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# Xenon isotopic constraints on the history of volatile recycling into the mantle

## Abstract

The long-term exchange of volatile species (such as water, carbon, nitrogen and the noble gases) between deep Earth and surface reservoirs controls the habitability of the Earth’s surface. The present-day volatile budget of the mantle reflects the integrated history of outgassing and retention of primordial volatiles delivered to the planet during accretion, volatile species generated by radiogenic ingrowth and volatiles transported into the mantle from surface reservoirs over time. Variations in the distribution of volatiles between deep Earth and surface reservoirs affect the viscosity, cooling rate and convective stress state of the solid Earth. Accordingly, constraints on the flux of surface volatiles transported into the deep Earth improve our understanding of mantle convection and plate tectonics. However, the history of surface volatile regassing into the mantle is not known. Here we use mantle xenon isotope systematics to constrain the age of initiation of volatile regassing into the deep Earth. Given evidence of prolonged evolution of the xenon isotopic composition of the atmosphere1,2, we find that substantial recycling of atmospheric xenon into the deep Earth could not have occurred before 2.5 billion years ago. Xenon concentrations in downwellings remained low relative to ambient convecting mantle concentrations throughout the Archaean era, and the mantle shifted from a net degassing to a net regassing regime after 2.5 billion years ago. Because xenon is carried into the Earth’s interior in hydrous mineral phases3,4,5, our results indicate that downwellings were drier in the Archaean era relative to the present. Progressive drying of the Archean mantle would allow slower convection and decreased heat transport out of the mantle, suggesting non-monotonic thermal evolution of the Earth’s interior.

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## Change history

• ### 24 September 2018

In this Letter, owing to a production error, the arrows in the middle panel of Fig. 1 were wrongly coloured and there were some some typos elsewhere. These errors have been corrected online.

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## Acknowledgements

The project was funded by NSF grant EAR-1250419 to S.M. We thank D. Fike, C. Jackson, M. Krawczynski and S. Turner for discussions that improved the manuscript.

### Reviewer information

Nature thanks M. Kendrick and D. Porcelli for their contribution to the peer review of this work.

### Extended data

is available for this paper at https://doi.org/10.1038/s41586-018-0388-4.

## Author information

• Rita Parai

### Contributions

S.M. and R.P. developed the conceptual model and the ideas presented in the manuscript. R.P. wrote the Matlab scripts for the numerical modelling. R.P and S.M. analysed the results and R.P. wrote the manuscript with input from S.M.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Rita Parai.

## Extended data figures and tables

1. ### Extended Data Fig. 1 Atmospheric Xe mass fractionation relative to the modern composition over time.

Figure adapted from ref. 2. Xe measured in Archaean barites, fluid inclusions in quartz from Archaean cherts and deep crustal fluids of various age are shown with associated 2σ uncertainties1,2,20,41,54,55. The blue line shows the model atmospheric Xe mass fractionation over time. We assume that the initial Xe isotopic composition of the atmosphere is Rayleigh-mass-fractionated by ~39‰ amu−1 relative to the modern atmosphere and that the degree of mass fractionation decreases linearly until 2 Gyr ago (Ga), when the atmosphere reaches its present composition.

2. ### Extended Data Fig. 2 Sum of squared residuals from least-squares fitting of mantle source compositions using either modern or ancient atmospheric Xe.

Mantle source 130,131,132,134,136Xe compositions are modelled as four-component mixtures of initial mantle Xe, recycled atmospheric Xe, and Xe from the fission of Pu and U. A sum of squared residuals of zero indicates that the mantle source composition can be fitted perfectly by mixing the four end-member components. Sums of squared residuals greater than zero indicate the sigma-normalized error in the best fit compared to the mantle source composition. Using modern atmospheric Xe as the regassed atmospheric Xe component, sums of squared residuals are zero or near-zero. Using ancient atmosphere, sums of squared residuals are much higher than zero, indicating that mantle source compositions cannot be explained by regassing of only ancient atmospheric Xe. The ancient atmospheric Xe composition used here corresponds to 20‰ amu−1 Rayleigh fractionation applied to the modern atmospheric composition and agrees with fission-corrected ancient atmosphere derived from fluid inclusions in Archaean rocks2. ae, Mantle source compositions for Equatorial Atlantic depleted mid-ocean ridge basalt (MORB)14 (a), Southwest Indian Ridge Eastern Orthogonal Supersegment MORB16 (b), Harding County well gas23 (c) and Bravo Dome well gas11 (d) are fitted using the Monte Carlo method (n = 10,000) described in ref. 16, with average carbonaceous chondrite as the initial mantle composition22, and either modern or 20‰ amu−1fractionated atmosphere (e) as the recycled component.

3. ### Extended Data Fig. 3 Continental crust growth models and exponential 130Xed time series examples.

a, 238U (and a small amount of 244Pu) extraction from the mantle by partial melting is offset by recycling of sediments at subduction zones at each time step. We model net extraction of U and any extant Pu from the mantle as directly tracking continental crust growth over time (Methods). Three CCs are adopted: two sigmoidal curves that approximate literature continental crust growth curves (‘CC = 1’ and ‘CC = 2’) and one linear growth curve (‘CC = 3’)39,40,41. b, Example of exponential 130Xed time series tested with our forward model of mantle Xe evolution. Two parameters describe the exponential function (Methods): $${}^{130}{{\rm{Xe}}}_{{\rm{d}}}^{{\rm{final}}}$$, the final 130Xe concentration in downwellings, and τ, the exponential time constant. Grey lines represent a collection of exponentials with discrete variation in $${}^{130}{{\rm{Xe}}}_{{\rm{d}}}^{{\rm{final}}}$$ and τ. A subset with a constant $${}^{130}{{\rm{Xe}}}_{{\rm{d}}}^{{\rm{final}}}$$ and varying τ is highlighted in red. The time constant τ is varied from 10−11 yr−1 to 5 × 10−8 yr−1, with small τ corresponding to slow growth. Examples for nine different $${}^{130}{{\rm{Xe}}}_{{\rm{d}}}^{{\rm{final}}}$$values are shown, with an upper bound of 5 × 108 atoms 130Xe per gram (Methods).

4. ### Extended Data Fig. 4 Characterization of successful regassing histories.

Diverse regassing history shapes are generated by sampling a limited time interval for a variety of growth rates and inflection times (Fig. 2). To provide a common point of comparison for the evolving conditions within downwellings, we sort results by the time when 130Xed has increased by 10% between its initial and final values (time of 10% rise). a, Times of 10% rise for successful regassing histories. Most successful model realizations have a time of 10% rise later than 2.5 Gyr ago. b, Model realizations with high present-day 130Xed values are uniformly characterized by late 10% rise times, indicating that in these model realizations downwelling Xe concentrations remain very low throughout most of Earth history. c, Variation in sigmoidal growth rates (parameter α) allows testing of near-linear (low α, sampling for a limited time interval) or near-step (high α) functions. Near-linear model realizations have a time of 50% rise that is about five times the time of 10% rise (dashed light-grey line), whereas step functions approach a 1:1 line (solid dark-grey line). Successful regassing histories with late times of 10% rise are characterized by rapid growth, approaching a step function, to a relatively high present-day 130Xed.

5. ### Extended Data Fig. 5 Successful regassing histories for varying model parameters.

ad, To test model sensitivity to the input parameters, we vary the number of mantle reservoir masses processed (Nres), convecting mantle reservoir mass (Mres), initial 130Xe concentration (LV) and continental crust model (CC), and collect all successful 130Xed (a, c) and mantle 130Xe concentrations (b, d) over time. For sigmoidal 130Xed, solutions are found for Nres = {5, 6, 7, 8, 9}, Mres of 50%, 75% and 90% of the whole mantle mass, LV of 0.1%, 0.5% and 1% chondritic late veneers, and all three CCs. Extended Data Figs. 6, 7 illustrate trade-offs between individual parameters; for instance, high Nres values generate solutions only with high LV. For all sigmoidal solutions, regassing is limited early in Earth history, and the mantle shifts from net degassing to net regassing after ~2.5 Gyr ago. For exponential 130Xed, solutions are found for Nres = {5, 6, 7, 8, 9}, Mres of 50%, 75% and 90% of the whole mantle mass, LV of 0.1%, 0.5% and 1% chondritic late veneers, and all three CCs. For all solutions, regassing is limited early in Earth history, and the mantle shifts from net degassing to net regassing after ~2.5 Gyr ago.

6. ### Extended Data Fig. 6 Sensitivity of 130Xe and 128Xe/130Xe to model parameters.

Present-day mantle 130Xe concentration and the ratio of two primordial stable isotopes, 128Xe and 130Xe are shown for different model parameter combinations. Four parameters are explored: those affecting the mantle processing-rate history (Mres and Nres), LV (initial 130Xe concentrations corresponding to a late veneer fraction between 0.1% and 1%) and CC (Extended Data Fig. 3). In each panel, three of these parameters are held constant and the other is varied to illustrate model sensitivity to the varied parameter. Each cloud of points represents the range of present-day 130Xe and 128Xe/130Xe generated by different regassing histories for the specified Nres, Mres, LV and CC. The red rectangle indicates the estimated present-day mantle 130Xe concentration and 128Xe/130Xe range. Dots that fall within the red rectangle represent the family of regassing histories that successfully reproduce the present-day mantle composition for each parameter combination. The reference case shown in Figs. 3, 4 (Mres = 90%, Nres = 8, LV = 1%, CC = 1) is shown as a cloud of black points in all panels. a, A higher mantle processing rate (Nres = 10) results in low 130Xe concentrations for successful 128Xe/130Xe ratios, and 128Xe/130Xe ratios that are too low for successful 130Xe concentrations. b, Higher late-veneer fractions correspond to higher initial 130Xe concentrations in the mantle. For the same mantle processing-rate history, LV = 0.1% yields present-day mantle 130Xe concentrations that are too low given successful 128Xe/130Xe ratios. The effect of low LV can be offset by lowering Nres and thus decreasing the total amount of degassing over Earth history; thus, Nres and LV can be co-varied to find solutions. c, The effect of Mres is minimal because degassing is parameterized through the number of reservoir masses processed over Earth history. Some difference is evident at high present-day mantle 130Xe abundances because the same 130Xed regassing rate parameter space is explored against different absolute degassing rates. d, The continental crust model has no effect on budgets of primordial Xe isotopes.

7. ### Extended Data Fig. 7 Sensitivity of fissiogenic Xe to model parameters.

Present-day outcomes are shown in 128Xe–132 Xe–136Xe isotopic space for different model parameter combinations. Four parameters are explored: parameters affecting the mantle processing-rate history (Mres and Nres), the initial mantle 130Xe concentration (LV = 0.1%–1%), and CC (Extended Data Fig. 3). In each panel, three of these parameters are held constant and the other is varied to illustrate model sensitivity to the varied parameter. Each cloud of points represents the range of present-day 128Xe/132Xe and 136Xe/132Xe generated by different regassing histories given the specified Nres, Mres, LV and CC. The red rectangle indicates the estimated present-day mantle 128Xe/132Xe and 136Xe/132Xe range. Dots that fall within the red rectangle represent the family of regassing histories that successfully reproduce present-day mantle composition for each parameter combination. The reference case shown in the main-text figures (Mres = 90%, Nres = 8, LV = 1%, CC = 1) is shown as a cloud of black points in all panels. The orange square is U-Xe, the brown diamond is average carbonaceous chondrites (AVCC) and the blue circle is the modern atmosphere. a, Higher mantle processing rates push present-day compositions towards fissiogenic Xe components. b, Lower late-veneer fractions correspond to present-day compositions closer to fissiogenic Xe components. c, A relatively low mass of the convecting mantle means that the mantle must be more depleted in U to satisfy mass balance with the continental crust (Methods). Thus, for low Mres, the impact of fission is muted compared to high Mres. d, The continental crust model has a limited effect on present-day Xe isotopic compositions.

8. ### Extended Data Fig. 8 130Xe fluxes over time in successful model realizations.

al, Regassing fluxes (ac), degassing fluxes (df), net fluxes (g), 130Xed concentrations (h, i), mass flux (j) and mantle 130Xe concentrations (k, l) are illustrated for an initial mantle 130Xe concentration of 3.2 × 108 atoms per gram (LV = 1%), a convecting mantle reservoir that is 90% of the mass of the whole mantle, and 8 mantle reservoir masses processed over Earth history. Fluxes are reported in moles per year and concentrations are reported in moles per gram. Panels in the left column show results from all successful model realizations (same results as those shown in Figs. 3, 4) and illustrate the 130Xe regassing flux (a), 130Xe degassing flux (d), 130Xe net flux (g) and mass flux over time (j). Panels in the central column show zoomed-in windows with only low-130Xed successful model realizations (light-blue lines), as these largely overlap with each other and are difficult to resolve in the full-scale panels. The right column replicates the central column with semi-logarithmic axes. The regassing 130Xe flux time series (ac) is the product of the downwelling mass flux time series (j; exponentially decreasing with time) and the 130Xed concentration over time (sigmoidally increasing; h, i). Time series for 130Xe regassing fluxes with high present-day 130Xed (darkest-blue lines in a) start near zero owing to near-zero 130Xe concentrations and then rapidly rise as the 130Xed concentration increases faster than the modest decline in mass flux later in Earth history. 130Xe flux time series with low present-day 130Xed (lightest-blue lines in ac) start a protracted, low-magnitude rise relatively early in Earth history. These translate to regassing flux time series that start near zero, rise and then decline with the exponentially decreasing mass flux (b, c). Time series for 130Xe degassing fluxes (df) are the product of the downwelling mass flux time series (j) and the mantle 130Xe concentration over time (k, l), which responds to both degassing and regassing. The net flux over time (g) is the difference between the regassing flux and degassing flux at any given time. The mantle shifts from net degassing to net regassing at some time after 2.5 Gyr ago.