18 mol of 132 Xe.
Error propagation and compilation of the results. Twenty-seven crushing experiments on seven distinct samples were conducted in total. Isotopic ratios of Xe released during each crushing experiment are shown in Supplementary Fig. 4. Very reproducible results were used to calculate an error-weighted average for each isotopic ratio (Supplementary Table 2) with MSWD values between 0.43 and 1.3. These values are satisfactory since MSWD values close to 1 indicate that errors are representative of the analytical uncertainty.
Degassing rate inferred from low 129 Xe(I) excess. All errors given in this section are at ±1s, s.d. The modern atmosphere contains (4.06±0.05) Â 10 12 mol of 129 Xe (ref. 12) and an excess of 6.8 ± 0.3% of 129 Xe(I) (ref. 35). This corresponds to 2.76 ± 0.13 Â 10 11 mol of 129 Xe(I). Barberton 129 Xe/ 130 Xe ratio has a d 129 Xe air value of 6.3±1.3 % (Fig. 2a in the main text). Propagation of the isotopic fractionation computed on light isotopes (see above) toward 129 Xe leads to a theoretical non-radiogenic delta value (d 129 Xe theor. ) of 12.9 ± 1.2 % for 129 Xe. The difference of 6.6±1.8 % between theoretical and measured deviations relative to the isotopic composition of the atmosphere (Fig. 4) indicates that the 3.3 Ga-old atmosphere contained a 129 Xe(I) excess of only 6.14±0.35% corresponding to (2.50 ± 0.07) Â 10 11 mol of 129 Xe(I) with the conservative assumption that no Xe was lost from the atmosphere. This result enables calculation of a lower limit of 8±4 mol a À 1 for the degassing rate of 129 Xe(I) during the last 3.3 Ga.
Data availability. The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information files.