A Portrait of Terrestrial Volatile Evolution from Mantle Noble Gases

A Portrait of Terrestrial Volatile Evolution From Mantle Noble Gases

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a dissertation presented by Jonathan M. Tucker to The Department of Earth and Planetary Sciences

in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Earth and Planetary Sciences

Harvard University Cambridge, Massachusetts October 2016 ©2016 – Jonathan M. Tucker all rights reserved. Dissertation advisors: Jonathan M. Tucker Professor Sujoy Mukhopadhyay Professor Charles H. Langmuir

A Portrait of Terrestrial Volatile Evolution from Mantle Noble Gases

Abstract

Volatile elements and compounds provide important insights into large-scale planetary and tectonic processes. The chapters in this thesis exploit the wealth of information provided by noble gas measurements to address a variety of questions regarding the origins and distributions of volatiles in the Earth.

Chapter 1 presents new He-Ne-Ar-Xe data from basalts from the equatorial Mid-Atlantic

Ridge, demonstrating a large degree of heavy noble gas heterogeneity in mid-ocean ridge basalts (MORBs). The He and Ne data can be explained primarily by a mixture of a depleted mantle component and a HIMU-like component, with the constraint that the HIMU component is a combination of recycled and primitive material. While most mantle-derived

Xe is recycled atmospheric Xe, the compositions of depleted MORBs, HIMU-type MORBs, and the Iceland plume cannot be related solely by different amounts of recycled air. Rather,

HIMU-type MORBs and the Iceland plume sample a less degassed reservoir. Furthermore, differences in the amount of 129I-derived 129Xe between the depleted and HIMU-type MORBs suggests that HIMU-type MORBs are sampling a reservoir that formed within the first 100

Myr of solar system history and has not extensively mixed with the depleted mantle since.

Chapter 2 explores the hypothesis that high 3He/22Ne ratios intrinsic to the depleted mantle were generated by multiple episodes of magma ocean outgassing and atmospheric loss during Earth’s accretion. We argue that magma ocean outgassing in the aftermath of giant impacts during accretion can raise the mantle 3He/22Ne ratio, but multiple episodes of outgassing and atmospheric loss are required to achieve the ratio observed in the depleted mantle. The preservation of low 3He/22Ne ratios in primitive plumes suggests that later giant impacts such as the Moon-forming giant impact did not homogenize the whole mantle. The

iii requirement for episodes of atmospheric loss to achieve high 3He/22Ne ratios during accre-

tion may also provide an explanation for Earth’s nonchondritic volatile element ratios such as

N/H as N would be more susceptible to loss processes than H.

Chapter 3 uses the combined constraints of the radiogenic noble gases 4He*, 21Ne*, 40Ar*,

136 and Xe*U to examine degassing processes at mid-ocean ridges. We show that ratios of radiogenic noble gases cannot be simultaneously explained by any equilibrium degassing model,

questioning the use of such models to reconstruct pre-degassing magmatic contents and hence

mantle fluxes of elements like C. We argue that kinetic fractionation prevents slowly diffusing

volatiles from achieving their equilibrium partitioning between vesicles and melt and present

4 a new simple model of disequilibrium degassing that self-consistently explains CO2- He*- 21Ne*-40Ar* compositions in MORBs. Application of this model suggests that the average

MORB mantle C/3He ratio and C flux may be a factor of 2 higher than that inferred from

equilibrium degassing-based estimates.

Chapter 4 presents new He data on depleted MORBs from the subtropical north Mid-

Atlantic Ridge. Correlations between He and Pb isotopic compositions in this region as well

as others globally suggest that, absent plume influence, He isotopes in MORBs can beex-

plained by a mixture of an intrinsic, relatively unradiogenic depleted component and highly

radiogenic recycled oceanic crust, a manifestation of the “marble cake” mantle. With a sim-

ple mixing model, we estimate that the mantle source of average MORBs has ~1-5% recycled

oceanic crust.

Chapter 5 presents new He-Ne-Ar-Xe data on a subset of the depleted MORB samples de-

scribed in Chapter 4. Ne isotopic compositions are less nucleogenic than average MORBs, in-

dicating the influence of a relatively undegassed component, which may be especially strongly

sampled near 29◦N. Ar, and Xe isotopic compositions extend from moderately radiogenic val-

ues to highly unradiogenic values, demonstrating extreme variability absent significant vari-

ability in lithophile chemistry. Globally, Ar and Xe isotopic compositions correlate in oceanic

basalts, interpreted to result from mixtures of degassed material having radiogenic Ar and Xe

with undegassed material and recycled air having unradiogenic Ar and Xe.

iv Contents

0 Introduction 1

1 The heavy noble gas composition of the depleted MORB mantle (DMM) and its implications for the preservation of heterogeneities in the

mantle 4

1.1 Introduction ...... 7

1.2 Methods ...... 9

1.3 Results ...... 13

1.4 Discussion ...... 20

1.5 Conclusions ...... 29

2 Evidence for multiple magma ocean outgassing and atmospheric loss

episodes from mantle noble gases 36

2.1 Introduction ...... 38

2.2 Determining MORB mantle source 3He/22Ne ratios ...... 40

2.3 The 3He/22Ne ratio of the depleted mantle ...... 42

2.4 3He/22Ne ratios in the present-day mantle and in planetary materials ...... 44

2.5 Can plate tectonics generate reservoirs with high 3He/22Ne ratios? ...... 46

2.6 Implications for Earth’s accretional history ...... 57

v 2.7 Conclusions ...... 61

3 Kinetic controls on volatile fluxes at mid-ocean ridges and impli-

cations for the mantle carbon flux 71

3.1 Introduction ...... 73

3.2 Equilibrium degassing models do not explain MORB data ...... 76

3.3 Kinetic fractionation during degassing ...... 81

3.4 Reconstructing initial noble gas contents in individual samples ...... 89

3.5 Implications for the mantle carbon content and flux ...... 94

3.6 Conclusions ...... 103

4 Using helium isotopes to constrain the amount of recycled crust

in the average MORB source 112

4.1 Introduction ...... 114

4.2 Coupled He-Pb variations in MORBs imply a ubiquitous marble cake mantle . . 116

4.3 Geodynamic consequences ...... 125

4.4 Where does subducted oceanic crust reside? ...... 133

4.5 Conclusions ...... 135

5 Extreme Ne, Ar, and Xe heterogeneity in depleted MORBs from the

subtropical north Mid-Atlantic Ridge 144

5.1 Introduction ...... 146

5.2 Methods ...... 148

5.3 Results ...... 150

5.4 Discussion ...... 155

5.5 Global variations in heavy noble gases ...... 170

5.6 Summary and conclusions ...... 173

Appendix A Supplemental material for Chapter 1 180

A.1 Data tables ...... 181

vi A.2 Supplementary figures ...... 186

Appendix B Supplemental material for Chapter 2 188

3 22 B.1 Calculation of He/ Nem by correcting for air contamination and degassing (Method 2) ...... 189

B.2 Three-component mixing model ...... 190

B.3 Calculation of 3He/22Ne ratios in primordial and modern terrestrial reservoirs . 191

B.4 Coupled hydrodynamic escape/magma ocean outgassing model ...... 198

B.5 Terrestrial noble gas abundances ...... 200

B.6 21Ne*/40Ar* vs. 4He*/40Ar* ...... 202

Appendix C Supplemental material for Chapter 3 205

C.1 Calculation of radiogenic noble gas abundances ...... 206

C.2 Derivation of Rayleigh-like degassing formulation ...... 207

C.3 Data tables ...... 211

Appendix D Supplemental material for Chapter 4 212

D.1 The effect of intermediate reactions on mixed lithology mixing calculation . . . . 213

D.2 Data tables ...... 215

Appendix E Supplemental material for Chapter 5 216

E.1 Data tables ...... 217

vii List of figures

1.1 Map of sample locations ...... 10

1.2 Ne-Ne plots ...... 12

1.3 4He/3He vs. 206Pb/204Pb and 143Nd/144Nd ...... 15

21 22 206 204 143 144 1.4 Ne/ NeE vs. Pb/ Pb and Nd/ Nd ...... 16

21 22 4 3 1.5 Ne/ NeE vs. He/ He ...... 17 1.6 Ne-Ar hyperbolas ...... 17

1.7 Ar-Xe hyperbolas ...... 18

1.8 Xe-Xe plots ...... 24

3 22 2.1 Correlation diagrams to determine He/ Nem ...... 41

3 22 2.2 He/ Nem vs. Ne, Nd, and Pb isotopes ...... 43 2.3 3He/22Ne in terrestrial and solar system reservoirs ...... 45

2.4 3He/22Ne evolution via plate tectonic cycling ...... 50

2.5 He/Ne solubility ratio ...... 51

2.6 Proposed chronology to explain mantle 3He/22Ne ratios via magma oceans . . . 53

2.7 Coupled hydrodynamic escape and magma ocean outgassing model ...... 57

2.8 Terrestrial volatile element ratios ...... 59

4 21 4 40 4 136 3.1 Literature He*/ Ne*, He*/ Ar*, and He*/ Xe*U data ...... 78

viii 3.2 θ parameter as a function of diffusivity and characteristic timescale ...... 83

3.3 Example disequilibrium degassing paths ...... 87

3.4 Experimental determinations of solubilities and diffusivities ...... 88

3.5 Reconstructed initial 3He and 22Ne ...... 91

3.6 Initial 3He and 22Ne from Monte Carlo simulation ...... 92

3.7 Measured and reconstructed 3He/22Ne in MORBs and OIBs ...... 94

3.8 Mismatch between C/3He predicted from 4He*/40Ar* and 4He*/21Ne* ...... 96

3.9 DC from vesicle data ...... 98

3.10 Reconstructed initial CO2 contents in 10 MORBs ...... 98 3.11 Reconstructed C/3He vs. La/Sm and Th/La ...... 100

3.12 Reconstructed CO2 vs. Ba with literature data ...... 101

4.1 4He/3He and 206Pb/204Pb vs. Latitude ...... 118

4.2 4He/3He vs. 206Pb/204Pb in Atlantic and Pacific MORBs ...... 120

4.3 Results of mixing calculation ...... 129

4.4 Amount of recycled crust in average MORB source ...... 131

5.1 Sample locations ...... 149

5.2 20Ne/22Ne vs. 21Ne/22Ne for nine samples ...... 152

5.3 40Ar/36Ar vs. 20Ne/22Ne hyperbolic fits ...... 154

5.4 129Xe/130Xe vs. 40Ar/36Ar hyperbolic fits ...... 156

206 204 143 144 5.5 Pb/ Pb, Nd/ Nd, La/Sm, and K2O/TiO2 vs. Latitude for the subtropical Mid-Atlantic Ridge...... 158

5.6 4He/3He vs. Latitude from Kane to Hayes ...... 159

5.7 Mantle source Ne isotopic compositions versus latitude...... 161

5.8 Mantle source Ar and Xe compositions versus latitude ...... 165

5.9 129Xe/136Xe vs. 130Xe/136Xe ...... 168

5.10 He, Ne, Ar, Xe cross plots ...... 171

A.1 Determination of 129Xe/132Xe ...... 186

ix 87 86 4 3 21 22 A.2 Relationship between Sr/ Sr, He/ He, and Ne/ NeE ...... 186 A.3 Plots of fissiogenic isotopes ...... 187

B.1 3-component mixing model ...... 192

B.2 21Ne/40Ar)* vs (4He/40Ar)* ...... 202

x List of Tables

1.1 Mantle source compositions ...... 14

1.2 Xenon component analysis ...... 27

2.1 MORB source 3He/22Ne ratios ...... 42

2.2 He and Ne partition coefficients ...... 47

3.1 Standard solubility and diffusivity values ...... 86

5.1 Mantle source noble gas compositions ...... 151

A.1 C, He, Ne, Ar abundances and isotope ratios ...... 181

A.2 Xe abundances and isotope ratios ...... 184

B.1 Concentrations ...... 190

B.2 Isotope ratios ...... 191

C.1 Measured and reconstructed initial gas contents ...... 211

D.1 He isotope compositions and dredge location ...... 215

E.1 He isotope compositions ...... 217

E.2 Ne, Ar, Xe abundances and isotopic ratios and CO2, He abundances ...... 218

xi 0 Introduction

To understand the composition and structure of the Earth’s mantle is to study the origin and evolution of the Earth itself. Basaltic magmas from mid-ocean ridges are win- dows into the mantle, but the view through them is not clear. Inferring the mantle composition from its basalt derivatives has remained an elusive and controversial pursuit for decades.

Volatile elements and compounds are critical components of the Earth’s composition. The presence of volatile compounds like water affects the physical properties of the mantle and its behavior during melting. Volatiles like carbon dioxide regulate the Earth’s climate and allow for a habitable surface. Studying volatiles at mid-ocean ridges is especially important,

1 as magmatic processes at mid-ocean ridges mediate fluxes of volatiles between the mantle and surface reservoirs on geological timescales.

Due to their nonreactive tendancy, the noble gases helium, neon, argon, krypton, and xenon form a special group of volatiles. Embedded within the noble gases are myriad nonradiogenic isotopes, as well as products of both long-lived and short-lived radioactivity. Thus, they are witnesses to the tectonic and planetary-scale processes that have been occurring since the start of the solar system, billions of years ago.

The geochemistry of mantle-derived helium dates back to the 1970s, and thousands of analyses on oceanic basalts (mid-ocean ridge basalts or “MORBs”, and ocean island basalts or “OIBs”) have been published since. However, it has been recognized for decades that heavy noble gas (neon, argon, krypton, and xenon) compositions of oceanic basalts are particularly susceptible to syn- to post-eruptive atmospheric contamination, the origin of which largely remains a mystery. This contamination plagues heavy noble gas analyses in oceanic basalts, dramatically lowering the number of individual samples for which the mantle source composition can be confidently determined. Neon determinations number in the hundreds but, including those presented in this thesis, only around 20 individual samples have robustly determined mantle source argon and xenon isotopic compositions. Therefore, any new data, especially for argon and xenon, has the capacity to reshape our understanding of noble gas geochemistry and reveal new insights into the origin and evolution of the Earth itself.

This thesis develops uses of noble gas isotopic and elemental systems to elucidate a variety of mysteries regarding the Earth’s origin and evolution. Some applications of the noble gases involve addressing the delivery of volatile elements to the primordial Earth and how major processes during accretion shaped the Earth’s volatile budgets. Others involve addressing how material has cycled into and out of the mantle over Earth history, and how these fluxes affect the composition of both the solid and fluid Earth.

The following chapters present new helium, neon, argon, xenon, and CO2 data from two localities along the Mid-Atlantic Ridge. Combined with literature noble gas data as well as

lithophile isotope systems like strontium, neodymium, and lead, the chapters illustrate how

2 the noble gases provide new dimensions to mantle isotope geochemistry.

3 1 The heavy noble gas composition of the depleted MORB mantle (DMM) and its implications for the preservation of heterogeneities in the mantle

Jonathan M. Tucker1, Sujoy Mukhopadhyay2, Jean-Guy Schilling3 1 Harvard University 2 University of California, Davis

3 The University of Rhode Island

The contents of this chapter have been published as:

Tucker, J.M., Mukhopadhyay, S., Schilling, J.-G., 2012. The heavy noble gas composition of the depleted MORB mantle (DMM) and its implications for the preservation of heterogeneities in the mantle. Earth and Planetary Science Letters 355–356, 244-254.

4 Abstract

To characterize the heavy noble gas composition of MORBs we present new He, Ne, Ar, and

Xe abundances and isotopic compositions from the equatorial Mid-Atlantic Ridge. Both depleted MORBs nominally devoid of plume influence and more enriched MORBs thought to represent the influence of a HIMU mantle plume are present in close geographical proxim- ity in this region. Ne–Ar–Xe isotopic compositions in individual step-crushes are correlated, which, along with significant radiogenic excesses, allows correction for shallow-level air contamination. Based on the relationship between the noble gases and the lithophile isotopes

(Sr, Nd and Pb), the depleted MORB mantle has a 21Ne/22Ne between 0.0617 and 0.0646,

40Ar/36Ar ratio of 41, 500 ± 9000 and 129Xe/130Xe ratio of 7.77 ± 0.06. On the other hand,

the HIMU-type MORBs are characterized by far less radiogenic Ne, Ar and Xe isotopic

compositions with mantle source 21Ne/22Ne between 0.0544 and 0.0610, and 40Ar/36Ar and

129Xe/130Xe ratios of 18, 100 ± 600 and 7.21 ± 0.06, respectively. The observation of less

nucleogenic 21Ne/22Ne in HIMU-type MORBs is similar to observations from HIMU ocean is-

lands and requires the HIMU plume to be comprised of both recycled and primitive material.

Within the depleted MORBs we observe He and Ne to be negatively correlated. The obser-

vation suggests that along the equatorial Atlantic the most depleted MORBs are related to

normal MORBs through the addition of a small proportion of a HIMU plume component.

Our new Xe isotopic measurements demonstrate distinct 129Xe/136Xe ratios in the mantle

sources of depleted MORBs, HIMU-type MORBs and the Iceland plume. While substantial

injection of atmospheric Xe into these mantle sources is implied, the differences in Xe iso-

topic composition cannot result solely from recycling of air. Rather, they require that mantle

plumes sample a reservoir less degassed than the depleted MORB mantle. This conclusion is

consistent with a higher proportion of Pu- to U-derived fission Xe in Iceland and HIMU-type

MORBs compared to the depleted MORBs. Overall, the Xe isotopic compositions imply that

mantle plumes tap a reservoir that separated from the MORB source within the first 100 mil-

lion years of Earth’s history and that the two reservoirs have had limited direct mixing since

5 then.

6 1.1 Introduction

Noble gas isotope ratios in mantle-derived rocks are powerful tools for understanding the

structure and evolution of the Earth’s mantle, the acquisition of terrestrial volatiles, and the

exchange of material between the solid and fluid Earth (Allegre et al., 1987, Coltice etal.,

2011, Gonnermann and Mukhopadhyay, 2009, Holland et al., 2009, Honda and McDougall,

1998, Marty, 1989, Ozima and Igarashi, 2000, Pepin, 1991, Porcelli and Wasserburg, 1995,

Sarda, 1999, Marty and Tolstikhin, 1998 and Trieloff and Kunz, 2005). Their low abun-

dances, unreactive nature, and preponderance of radiogenic and nonradiogenic (primordial)

isotopes allow them to be ideal tracers of the degassing history of mantle reservoirs and the

long-term interaction between these reservoirs. This is because small amounts of radiogenic

ingrowth of noble gas daughter nuclides or admixtures of different material can dramatically

alter noble gas isotope ratios, often in excess of other isotope systems by orders of magnitude.

Low ratios of the radiogenic to non-radiogenic noble gas nuclides (e.g. 21Ne/22Ne,

40Ar/36Ar, 129Xe/130Xe) in ocean island basalts (OIB) compared to mid-ocean ridge basalts

(MORB) are often used as evidence for a less degassed deep mantle and a more degassed,

more processed upper mantle (e.g. Allegre et al., 1983, Allegre et al., 1996, Gonnermann

and Mukhopadhyay, 2009, Kurz et al., 1982 and Porcelli and Wasserburg, 1995). The low

ratios of 40Ar/36Ar and 129Xe/130Xe in OIBs have also been attributed to the recycling of

atmospheric noble gases (e.g. Holland and Ballentine, 2006 and Trieloff and Kunz, 2005).

However, Mukhopadhyay (2012) showed that the 40Ar/36Ar and 129Xe/130Xe in the mantle sources of the Iceland plume and the gas-rich MORB (“popping rock”) from the north At- lantic (Kunz et al., 1998 and Moreira et al., 1998) cannot be related solely through recycling of atmospheric noble gases; differences in the degree of mantle degassing are required toex- plain the observed Ar and Xe isotopic compositions.

The extent to which the noble gas composition of popping rock is representative of the depleted MORB mantle, however, is not clear. This is because the sample is highly enriched in trace elements (La/SmN = 2.1; Dosso et al., 1991 and Dosso et al., 1993) compared to the

7 normal depleted MORBs (N-MORBs; La/SmN ≤ 1) that erupt along >70% of the mid-ocean ridge system. Furthermore, recent work suggests that atmospheric noble gases are subducted

into the mantle (Holland and Ballentine, 2006, Holland et al., 2009, Sumino et al., 2010 and

Kendrick et al., 2011) although the extent to which recycling affects the mantle noble gas

budget is debated (Moreira and Raquin, 2007). Nonetheless, if the recycled component is

distributed heterogeneously, large variations in MORB source Ar and Xe isotopic compo-

sitions would be expected. In this regard, Sarda et al. (1999) showed that maximum mea-

sured 40Ar/36Ar ratios in Atlantic MORBs were negatively correlated with 206Pb/204Pb, such

that the Pb isotopic evidence for recycled material was associated with maximum measured

40Ar/36Ar ratios that were closer in composition to the atmospheric 40Ar/36Ar. The corre-

lation suggests recycling of atmospheric Ar to the mantle via subducting plates. Burnard

(1999), however, challenged Sarda et al.’s (1999) interpretation of Ar recycling as basalts with

elevated 206Pb/204Pb are commonly found on topographic highs and those magmas would be

more extensively degassed and more susceptible to atmospheric contamination, lowering their

40Ar/36Ar closer to the atmospheric ratio. Consequently, the extent to which noble gases are

recycled, whether the recycled gases are distributed homogeneously throughout the mantle,

and the average and variance of the Ne, Ar and Xe isotopic composition of the MORB source

all remain poorly constrained.

To better characterize the variability in the noble gas composition of the MORB source we

present new He, Ne, Ar, and Xe observations from the equatorial Mid-Atlantic Ridge. Basalts

from the region of 5◦N to 7◦S span a range of compositions from among the most depleted

206 204 MORBs (La/SmN=0.42, Pb/ Pb=17.64) to among the most enriched (La/SmN=3.1, 206Pb/204Pb=20.09). The enriched MORBs are thought to be related to the interaction

of the HIMU-type (high µ, where µ is the U/Pb ratio) Sierra Leone plume with the Mid-

Atlantic Ridge, whereas the depleted MORBs are devoid of plume influence (Hannigan et

al., 2001, Schilling et al., 1994 and Schilling et al., 1995). Such large geochemical variations

spanning nearly the entire range of Pb isotopic compositions seen in MORBs over a short

geographical distance provide a unique opportunity to characterize the heavy noble gas vari-

8 ations in the MORB source, study the relationship between the noble gases and lithophile tracers, and thereby understand the relationship between the depleted MORBs and enriched

MORBs. We use our new noble gas observations to address the following key questions:

1. What is the Ne, Ar, and Xe isotopic composition of depleted MORB mantle (DMM)

and of the extremely depleted MORBs (D-DMM; Workman and Hart, 2005)?

2. What is the degree of heterogeneity in Ne, Ar and Xe in the MORB source and how

were these heterogeneities created?

3. Are the HIMU-type MORBs also associated with primitive material as postulated for

HIMU ocean islands (Day and Hilton, 2011; Parai et al., 2009)?

4. Are Ar and Xe being recycled back into the mantle, and if so, does this explain the

differences in observed 40Ar/36Ar and 129Xe/130Xe ratios between MORBs and OIBs?

1.2 Methods

1.2.1 Samples

The samples used in this study were dredged from the equatorial Mid-Atlantic Ridge during the cruises of R/V Endeavor EN061 and R/V Conrad RC2806. They have been previously characterized for major elements, trace elements, Sr, Nd, and Pb isotopic compositions

(Hannigan et al., 2001, Schilling et al., 1994 and Schilling et al., 1995). Some samples were reanalyzed for Pb isotopes (Agranier et al., 2005), and we use the newer measurements where applicable. For two of the samples, He isotopic compositions were previously determined by

Graham et al. (1992b). We measured nine samples from between 5◦N and 5◦S for heavy no-

ble gas abundances and isotope ratios. Four samples are depleted MORBs from between the

Ascension and Chain fracture zones and five samples are HIMU-type MORBs from between

5◦N and the Romanche fracture zone (Fig. 1.1).

Fresh basaltic glass for each sample was prepared by leaching in 5% HNO3 and/or in 1%

oxalic acid to remove minor surface alteration. Approximately 3–5 g of glass was loaded into

9 Figure 1.1: Map of the Equatorial Atlantic showing the locations of the samples and the Sierra Leone Rise. The solid symbols between the Ascension and Chain fracture zones are the MORBs from the depleted group while the open symbols north of the Romanche fracture zone are the enriched HIMU-type MORBs. a piston crusher and baked under vacuum at 90–100 ◦C for ~18 h to remove adsorbed gas.

Glasses were step-crushed under vacuum, releasing the gas trapped in vesicles. Approxi-

mately 5–10 crushing steps were performed per sample, with each crushing step yielding a

set of C, He, Ne, Ar, and Xe measurements.

1.2.2 Measurements

CO2 concentrations were determined by manometry using 10 Torr MKS manometers directly attached to the crusher volume. Gases were purified by sequential exposure to hot and cold

SAES getters and a small split of the gas was let into a quadrupole mass spectrometer to de-

termine the Ar abundance and an approximate 40Ar/36Ar ratio. The noble gases were frozen

onto a cryogenic cold trap and then sequentially released and let into the mass spectrometer.

He, Ne, Ar and Xe abundances and isotopic compositions were measured on a Nu Noblesse

noble gas mass spectrometer operating in multicollection mode. 20Ne and 22Ne were corrected

40 44 ++ + for isobaric interferences from doubly-charged Ar and CO2 respectively. The Ar /Ar ± ++ + ± was 0.061 0.002 and the CO2 /CO2 was 0.0055 0.0005. For the Ar measurements, depending upon the Ar abundance and approximate isotope ratio previously determined by

the quadrupole mass spectrometer, a fraction of the gas was let into the mass spectrometer

for more precise isotope ratio determination. Mass spectrometric procedure is described in

Mukhopadhyay (2012). Typical procedural blanks for 4He, 22Ne, 36Ar and 130Xe prior to the

10 starting crush were 2 × 10−11, 5.7 × 10−14, 3.7 × 10−13, and 1.8 × 10−16 cc, respectively.

Blank levels were stable or decreasing during the course of crushing, with the exception of

He, which increased by up to a factor of 2–4. Ne, Ar, and Xe blank isotopic ratios were statistically indistinguishable from atmosphere, and because the sample gases themselves are a mixture of mantle and shallow-level air contamination, no blank corrections were applied to the step–crushes. Mass discrimination for He was determined using the HH3 standard with a

3 4 He/ He ratio of 8.81 RA (Gayer et al., 2008) and for Ne, Ar, and Xe using air standards. Instrumental drift in sensitivity and mass discrimination was monitored through sample- standard bracketing with additional standards run overnight. Abundances and isotope ratios are reported in Tables A.1 and A.2.

1.2.3 Determination of mantle source isotopic ratios

For Ne, Ar, and Xe, each crushing step samples a population of bubbles reflecting variable mixtures of mantle-derived noble gases and syn- to post-eruptive atmospheric contaminants.

As a result, noble gas compositions of bubbles define a mixing array that lies between the atmospheric end-member and the mantle end-member. In 20Ne/22Ne vs. 21Ne/22Ne space, the array is linear, while in Ne–Ar, Ne–Xe, or Ar–Xe space the array can be described by a hyperbolic mixing equation. Assuming the 20Ne/22Ne ratio of the MORB source mantle is

12.5 (see Section 3.3), a particular isotope ratio (e.g. 21Ne/22Ne, 40Ar/36Ar) can be regressed against 20Ne/22Ne and extrapolated to a 20Ne/22Ne of 12.5 to determine the mantle source value.

The mantle source 21Ne/22Ne was determined by x and y error-weighted least squares regression forced through the atmospheric composition (y = mx) and extrapolation to

20Ne/22Ne of 12.5 (Fig. 1.2). Ar and Xe isotope ratios for the mantle source were determined using an iterative nonlinear least squares hyperbolic fit constrained to go through the atmospheric composition (Ax+Bxy+Cy = 0). We present Ar and Xe mantle source values for two samples that show well-defined hyperbolic mixing arrays. Such hyperbolic arrays are likely to reflect either a single atmospheric contaminant or two elementally-fractionated atmospheric

11 Figure 1.2: Linear arrays in 21Ne/22Ne-20Ne/22Ne space for all nine samples that result from syn- to post- eruptive air contamination of bubbles containing mantle Ne. The mantle source 21Ne/22Ne was determined by x and y error-weighted least squares regression. Data points were translated such that the atmospheric composition was at (0,0). The y data were then scaled by the square root of the ratio of the variance in x to the variance in y so as to put x and y on the same scale and fitted with an equation of the form y = m x. The uncertainties in the slopes (shown by the 1σ error bands) were calculated using a Monte Carlo technique by randomly perturbing the data assuming normally distributed errors and refitting the slopes. 21 22 20 22 The mantle value ( Ne/ NeE) was determined by extrapolation to Ne/ Ne of 12.5. The extrapolated values and their uncertainties are given in each panel. contaminants present in nearly fixed proportions. We denote all extrapolated mantle source isotope ratios extrapolated to a 20Ne/22Ne ratio of 12.5 with a subscript “E”.

1.2.4 Decolvolution of Pu- and U-derived fission Xe

To deconvolve U- from Pu-derived fissiogenic Xe, four mantle source Xe isotope ratios were

130,131,134,136 132 used ( Xe/ XeE) following the methodology employed by Caffee et al. (1999) and Mukhopadhyay (2012). Because of the larger analytical uncertainty of 130Xe-normalized ratios, we use 132Xe-normalized ratios. We assume the present-day mantle source values rep-

12 resent a mixture of four end-members: initial Xe, 238U-produced Xe, 244Pu-produced Xe, and subducted atmospheric Xe. The solution x to the system Ax = b was found by a least-squares inversion with the additional constraints Σxi = 1 and 0 ≤ xi ≤ 1. A is a matrix that defines the four end-members in terms of the four isotope ratios; x is a vector that defines the fraction of each of the four components in the present-day composition; and b is a vector with

the mantle source compositions (free of post-eruptive air contamination). To determine the

129 132 elements of b, the mantle source Xe/ XeE was first determined from an Ar–Xe least- squares hyperbolic fit (Fig. A.1). 130,131,134,136Xe/132Xe ratios were then linearly regressed against the 129Xe/132Xe ratio for the individual step-crushes. The linear regressions followed the same procedure as in Section 1.2.3 (see also Fig. 1.2). The slope and uncertainty in slope

130,131,134,136 132 from the regressions were used to calculate the mantle Xe/ XeE ratios along

129 132 with their uncertainties for the given mantle Xe/ XeE ratio. End-member and mantle source compositions (A and b, respectively) were normalized to the standard deviations in

the mantle source isotope ratios to assign equal weight to each isotope ratio. To compute the

uncertainties in the deconvolution, a Monte Carlo technique was utilized; the mantle source

compositions were varied at random within their 1σ uncertainties and the least-squares fit

recomputed using the new values. For all simulations it was verified that convergence toa

minimum was achieved.

1.3 Results

1.3.1 Depleted MORB noble gases

Samples between the Ascension and Chain fracture zones have been previously classified as depleted MORBs on the basis of isotopic and incompatible element ratios (Schilling et al., 1994). We note that the depleted MORB samples span the range of extremely depleted

MORBs (206Pb/204Pb=17.68; 87Sr/86Sr=0.7021) to MORBs showing an average degree of depletion (206Pb/204Pb=18.35; 87Sr/86Sr=0.7026).

The 4He/3He ratios of the depleted MORBs vary between 80,800–86,700 with the more de-

13 Table 1.1: Mantle source compositions

pleted Sr, Nd, and Pb isotopic composition associated with the lower 4He/3He ratios (Figs.

21 22 1.3 and A.2a). Ne/ NeE values for the depleted MORB samples range from 0.062 to 0.065 (Table 1.1; Fig. 1.2 and Fig. 1.4 and A.2b). For the depleted MORBs, the He and Ne isotopic compositions are negatively correlated (Fig. 1.5).

The highest measured 40Ar/36Ar ratio in the depleted samples is 30, 400 ± 300. We note

that sample RC2806 3D-2 has a lithophile isotopic composition very similar to average N-

MORB source (206Pb/204Pb=18.35, 87Sr/86Sr=0.7026, 143Nd/144Nd=0.513126; cf. DMM:

18.275, 0.70263, 0.51313, Workman and Hart, 2005) and is also the only depleted sample for

which the mixing hyperbolas in Ne–Ar–Xe space are well defined. Since the He and Ne iso-

topic composition of the depleted MORBs vary over a limited range, the Ar and Xe isotopic

composition of the depleted samples may also show limited variations. However, given the

sample’s lithophile isotopic composition, and in the absence of substantial number of step-

crushes for the other samples, we assume the extrapolated Ar and Xe isotopic composition

for RC2806 3D-2 is broadly representative of the depleted group. The best fit hyperbola for

40 36 this sample yields a mantle source Ar/ ArE of 41, 500 ± 9000 (Table 1.1; Fig. 1.6a). The

40 36 uncertainty in Ar/ ArE is related to a small number of data points with respect to the scatter in the data and suggests additional measurements on this sample in the future will

be able to better constrain the hyperbolic fit. For a consistent comparison, we refit the step-

crushing popping rock data (Moreira et al., 1998) using the same technique (Section 1.2.3),

40 36 which yielded a mantle source Ar/ ArE of 25, 200 ± 600 (Fig. 1.6a), consistent with the estimate of 27, 000 ± 4000 from UV laser ablation of individual bubbles (Raquin et al., 2008).

14 Figure 1.3: Relationship between 4He/3He ratios and (a) 206Pb/204Pb and (b) 143Nd/144Nd. The solid symbols are the depleted MORBs and the open symbols are the enriched HIMU-type MORBs. He shows a coherent relationship with the other lithophile isotopes and indicates that more radiogenic He isotope ratios are associated with more radiogenic Pb and unradiogenic Nd, consistent with the presence of recycled material in the source of HIMU-type MORBs. The popping rock (2ΠD43) from the North Mid- Atlantic Ridge is indicated by the square. Popping rock data is from Moreira et al. (1998) and Dosso et al. (1991). He data for the samples EN061 2D and EN061 4D are from Graham et al. (1992b). The solid lines are illustrative two-component mixing hyperbolas between a depleted mantle (D-DMM) and a HIMU plume component. The 206Pb/204Pb ratios of D-DMM and HIMU are taken to be 17.5 and 23, and the 143Nd/144Nd ratios of D-DMM and HIMU are taken to be 0.51330 and 0.51295, respectively. The 4He/3He ratio of D-DMM is 80,000, similar to the low end of plume-free MORB (Graham, 2002), and the 4He/3He ratio of HIMU is 160,000, similar to the highest values measured at HIMU OIB (Gra- ham et al., 1992a). The curvature of the hyperbola is controlled by the parameter r, defined as, e.g., 3 204 3 204 ( He/ Pb)D-DMM/( He/ Pb)HIMU.

15 21 22 206 204 143 144 Figure 1.4: Relationship between Ne/ NeE ratios and (a) Pb/ Pb and (b) Nd/ Nd. Sym- bols as in Fig. 1.3. The solid lines are illustrative two-component mixing hyperbolas for mixing between a depleted mantle (D-DMM) and the HIMU plume component. The Pb and Nd isotope ratios of the two components are as in Fig. 1.3. The 21Ne/22Ne ratio of D-DMM is 0.065 (this work) and the 21Ne/22Ne ratio of HIMU is 0.05 (Parai et al., 2009). The curvature of the hyperbola is controlled by the parameter r, 22 204 22 204 defined as, e.g., ( He/ Pb)D-DMM/( He/ Pb)HIMU.

16 4 3 21 22 Figure 1.5: Relationship between He/ He ratios and Ne/ NeE ratios. Symbols as in Fig. 1.3. Note that the sample with the most depleted Pb, Sr, and Nd isotopic composition has a lower 4He/3He ratio 21 22 4 3 but higher nucleogenic Ne/ NeE. Overall, there is a general tendency for increasing He/ He ratios to 21 22 be associated with decreasing Ne/ NeE within the depleted MORB group. The HIMU-type MORBs are displaced to more radiogenic He and less nucleogenic Ne than the depleted MORBs. Overall, the He– Ne relationships of the MORBs can be explained by a mixture of depleted mantle (D-DMM) and HIMU, with the requirement that HIMU is composed of both recycled and less degassed mantle material, such as FOZO (Hart et al., 1992). The solid line is an illustrative mixing hyperbola using the end-member compo- 3 22 3 22 sitions as in Fig. 1.3 and Fig. 1.4. The curvature r=( He/ Ne)D-DMM/( He/ Ne)HIMU=5.6 is consistent with the hyperbolas in Fig. 1.3 and Fig. 1.4, e.g. rHe–Pb/rNe–Pb=rHe–Ne.

Figure 1.6: (a) Ne–Ar hyperbola for the depleted MORB sample RC2806 3D-2 (thick solid line). Only crushes from the first aliquot are plotted as the crushes from the second aliquot define a poorly-constrained hyperbola with a different (Ne/Ar)mantle/(Ne/Ar)atm ratio. The best-fit hyperbola to the step-crushes for popping rock (2ΠD43; Moreira et al., 1998) is shown for reference (thin line). Symbols as in Fig. 1.3 and the open diamond represents the atmospheric composition. (b) Ne–Ar hyperbolic fit for the HIMU-type MORB, RC2806 57D-1. Because of the curvature, the Ar isotopic composition of the mantle source corresponding to a mantle 20Ne/22Ne of 12.5 (Ballentine and Holland, 2008; Raquin et al., 2008) is well determined.

17 Figure 1.7: (a) Ar–Xe mixing systematics for the depleted MORB RC2806 3D-2. Based on its lithophile isotopic composition this sample may be representative of average DMM in noble gas isotopic composition. The solid line is the best-fit hyperbola through the step-crushes. The best-fit hyperbola to the step-crushes for popping rock (2ΠD43) is shown for reference (thin line). The popping rock data is from Moreira et al. (1998). Symbols as in Fig. 1.3 and the open diamond represents the atmospheric composition. (b) Ar–Xe mixing systematics for the HIMU-type MORB, RC2806 57D-1. Note that the HIMU-type mantle source must have a lower 129Xe/130Xe ratio than DMM.

The highest measured 129Xe/130Xe in the depleted sample group is 7.81 ± 0.06. Xe isotopes

(129Xe/130Xe) correlate better with Ar isotopes than with Ne isotopes. Consequently, we obtained the best-fit hyperbola in Ar–Xe space for sample RC2806 3D-2 to constrain the mantle

129 130 40 36 source Xe/ XeE to 7.77±0.06 at a Ar/ Ar of 41,500 (Table 1.1; Fig. 1.7a). Because of

129 130 the curvature of the best-fit hyperbola, the mantle Xe/ XeE is not particularly sensitive

40 36 to the uncertainty in Ar/ ArE.

1.3.2 HIMU-type MORB noble gases

Samples north of the Romanche fracture zone are classified as enriched HIMU-type MORBs and span the range of 206Pb/204Pb from 18.75 to 19.64 and 87Sr/86Sr from 0.7026 to 0.7029.

Although the Pb isotopic compositions in these samples do not reach the extreme HIMU compositions observed in OIBs, we refer to them as “HIMU-type” following the identification of a HIMU component in these basalts (Schilling et al., 1994) to distinguish them from the depleted MORBs south of the equator.

4He/3He ratios of the HIMU-type MORBs are between 93,200 and 99,000—more radio-

21 22 genic than the depleted MORBs (Figs. 1.3 and A.2a). Ne/ NeE values for the HIMU-type MORB samples are between 0.056 and 0.061, which is less nucleogenic than the depleted

18 MORBs (Table 1.1; Figs. 1.2, 1.4, 1.5 and A.2b). The highest measured 40Ar/36Ar ratio in the HIMU-type lavas is 17, 800 ± 178, significantly lower than the highest measured values in the depleted sample group. Sample RC2806 57D-1 yields the best mixing hyperbola in Ne–

40 36 Ar space, which constrains the source Ar/ ArE ratio to be 18, 100 ± 600 (Table 1.1; Fig. 1.6b) and, like for the depleted MORB group, we assume this sample’s Ar and Xe isotopic composition is broadly representative of the enriched HIMU-type MORBs. The highest measured 129Xe/130Xe in the depleted sample group is 7.26 ± 0.05. The Ar–Xe mixing array for

129 130 the same sample (RC2806 57D-1) defines the mantle source Xe/ XeE of 7.21 ± 0.02 at a 40Ar/36Ar of 18,100 (Table 1.1; Fig. 1.7b). The curvature of the best-fit hyperbola indicates

129 130 40 36 that Xe/ XeE is not particularly sensitive to the uncertainty in the mantle Ar/ Ar.

1.3.3 A note on the mantle 20Ne/22Ne ratio

We recognize that the 20Ne/22Ne value of the whole mantle may not be 12.5, and the source of mantle plumes may be associated with 20Ne/22Ne of 12.9, or higher (Mukhopadhyay, 2012 and Yokochi and Marty, 2004). We choose a MORB source value of 12.5 based on the mantle source composition of continental well gases (Ballentine and Holland, 2008 and Holland and Ballentine, 2006) and the gas-rich popping rock (Raquin et al., 2008). Furthermore, our highest measured value in both sample groups (12.36 in depleted samples; 12.43 in HIMU- type samples), and MORBs in general (Kunz, 1999, Moreira et al., 1998, Moreira et al., 2011,

Raquin and Moreira, 2009 and Sarda et al., 1988) are close to 12.5. Correcting all the isotope ratios to a common 20Ne/22Ne allows for a consistent comparison between samples.

Our primary results are not affected if a higher value is chosen. For example, if the mantle

20Ne/22Ne and 21Ne/22Ne varied as a mixture between the “MORB array” (12.5, 0.059; Sarda et al., 1988) and “Iceland array” (13.8, 0.0375; Mukhopadhyay, 2012) the least nucleogenic sample in our dataset would intersect this mixture at 20Ne/22Ne=12.65, causing a negligi-

40 36 129 130 20 22 ble shift in the extrapolated Ar/ ArE and Xe/ XeE. If the mantle Ne/ Ne of the MORB source were higher than ~13, our results would actually be strengthened. Because of

the curvature of the hyperbolas (Fig. 1.6 and Fig. 1.7), the depleted sample would extrap-

19 olate to higher 40Ar/36Ar and 129Xe/130Xe while the HIMU-type sample would be little af-

fected, amplifying the compositional difference between them.

1.4 Discussion

1.4.1 A primitive Ne component in HIMU-type basalts

The 4He/3He ratios in the HIMU-type MORBs span the range of ~80,000–100,000, within the typical MORB range (Graham, 2002). The 4He/3He ratios of the HIMU-type lavas are, how-

ever, all more radiogenic than the depleted MORBs and are associated with more radiogenic

206Pb/204Pb (Fig. 1.3). Since HIMU mantle plumes are characterized by radiogenic He and

Pb isotopic ratios (Chauvel et al., 1992, Day and Hilton, 2011, Graham et al., 1992a, Hanyu

et al., 1999, Hanyu et al., 2011 and Hauri and Hart, 1993; Hilton et al., 2000 and Parai et al.,

2009), the He–Pb co-variation is consistent with the injection of a HIMU-type plume into the

Equatorial Mid-Atlantic Ridge (Schilling et al., 1994).

The relationship between Ne and He isotopic compositions provides insight into the genesis

of the HIMU plume sampled at the equatorial Mid-Atlantic Ridge. HIMU plumes are often

assigned to recycled oceanic crust (Chauvel et al., 1992, Hauri and Hart, 1993 and Hofmann,

1997). In addition to radiogenic 206Pb/204Pb, such a component should have both radiogenic

He and nucleogenic Ne isotopic ratios. This is because in highly degassed oceanic crust, nucleogenic 21Ne will be produced from 18O(α,n) and 24Mg(n,α) reactions with the reacting alpha particles and neutrons ultimately sourced from U and Th decay. Thus, the less nucleogenic Ne in the HIMU-type lavas compared to the depleted MORBs cannot be generated solely through sampling of recycled material or mixing recycled material with DMM.

Our observation of less nucleogenic Ne and more radiogenic He have been observed in other HIMU localities, such as the Cameroon line of volcanoes (Barfod et al., 1999) and the

Cook–Austral islands (Parai et al., 2009). The simplest explanation for the less nucleogenic signature is the involvement of a relatively undegassed mantle, such as FOZO. In this regard,

Parai et al. (2009) attributed the association of more radiogenic He than MORBs with less

20 nucleogenic Ne in the HIMU Cook–Austral islands to mixing between degassed recycled crust and FOZO (also see Day and Hilton, 2011). Based on the lithophile isotopes, Schilling et al.

(1994) suggested that the plume-influenced MORBs north of the equator reflect mixing between a depleted mantle, recycled crust (HIMU) and FOZO. Our present study is consistent with the suggestion of a HIMU component in the north equatorial Atlantic MORBs (Schilling et al., 1994) and provides further evidence that HIMU is a hybrid of at least two different materials—a degassed recycled component and a relatively undegassed mantle.

1.4.2 A negative correlation between He and Ne in depleted MORBs

Our new observations from the equatorial Atlantic indicate that within the depleted group

21 22 there appears to be an overall trend of more nucloegenic Ne/ NeE associated with less radiogenic He and more depleted Sr, Nd and Pb isotopic compositions (Fig. 1.3, Fig. 1.4 and

4 3 21 22 Fig. 1.5). This observation places constraints on the He/ He and Ne/ NeE variability in MORBs, and the relationship between the most depleted MORBs (D-DMM; Workman and

Hart, 2005) and N-MORBs (DMM).

Helium and neon isotopic variations in the MORB source are often interpreted in terms of

a flux of 3He and 22Ne from the OIB source into the MORB source followed by mixing with

in situ radiogenic 4He and nucleogenic 21Ne (e.g. Allegre et al., 1987; Porcelli and Wasser-

burg, 1995 and Tolstikhin and Hofmann, 2005). However, differences in 20Ne/22Ne and

3He/22Ne ratios between MORBs and OIBs suggests that not all the primordial He and Ne

in the MORB mantle can be derived from the OIB mantle source (Honda and McDougall,

1998, Mukhopadhyay, 2012 and Yokochi and Marty, 2004). Assuming 3He is indigenous to the MORB source, variations in MORB 4He/3He ratios may be explained in the framework of a marble cake assemblage comprising pyroxenite veins in a depleted peridotite matrix

(e.g. Graham et al., 2001 and Hamelin et al., 2011). The 4He/3He ratio of the most depleted

MORB in our dataset lies at the lower limit of the MORB range from 74,000 to 120,000 for regions removed from obvious influences of mantle plumes (Georgen et al., 2003, Graham,

2002, Graham et al., 1992b and Graham et al., 2001). The addition of pyroxenites (recycled

21 crust) with radiogenic 4He to this depleted peridotitic matrix could then produce the range

of 4He/3He ratios and lithophile isotopes in non-plume influenced MORBs (Figs. 1.3 and

A.2a). Within the marble cake framework, recycled oceanic crust should be associated with

nucleogenic 21Ne/22Ne ratios in addition to radiogenic 4He/3He ratios. So as 4He/3He ratios become more radiogenic in MORBs through sampling a greater proportion of pyroxenites,

21Ne/22Ne ratios should become more nucleogenic, opposite to the observed relation between

He and Ne (Fig. 1.5). Hence, the observed isotopic relations (Fig. 1.3, Fig. 1.4 and Fig. 1.5) cannot be generated by mixing depleted peridotites with pyroxenites that have radiogenic He and nucleogenic Ne.

Instead, we hypothesize that the observed He–Ne relationship requires the equatorial At- lantic N-MORBs to be produced by the addition of a small proportion of a HIMU plume component to a very depleted MORB source (D-DMM; e.g. Fig. 1.5). We note that based on lithophile isotopes Schilling et al. (1994) suggested that the depleted section of the Mid-

Atlantic Ridge between the Ascension and Romanche fracture zones resulted from mixing between an extremely depleted MORB source and an enriched HIMU component. Our results are consistent with this interpretation with the additional requirement that HIMU is itself a mixture of recycled and primitive components (Section 1.4.1). While a marble cake mantle remains a viable way of interpreting the geochemical observations in depleted MORBs, based on our new He–Ne observations, it appears to be richer in flavor than a simple mixture of recycled pyroxenites and depleted peridotites.

1.4.3 Argon isotopic composition of DMM and the HIMU-type MORB source

40 36 The depleted MORB sample RC2806 3D-2 has a mantle source Ar/ ArE ratio of 41, 500 ± 9000 (Fig. 1.6a). This is similar to the 40Ar/36Ar ratio of 41, 050 ± 2670 for the Bravo Dome

well gas and the maximum measured 40Ar/36Ar in MORBs of 42, 400 ± 9700 (Marty and

40 36 Humbert, 1997). In contrast, we compute the popping rock mantle source Ar/ ArE to be 25, 200 ± 600 from the published step-crushing data (Fig. 1.6a) (Moreira et al., 1998), similar

22 to the value of 25,000 reported in that work and 27, 000 ± 4000 obtained by UV laser ablation

of individual bubbles (Raquin et al., 2008). We note that a laser ablation study by Burnard

et al. (1997) yielded a 40Ar/36Ar ratio of 40, 000 ± 4000 in an individual bubble in the pop-

ping rock sample, higher than the values reported by Raquin et al. (2008) and those of Mor-

eira et al. (1998). While the mantle source composition of popping rock is debatable (see

Raquin et al., 2008 for further discussion), DMM has a 40Ar/36Ar ratio of at least 41,000.

40 36 The HIMU-type MORB sample RC2806 57D-1 has a mantle source Ar/ ArE ratio of 18, 100 ± 600, unequivocally lower than both DMM and the popping rock mantle source

(Fig. 1.6b). The result demonstrates that large variations (factor of 2) in the MORB mantle source 40Ar/36Ar ratio exist even when variations in He and Ne isotopic compositions are

40 36 more muted. The low Ar/ ArE ratio in the HIMU-type MORBs likely results from the injection of a HIMU mantle plume with low 40Ar/36Ar into the Mid-Atlantic Ridge. Plumes feeding OIB are often characterized by low 40Ar/36Ar (Honda et al., 1993, Mukhopadhyay,

2012, Raquin and Moreira, 2009, Trieloff et al., 2000, Trieloff et al., 2002 and Valbracht et al., 1997). The low 40Ar/36Ar in plumes and the HIMU-type MORBs of the north equatorial

Atlantic could be due to sampling of a less degassed reservoir with low K/36Ar ratio, an explanation that would be consistent with Ne isotopic evidence for a less degassed component in the HIMU plume. Alternatively, the low 40Ar/36Ar ratio could be a result of recirculation of atmospheric Ar associated with recycled crust to the mantle source of plumes (Holland and

Ballentine, 2006). We discuss these two separate hypotheses while discussing Xe isotopes in the next section.

1.4.4 Xenon isotopic differences between DMM, HIMU-type MORB and Iceland plume sources

129 130 The depleted MORB sample RC2806 3D-2 has a mantle source Xe/ XeE ratio of 7.77 ± 0.06 (Fig. 1.7a). This ratio overlaps with the 129Xe/130Xe ratio of 7.9 ± 0.14 for the mantle source of the Bravo Dome well gas (Holland and Ballentine, 2006). On the other

129 130 hand, the HIMU-type MORB sample RC2806 57D-1 has a mantle source Xe/ XeE of

23 Figure 1.8: (a) 129Xe/130Xe vs. 136Xe/130Xe ratios of step-crushes for depleted and HIMU-type MORB. Symbols as in Fig. 1.3. The solid lines represent the x–y error weighted best fit line and the gray bands denote the 1σ error envelopes. The methodology for the least squares regression was outlined in Section 1.2.3 and in Fig. 1.2. The slope of the line is a function of the time integrated (244Pu+238U)/129I ratio. The slopes are 0.375 ± 0.009 and 0.334 ± 0.009 for depleted and HIMU-type MORBs, respectively. The slope with all data taken together is 0.358 ± 0.006, which does not overlap the slope of either group. The difference in slopes demonstrates a difference in the time integrated244 ( Pu+238U)/129I ratio within MORBs. (b) 130Xe/136Xe vs. 129Xe/136Xe isotope plot showing the weighted average composition of DICE 10 (Ice- land; Mukhopadhyay, 2012), depleted MORB and HIMU-type MORB step-crushes. Symbols as in Fig. 1.3. The air-Iceland mixing line is distinct from the air-depleted MORB mixing line. Consequently, the plume Xe signal cannot be related to MORBs solely through addition of subducted atmospheric Xe or through addition of 238U-produced fission 136Xe. Sampling of a reservoir that is less degassed than DMM is required to explain the Xe isotopic composition of the HIMU-type MORBs and the Iceland plume.

7.21 ± 0.05, significantly lower than the depleted MORB source (Fig. 1.7b). Like theless

21 22 40 36 129 130 nucleogenic Ne/ NeE ratio and less radiogenic Ar/ ArE ratio, the lower Xe/ XeE in the HIMU-type MORBs could reflect sampling of a less degassed reservoir with alower

I/130Xe ratio than the DMM source. 129I, which produces 129Xe, became extinct at 4.45

Ga and therefore differences in the degree of degassing between DMM and the less degassed reservoir would have to have been initiated prior to 4.45 Ga and the reservoirs could not have

129 130 subsequently been homogenized. Alternatively, the lower Xe/ XeE in the HIMU-type MORBs could reflect preferential recycling of atmospheric Xe into the HIMU plume source.

These two hypotheses can be addressed by considering the 129Xe/136Xe ratio, which reflects the time-integrated 129I/(244Pu+238U) ratio (Fig. 1.8).

Given the uncertainties in Xe isotopic ratios, we cannot yet identify possible Xe isotopic differences within the depleted or HIMU-type groups. As a result, in Fig. 1.8,wecom- bine the step-crushes for each sample group to investigate whether differences in Xe iso-

24 topic composition exist between the depleted and HIMU-type groups and whether the depleted MORBs are isotopically distinct from the Iceland plume. Fig. 1.8a shows our data in 129Xe/130Xe vs. 136Xe/130Xe space. In this space, the Xe–Xe slopes for the depleted and

HIMU groups are statistically distinct from each other and from the slope calculated for all

the data taken together.

The distinct 129Xe/136Xe ratios for the two MORB groups can be clearly seen in

129Xe/136Xe vs. 130Xe/136Xe space when the error-weighted average compositions of the crushing steps are plotted (Fig. 1.8b). The data are not corrected for post-eruptive contamination, so the true mantle source (extrapolated) values lie further along the particular mixing line with air. But extrapolation is unnecessary to demonstrate the simple conclusion that the HIMU-type MORBs have a 129Xe/136Xe ratio in excess of air while the depleted MORBs have a ratio lower than air. The data in Fig. 1.8, therefore, clearly demonstrate that the depleted MORBs and the HIMU-type MORBs have distinct 129Xe/136Xe ratios. Furthermore,

a clear distinction is observed between the Iceland plume composition (Mukhopadhyay, 2012)

and the depleted MORBs, with the HIMU-type MORBs intermediate between the two.

In both of the Xe–Xe isotopic spaces (Fig. 1.8a and b), recycling of atmospheric Xe would

shift the composition of a reservoir linearly towards air. Thus, neither the small difference in

slope (Fig. 1.8a) nor the measured difference in the 129Xe/136Xe ratio (Fig. 1.8b) between

the depleted and HIMU-type MORBs can be produced solely through recycling of atmo-

spheric Xe. We conclude that 129I/(244Pu+238U) ratios are different between the two groups

of MORBs, reflecting different degrees of mantle outgassing. The lower 129Xe/136Xe ratio

of DMM is consistent with a more degassed source than the mantle source of HIMU-type

MORBs (Fig. 1.8). This is because a more degassed source will have lower concentrations of

primordial Xe isotopes (130Xe), and lower concentrations of 129Xe from decay of extinct 129I

and 136Xe from fission of extinct 244Pu. Adding 136Xe from 238U fission or 244Pu fission while

244Pu is still alive to such a degassed source will lead to a decrease in 129Xe/136Xe ratio. The higher 129Xe/136Xe ratio of the HIMU-type MORBs likely reflects mixing between a less degassed source, such as the reservoir supplying primordial noble gases to the Iceland plume

25 (Mukhopadhyay, 2012), and more degassed sources, such as recycled crust and DMM. In this

129 136 40 36 regard, the Xe/ Xe evidence suggests that the lower Ar/ ArE ratio in the HIMU-type MORBs also cannot originate solely from recycling of atmospheric Ar; sampling of a less de-

gassed mantle reservoir with low 40Ar/36Ar ratio is required.

1.4.5 Pu-U-I derived Xe in the depleted and the HIMU-type MORB mantle source

The proportion of Pu- to U-derived Xe provides powerful independent constraints on the degree of outgassing of a mantle source that augments arguments from the other noble gas isotope ratios. Because fission Xe yields from Pu are significantly larger than from U,areser-

136 136 voir that has remained completely closed over Earth’s history will have XePu*/ XeU* of ~27, where ‘*’ refers to fissiogenic Xe. Because 244Pu became extinct at ~4 Ga, reservoirs open to substantial volatile loss over the past 4 billion years will have a large proportion of

238 136 136 fission Xe derived from U; i.e., XePu*/ XeU* in degassed reservoirs will be ≪27 (Kunz et al., 1998, Ozima et al., 1985, Tolstikhin and O’Nions, 1996 and Yokochi and Marty, 2005).

In the present day mantle, 131,132,134,136Xe isotopes reflect a mixture of the initial mantle

Xe, Pu- and U-produced fission Xe, and subducted atmospheric Xe, if any. For the initial mantle composition we investigated solar and chondritic Xe (AVCC) (Caffee, 1999, Holland and Ballentine, 2006, Holland et al., 2009 and Pujol et al., 2011). The deconvolution of the four Xe components was performed with the mantle source ratios listed in Table 1.1 and the methodology discussed in Section 1.2.4. Here we will note four major implications of the fission deconvolution: (a) recycling of atmospheric Xe to the mantle, (b) the ratio of Pu- to U- derived Xe in the depleted MORB source, (c) the ratio of Pu- to U-derived Xe in the HIMU- type MORB source, and (d) I/Pu ratios in the depleted and HIMU-type MORB sources.

For a mantle starting composition of either solar Xe or chondritic Xe, substantial injection of atmospheric Xe back into the mantle is required. We find that on order 80–90% of the

132Xe in the mantle source is derived from recycled atmospheric Xe (Table 1.2). The proportion of recycled Xe in the HIMU-type MORBs, however, does not appear to be larger than

26 Table 1.2: Xenon components in the depleted MORB and HIMU-type mantle sources

in the depleted MORBs (Table 1.2). Thus, we suggest that the lower 129Xe/130Xe ratios in the enriched HIMU-type MORBs do not result from preferential recycling of atmospheric Xe into the plume source. Rather the HIMU-type MORBs must sample a reservoir with a lower

129I/130Xe than the depleted MORBs.

The requirement that a significant fraction of the fissiogenic Xe isotopes in the mantle is recycled from the atmosphere (Table 1.2) is consistent with previous work that suggests

Xe can be recycled back into the mantle (Holland and Ballentine, 2006 and Kendrick et al.,

2011; Sumino et al., 2010). The recycling of atmospheric Xe could have happened all through

Earth’s history associated with plate subduction (Holland and Ballentine, 2006), or very early on in Earth’s history (Moreira and Raquin, 2007). However, since the 129Xe/130Xe ratio can

only evolve during the first 100 Myr of solar system history, the distinct atmospheric and

mantle compositions require that recycling efficiency of atmospheric Xe must be relatively

low so as not to homogenize the mantle and atmospheric compositions over 4.45 Ga. In this

regard, since at most 80–90% of the Xe in the mantle is recycled (Table 1.2), the mantle

129Xe/130Xe ratio can still be distinctly different from the atmospheric ratio.

Depending on whether the initial mantle Xe composition is solar or chondritic, the frac-

136 +0.17 +0.14 tion of Xe derived from Pu fission in the depleted MORB source is 0.25−0.10 or 0.29−0.12, 136 136 respectively (Table 1.2). The corresponding XePu*/ XeU* is 0.33 ± 0.12 or 0.41 ± 0.1.

136 136 The XePu*/ XeU* ratios are ~1% of the closed system value of 27 and suggest that the

27 depleted MORB source has lost 99% of its Pu-produced Xe as a result of mantle outgassing from a combination of giant impacts and mantle convection.

In the HIMU-type MORB source, the fraction of 136Xe derived from Pu fission is 0.52 ±

0.13 (solar) or 0.63 ± 0.18 (chondritic) (Table 1.2). Although the uncertainties are large,

the result suggests that the HIMU-type MORBs may have a higher proportion of Pu- to U-

derived fission Xe than the depleted MORBs but lower than the Iceland plume (Table 1.2;see

also Fig. A.3). The high proportion of Pu-derived Xe in the HIMU-type MORBs compared

to the depleted MORBs is inconsistent with the HIMU component being comprised only of

recycled crust or a mixture of recycled crust and DMM. This is because recycled crust should

be highly degassed and will have fission Xe produced only from 238U fission during its resi-

dence in the mantle. Pu-produced Xe could be present in recycled crust only if the crust were

produced and subducted back into mantle prior to 4 Ga when 244Pu was still alive. However,

Re–Os and Pb isotopic systematics indicate an age of 1–2 Ga for the HIMU mantle (Chau- vel et al., 1992 and Hauri and Hart, 1993). Therefore, the relatively high proportion of Pu- to U-derived fission Xe in the HIMU-type mantle provides further evidence that HIMUisa hybrid of a recycled and a less degassed mantle component and requires the Xe contribution from the less degassed mantle component to dominate over the 238U-produced fission Xe in the recycled crust. Such a conclusion is consistent with the HIMU-type MORBs having a

129Xe/136Xe ratio that is intermediate between Iceland and the depleted MORBs.

The combined I–Pu–Xe system has been used to constrain the closure time for volatile loss

129 136 129 of a mantle reservoir through the Xe*/ Xe*Pu ratio, where Xe* is the decay prod-

129 136 136 244 uct of I decay and Xe*Pu is Xe produced from Pu fission (Allegre et al., 1987, Azbel and Tolstikhin, 1993, Kunz et al., 1998, Ozima et al., 1985, Pepin and Porcelli, 2006 and Yokochi and Marty, 2005). 129I has a shorter half-life than 244Pu and as a result, higher

129 136 Xe*/ Xe*Pu ratios are indicative of earlier closure to volatile loss. We find that for the

129 136 +7.4 +6.5 depleted MORB source, the Xe*/ Xe*Pu ratio is 10.7−4.6 or 8.9−3.1 depending on an 129 136 initial mantle composition of solar or chondritic Xe; the Xe*/ Xe*Pu for the HIMU-

+1.9 +1.9 type MORB source is 4.1−1.0 or 4.6−1.0 (Table 1.2). Interpreting these values as closure ages

28 129 136 for a mantle with an initially homogenous I/Pu ratio, the higher Xe*/ Xe*Pu ratio in the depleted MORB source would imply that the shallow upper mantle became closed to volatile loss prior to the deep mantle reservoir supplying noble gases to the HIMU plume.

Such a conclusion appears paradoxical. Rather, a simpler explanation is that the lower

129 136 Xe*/ Xe*Pu in the HIMU-type MORB source reflects a lower initial I/Pu ratio for the plume source compared to the MORB source. This is consistent with the conclusions inferred from the Xe data in the Iceland plume (Mukhopadhyay, 2012) and suggests that the initial phase of Earth’s accretion was volatile poor compared to the later stages of accretion because

Pu is a refractory element while I is a volatile element.

Differences in I/Pu ratios and I/Xe ratios in the mantle are relicts of accretion andearly

Earth processes. The preservation of these differences in the present day mantle reflects the relatively low recycling efficiency of the noble gases with respect to the lithophile and siderophile elements. Importantly, since 129I became extinct 100 Myr after the start of the so-

129 130 lar system, the differences in Xe/ XeE ratios (Fig. 1.7) between the reservoir supplying Xe to the Iceland and HIMU plumes and DMM must have been established by 4.45 Ga. If the two reservoirs were completely homogenized after 4.45 Ga, the different Xe isotopic compositions in the present day mantle could not have been maintained.

1.5 Conclusions

We present new heavy noble gas data in MORBs from the equatorial Mid-Atlantic Ridge.

Based on our observations we conclude:

1. He–Ne are tightly coupled to variations in the lithophile isotopes. The depleted end of

the MORB array (D-DMM) is less radiogenic in He but more nucleogenic in Ne than

N-MORBs (DMM). We conclude that N-MORBs in the equatorial Atlantic are pro-

duced by mixing a small proportion of a HIMU plume component to a very depleted

MORB matrix.

2. Despite having more radiogenic Pb and He isotopic compositions, the HIMU-type

29 MORB mantle source is less nucleogenic in 21Ne/22Ne and less radiogenic 40Ar/36Ar

and 129Xe/130Xe ratios than DMM. 129Xe/136Xe ratios preclude air or seawater sub-

129 130 duction as the sole cause of the lower Xe/ XeE in the HIMU-type MORB source compared to the depleted MORB source; a less degassed component is required in the

21 22 40 36 129 130 HIMU source. Consequently, the lower Ne/ NeE, Ar/ ArE and Xe/ XeE are also interpreted as evidence for a less degassed mantle reservoir contributing to the

HIMU plume. We emphasize that our results do not imply that air or seawater subduc-

tion do not occur; rather by itself it cannot account for the differences between the two

groups of MORBs.

3. The ratio of Pu- to U-derived fission 136Xe in the depleted MORB source is ~0.4, sug-

gesting it has lost 99% of its Pu-derived Xe, and thus at least 99% of its original pri-

mordial volatile inventory. The HIMU-type MORBs have a higher ratio of Pu- to U-

derived fission Xe than the depleted MORB group, consistent with the sampling ofa

less degassed mantle reservoir in the HIMU plume.

129 136 4. Differences in Xe*/ Xe*Pu suggest a lower I/Pu ratio for the relatively undegassed mantle reservoir compared to the depleted MORB source and thus supports heteroge-

neous volatile accretion with early accretion being drier than later accreting material.

Overall the Xe isotopic compositions require the preservation of early (pre-4.45 Ga)

formed heterogeneities in the present day mantle.

Acknowledgments

We thank Rita Parai for helping to quantify the long-term Xe isotopic performance of the instrument. We thank Masahiko Honda and two anonymous reviewers for constructive comments and Bernard Marty for editorial handling. This work was supported by NSF Grant

OCE 092919.

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35 2 Evidence for multiple magma ocean outgassing and atmospheric loss episodes from mantle noble gases

Jonathan M. Tucker1, Sujoy Mukhopadhyay2 1 Harvard University

2 University of California, Davis

The contents of this chapter have been published as: Tucker, J.M., Mukhopadhyay, S., 2014.

Evidence for multiple magma ocean outgassing and atmospheric loss episodes from mantle noble gases. Earth and Planetary Science Letters 393, 254–265.

36 Abstract

The energy associated with giant impacts is large enough to generate global magma oceans during Earth’s accretion. However, geochemical evidence requiring a terrestrial magma ocean is scarce. Here we present evidence for at least two separate magma ocean outgassing episodes on Earth based on the ratio of primordial 3He to 22Ne in the present-day mantle.

We demonstrate that the depleted mantle 3He/22Ne ratio is at least 10 while a more prim-

itive mantle reservoir has a 3He/22Ne ratio of 2.3 to 3. The 3He/22Ne ratios of the mantle

reservoirs are higher than possible sources of terrestrial volatiles, including the solar nebula

ratio of 1.5. Therefore, a planetary process must have raised the mantle’s 3He/22Ne ratio.

We show that long-term plate tectonic cycling is incapable of raising the mantle 3He/22Ne ratio and may even lower it. However, ingassing of a gravitationally accreted nebular atmosphere into a magma ocean on the proto-Earth explains the 3He/22Ne and 20Ne/22Ne ratios

of the primitive mantle reservoir. Increasing the mantle 3He/22Ne ratio to a value of 10 in

the depleted mantle requires at least two episodes of atmospheric blow-off and magma ocean

outgassing associated with giant impacts during subsequent terrestrial accretion. The preser-

vation of a low 3He/22Ne ratio in a primitive reservoir sampled by plumes suggests that the

later giant impacts, including the Moon-forming giant impact, did not generate a whole man-

tle magma ocean.

Atmospheric loss episodes associated with giant impacts provide an explanation for Earth’s

subchondritic C/H, N/H, and Cl/F elemental ratios while preserving chondritic isotopic ra-

tios. If so, a significant proportion of terrestrial water and potentially other major volatiles

were accreted prior to the last giant impact, otherwise the fractionated elemental ratios

would have been overprinted by the late veneer.

37 2.1 Introduction

Global magma oceans are thought to be a natural result of the highly energetic giant impact

phase of planetary accretion (Abe and Matsui, 1985, Benz and Cameron, 1990, Canup, 2008,

Elkins-Tanton, 2012, Sasaki and Nakazawa, 1986, Stevenson, 1987 and Tonks and Melosh,

1993). The best evidence for a terrestrial magma ocean is the relative concentrations of

siderophile elements in the mantle, which suggest core formation occurred when at least part

of the Earth’s mantle was molten (Li and Agee, 1996, Righter et al., 1997 and Rubie et al.,

2007). However, elements that trace silicate differentiation do not show strong signatures for

a magma ocean. For example, Kato et al. (1988) and Ringwood (1990) argued that refrac-

tory lithophile trace elements should have been highly fractionated by magma ocean crystal-

lization and that fractionation is not observed in Hadean zircons, which preserve chondritic

ratios. On the other hand, magma ocean crystallization models have been used to explain in-

congruent Sm-Nd and Lu-Hf isotope systematics in Archean rocks (Caro et al., 2005 and Rizo

et al., 2011) as well a slightly superchondritic mantle Ca/Al ratio (Walter et al., 2004). Geo-

chemical evidence for a magma ocean may be difficult to find in the present-day mantle, as

crustal recycling and mantle mixing throughout Earth’s history may have erased the chemical

fractionations of the lithophile elements produced by magma ocean crystallization.

The noble gases may provide unique information on the occurrence of magma oceans, as

magma ocean ingassing or outgassing will create large fractionations in noble gas elemental

ratios due to their different solubilities in magma. The present-day budgets of nonradiogenic

Ar, Kr, and Xe in the mantle are dominated by recycled air (Holland and Ballentine, 2006,

Kendrick et al., 2011, Mukhopadhyay, 2012, Pető et al., 2013, Sumino et al., 2010 and Tucker

et al., 2012), so possible magma ocean degassing signatures involving Ar, Kr, and Xe would

have been overprinted by subduction. On the other hand, He and Ne are not recycled back

into the mantle in significant quantities, and may preserve ancient magma ocean signatures

(Harper and Jacobsen, 1996, Honda and McDougall, 1998, Porcelli et al., 2001, Shaw et al.,

2001 and Yokochi and Marty, 2004).

38 Honda and McDougall (1998) observed that the mantle 3He/22Ne ratio, as determined

from measurements of mid-ocean ridge basalts (MORBs) and ocean island basalts (OIBs),

was twice the solar value, and suggested that this fractionation resulted from the higher sol-

ubility of He compared to Ne during magma ocean outgassing. Ingassing, i.e. dissolution of

volatiles from an accreted nebular atmosphere into a magma ocean (Harper and Jacobsen,

1996 and Mizuno et al., 1980), could also have the same effect on the mantle 3He/22Ne ratio.

However, magma ocean equilibration (ingassing or outgassing) has been regarded as a spec-

ulative explanation of the high mantle 3He/22Ne ratios (e.g., Graham, 2002). Yokochi and

Marty (2004) advocated magma ocean ingassing based on observations of 20Ne/22Ne ratios of

>13.0 in the Kola plume, a Ne isotopic composition similar to the solar wind. The authors

also noted that the high 3He/22Ne ratio (~7.9) observed in the Kola plume and in present-

day MORBs requires additional fractionation beyond that capable through magma ocean

ingassing. They speculated that the fractionation mechanism was fluid-melt partitioning dur-

ing high pressure melt segregation and fluid phase formation in the deep mantle. However, it

is unclear whether fluid phases would nucleate at the P-T conditions of the deep mantle.

Here we present evidence for ancient magma ocean degassing based on high 3He/22Ne ra-

tios in the depleted mantle that are more extreme than the average MORB value. To estab-

lish the 3He/22Ne ratio of the depleted mantle, we characterize how 3He/22Ne variations are linked to lithophile (Pb, Sr, Nd) and noble gas isotope ratios in very depleted to enriched

MORBs using published data from the equatorial Atlantic (Agranier et al., 2005, Schilling et al., 1994 and Tucker et al., 2012). We then show that magma ocean degassing is the most likely explanation for the large 3He/22Ne fractionation observed in the present-day mantle.

We demonstrate that extraction of He and Ne from the mantle through partial melting and

plate subduction associated with plate tectonics either has a negligible effect or decreases the

mantle 3He/22Ne ratio. We argue that the magnitude of the 3He/22Ne fractionation requires

atmospheric loss followed by solubility-controlled degassing of at least two separate magma

oceans during the giant impact phase of Earth’s accretion.

39 2.2 Determining MORB mantle source 3He/22Ne ratios

Direct measurements of 3He/22Ne ratios in mantle-derived basalts are not likely to represent the mantle value because the ratio can be changed by magmatic degassing during eruption and ubiquitous shallow-level air contamination. We therefore calculate the mantle source

3 22 3 22 He/ Ne ( He/ Nem) ratio from measured He and Ne isotope ratios in basalts, after Honda and McDougall (1998) and Porcelli and Ballentine (2002) (Method 1):

21 22 −21 22 3 22 Ne/ NeE Ne/ Nei × 4 21 ∗ He/ Ne = 4 3 4 3 ( He/ Ne)production (2.1) He/ Hemeas − He/ Hei

21 22 21 22 Ne/ NeE is the mantle source Ne/ Ne ratio corrected for shallow-level air contamination by extrapolation of measured 21Ne/22Ne ratios to the mantle 20Ne/22Ne ratio of 12.5

21 22 21 22 (Tucker et al., 2012). Ne/ Nei, the initial Ne/ Ne ratio for the mantle, is 0.0313, corre-

20 22 4 3 sponding to a Ne/ Ne ratio of 12.5. The primordial He isotope ratio He/ Hei is 6024 (120

4 21 ∗ RA), as observed in the Jovian atmosphere (Mahaffy et al., 1998), and ( He/ Ne)production is the production ratio of radiogenic 4He to nucleogenic 21Ne in the mantle.

3 22 We additionally calculate the He/ Nem ratio (Method 2) by first correcting the sam-

3 22 4 21 3 22 ple’s measured He/ Ne and He/ Ne ratios for air contamination ( He/ NeE and

4 21 4 21 He/ NeE; Fig. 2.1) and computing ( He/ Ne)* (where ‘*’ refers to the mantle-derived

4 21 3 22 radiogenic/nucleogenic species) from He/ NeE. He/ NeE is corrected for magmatic degassing by the degree to which the sample’s (4He/21Ne)* ratio is fractionated from the ex-

pected production ratio (e.g., Graham, 2002; see supplementary material). The two methods

give comparable results for our MORB samples (Table 2.1).

In our calculations, we assume the MORB mantle 20Ne/22Ne ratio is 12.5 (Ballentine et

al., 2005, Holland and Ballentine, 2006, Raquin et al., 2008 and Trieloff et al., 2000). Ifwe

instead assume a MORB mantle 20Ne/22Ne ratio of 13.8, corresponding to the solar wind

3 22 value (Grimberg et al., 2006), calculated He/ Nem ratios increase by ~50%, strengthening

3 22 our conclusions. Additionally, we report He/ Nem ratios using two different determinations 4 21 ∗ × 7 × 7 of ( He/ Ne)production: 2.2 10 (Yatsevich and Honda, 1997) and 2.8 10 (Ballentine and

40 3 22 3 22 Figure 2.1: Example of correlation diagrams to determine the MORB source He/ Ne ( He/ Nem) ratios. Each point represents a single crushing step of the equatorial Atlantic MORB sample RC2806 42D-7 (data presented in Tucker et al., 2012). Step-crushing releases gas trapped in vesicles that reflects magmatic gas variably contaminated with a post-eruptive atmospheric contaminant. Extrapolation of the (a) 20Ne/22Ne–3He/22Ne and (b) 4He/21Ne–22Ne/21Ne correlation trends to the uncontaminated mantle values of 20Ne/22Ne = 12.5 and 22Ne/21Ne (determined by correlation of 20Ne/22Ne with 21Ne/22Ne; Tucker et al., 2012) corrects for post-eruptive air contamination and establishes the magmatic 3He/22Ne and 4He/21Ne ratios. This magmatic 3He/22Ne ratio is corrected for potential magmatic degassing though the degree to which the magmatic (4He/21Ne)* ratio is fractionated from the mantle (4He/21Ne)* production ratio (see supplementary material).

41 Table 2.1: MORB source 3He/22Ne ratios

3 22 Burnard, 2002 and Leya and Wieler, 1999). For consistency, we refer to the He/ Nem ratios

3 22 calculated with the lower production ratio, noting this yields a lower bound on He/ Nem

4 3 ratios. We further note that using He/ Hei ratios of ~2000–3000, corresponding to modern solar wind, or using a mantle 20Ne/22Ne ratio of ~12.4, corresponding to highest measured

3 22 values in our samples, has a negligible effect on the computed He/ Nem ratio.

2.3 The 3He/22Ne ratio of the depleted mantle

The equatorial Atlantic MORBs are derived from a heterogeneous source with 3He/22Ne ra-

tios of 6.1 to 9.8 (Table 2.1). The most depleted MORBs are derived from a mantle with

the highest 3He/22Ne ratios and the more enriched MORBs (Schilling et al., 1994) are de-

rived from a mantle with lower 3He/22Ne ratios (Fig. 2.2). We note that an average MORB

3 22 He/ Nem ratio of 10.2 ± 1.6 was calculated by Honda and McDougall (1998) and 8.8 ± 3.5 by Graham (2002). These values were calculated assuming a mantle 20Ne/22Ne ratio of 13.8,

3 22 and under this assumption, our samples range from 8.9–14.3. The average He/ Nem ratios of Honda and McDougall (1998) and Graham (2002) recalculated to 20Ne/22Ne = 12.5 are

7.3 ± 1.2 and 6.1 ± 2.4, respectively, at the mid to low end of our range (Table 2.1; supplementary material).

42 3 22 21 22 4 Figure 2.2: Correlation between He/ Nem and (a) Ne/ NeE, (b) εNd where ε is the part in 10 deviation from the chondritic 143Nd/144Nd value, and (c) 206Pb/204Pb. These correlations establish the 3 22 depleted mantle value to be at least 9.8 and indicate that the variability in MORB He/ Nem ratios is caused by recent mixing between a depleted mantle source and a more enriched plume source with a lower 3He/22Ne ratio.

43 3 22 Since He/ Nem ratios are strongly correlated with the lithophile isotopic composition

3 22 of the MORBs (Fig. 2.2), the variations in He/ Nem ratios must have been produced by recent mixing between a depleted mantle with a high 3He/22Ne ratio (≥ ~10) and an enriched mantle with a low 3He/22Ne ratio. Specifically, intermediate values can be explained by mixing depleted mantle with primitive and recycled material (e.g., Schilling et al., 1994 and Tucker et al., 2012; see supplementary material). Because the lithophile isotopic composition of the depleted samples defines the depleted end of the MORB array (Schilling etal.,

3 22 3 22 1994), the depleted mantle He/ Ne ratio must be at least 9.8 (Fig. 2.2). As the He/ Nem value of 9.8 is itself a lower limit for the most depleted sample (Section 2.2), in subsequent discussions we take the depleted mantle to have a 3He/22Ne ratio of ≥ ~10.

3 22 Previous studies have attributed variations in He/ Nem ratios in mantle-derived rocks to either source heterogeneity (Coltice et al., 2011, Kurz et al., 2009, Moreira et al., 2001,

Mukhopadhyay, 2012, Raquin and Moreira, 2009 and Yokochi and Marty, 2004) or to frac-

tionation resulting from partial melting and degassing of melts derived from a mantle with

a uniform 3He/22Ne ratio (Hopp and Trieloff, 2008, Moreira and Allègre, 1998, Moreira et

al., 2001, Sarda et al., 2000 and Trieloff and Kunz, 2005). However, the correlations between

3 22 the He/ Nem and lithophile isotopic ratios in the MORB samples (Fig. 2.2) clearly demonstrate the existence of mantle domains with different 3He/22Ne ratios. We further note that

the correlations argue against source variations in 3He/22Ne arising from fractionation due to fluid/melt partitioning of gases in the deep mantle (Yokochi and Marty, 2004).

2.4 3He/22Ne ratios in the present-day mantle and in planetary materials

Based on the mixing trends in Fig. 2.2, the present-day depleted mantle has a 3He/22Ne ratio of ≥10. In contrast, plumes tend to have lower 3He/22Ne ratios (e.g. Füri et al., 2010, Gra-

ham, 2002, Honda and McDougall, 1998, Jackson et al., 2009, Kurz et al., 2009, Moreira et

al., 2001, Mukhopadhyay, 2012, Raquin and Moreira, 2009 and Yokochi and Marty, 2004).

21 22 3 22 OIBs with the most primitive Ne/ Ne ratios (e.g., Galapagos, Iceland), have He/ Nem

44 3 22 3 22 Figure 2.3: He/ Nem ratios in modern terrestrial reservoirs along with the He/ Ne ratios in possible sources that may have contributed primordial He and Ne to the Earth. Note that the depleted mantle value is at least a factor of 6.5 higher than the value in possible primordial materials. MORBs also have higher values than the primitive reservoir sampled by OIBs at Galapagos and Iceland. 3He/22Ne ratios for terrestrial reservoirs are computed by Method 1. Details of the calculations are given in the supplementary material. Data sources are as follows: MORB average (H&M) from Honda and McDougall (1998); MORB average (Graham) from Graham (2002); Mangaia from Parai et al. (2009); Samoa from Jackson et al. (2009); Iceland from Mukhopadhyay (2012); Galapagos from Kurz et al. (2009) and Raquin and Moreira (2009); solar nebula from Grimberg et al. (2006), Mahaffy et al. (1998), and Pepin et al. (2012); implanted solar wind from Raquin and Moreira (2009); chondrite from Ott (2002); iron (Washington County; unclassified) from Becker and Pepin (1984); pallasite (Brenham; olivine) from Mathew and Begemann (1997); howardite (Kapoeta and Jodzie) from Mazor and Anders (1967); aubrites (various) from Lorenzetti et al. (2003); angrite (D’Orbigny) from Busemann et al. (2006). The chondrite, pallasite, howardite, and angrite values are maximum values (see supplementary material). ratios of 2.3 to 3 (Kurz et al., 2009, Mukhopadhyay, 2012 and Raquin and Moreira, 2009; also see supplementary material).

The present-day mantle is also enriched in 3He relative to 22Ne compared to the sources that may have contributed primordial He and Ne to Earth (Fig. 2.3). These sources include the solar nebula (3He/22Ne = 1.46 ± 0.06), the implanted solar (Ne-B) component in gas-rich meteorites (3He/22Ne = 0.9 ± 0.1), the chondritic value (3He/22Ne ≤ 0.89 ± 0.11), as well as differentiated meteorites (Fig. 2.3; also see supplementary material).

The particular source(s) of He and Ne to the Earth are unclear, but must be consistent with Ne isotopes. For example, the observation of 20Ne/22Ne ratios >12.9 in the Iceland and

Kola plumes (Mukhopadhyay, 2012 and Yokochi and Marty, 2004) implies a nebular origin

45 for Ne, corresponding to a 3He/22Ne of 1.46 ± 0.06. The 3He/22Ne ratio of the primitive reservoir sampled by plumes is, therefore, fractionated from the nebular value by approximately a factor of 1.5 to 2. The MORB source 20Ne/22Ne ratio of ~12.5 is similar to the Ne-

B component observed in some primitive meteorites (Ballentine et al., 2005, Holland and Bal- lentine, 2006 and Raquin et al., 2008), thought to represent implantation of solar wind into dust grains (Grimberg et al., 2006 and Raquin and Moreira, 2009). Alternatively, the MORB source 20Ne/22Ne ratio of ~12.5 could have originated through a limited amount of recycling of atmospheric Ne (20Ne/22Ne = 9.8) into a mantle with nebular Ne (Kendrick et al., 2011).

In either case, the 3He/22Ne ratio of the material that contributed He and Ne to the MORB source must have been ≤ 1.46 ± 0.06 (Fig. 2.3). Therefore, the present-day depleted mantle

3He/22Ne ratio is fractionated by at least a factor of 6.5 from possible sources of terrestrial volatiles (Fig. 2.3). Additionally, because of mixing between the depleted mantle and the primitive reservoir over time, the depleted mantle 3He/22Ne ratio was likely higher than 10 in the past. Thus, a factor of 6.5 is a lower limit for the degree of 3He/22Ne fractionation of the depleted mantle.

2.5 Can plate tectonics generate reservoirs with high 3He/22Ne ratios?

We now address the puzzling observation: how has the Earth’s interior acquired 3He/22Ne

ratios higher than even the solar nebula? We investigate whether processes associated with

the present style of plate tectonics can generate the high 3He/22Ne ratio in the depleted man-

tle and the difference between the depleted mantle and the primitive reservoir. Specifically,

the mechanisms that could change the 3He/22Ne ratio are (i) partial melting that generates oceanic crust and a depleted mantle residue and (ii) recycling and mixing of tectonic plates.

2.5.1 Partial melting

Partial melting could raise or lower the He/Ne ratio of lavas if the two elements have different partition coefficients during mantle melting. Such fractionation has been advocated to

46 Table 2.2: He and Ne partition coefficients

3 22 explain the apparent difference in He/ Nem ratios between MORBs and OIBs under the assumption of a uniform mantle 3He/22Ne ratio (Füri et al., 2010, Hopp and Trieloff, 2008,

Moreira and Allègre, 1998, Sarda et al., 2000 and Trieloff and Kunz, 2005). Hopp and Trieloff

3 22 (2008) presented a hypothesis for generating a low He/ Nem ratio in OIBs compared to MORBs. They proposed that melting of the MORB source does not fractionate the 3He/22Ne

ratio, while low degree melting of mantle plumes produces melts with significantly lower

3He/22Ne ratios than the source. Mixing of melts derived from the MORB source with the

3 22 low degree melts from the plume source then generates the range of He/ Nem ratios measured in mantle-derived rocks.

Experimentally determined partition coefficients, however, rule out partial melting asthe

3 22 primary mechanism for producing the large range of observed He/ Nem ratios (Table 2.2; Brooker et al., 2003, Heber et al., 2007 and Jackson et al., 2013). For example, generating

the observed MORB/OIB fractionation of ~3–4× would require a degree of partial melting on

the order of 0.01%, far too low for the generation of OIBs. Given a typical degree of melting

of 1–10% for OIBs and MORBs, the 3He/22Ne ratio of the melt would be different from the

source by at most 0.3–3.6% compared to the large (>100%) variability observed (Fig. 2.2 and

3 22 Fig. 2.3). Therefore, we conclude that variability in He/ Nem ratios reflects differences in the 3He/22Ne ratio of the mantle and not fractionation produced through partial melting.

47 2.5.2 Recycling and mixing of slabs

The process of generating slabs and recycling them back to the mantle creates chemical heterogeneity in the mantle and has likely occurred since the Hadean (Coltice and Schmalzl,

2006, Harrison et al., 2005 and Hopkins et al., 2008). Partial melting of the mantle generates the oceanic crust and depleted residue. The partial melt (oceanic crust) degasses, and the slab, comprised of the degassed crust and depleted residue, is recycled during subduction and mixed back into the mantle.

The partial melt will have the same 3He/22Ne ratio as the mantle source (Section 2.5.1).

Degassing of the partial melt prior to solidification into oceanic crust could then generate

high 3He/22Ne ratios in the crust as He is more soluble in the melt than Ne. However, recycling and mixing of oceanic crust back into the mantle could not have increased the mantle

3He/22Ne ratio for a number of reasons. First, direct measurements reveal that old basaltic and gabbroic portions of the oceanic crust have 3He/22Ne ratios of ~0 due to the ubiquitous introduction of atmospheric noble gases (Moreira et al., 2003 and Staudacher and Allègre,

1988). Recycling and mixing of oceanic crust would, therefore, serve to lower the mantle

3He/22Ne ratio over time. Second, if recycling of partially degassed oceanic crust introduced a high 3He/22Ne ratio into the mantle, then HIMU (high-µ, where µ is the U/Pb ratio) OIBs, known to sample recycled oceanic crust (e.g., Cabral et al., 2013) and enriched MORBs from the equatorial Atlantic that likely sample recycled crust (Schilling et al., 1994) should have

3 22 the highest He/ Nem ratios. However, the observations show the opposite to be true (Fig. 2.2 and Fig. 2.3). The enriched MORBs from the equatorial Atlantic have significantly lower

3 22 He/ Nem ratios than the depleted MORBs, and HIMU OIBs from the Cook-Australs and

3 22 Cameroon line have He/ Nem ratios of 4.6 ± 0.3 and 4.8 ± 1.1, respectively (Fig. 2.3; Bar- fod et al., 1999 and Parai et al., 2009). Furthermore, trace element and isotopic compositions demonstrate that compared to enriched mantle domains, depleted mantle domains are less influenced by recycled oceanic crust. Therefore, partially degassed recycled oceanic crustcan-

3 22 not produce the high He/ Nem ratios observed in the depleted MORBs. Instead, we explore whether mixing the residue of partial melting back into the mantle

48 can generate the high 3He/22Ne ratios. Because our goal is to understand how the mantle

3He/22Ne ratio can increase to values ≥10, and because old oceanic crust has a 3He/22Ne ra-

tio of ~0, we will assume quantitative extraction of He and Ne from the oceanic crust during

subduction in our simple model. For the simplest case where slabs (oceanic crust + residual

mantle) are mixed instantaneously with the mantle, the concentration of a primordial isotope

(3He or 22Ne) in the mantle reservoir is:

(f−1)N C = C0e (2.2)

where C is the present-day concentration of the isotope in the mantle reservoir, C0 the initial concentration, f the fraction of gas retained in the mantle residue, and N the number of

reservoir masses processed through partial melting over 4.5 Ga (Gonnermann and Mukhopad-

hyay, 2009). The fraction of He and Ne in the residue depends on that element’s bulk parti-

tion coefficient, D, and the extent of partial melting, F . Assuming batch melting, the concen-

tration of the primordial isotope in the mantle as a function of N is:

( ) D − F +D(1−F ) 1 N C = C0e (2.3)

To generate the largest 3He/22Ne fractionation, we use the extremes in the ranges of He

and Ne partition coefficients (Table 2.2) during partial melting of a mantle with 60% olivine,

20% clinopyroxene, 20% orthopyroxene and a global average F of 0.05. We observe that the

3He/22Ne ratio of the mantle changes by at most 13% even after 20 reservoir masses have

been processed (Fig. 2.4). Hence, starting with a solar nebular 3He/22Ne ratio of 1.46 ± 0.06 does not produce the present-day OIB source of ~2.3 to 3 and starting with the OIB value does not produce the present-day depleted mantle value of ≥ 10 (Fig. 2.4). Furthermore, compared to fractional or dynamic melting, batch melting produces the largest effect on the mantle 3He/22Ne ratio. For example, using the highest partition coefficients within the 1σ ranges ( Table 2.2) and for a 1% partial melt, batch melting produces residues depleted in He and Ne by 2 orders of magnitude, while fractional melting produces residues depleted by 12–

49 Figure 2.4: Model calculation showing the 3He/22Ne evolution of a hypothetical mantle reservoir by plate tectonic cycling. The 3He/22Ne ratio evolves as a function of the number of reservoir masses processed through partial melting. The Earth’s mantle has likely experienced <9 overturns in 4.5 Ga (Coltice et al., 2009 and Gonnermann and Mukhopadhyay, 2009), so plate tectonic cycling cannot significantly change the mantle 3He/22Ne ratio. This result is not sensitive to the initial value chosen; starting from the solar nebula value of ~1.5, the mantle cannot evolve to the primitive reservoir values of ~2.3–3 sampled by OIBs, and starting from 2.3, the mantle cannot evolve to the value of ≥ 10 observed in the depleted mantle. The plot shows the range of possible 3He/22Ne evolution by combining the two extremes (1σ) in the He and Ne partition coefficients of Brooker et al. (2003) and Heber et al. (2007) (Table 2). For example,we pair the +1σ in the He partition coefficient with theσ −1 in the Ne partition coefficient. We note that if the average degree of melting is greater than 5%, or the melt is extracted more efficiently than in batch melting, or the mantle has experienced fewer than 20 overturns, the overall change in the mantle 3He/22Ne ratio would be less than that shown in the figure. Additionally, if recycled crust carries Ne but not He, then the mantle 3He/22Ne would decrease over time.

13 orders of magnitude. As a result, residues produced by fractional melting cannot affect the mantle’s 3He/22Ne ratio. Overall, our simple model demonstrates that recycling of slabs and extracting He and Ne from the mantle through partial melting cannot significantly increase the mantle 3He/22Ne ratio.

2.5.3 Generating high 3He/22Ne ratios via magma ocean ingassing and outgassing

While extraction of He and Ne from the mantle through partial melting and subsequent recycling of plates cannot significantly increase the mantle 3He/22Ne ratio, ingassing or outgassing of a magma ocean would produce a mantle with a higher 3He/22Ne ratio. The higher

50 Figure 2.5: The solubility ratio of He to Ne (SHe/SNe) corresponding to three magma ocean compositions, based on three proposed bulk silicate Earth compositions, as a function of temperature. Solubility S (Henry’s constant) is the melt/vapor partition coefficient, computed from the solubility model of Iacono- Marziano et al. (2010). SHe/SNe is at most 1.96, corresponding to the peridotite liquidus temperature of 2053 K at 1 bar. magmatic solubility of He compared to Ne results in preferential partitioning of Ne into the atmosphere and an increase in the 3He/22Ne ratio of the mantle. In an equilibrium between

a magma ocean and an atmosphere, the magma 3He/22Ne ratio can be increased by up to a factor of the He/Ne solubility ratio (SHe/SNe) relative to the atmosphere. Previous sug- gestions of a magma ocean based on He/Ne studies (Honda and McDougall, 1998, Shaw et al., 2001 and Yokochi and Marty, 2004) have used SHe/SNe = 2 based on experiments in basaltic magmas at 1573–1623 K (Jambon et al., 1986 and Lux, 1987). To investigate whether SHe/SNe of 2 is applicable to discussions of a magma ocean, we used the ionic porosity model of noble gas solubility (Carroll and Stolper, 1993 and Iacono-Marziano et al., 2010) to calculate SHe/SNe for a bulk silicate Earth (pyrolite) magma composition (McDonough and Sun, 1995). We obtain SHe/SNe of 1.96 in a magma ocean at 2053 K, the peridotite liquidus temperature at 1 bar (Katz et al., 2003), noting that the surface of a magma ocean should be at least this hot initially. Because SHe/SNe decreases at higher temperatures (Fig. 2.5) and other proposed compositions of the bulk silicate Earth (Javoy et al., 2010 and Palme

and O’Neill, 2003) also yield SHe/SNe < 2, we adopt a value of 2, noting that the relevant value may be lower and not constant.

51 In the following discussion, we outline a possible chronology that includes at least three major accretionary events terminating with the Moon-forming giant impact: (i) ingassing of nebular gases into a magma ocean on the proto-Earth (Fig. 2.6a); (ii) loss of the nebular atmosphere, production of a partial mantle magma ocean by a giant impact, and subsequent outgassing to produce a secondary atmosphere (Fig. 2.6b); (iii) loss of the secondary atmosphere and generation and outgassing of another partial mantle magma ocean likely associated with the Moon-forming giant impact (Fig. 2.6c). This highly simplified chronology may be thought of as a minimum sequence of events that explains the main observation of a preserved low 3He/22Ne ratio in the deep plume mantle and a high 3He/22Ne ratio in the MORB

mantle.

2.5.4 Magma ocean ingassing and the OIB mantle

Ingassing of nebular gas from a gravitationally accreted nebular atmosphere into a magma ocean has been proposed as the mechanism responsible for acquisition of terrestrial He and

Ne (Harper and Jacobsen, 1996, Mizuno et al., 1980, Porcelli et al., 2001 and Yokochi and

Marty, 2004). The observation of solar-like 20Ne/22Ne ratios (>12.9) in primitive OIBs supports the presence of nebular He and Ne in the deep mantle (Mukhopadhyay, 2012 and

Yokochi and Marty, 2004). During nebular ingassing into a magma ocean, the 3He/22Ne ratio

of the magma ocean would be fractionated from the nebular value of ~1.5 by SHe/SNe of ≤2 to values of ~2.3–3 (Fig. 2.6a). Thus, the solar-like 20Ne/22Ne ratios and the 3He/22Ne ratios

observed in plumes with the most primitive 21Ne/22Ne ratios (Fig. 2.3) are strong evidence for nebular ingassing.

The ingassing hypothesis is consistent with the timescales for planet formation and dissipation of nebular gases. The median timescale of dissipation for nebular gas is ~3 Ma, but nebular gas may be present for up to 10–12 Ma (Wyatt, 2008). Mars reached approximately half its present size in 1.8 ± 1 Ma (Dauphas and Pourmand, 2011) and the mean age of Earth’s

accretion is around 11 ± 1 Ma (Yin et al., 2002). Embryos of at least the mass of Mars are required for gravitational capture of substantial amounts of nebular gases (Hayashi et al.,

52 Figure 2.6: A proposed conservative chronology of events to explain the highly fractionated 3He/22Ne ratio of the depleted mantle. (a) Nebular ingassing. A gravitationally accreted nebular atmosphere surrounds the molten proto-Earth. Gases are dissolved into the magma ocean and fractionated by a factor up to their solubility ratio. The magma ocean solidifies, and the mantle inherits the fractioned 3He/22Ne ratio. Neb- ular ingassing probably happened on multiple embryos that later collided to form the Earth. (b) Magma ocean outgassing. A giant impact (or hydrodynamic escape) leads to loss of the existing atmosphere and produces a new partial mantle magma ocean, preserving the low 3He/22Ne reservoir sampled by deep mantle plumes. This magma ocean outgasses, forming a secondary atmosphere, and leaving residual He and Ne fractionated. (c) Moon-forming giant impact. A second giant impact blows off the existing secondary atmosphere and induces a new partial mantle magma ocean. This magma ocean outgasses, forming a new secondary atmosphere, and leaving He and Ne fractionated. Because the amount of 3He/22Ne fractionation in each step is at most a factor of 2, our data require at least two giant impact-induced magma ocean outgassing episodes to achieve a 3He/22Ne ratio ≥ 10.

53 1979). We suggest that the proto-Earth, poorly constrained to between 10% to ~60% of the present mass of Earth, gravitationally captured a nebular atmosphere that equilibrated with a magma ocean. This early magma ocean could have been produced through early radiogenic heating, the energy of accretion, and the blanketing effect of the massive nebular atmosphere, and may have occurred on multiple embryos that later accreted to form the Earth.

2.5.5 Multiple magma oceans and the depleted mantle

After the initial episode of ingassing, the 3He/22Ne ratio of the shallower portion of the mantle increased to ≥10 while the deep mantle preserved values of ~2.3–3. If the origin of noble gases in the shallower mantle is meteoritic as opposed to solar (Section 2.4), the required fractionation is even higher (Fig. 2.3). Because SHe/SNe is at most 2 (Fig. 2.5), multiple episodes of magma ocean outgassing are required to increase the mantle 3He/22Ne ratio from the value preserved in primitive plumes of at most 3 to the value in the depleted mantle of at least 10.

Magma ocean outgassing of the whole Earth was proposed by Honda and McDougall

(1998) as a mechanism to increase the mantle 3He/22Ne ratio. They derived an average mantle 3He/22Ne ratio of 7.7 ± 2.6 from various MORBs and OIBs, and noted that this value is twice the solar value of 3.8. The authors argued that because SHe/SNe in basaltic liquids is 2, the mantle’s apparent 2× fractionation from the solar nebular value could be explained by solubility-controlled outgassing of a magma ocean. They also noted that the MORB average seemed higher than the OIB average, but based their arguments on the combined average.

We argue that the average 3He/22Ne ratio of the mantle is not particularly meaningful in the discussion of the extent of magma ocean degassing as the depleted mantle and the primordial

3 22 reservoir clearly have different He/ Nem ratios (Fig. 2.3). Furthermore, the solar value of 3.8 is an unlikely primordial value because the solar nebula 3He/22Ne ratio is 1.46 ± 0.06 and implanted solar gas has a 3He/22Ne ratio of 0.9 ± 0.1 (Fig. 2.3).

We propose that after loss of the nebular atmosphere and during the giant impact phase of terrestrial growth, at least two separate partial mantle magma ocean episodes raised the

54 3He/22Ne ratio of the shallower mantle to ≥10 (a modification of the hypothesis proposed by

Honda and McDougall, 1998). The last of the magma ocean episodes would have been asso-

ciated with the Moon-forming giant impact. Equilibrium outgassing of a magma ocean can

3 22 increase the magmatic He/ Ne ratio by up to a factor of SHe/SNe, which is ≤2 (Fig. 2.5). Loss of the nebular atmosphere, either before or during a giant impact, followed by solubility- controlled outgassing from the impact-generated magma ocean, raised the 3He/22Ne ratio

from at most 2.3–3 to as high as 5–6 (Fig. 2.6b). A minimum of one additional episode of atmospheric loss and impact-induced magma ocean outgassing is then required to achieve the

3He/22Ne ratio of ≥10 that characterizes the depleted mantle (Fig. 2.6c).

Partial or complete loss of the preexisting atmosphere prior to magma ocean generation

is a requirement to drive the 3He/22Ne fractionation in the magma ocean. If an atmosphere

that had equilibrated with a previous magma ocean remained intact during a giant impact,

the new magma ocean would not outgas and fractionate 3He from 22Ne because it would al- ready be in equilibrium with the atmosphere. Complete loss would lead to the highest degree of He/Ne fractionation, up to SHe/SNe, whereas partial loss would lead to fractionation less than SHe/SNe. Therefore, if atmospheric loss between magma ocean episodes were incom- plete, more than the minimum of two magma ocean outgassing events would be required to attain 3He/22Ne ratios of ≥ 10.

Hydrodynamic escape and impact erosion could provide the mechanisms for the atmo-

3 22 spheric loss required by the He/ Ne observations. The H2-rich primary nebular atmosphere captured by embryos or the proto-Earth may have been partially or substantially lost through hydrodynamic escape after the nebula dissipated (e.g., Pepin, 1991, see Section

2.7.1). However, secondary (outgassed) atmospheres are unlikely to be H2-rich even if core formation is ongoing (Hirschmann, 2012) and consequently, hydrodynamic escape may not be an important process for loss of outgassed atmospheres. Furthermore, the process would result in chemical fractionations that are not observed (Marty, 2012 and Sharp and Draper,

2013). We therefore propose that loss of secondary atmospheres was driven by giant impacts during terrestrial accretion. Although numerical simulations suggest that atmospheres are

55 not necessarily lost during a giant impact (Genda and Abe, 2003), atmospheric loss becomes more efficient if the planet has an ocean (Genda and Abe, 2005) and/or if the planet isrotat- ing quickly (Lock and Stewart, 2013 and Stewart and Mukhopadhyay, 2013). Irrespective of the precise mechanism for atmospheric loss, we reiterate that atmospheric loss is a requirement for driving 3He/22Ne fractionation in a magma ocean (Fig. 2.6).

These atmospheric loss and magma ocean episodes would have occurred as planetary embryos started colliding with each other following dissipation of the nebula. While the last of these magma oceans must have occurred on the Earth in association with the Moon-forming impact, the previous magma ocean outgassing episode(s) may have happened on the planetary embryos that collided with the proto-Earth. However, giant impacts were prevalent during accretion (e.g., O’Brien et al., 2006 and Walsh et al., 2011) and two giant impacts on the Earth itself are implied in a recent hypothesis for the formation of the Moon (Ćuk and

Stewart, 2012). To obtain a lunar disk with the same bulk composition as the Earth, the hypothesis posits a giant impact onto a fast-spinning Earth. To spin the Earth up requires an additional giant impact prior to the Moon-forming impact.

Our proposed scenario explains the increase in the mantle 3He/22Ne ratio through equilibrium outgassing of at least two partial mantle magma oceans. If there were disequilibrium degassing, the fractionation between He and Ne would be suppressed (e.g., Gonnermann and

Mukhopadhyay, 2007 and Paonita and Martelli, 2007). Consequently, the 3He/22Ne ratio in the magma ocean would be fractionated by less than SHe/SNe, requiring additional magma ocean outgassing and atmospheric loss events. In volcanic systems, open-system degassing can fractionate elemental ratios beyond the solubility ratio (e.g., Moreira and Sarda, 2000) and open system magma ocean degassing has been proposed (Shaw et al., 2001). Open- system degassing of a magma ocean implies that the degassed gases are immediately lost from the atmosphere, even though Ne is gravitationally bound. Such gas loss could be driven by hydrodynamic escape during outgassing of the magma ocean, perhaps precluding the need for multiple outgassing episodes. To test this possibility, we performed a coupled magma ocean outgassing/hydrodynamic escape calculation. In our calculation, EUV flux from the

56 Figure 2.7: Coupled magma ocean outgassing and hydrodynamic escape model. Plotted are the dissolved magmatic 3He abundance (left axis) and magma ocean and atmospheric 3He/22Ne ratios (right axis) as a function of atmospheric H2 inventory, a proxy for time. In this model, solar EUV radiation, 100× the present value (Ribas et al., 2005), drives H2 loss from a nebular atmosphere, which lifts He and Ne from the atmosphere. The underlying magma ocean is always assumed to be in equilibrium with the atmospheric composition above it so the maximum amount of outgassing can occur. In the calculation shown we assume a proto-Earth of 0.3× Earth mass, an initial surface pressure of 30 bar, surface temperature of 2000 K, and H2 escape flux that decays with a time constant of 90 Myr (Pepin, 1991); the corresponding initial crossover mass are 541 and 762 amu for He and Ne, respectively. Equations are given in the supplementary material. We note that the 3He/22Ne ratios in the atmosphere and magma ocean decrease regardless of the particular parameters used, and therefore conclude that open-system degassing accommodated by hydrodynamic escape cannot raise the mantle 3He/22Ne ratio.

young Sun drives H2 loss that in turn lifts He and Ne from the atmosphere. Since the atmosphere and magma ocean remain in equilibrium, atmospheric loss leads to further outgassing from the magma ocean (Fig. 2.7; equations in supplementary material). We find that despite the open-system nature of outgassing, hydrodynamic escape is significantly more efficient at removing He from the atmosphere than Ne, such that the 3He/22Ne ratios of the atmosphere and magma ocean decrease (Fig. 2.7). Hence, we conclude that two outgassing episodes are the minimum required to explain the fractionated 3He/22Ne of the depleted mantle.

2.6 Implications for Earth’s accretional history

The observation of large differences in 3He/22Ne ratios in the mantle and the requirement for atmospheric loss in our magma ocean outgassing hypothesis have significant implications for

57 the terrestrial inventories of volatile elements, early mantle mixing, and the origin of mantle heterogeneities.

2.6.1 The terrestrial volatile budget

Magma ocean outgassing can efficiently transfer volatiles (e.g., N2,H2O, and CO2) from the mantle to the exosphere (Elkins-Tanton, 2008 and Zahnle et al., 2007). Consequently, the

mantle was dried by giant impacts and the terrestrial volatile budget was concentrated at the

surface prior to the Moon-forming giant impact. As a result, the volatiles would have been

susceptible to loss through atmospheric blow-off during the Moon-forming giant impact.

Multiple atmospheric loss and magma ocean outgassing episodes are compatible with the

He and Ne abundances inferred for the present-day mantle, although these abundances are

poorly known (see supplementary material). However, the atmospheric loss episodes, which

are necessary to explain 3He/22Ne fractionation during magma ocean outgassing, may also

provide explanations for other curious features of the terrestrial volatile budget.

The combined silicate mantle and exosphere of the Earth has a low C/H ratio and ex-

tremely low N/H ratio compared to CI chondrites (Fig. 2.8; Halliday, 2013, Hirschmann and

Dasgupta, 2009 and Marty, 1995), which is surprising considering the Earth’s chondritic-like

C, H, and N isotopic ratios (e.g., Alexander et al., 2012 and Marty, 2012). The depletion of carbon has been linked to atmospheric loss or to partitioning of C into the core (Hirschmann and Dasgupta, 2009). Likewise, Marty (2012) argued that nitrogen depletion is due to seques- tration of N in the core. However, the depletion of N by core formation is unlikely because it metal−silicate ≤ would be accompanied by a significantly greater depletion of C; DC 10 (Kadik metal−silicate et al., 2011), whereas DC may be >1000 (Dasgupta et al., 2013). We suggest that the observed moderate depletion in C and extreme depletion in N can be explained if the

Earth had a water ocean prior to the last giant impact. The presence of liquid water on an

accreting Earth is likely if the time between giant impacts is >107 years (Elkins-Tanton, 2008

and Zahnle et al., 2007). A giant impact would fractionate the C/H and N/H ratios as it

would preferentially remove the atmosphere compared to the ocean (Genda and Abe, 2005).

58 Figure 2.8: Relative terrestrial abundances of C, N, H, and halogens. The relative depletions of C and N with respect to H can be explained by atmospheric loss during a giant impact if H is condensed as a water ocean as atmosphere would be lost in preference to liquid water. The greater depletion of N could reflect some C retention as bicarbonate and carbonate ions in the ocean and/or carbonated crust. Thefigure also illustrates the relative depletion of Cl and Br with respect to F, a surprising feature of the terrestrial volatile pattern. At least two episodes of magma ocean outgassing, as inferred from the 3He/22Ne data, would have outgassed Cl and Br and concentrated them in the exosphere prior to the last giant impact. The higher solubility of F in magmas would cause F to be preferentially retained in the mantle. Loss of the atmosphere or partial loss of the hydrosphere during a giant impact may explain the relative depletion Cl and Br compared to F. Terrestrial and chondritic C, N, and H abundances from Halliday (2013); terrestrial halogen abundances from McDonough (2003); chondritic halogen abundances from Lodders (2003).

Because C can form bicarbonate and carbonate ions, a significantly larger proportion ofC would be in the ocean (or in the crust) compared to N. Therefore, preferential loss of the atmosphere would lead to a large decrease in the N/H ratio compared to a modest decrease in the C/H ratio (Fig. 2.8).

An atmospheric loss event that also involved partial loss of an ocean could explain why the heavy halogens (Cl, Br) are depleted in the Earth relative to fluorine and other highly volatile elements (Fig. 2.8; McDonough, 2003 and Sharp and Draper, 2013). This is another peculiar aspect of terrestrial volatile abundances (Marty, 2012), especially considering that the Earth has a chondritic Cl isotope ratio (Sharp and Draper, 2013). F is highly soluble in magmas compared to Cl and Br (e.g. molar SF/SCl =~4 where S is the melt/vapor solubility coefficient; Aiuppa, 2009). Consequently, during magma ocean outgassing Cl and Brwould

be outgassed while F would be preferentially retained in the magma ocean. Removal of the

atmosphere or partial removal of an ocean during a giant impact could, therefore, explain the

depletion of the heavy halogens on the Earth with respect to F.

59 We argue that the relative proportions of major volatiles (H, C, N, halogens) on Earth record the violent events during accretion. Thus, most of Earth’s water, and possibly the other major volatiles, were acquired prior to and during the giant impact phase of terrestrial accretion (also see Halliday, 2013 and Saal et al., 2013). The observed fractionations in the major volatiles (Fig. 2.8) could have been larger in the immediate aftermath of the Moon- forming giant impact, as the late veneer also contributed volatiles to Earth (e.g., Albarède,

2009 and Wänke, 1981). However, the late veneer contribution was not sufficiently large to overprint the volatile characteristics acquired during the main stages of Earth’s accretion

(Halliday, 2013).

2.6.2 Preservation of early-formed heterogeneity and depth of the magma oceans

The observation of different 3He/22Ne ratios in the OIB and MORB mantle reservoirs requires the formation and preservation of two distinct mantle domains during accretion. This implies that the later magma oceans, including the one created by the Moon-forming giant impact, did not homogenize the whole mantle. Because the timescale for turnover of a tur- bulently convecting magma ocean may be as short as a few weeks (Elkins-Tanton, 2008 and

Pahlevan and Stevenson, 2007), a magma ocean would be expected to be chemically homogeneous. The deep mantle could preserve a low 3He/22Ne ratio if the later giant impacts did not melt the whole mantle (Fig. 2.6b, c). Regions in the deep mantle could escape melting because the distribution of energy during a giant impact is heterogeneous (Solomatov, 2000).

Along with 3He/22Ne ratios, the differences in 20Ne/22Ne (Mukhopadhyay, 2012 and Yokochi

and Marty, 2004) and 129Xe/130Xe ratios between the deeper plume mantle and shallower de-

pleted MORB mantle (Mukhopadhyay, 2012, Parai et al., 2012, Pető et al., 2013 and Tucker

et al., 2012) support the notion that the mantle was never completely homogenized during or

since Earth’s accretion.

60 2.6.3 Formation of the LLSVPs

Large Low Shear-Velocity Provinces (LLSVPs), two large antipodal seismically imaged structures at the base of the mantle, have been linked to OIB volcanism (e.g., Burke et al., 2008,

Thorne et al., 2004 and Wen and Anderson, 1997). LLSVPs are often associated with crystal fractionation from a basal magma ocean (e.g., Coltice et al., 2011 and Labrosse et al.,

2007) and Coltice et al. (2011) have suggested that the primitive He and Ne signature in

OIBs reflects the signature of a basal magma ocean. However, the primitive reservoir with a low 3He/22Ne ratio cannot have its origin in a basal magma ocean produced by the last

giant impact (the Moon-forming giant impact) because that magma ocean must have pro-

duced the high 3He/22Ne ratio now sampled in the depleted mantle (Section 2.6.2). A basal

magma ocean sequestering low 3He/22Ne ratios in the deep mantle could have formed from a previous whole-mantle magma ocean. In this case, subsequent giant impacts including the

Moon-forming giant impact must not have disrupted the basal magma ocean, whose lifetime is >1 Gyr (Labrosse et al., 2007), or else this reservoir of primitive material would not remain intact. In summary, LLSVPs may have formed as crystallization products of previous magma oceans and survived the Moon-forming giant impact. Otherwise, their formation is unrelated to magma oceans.

2.7 Conclusions

3 22 We observe He/ Nem ratios in equatorial Atlantic MORBs to be correlated with Ne, Pb, and Nd isotopic ratios, which allows us to constrain the depleted mantle 3He/22Ne ratio to be

≥10. In contrast, the deep primitive reservoir sampled by plumes has a ratio of ~2.3 to 3. We

find that processes associated with the long-term plate tectonic cycle, such as partial melting

and recycling of plates, are incapable of changing the mantle 3He/22Ne ratio appreciably in

4.5 Ga.

Solubility-controlled fractionation associated with ingassing of a gravitationally captured

nebular atmosphere on the proto-Earth raised the mantle 3He/22Ne ratio from a primordial

61 value of ≤1.5 to that sampled in primitive plumes. Atmospheric loss and magma ocean outgassing associated with at least two separate giant impacts subsequently increased the mantle

3He/22Ne ratio to ≥10. These giant impacts, including the Moon-forming impact, likely did not melt the whole mantle or else the low 3He/22Ne ratios sampled in primitive plumes could

not be preserved. Atmospheric loss and magma ocean outgassing also provide an explana-

tion for the lower than chondritic C/H and N/H ratios as well as Cl/F and Br/F ratios in the

Earth.

Acknowledgments

We thank Marc Hirschmann, Simon Lock, Rita Parai, and Sarah Stewart for helpful discus-

sions, and editor Tim Elliott and two anonymous reviewers for helpful comments. This work

was supported by NSF grant OCE 0929193.

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70 3 Kinetic controls on volatile fluxes at mid-ocean ridges and implications for the mantle carbon flux

Jonathan M. Tucker1, Sujoy Mukhopadhyay2, Helge M. Gonnermann3 1 Harvard University 2 University of California, Davis

3 Rice University

71 Abstract

The flux of carbon from the mantle is the basis for Earth’s long-term climate stabilityand the biogeochemical carbon cycle. This flux can be quantified from the mid-ocean ridge 3He flux and measurements 3of C/ He ratios in MORBs. However, C/3He and other volatile ratios in MORBs may be strongly influenced by degassing. One widely applied methodology tore- construct pre-degassing C/3He ratios uses an equilibrium degassing model based on measured

4He*/40Ar* ratios (where * refers to the radiogenic abundance of an isotope). This methodology has established the ‘canonical’ upper mantle C/3He ratio of 2 × 109 and corresponding

13 mid-ocean ridge CO2 flux of 5 × 10 g/year. However, other recent estimates independent of degassing corrections have estimated significantly higher CO2 fluxes. Using global MORB data, we demonstrate that 4He*/21Ne*, 4He*/40Ar*, and

4 136 He*/ Xe*U ratios do not simultaneously conform to any equilibrium degassing model, questioning the validity of these models for correcting ratios involving C. We argue that kinetic effects prevent slowly diffusing gases such as Ar and Xe from reaching their equilibrium distributions between melt and vesicles. We present a new simple model of disequilibrium degassing that can quantitatively reconstruct pre-degassing volatile contents. Application of our

3 model suggests that pre-degassing MORB C/ He ratios, and consequently the mantle CO2 flux, may be higher than the canonical ratio by more than a factor of 2. Therefore, consideration of kinetic fractionation during degassing can bring degassing-based estimates of the mid-ocean ridge CO2 flux into accord with estimates independent of degassing.

72 3.1 Introduction

The abundances of volatile elements such as carbon, nitrogen, hydrogen, and the noble gases

place critical constraints on the provenance and timing of delivery of Earth’s volatiles (e.g.

Wanke, 1981; Morbidelli et al., 2000; Marty, 2012; Bergin et al., 2015). The flux of volatiles

between the mantle and surface also controls climate stability and the habitability of Earth’s

surface (e.g. Sleep and Zahnle, 2001; Hayes and Waldbauer, 2006). However, the mantle

volatile budgets, fluxes, and distribution remain highly uncertain.

The mantle carbon content and flux out of mid-ocean ridges, for example, is difficult to

ascertain from measurements of oceanic basalts because carbon may degas to a large extent

during volcanism. This has resulted in a plethora of indirect methods and proxies used to

estimate these quantities or the reliance on individual samples or small sample suites (e.g.,

Javoy and Pineau, 1991; Marty, 2012; Hirschmann and Dasgupta, 2009; Halliday, 2013;

Dauphas and Morbidelli, 2014; Michael and Graham 2015; Saal et al., 2002; Shaw et al.,

2010). These estimates vary by an order of magnitude, rendering volatile abundances the

least constrained aspect of Earth’s composition. Reconciling these diverse estimates, as well

as studying the variation in volatile content between different samples, requires understand-

ing how magmatic degassing affects volatile contents and ratios measured in individual sam-

ples.

The noble gases are ideal tracers of degassing processes because physical properties are

generally governed by size or mass, so degassing should affect them in systematic, predictable

ways. But more importantly, the ratios of the radiogenic noble gases 4He*, 21Ne*, 40Ar*, and

136 Xe*U (where ’*’ refers to the radiogenic abundance, that is, free of air contamination, recycled air, or primordial abundance; ‘U’ refers to the 136Xe* deriving from spontaneous 238U fission as opposed to 244Pu fission), are produced at known rates in the mantle, resulting in constant mantle ratios (Ozima and Podosek, 1983; Jambon et al., 1985; Yatsevich and Honda

1997; Leya and Wieler, 1999). Therefore, deviations of measured radiogenic noble gas ratios from so-called mantle “production ratios” may be used to assess and quantitatively correct

73 other volatile element ratios for the effects of degassing. The most widely used ratio forthis purpose is the ratio of radiogenic He to radiogenic Ar. Because Ar is less soluble than He in magmas, the residual magmatic 4He*/40Ar* ratio will increase during equilibrium degassing

(e.g. Jambon et al., 1985). Consequently, values close to the mantle production ratio indicate relatively undegassed samples whereas high values indicate extensively degassed samples (e.g.,

Marty, 1995; Marty and Tolstikhin, 1998; Burnard et al., 2002).

Because the parent elements K, U, and Th have different half-lives, the mantle 4He*/40Ar* production ratio is a function of the residence time as well as the mantle K/U and Th/U ratios. Using the average MORB K/U and Th/U of Gale et al. (2013), the mantle 4He*/40Ar* production ratio ranges from an “instantaneous” value of 4.4 to a value of 1.7 for a residence time equal to the age of the Earth. In this paper, we will assume a value of 2.5 but note that using a different value has little effect as measured 4He*/40Ar* ratios vary by two orders of magnitude.

4 21 4 136 In contrast, the mantle He*/ Ne* and He*/ Xe*U production ratios are very weak functions of composition and time. In this paper we will use a 4He*/21Ne* production ratio of 2.2 × 107 (Yatsevich and Honda, 1997). However, calculating 21Ne* requires relatively precise Ne isotopic ratios and abundances with low levels of atmospheric contamination (see supplemental material). This calculation is possible for fewer samples than 4He*/40Ar*, and sub-

sequent relative uncertainties on 4He*/21Ne* in samples are much larger than 4He*/40Ar*,

despite a more constant mantle production ratio. We calculate 4He*/21Ne* values by the

methodology introduced by Honda et al. (1991) and summarized by Graham (2002) and the

supplemental material.

136 136 Xe*U is the most challenging because Xe contributions from U fission, Pu fission, recycled air, air contamination, and primordial must be deconvolved, which is possible only for

a handful of MORB samples (see compilation in Parai and Mukhopadhyay, 2015). For sim-

plicity, we will use the approximate calculation of 136Xe* from Graham (2002) with a factor

74 discriminating U- from Pu-derived 136Xe*:

( ) 136 ∗ 130 × 136 130 −136 130 ×136 ∗ XeU = Xemeas Xe/ Xemeas Xe/ Xeair XeU/(U+Pu) (3.1)

On average, around 90% of the mantle-derived Xe in oceanic basalts is recycled atmosphere

(Parai and Mukhopadhyay, 2015), whereas this formulation assumes that all measured 130Xe is atmospheric. However, it does not distinguish between recycled atmosphere and post- eruptive contamination, assuming they carry the same isotope ratio. Furthermore, the fraction of the total 136Xe* that is U-derived in MORBs is on average 0.69±0.11 (Parai and

Mukhopadhyay, 2015), so we assume a constant fraction of 0.7, and note that uncertainties

136 of 10-20% in our approximate calculation of Xe*U have no effect on our primary conclu-

4 136 −8 sions. We use a mantle He*/ Xe*U production ratio of 3.5 × 10 (calculated using the fission yield of Ragettli et al., 1994).

One special volatile-rich MORB sample called “popping rock” (2ΠD43) has radiogenic elemental ratios thought to resemble the mantle production ratios of

4 21 40 136 He*/ Ne*/ Ar*/ Xe*U, and is thought not to have lost bubbles. Consequently, its nonradiogenic noble gas ratios e.g. 3He/22Ne/36Ar/130Xe and C/3He are often taken as representative of the upper mantle (Staudacher et al., 1989; Sarda and Graham, 1990; Javoy and

Pineau, 1991; Moreira et al., 1998; Moreira and Sarda, 2000). However, this sample is extremely enriched in trace elements (e.g. K2O/TiO2=0.4, La/Sm=3, Bougault et al. 1988) and has an unusually high vesicularity, so the extent to which its noble gas composition is representative of the upper mantle is unclear (e.g. Saal et al., 2002). Because undegassed samples like popping rock are rare, reliance on them to study the mantle volatile distributions is extremely difficult.

In this study, we will develop the noble gases as passive tracers of the degassing process at mid-ocean ridges for the purpose of understanding the elemental fractionations that occur during degassing. We will show that simultaneous consideration of multiple systems such as

4He*/21Ne* and 4He*/40Ar* provide much more stringent constraints on the degassing mech-

75 anisms than 4He*/40Ar* alone. Importantly, we will demonstrate that the widely employed

equilibrium Rayleigh distillation model, or any solubility-based equilibrium model, cannot

4 21 40 136 explain the He*/ Ne*/ Ar*/ Xe*U composition of MORBs and should not be used for correcting ratios such as C/3He that are perturbed due to magmatic degassing. We will argue that disequilibrium in the form of kinetic fractionation is responsible for diminishing the fractionation of ratios such as 4He*/40Ar* from that expected by solubility alone. Finally, we will

present a new simple model of disequilibrium degassing to demonstrate how initial magmatic

noble gas and C abundances may be quantitatively reconstructed from measured data.

3.2 Equilibrium degassing models do not explain MORB data

3.2.1 Introduction to Rayleigh distillation

The composition of volatile elements in MORB glasses is thought to be controlled by transfer of dissolved volatiles from the magma to CO2 vesicles and the loss of these vesicles (e.g. Jambon et al., 1985; Gerlach, 1989; Sarda and Graham, 1990). Given sufficient time for equi-

libration, volatiles partition between melt and bubbles according to their solubility or Henry’s

constant k. The magmatic solubility of noble gases decreases with increasing size such that

kHe > kNe > kAr > kXe (Jambon et al., 1986; Lux, 1987). Because the larger noble gases are more insoluble, equilibrium degassing causes ratios such as He/Ne, He/Ar, and He/Xe to increase in the residual magma; He/Xe increases the most and He/Ne the least.

If bubbles are lost continuously as they form, the evolution of the magmatic composition is described mathematically by a Rayleigh distillation, perhaps the most widely used degassing model to explain the C isotopic composition (Pineau et al., 1976; Javoy et al., 1982; Pineau and Javoy, 1983; Cartigny et al., 2008) and volatile elemental composition (Sarda and Gra- ham, 1990; Marty, 1995; Marty and Tolstikhin, 1998; Burnard, 1999; Marty and Zimmer- mann, 1999; Cartigny et al., 2001; Burnard et al., 2002; Colin et al., 2013) of MORBs. Us- ing a Rayleigh distillation model framework, the measured 4He*/40Ar* ratio can be used to quantitatively correct any other volatile element ratio for degassing, where the fractionation

76 factor is related simply to equilibrium solubilities. A full derivation is given for reference in the supplement.

Because of the exponential dependence on the fractionation factor, the composition of a magma evolving by equilibrium Rayleigh distillation is a straight line path in a log-log plot of any elemental abundance or ratio, and the slope is related to the relative solubilities. The line must also pass through the initial composition—the mantle production ratios in the case of radiogenic noble gas ratios. The instantaneous vesicle compositions follow a parallel but offset path.

3.2.2 MORB data fail tests of equilibrium models

4 21 40 136 The combined He*- Ne*- Ar*- Xe*U systems provide stringent independent tests of the equilibrium Rayleigh distillation model because the initial composition is fixed by the mantle production ratios and slope of degassing path (in log-log space) by the solubilities. Fig-

4 21 4 40 4 136 ure 3.1 shows literature He*/ Ne*, He*/ Ar*, and He*/ Xe*U data along with the compositional evolution of a magma and instantaneous vesicle compositions by equilibrium

4 21 40 136 Rayleigh distillation. By using only He*- Ne*- Ar*- Xe*U, we have not assumed any- thing about the composition of the unradiogenic isotopes in the mantle (e.g. 3He/22Ne). Fig- ure 3.1 clearly demonstrates that equilibrium Rayleigh distillation alone cannot explain most of the data, as many points fall significantly off the fixed model degassing lines. This is especially true for ratios involving Xe (Figure 3.1c). Rayleigh distillation is the extreme case of

multi-step open system degassing where the step sizes are infinitesimal. If the steps are finite

or discrete, the degassing path follows a similar path that travels slightly closer to the data

(Figure 3.1b). However, discrete multi-step paths still cannot pass through the majority of the data.

A possible explanation for most of the data not following the equilibrium degassing paths could be that true noble gas solubilities are different from experimentally determined values.

We can explore what values are needed to explain the data, a possibility raised by Burnard

(1999) and Moreira and Sarda (2000). A simple way to ascertain the solubilities required to

77 Figure 3.1: (a) 4He*/40Ar* vs. 4He*/21Ne* in literature fusion (orange, n=67) and crushing (blue, n=54) 4 40 4 21 4 21 4 136 data. (b) He*/ Ar* vs. He*/ Ne* (n=35) and (c) He*/ Ne* vs. He*/ Xe*U for crushing data from Tucker et al. (2012), Parai et al. (2012), and Peto (2014) (n=33). Error bars reflect propagated uncertainty from reported elemental abundances. The yellow point in panel (a) is the sample AMK3376, high- lighted below. Also plotted are Rayleigh distillation trajectories for magmatic (green) and instantaneous vesicle (red) compositions using the solubilities of Jambon et al. (1986), and open-system degassing paths with discrete vesicularities of 0.1%, 1%, and 10% per step in panel (b). Much of the data plot far from the equilibrium paths indicating the prevalence of some process other than equilibrium degassing. Data in (a) from Hiyagon et al., 1992; Moreira et al., 1995; 1996; 2011; Niedermann et al., 1997; Niedermann and Bach, 1998; Sarda et al., 2000; Burnard et al., 2002; 2003; Moreira and Allegre, 2002; Stroncik and Nider- mann, 2007; 2016; Raquin et al., 2009; Colin et al., 2011; Furi et al., 2011; and Barry and Hilton, 2016.

78 explain the data by an equilibrium model is to notice that many samples in Figures 3.1a and b plot close to a hypothetical line where the extent of He/Ne fractionation equals the extent of He/Ar fractionation; a 1:1 line originating at the production ratios. Similarly, in Figure

3.1c, an equal extent of He/Ne and He/Xe fractionation approximately traces the boundary

of the data. Equal extents of fractionation in an equilibrium Rayleigh distillation are possi-

ble only if the He/Ne, He/Ar, and He/Xe solubility ratios are equal. This possibility is ex-

tremely unlikely given the preponderance of experimental data, which consistently finds Ne

at least 4× and 10× more soluble than Ar and Xe (see section 3.3.4). Noble gas solubilities

can change as functions of composition, pressure, and temperature, however the ranges in

these parameters are too limited among most MORBs to significantly change solubility ra-

tios (e.g. Yamamoto and Burnard, 2005). We also note that changing only the He solubil-

ity, per the suggestion of Moreira and Sarda (2000), cannot change the slope significantly

enough to intersect the data. Therefore, while some of the data could be fit with an equilib-

rium Rayleigh distillation model, we argue that a process other than equilibrium Rayleigh

distillation must be required to explain most of the elemental data.

3.2.3 Degassing paths from individual vesicles

One of the most powerful ways to investigate degassing is by analyzing compositions of individual vesicles that preserve a degassing path within a sample. Some such samples show ex-

4 40 ceptionally coherent He- Ar*-CO2 variations, forming linear correlations in log-log space interpreted as equilibrium Rayleigh distillation trajectories (Burnard, 1999; Colin et al., 2013).

We now investigate the conundrum that bulk crushing and fusion data rule out equilibrium

Rayleigh distillation (Figure 3.1), yet individual vesicle data appear to support it.

4 21 40 4 40 Unlike in He*- Ne*- Ar* space, the initial composition in He- Ar*-CO2 space is not fixed so the same strict constraints on the degassing path are not available. However,the

slope of the degassing path still depends only on the solubility ratios. Therefore one test of

the equilibrium Rayleigh distillation model is to solve for the apparent CO2/Ar or CO2/He solubility ratio and compare it to experimental values. In the single sample of Burnard

79 (1999) that could be fit in this way (AMK3376), the empirical He/CO2 solubility ratio was 5, whereas the experimentally determined ratio is ~2 (e.g. Jambon et al., 1986; Lux, 1987;

Pan et al., 1991). In three samples, Colin et al. (2013) found empirical He/CO2 solubility ratios of 1.06, 1.45, and 1.73, up to a factor of 2 lower than experimental values, but with 1σ

uncertainties close to 100%. Therefore, while the individual vesicle data appear to preserve

degassing paths suggestive of an equilibrium volatile loss process, the disagreement between

the experimentally determined and empirical He/CO2 solubility ratios (Burnard, 1999) and large uncertainties in fitted solubilities (Colin et al., 2013) leave room for the possibility that

processes other than equilibrium Rayleigh distillation are operating.

As with the data in Figure 3.1, another critical test of the equilibrium Rayleigh distillation model is whether 4He*/21Ne* and 4He*/40Ar* ratios simultaneously conform to the model.

Unfortunately, Ne data are not available for these vesicles. However, Ne data are available

from step-crushing for one of the samples, AMK3376 (Burnard, 1999; Burnard et al., 2003).

For this sample, both the step-crushing and individual vesicle measurements yield the same

bulk 4He*/40Ar* values around 81. For a value of 8, the corresponding vesicular 4He*/21Ne* predicted from a Rayleigh distillation is 1.2 × 107, and residual dissolved 4He*/21Ne* is 2.6 ×

107 (assuming solubilities of Jambon et al., 1986). However, the measured 4He*/21Ne* is ~5×

107, significantly higher than either of these predicted values. In fact, this sample plotswith the majority of the data away from the equilibrium Rayleigh distillation lines (Figure 3.1a).

4 40 We therefore conclude that while the He- Ar*-CO2 data in individual vesicles may appear suggestive of equilibrium Rayleigh distillation, it can be ruled out in the case of AMK3376 on

the basis of the empirically derived solubility ratios and misfit of Ne data. The other samples

where individual vesicles were analyzed do not have Ne data and for these samples we cannot

rule out equilibrium degassing. However, the very large uncertainties in derived solubility

ratios allow for alternative interpretations. Overall, we suggest that tight constraints on the

degassing path afforded by 4He*/21Ne* makes acquisition of Ne data on single vesicles, or

at the least from bulk crushing of the same sample, a high priority to understand degassing

1We believe the units of the carbon data reported in Table 2a of Burnard et al. (2003) may be misreported; for example they imply C/3He ratios of ~106.

80 pathways.

3.3 Kinetic fractionation during degassing

We have demonstrated that equilibrium or solubility-based degassing models do not fit the

MORB noble gas data when multiple noble gas isotope ratios are considered. In the following

section, we argue that the noble gases are kinetically inhibited from diffusing into vesicles,

resulting in magmatic retention of some volatiles in quantities greater than their equilibrium

solubility. A simple model of this disequilibrium degassing can indeed explain the noble gas

data and be used to predict initial magmatic volatile concentrations.

3.3.1 Evidence for kinetic fractionation

Disequilibrium, in the form of kinetic fraction, has been argued to affect noble gas elemental ratios in OIBs (Hanyu et al., 2005; Gonnermann and Mukhopadhyay, 2007; Weston et al., 2015) and may also be important in MORBs (Burnard et al., 2003; Aubaud et al., 2004;

Paonita and Martelli, 2007; Gonnermann and Mukhopadhyay, 2007). The noble gases degas by diffusion into vesicles dominated 2by aCO vapor phase, so rapid vesicle ascent or low extents of vesicularity may hinder the ability of slowly diffusing species to partition into the

vapor.

It is generally thought that diffusivities of noble gases decrease with size (Lux, 1987; Guil-

lot and Sator, 2012), so diffusion-limited degassing will fractionate noble gases in the oppo-

site sense of solubility, as the larger noble gases do not diffuse as quickly into vesicles. In

principle, degassing is the combination of the solubility-based and diffusivity-based effects;

a small extent of disequilibrium might allow a ratio such as He/Ar to rise but not as much

as it would during equilibrium degassing. A large extent of disequilibrium could cancel out

the fractionation generated through solubilities or even reverse it such that the He/Ar ratio

remains constant or even decreases.

Diffusive fractionation therefore may explain why the MORB data tend to fallbelow

4 21 4 40 and to the right of equilibrium degassing paths in log10 He*/ Ne* vs He*/ Ar* or

81 4 136 He*/ Xe*U space (Figure 3.1). Because of their lower diffusivities, Ar and Xe would be preferentially retained in the magma in excess of their solubility, resulting in low He/Ar and

He/Xe ratios compared to He/Ne.

To quantitatively illustrate the potential influence of kinetic effects, Figure 3.2 shows a plot of a parameter θ, introduced into a degassing context by Gonnermann and Mukhopadhyay

(2007): ∑∞ 8 1 2 2 2 θ = e−D(2j+1) π (t/4a ) (3.2) π2 (2j + 1)2 j=0

(Equation 4.18 of Crank, 1975). θ is the ratio of the amount of a volatile species that diffuses

across a boundary (i.e. into a bubble) within a time t over the amount that would diffuse in infinite time. It can therefore be thought of as the fractional amount of disequilibrium. θ is a function of the magmatic diffusivity D of a volatile species (which itself may be a function of parameters such as pressure, temperature, and composition) as well as the characteristic diffusive lengthscale a and timescale t, which we will refer to jointly as the characteristic diffusion timescale of t/a2. If D and/or t/a2 are sufficiently large, θ approaches 0, indicating approach to equilibrium conditions, whereas if D and/or t/a2 are sufficiently small, θ approaches 1 and the volatile species is prevented from diffusing into the vapor. Figure 3.2 thus demonstrates that the different volatiles may experience different extents of disequilibrium based on their diffusivity. For example, He might achieve equilibrium partitioning, but

Xe could be nearly quantitatively retained in the melt, despite its lower solubility. And depending on the diffusivities, t/a2 must be extremely large (>~1011 s/m2) for all species to

experience purely equilibrium conditions.

The potential for disequilibrium to lessen or reverse the fractionation caused by solubil-

ity represents a significant caveat to using ratios such as 4He*/40Ar* to quantify the extent of degassing (Aubaud et al., 2004; Paonita and Martelli, 2007; Weston et al., 2015). During disequilibrium degassing, the magmatic 4He*/40Ar* ratio could stay relatively constant even while a significant amount of volatile loss occurs. A low measured 4He*/40Ar* could therefore

be misinterpreted as representing a low extent of degassing. For example, some samples have

82 Figure 3.2: θ parameter, the fractional extent of disequilibrium, as a function of characteristic degassing timescale and diffusivity. For a given sample, the characteristic timescale is constant for all volatiles (example cyan line) but each volatile has a different diffusivity (red, yellow lines). A volatile with high diffusivity such as He could achieve its equilibrium distribution, whereas a volatile such as Ar or C could be significantly affected by disequilibrium. This also demonstrates how a ratio such as He/Ar might bemuchmore affected by disequilibrium than He/Ne. The volatile diffusivities shown here are schematic only.

4He*/40Ar* < 5, very close to the mantle production ratio, yet 4He*/21Ne* > 6 × 107 (Figure

3.2).

3.3.2 A new disequilibrium degassing model

We now present a new model of disequilibrium degassing that can fit the MORB data with a minimum of assumptions. The primary purpose of this model is to demonstrate the importance of kinetic fractionation during degassing. We will use the degassing model to quantitatively predict initial (undegassed) magmatic volatile contents with the caveat that these predictions are subject to uncertainty in the physical parameters used.

Critically, this model uses the parameter θ to control the extent of disequilibrium of each

volatile species in a sample. Each sample has a common characteristic degassing timescale

but each volatile species has its own diffusivity and consequently θ value. We insert θ as a

83 “modification” to the solubility in a Henry’s law formulation:

Ci/Pi = ki/(1 − θi) (3.3)

where Ci, Pi, and ki are the dissolved concentration, partial pressure in the vapor phase, and solubility of volatile species i. As θ approaches 0, equation 3.3 becomes Henry’s law, and as

θ approaches 1, the partial pressure must approach 0, meaning degassing of the species does not occur. Because solubility is being modified by the factor (1-θ), we may refer to a modi-

fied or “effective” solubility k′ as k/(1 − θ).

For the demonstration purposes of this paper, we assume one of the simplest possible

degassing formulations where degassing proceeds by continuous open-system steps. This

model formulation reduces to a Rayleigh distillation but using effective solubilities. (A full

derivation is given in the supplement.) The model can then be thought of as “disequilibrium

Rayleigh distillation” in contrast to the equilibrium model often used. In analogy to equilib-

rium Rayleigh distillation, the magmatic ratio of any two species x and y can be written as

− ′ × (1 αx,y) (x/y) = (x/y)0 (x/x)0 (3.4) where ′ ′ ′ × − − αx,y = kx/ky (1 θy) / (1 θx) . (3.5)

And as with equilibrium Rayleigh distillation, any volatile element ratio composition of the magma (subscript m) and instantaneous coexisting vesicles (subscript v) are related by the

effective solubility ratio: ( ) ′ ′ (x/y)v = (x/y)m / kx/ky (3.6)

In order to study the effect of kinetic fractionation during mid-ocean ridge degassing iniso- lation, we attempt to introduce as few additional parameters as possible into the degassing framework. For example, the characteristic degassing timescale t/a2 is a complicated function of the dynamics of vesiculation and eruption, as well as initial CO2 content. But a full

84 bubble growth model requires a plethora of additional physical parameters (e.g. Paonita and

Martelli, 2007), so we instead assume the characteristic degassing timescale is a constant but free parameter for a given sample. Furthermore, we assume the solubility ratios and diffusivities are constant, while acknowledging that these physical parameters may evolve as the magma composition, temperature, and pressure evolve (e.g. Yamamoto and Burnard, 2005;

Weston et al., 2015). Therefore if the solubility ratios and diffusivities are specified, the only model variables are the characteristic degassing timescale and extent of volatile loss.

In addition to the minimal number of parameters, there are other advantages of a simple model. For example, the simple analytical formulation permits many rapid calculations of the same model with different parameters. Although we assume the solubility and diffusivity values are constant, these values are known to different degrees of certainty (section 3.3.4) so we may easily explore the effect of varying these parameters on the degassing paths. And importantly, even considering these uncertainties, the simple model will be able to predict reasonable initial magmatic volatile contents (section 3.4.2).

Despite the similar treatment of disequilibrium, this degassing model is quite different than those of Gonnermann and Mukhopadhyay (2007) and Weston et al. (2015). The most major difference is that degassing here proceeds in continuous infinitesimal open-system steps, as opposed to a specified or variable number of closed or open-system steps. We therefore do not need to compute volatile fugacities at each step, which was the main point of difference between the two aforementioned models. It also means that there is no explicit relationship between the initial CO2 content and extent of noble gas degassing—the extent of noble gas degassing is treated as a free parameter. This simplification does not allow us reconstruct initial CO2 contents from noble gas data alone as in the aforementioned models; we also require measured CO2 contents as a constraint.

3.3.3 Example disequilibrium degassing paths

Figure 3.3 shows degassing paths (blue lines) calculated using the above model, where the distance along the path is related to the amount of helium loss (grey lines). In log-log space,

85 Table 3.1: Standard solubility and diffusivity values used in calculations unless otherwise noted

Quantity Value −5 a kHe 56 × 10 ccSTP/g/bar −5 a kNe 25 × 10 ccSTP/g/bar −5 a kAr 5.9 × 10 ccSTP/g/bar −5 b kC 28 × 10 ccSTP/g/bar 2 c log10 DHe −8.5 m /s 2 c log10 DNe −9.0 m /s 2 c log10 DAr −10.5 m /s 2 d log10 DC −9.7 m /s a Jambon et al. (1986) b Pan et al. (1991) c Intermediate to Lux (1987), Nowak et al. (2004), Guillot and Sator (2012) d See §3.5.2 these paths are straight lines. The slope of the path is related to the characteristic degassing timescale: at sufficiently large timescales, θ values for all volatiles approach 0 and degassing approaches the equilibrium Rayleigh distillation; and as the timescale decreases, the extent of kinetic fractionation increases such that the degassing path passes through samples more distant from the equilibrium path. The shallowing of slopes with timescale results from the

He/Ar ratio being more susceptible to kinetic fractionation than He/Ne. Figure 3.3 therefore demonstrates how the characteristic degassing timescale and extent of volatile loss can be determined for any given sample.

However, Figure 3.3 also shows that the choice of parameters affects the degassing paths.

Panels a and b use the solubilities of Jambon et al. (1986) whereas panels c and d use the

−8.5 −9 tholeiite solubilities of Lux (1987). Panels a and c use DHe = 10 , DNe = 10 , DAr =

−10.5 2 −9.5 10 m /s (Table 3.1), while in panels b and d DNe is changed to 10 . Furthermore, these two panels demonstrate that not every combination of parameters is capable of produc-

ing degassing paths that can fit all samples. It is therefore worthwhile to investigate howwell

constrained noble gas solubilities and diffusivities are.

86 Figure 3.3: Example disequilibrium degassing paths (blue) with variable characteristic degassing timescales (blue text). At large timescales the model approaches equilibrium Rayleigh distillation. The grey lines are increments of constant He loss, or the extent of degassing along a path. The black line at He/He0 = 0.02 is for clarity. Black data points are those in Figure 3.1b. The stronger kinetic retention of Ar compared to He and Ne explains why the paths and samples fall below and to the right of the equilibrium path. The solubilities used in panels (a) and (b) are from Jambon et al. (1986), and in (c) and (d) from Lux (1987). −9.5 The diffusivities used are from Table 3.1 except in panels (b) and(d), DNe has been changed to 10 . This demonstrates that not all parameter sets can fit each data point.

87 Figure 3.4: (a) Experimentally determined solubility of noble gases in tholeiitic basalts (downward triangle = Hayatsu and Waboso, 1985; star = Jambon et al., 1986; square = Lux, 1987; x = White et al., 1989; plus = Carroll and Stolper, 1993; circle = Guillot and Sator, 2012). Determinations in alkali basalts or other compositions are not shown to minimize compositional dependence, but those values are similar. (b) Noble gas and C diffusivities from Lux (1987; squares), Guillot and Sator (2011; circles), andNowak et al. (2004; upward triangles). Points plotted in (b) are individual determinations from which Arrhenius relationships may be derived. Colors in both panels are: blue = He; green = Ne; red = Ar; black = Xe; orange = C (total).

3.3.4 Noble gas solubility and diffusivity are highly uncertain

Figure 3.4a shows the experimental determinations of He, Ne, Ar, and Xe solubility that have been reported for tholeiitic basalts, the most relevant composition for the majority of

MORBs. Experiments on alkali basalts have also been performed (e.g. Hayatsu and Waboso,

1985; Lux, 1987; Iacono-Marziano et al., 2010), but in general overlap with the ranges observed in Figure 3.4a. Experiments at 1200 ◦C, close to MORB eruptive temperatures, are shown where possible, however, noble gas solubilities are generally not strong functions of magmatic temperature. For example, both Jambon et al. (1986) and Lux (1987) found that

He, Ne, Ar, and Xe solubilities were less than 20% higher at 1500 ◦C than 1300 ◦C, and the temperature dependence of solubility ratios would be even smaller. Among the experimental determinations shown in Figure 3.4a, He solubility experiments are the most consistent, varying only by ~10%. However, despite the restricted compositional and other experimental parameter ranges, the Ne, Ar, and Xe solubilities vary widely; by factors of around 2, 4, and

3, respectively.

88 There has only been one experimental determination of the suite of noble gas diffusivities in basaltic melt (Lux, 1987) and one determination from molecular dynamics calculations

(Guillot and Sator, 2012), shown in Figure 3.4b. Both sets predict that noble gas diffusivity increases systematically with size from He to Xe. The 1 bar values from Lux (1987) are all higher than the 20 kbar Guillot and Sator (2012) runs by a factor varying from 1.3 to 3.5

(when Guillot and Sator, 2012 is extrapolated assuming an Arrhenius relationship to 1350

◦C, the experimental temperature of Lux, 1987). The discrepancy between the values from

Guillot and Sator (2012) and Lux (1987) might be related to different pressures at which the determinations were made, provided noble gas diffusivities in basaltic magmas are affected by pressure. Also plotted in Figure 3.4b is the Ar diffusivity in a synthetic iron-free tholeiitic

composition at 5 kbar (Nowak et al., 2004). These experiments are factors of 20 and 30 lower

than Guillot and Sator (2012) and Lux (1987) at 1350 ◦C, and a factor of 50 lower than Guil- lot and Sator (2012) at 1200 ◦C, despite being intermediate in pressure. This may be a result of the composition which is fairly alkali rich and iron-free, but it highlights the order of magnitude level uncertainty in noble gas diffusivity, and the potentially strong and unquantified compositional dependence. We therefore emphasize the need for better experimental quan- tification of noble gas diffusivities in magmatic systems because of the significant effectthese quantities have on degassing paths (Figure 3.3).

For simplicity, unless otherwise stated, we will use a constant set of solubilities and dif-

fusivites, listed in Table 3.1. These values are chosen to be from the middle of the range of

reported values.

3.4 Reconstructing initial noble gas contents in individual samples

3.4.1 Methodology

We now describe a methodology by which our degassing model may be used in combination with measured data to reconstruct initial magmatic noble gas concentrations. For a given set of solubilities and diffusivities, the slope of the degassing path (in log-log space) depends only

89 on the characteristic degassing timescale. When radiogenic noble gases are used, the slope of the degassing path for a sample is defined by the initial composition of the mantle production ratios and the measured final composition. The fractional extent of volatile loss, x/x0

, can then be found from Equation 3.4, and the initial volatile content x0 from a measured concentration x. The extent of volatile loss for any other species y is related to species x by

rearranging Equation 3.4:

′ αx,y y/y0 = (x/x0) (3.7)

Once the characteristic degassing timescale and extent of volatile loss for one species (for example He as shown in Figure 3.3) is obtained for a sample, θ values and, hence, any initial

ratios and concentrations for any other volatile species can be calculated from Equations 3.4 and 3.7.

In the following applications to published data we will make one additional assumption, that upon quenching, nearly all the noble gases are transferred to vesicles during a final closed-system vesiculation step. Such an assumption is justified by the fact that noble gas elemental ratios measured by crushing and by fusion are not systematically offset (Figure

3.1a), and similar assumptions have been previously used (e.g. Burnard, 1999; Marty and

Tolstikhin, 1998; Marty and Zimmerman, 1999).

3.4.2 Reconstructed initial volatile contents

We now apply this methodology to predict the initial nonradiogenic noble gas concentrations to 33 of the samples shown in Figure 3.1b. Fitting a degassing path taking advantage of the known mantle production ratios requires 4He*-21Ne*-40Ar* data for the sample, which can be computed with reasonable accuracy even for samples with only modest radiogenic excesses over atmospheric contamination (e.g. Graham, 2002; see supplemental material). Initial 3He concentrations can then be reconstructed for any sample with a measured 3He concentration, however, reconstructing the nonradiogenic heavy noble gas concentrations requires correcting the measured concentrations for atmospheric contamination, which is especially difficult for

90 Figure 3.5: Predicted initial 3He and 22Ne contents of samples shown in Figure 3.1b (black dots). Mea- sured values are red dots, and dashed lines represent degassing paths. The grey bars show the 3He content of an average primary MORB magma derived from the oceanic 3He flux of 527±102 mol 3He/year (Bianchi et al., 2010), a crustal production rate of 21 km3/year (Crisp, 1984), and 3He/22Ne of 6 (Tucker et al. 2014). The overlap of the middle of our reconstructed values with the independent estimates demonstrates that our degassing model yields reasonable values for initial He and Ne contents in MORBs.

Ar and Xe.

Using the noble gas solubilities and diffusivities listed in Table 3.1, we find initial 3He and 22Ne concentrations that range over approximately two orders of magnitude (Figure 3 +2.7 × −10 22 3.5). The median initial magmatic He is 2.1−1.1 10 ccSTP/g and median initial Ne +2.3 × −11 is 2.9−1.6 10 (uncertainties represent the central 68.2% confidence intervals). The reconstructed initial 3He and 22Ne broadly form an array indicating that the initial magmatic

3He/22Ne ratios are less variable than the initial noble gas contents; reconstructed 3He/22Ne varies by a factor of ~2 among these samples.

For comparison, average undegassed magmatic noble gas contents can also be predicted independently of MORB measurements. Using the mantle 3He flux of ±527 102 mol/year

(Bianchi et al., 2010), crustal production rate of 21 km3/year (Crisp 1984) and 3He/22Ne of 6

(Tucker and Mukhopadhyay, 2014), an average initial magma has 2.1 ± 0.4 × 10−10 ccSTP/g

3He and 3.5 ± 0.7 × 10−11 ccSTP/g 22Ne. These estimates are plotted as grey bars in Figure

91 Figure 3.6: Histograms of median 3He and 22Ne concentrations of 33 samples in 107 trials. 57% of tri- −5 als could not fit all samples and are not included. Parameter ranges used are kHe from 56- 64 × 10 cc- 2 STP/g/bar; kNe from 19-38; kAr from 2.3-9.9; log10 DHe from -8.7 to -8.2 m /s; log10 DNe from -9.4 to -8.6; log10 DNe from -11.5 to -9.2. The discontinuous nature of the histograms results from the discrete parameter ranges used. The overall median and 68.3% ranges are shown, and are centered near the values found in Figure 3.5.

3.5 and overlap the median reconstructed compositions of the 33 samples.

While the solubility and diffusivity values used were chosen because they are generally intermediate to the experimental values, there is considerable uncertainty in some of these values (section 3.3.4; Figure 3.4). To examine the effect of changing our assumed solubility and diffusivity values, we performed a Monte Carlo simulation with 107 trials varying the solubility and diffusivity values. For individual samples, the median initial 3He and 22Ne concentrations varied by only a factor of 3 (68.2% range) despite the wide ranges in parameters used. The median value for all 33 samples and 68.2% confidence intervals for the initial 3He 22 +2.4 × −10 +3.0 × −11 and Ne concentrations are 2.2−0.6 10 and 2.9−0.9 10 ccSTP/g (Figure 3.6), quite similar to the values found using the standard set of parameters (Table 3.1).

The correspondence between our estimates based on reconstructing initial magmatic volatile contents and the independent estimate based on the oceanic He flux is a heartening indication that our simple degassing model has the capacity to produce reasonable estimates of reconstructed initial magmatic volatile contents. Furthermore, we have not made any assumptions about initial concentrations or elemental ratios. And although these samples were not chosen as representative of global MORB, they span wide geographic and geochemical

92 ranges. Acknowledging the very large range in initial concentrations between the samples, and the potential bias that the best data often come from volatile-rich samples, this procedure must be applied to many more samples with high precision He, Ne, and Ar data to con- firm the robustness of our median initial magmatic noble gas concentrations.

3.4.3 A range in reconstructed initial elemental ratios

Our range in initial magmatic 3He/22Ne ratios contradicts a conclusion from other disequilib-

rium models that the variety of measured elemental ratios in MORBs (Paonita and Martelli,

2007), as well as OIBs (Weston et al., 2015), could be explained by disequilibrium degassing

of a uniform initial composition. However, neither of those models considered the strict con-

straints placed on the degassing path by the 4He*/21Ne* ratio. Any process that fraction-

ates He from Ne, such as equilibrium or disequilibrium degassing, or helium loss, affects the

3He/22Ne and 4He*/21Ne* ratios by the same relative amounts as long as there is no or mini-

mal isotopic fractionation. Therefore, initial mantle source 3He/22Ne ratios can be computed solely from the measured (air contamination-corrected) 3He/22Ne and 4He*/21Ne* ratios

(Tucker and Mukhopadhyay, 2014):

( ) ( ) ( ) ( ) 3 22 3 22 × 4 ∗ 21 ∗ 4 ∗ 21 ∗ He/ Ne mantle = He/ Ne measured He / Ne mantle / He / Ne measured (3.8)

4 21 where He*/ Ne*mantle is the production ratio—a relationship which is being implicitly ex- ploited in our degassing model.

The coupled relationship between 3He/22Ne and 4He*/21Ne* can also be demonstrated graphically (Figure 3.7) where the mantle source 3He/22Ne for a sample can be found by extrapolating a He/Ne fractionation line to the mantle 4He*/21Ne* production ratio. This figure demonstrates, similar to previous results (Honda and McDougall, 1998; Moreira et al.,

2001; Graham, 2002; Tucker and Mukhopadhyay, 2014), that in general the mantle source of

MORBs generally has higher 3He/22Ne than that of OIBs, but significant heterogeneity even within MORBs is apparent.

93 Figure 3.7: Measured 4He*/21Ne* vs 3He/22Ne (filled symbols; 22Ne is corrected for atmospheric contamination) and reconstructed mantle values (open symbols) for various OIBs (red) and MORBs (blue). Man- tle source values are reconstructed only by assuming the extent of 3He/22Ne fractionation from the source ratio is equivalent to the extent of 4He*/21Ne* fractionation from the mantle production ratio. The compositions must follow the dashed lines during any fractionation process. This figure clearly demonstrates that significant mantle source 3He/22Ne heterogeneity exists between MORBs and OIBs (indicated by the arrows), as well as within both groups, contrary to the conclusions of Paonita and Maretlli (2007) and We- ston et al. (2015) that the mantle has uniform noble gas elemental ratios. MORB data from Tucker et al. (2012); OIB data from Jackson et al. (2009), Kurz et al. (2009); Mukhopadhyay (2012).

We argue that just because a degassing model can fit a subset of observed data with a uniform initial 3He/22Ne ratio, one cannot conclude that the mantle ratio is indeed uniform. For example, the model of Gonnermann and Mukhopadhyay (2007) also assumed a constant mantle 3He/22Ne ratio only to minimize the number of model parameters, but acknowledged that the mantle ratio could be heterogeneous.

3.5 Implications for the mantle carbon content and flux

3.5.1 Estimates based on equilibrium noble gas degassing are not robust

A frequently used technique to quantify the CO2 flux from mid-ocean ridges and hence the

3 upper mantle CO2 content is via measurements of C/ He ratios in MORBs. Measured ratios are often corrected for fractionation during degassing assuming an equilibrium Rayleigh distillation model where the extent of 4He*/40Ar* fractionation from the mantle production

94 ratio is used to quantitatively correct the C/3He ratio for degassing (e.g. Marty and Jam- bon, 1987; Marty and Tolstikhin, 1998; Marty and Zimmermann, 1999; Burnard et al., 2002;

Parai et al., 2012; Colin et al., 2013). Because the magmatic solubilities of He and C are closer than He and Ar, the typically observed increase in 4He*/40Ar* of around an order of

magnitude (Figure 3.1) implies a decrease in C/He by only a few 10s of % during equilibrium degassing. Applying this equilibrium model to a variety of samples results in the “canonical” average undegassed magmatic, and hence mantle C/3He of ~2 × 109 (atomic; e.g. Marty and

Tolstikhin, 1998). Combined with an upper mantle 3He flux of 527 mol/year (Bianchi et al.,

13 2010), this corresponds to a CO2 flux of 5 × 10 g/year and average initial magmatic CO2 content of ~800 ppm.

A simple demonstration can assess the robustness of these results: in principle, C/3He ra-

tios corrected for degassing using the 4He*/40Ar* ratio should be identical to values corrected

using the 4He*/21Ne* ratio. Figure 3.8 shows the correction factor, that is, the amount the measured C/3He ratio is multiplied by to reconstruct the initial C/3He ratio calculated using

4He*/40Ar* and using 4He*/21Ne*. The figure demonstrates that reconstructed C/3He ratios using 4He*/21Ne* would be a factor of a few higher than if 4He*/40Ar* were used. Given the large discrepancy between the correction factor calculated using 4He*/40Ar* and using

4He*/21Ne*, Figure 3.8 strongly suggests that equilibrium degassing models cannot be used

to reconstruct initial magmatic C/3He ratios. We therefore explore including C in our dise-

quilibrium degassing model to obtain C/3He ratios in a self-consistent manner.

3.5.2 Carbon diffusivity is highly uncertain

Incorporation of C into our disequilibrium degassing model critically depends on the C diffusivity in basaltic magma. However, this quantity is complicated by C speciation: while most of the C in basaltic systems is dissolved as carbonate anion, the diffusivity of molecular

CO2 is much higher such that it still significantly affects the total C diffusivity (Nowak etal., 2004; Guillot and Sator, 2011). Two studies have quantified the total C diffusivity accounting

for both species but found vastly different results: the 1350 ◦C Nowak et al. (2004) value of

95 Figure 3.8: Mismatch between C/3He predicted from 4He*/40Ar* and 4He*/21Ne* and equilibrium degassing models. Plotted is the correction factor, or the amount C/3He has decreased during degassing assuming equilibrium Rayleigh distillation, calculated for 33 samples (from Figure 3.1b). If equilibrium Rayleigh distillation correctly described the degassing process, the two estimates should be equivalent and plot on a 1:1 line. The mismatch strongly suggests that equilibrium degassing models cannot be used to reconstruct initial magmatic C/3He ratios.

10−11.2 m2/s is 50× lower than the value of 10−9.5 from Guillot and Sator (2011) interpolated

to the same temperature, despite being at lower pressure (Figure 3.4b). Other determinations such as Watson et al. (1982) and Zhang and Stolper (1991) only consider carbonate and not molecular CO2 diffusion. This enormous uncertainty in C diffusivity has significant implications for its fate during degassing. For example, noble gas data from a typical MORB sample may be fit with a characteristic degassing timescale of around 109 s/m2 in which case C with a diffusivity of 10−9.5

would be only mildly affected by disequilibrium (θ = 0.37; Figure 3.2), whereas a value of

10−11.2 implies such a strong kinetic inhibition that C would hardly degas at all (θ = 0.91).

We can potentially use data from the samples themselves to constrain the likely C diffu-

sivity. The best sample for this purpose is AMK3376 for which both vesicle data and bulk

crushing data are available. Applying the methodology outlined in section 3.4.1 using the

noble gas solubilities and diffusivities in Table 3.1, the 4He*-21Ne*-40Ar* data of this sam-

ple are fit with a characteristic degassing timescale of 9.25 s/m2. With this timescale and a

96 C solubility of 28 × 10−5 ccSTP/g/bar (Pan et al., 1991), the slope of the degassing path

4 40 40 in elemental spaces involving C, such as He*/ Ar* vs. CO2/ Ar*, now depends only on the C diffusivity (Figure 3.9). In the case of AMK3376, the slope is also independently defined by the individual vesicle data, so the C diffusivity can be solved for.Figure 3.9 shows

4 40 40 degassing paths constrained to pass through the bulk He*/ Ar* and CO2/ Ar* composi-

−9.7 tions of this sample with variable C diffusivities, where the best fitting path has DC of 10 m2/s, similar to values of Guillot and Sator (2011) around 1200 ◦C and distinctly higher than

−11.2 the value from Nowak et al. (2004) of 10 . The precise value of DC found in this manner is dependent on the other parameters that have been used, but in general is found to be intermediate to DNe and DAr. A similar conclusion is reached if the above procedure is performed on step-crushed MORB samples with noble gas and C data with spreads in elemental ratios between individual crushing steps (although these spreads are in general much smaller than those found in individual vesicles). These results suggest that the C diffusivity may be closer the higher end of estimates, and that C is mildly affected by disequilibrium, perhaps more than Ne but less than Ar.

3.5.3 Reconstructed MORB carbon contents

Adopting the C diffusivity of 10−9.7 m2/s computed above, we can use the methodology outlined in Section 3.4.1 to solve for the extent of C loss during degassing for any sample in Fig- ure 3.1a or b. However, because our model treats C and noble gas degassing separately, the initial C content can only be estimated for samples with total residual (vesicular + glass) C analyses, presently possible for 10 MORB samples: 5 from the equatorial Mid-Atlantic Ridge

(Tucker et al., 2012; Le Voyer et al., 2015) and 5 from the Southwest Indian Ridge (Parai et al., 2012; Standish, 2006). Initial CO2 contents reconstructed for these samples range from 900 to 2500 ppm with a median value of 1700 ppm (Figure 3.10, Table C.1). Initial C/3He

ratios range from 1.6 × 109 to as high as 1.4 × 1010 (Table C.1), with a median value of

4.1 × 109, higher than the canonical value by a factor of 2.

The order of magnitude range in reconstructed C/3He ratios is enormous for a pair of

97 40 4 40 Figure 3.9: CO2/ Ar* vs. He*/ Ar* for individual vesicles from AMK3376 (Burnard, 1999). Because 4He*-21Ne*-40Ar* data are available for this sample (Burnard et al., 2003), a characteristic degassing timescale can be fit such that the slope in this space depends onlyon DC. log10 DC is constrained here 2 to be intermediate between log10 DNe (-9 m /s) and DAr (-10.5), much higher than the value from Nowak et al. (2004) of -11.2.

Figure 3.10: Reconstructed initial CO2 content of 10 MORB samples using our degassing model. The dotted dashed line and uncertainty band is the average MORB initial CO2 content based on equilibrium degassing models that find a 3C/ He of 2.2 ± 1.0 × 109 (Marty and Tolstikhin, 1998) and the mantle 3He flux of ±527 102 mol/year (Bianchi et al., 2010). The dashed line and uncertainty band is the initial MORB CO2 content estimate of Michael and Graham (2015). Despite the small number of samples, most of our samples are incompatible with the low average estimate based on equilibrium models. The median value of our samples is 1700 ppm.

98 highly incompatible elements in MORB. Even though the precise values depend on the other parameters assumed, the wide range is generally preserved regardless of the parameters.

Preliminarily, we observe correlations between C/3He and indications of source enrichment such as La/Sm and Th/La (Figure 3.11). While these correlations are mostly dominated by one or two samples, they suggest that enriched mantle domains have high C/3He ratios, sim-

ilar to the finding of Marty and Tolstikhin (1998). The origin of enriched mantle domainsis

the subject of considerable debate, although it is often thought to be related in some way to

recycled material (e.g. Hofmann, 1997). In that case, high C/3He in enriched MORBs could result from either enrichment in C, for example from post-arc subduction of marine carbon- ates or carbonated basalt, or 3He depletion from degassing, or both. However, a large number of well characterized samples would be required to fully deconvolve these possibilities.

Reconstructed C contents can also be placed in a global context by comparison to undegassed MORBs. It has been found that absent the effects of degassing, C contents in MORBs correlate with other highly incompatible elements such as Nb or Ba (Saal et al., 2002; Car- tigny et al., 2008; Michael and Graham, 2015; Rosenthal et al., 2015). For example, Michael and Graham (2015) showed that in depleted, undersaturated (and therefore undegassed) samples, dissolved C concentrations correlated with Ba concentration. The relative constancy of the CO2/Ba ratio, along with an estimate of the average MORB Ba content, allowed for an estimate of the average MORB mantle C content and flux.

In Figure 3.12, we plot Ba and our reconstructed CO2 concentrations along with the undersaturated samples considered by Michael and Graham (2015). We also plot the composi-

tion of the popping rock 2ΠD43 (Javoy and Pineau, 1991; Dosso et al., 1993) and undegassed

Axial Seamount melt inclusions (Helo et al., 2011) and Gakkel Ridge melt inclusions (Shaw

et al., 2010). While we observe a large degree of scatter, the median reconstructed CO2/Ba in our samples is 94, very similar to the value of 105 ± 9 found by Michael and Graham

(2015). It is also within the range of 133 ± 44 found by Rosenthal et al. (2015). The similar-

ity of these estimates suggests that estimates of the MORB mantle Ba content and flux may

be used as a proxy for CO2. However, we also acknowledge the possibility that the scatter at

99 Figure 3.11: Reconstructed C/3He vs. La/Sm and Th/La. The association of higher C/3He with more enriched trace element ratios suggests that the enriched mantle is characterized by a high C/3He ratio. Trace element data from Janney et al. (2005), Standish (2006), and Kelley et al. (2013).

100 Figure 3.12: Reconstructed CO2 vs. Ba with literature data. Reconstructed values from this study (red diamonds) are reported in Table C.1. Blue circles are undersaturated MORBs excluding Gakkel Ridge samples (see Michael and Graham, 2015); orange triangle is the popping rock 2ΠD43 (Javoy and Pineau, 1991; Dosso et al., 1993); green triangles are undegassed Axial Seamount melt inclusions (Helo et al., 2011). The thick black line is the median CO2/Ba ratio of 97 from all samples plotted except VAN7 89-02 which has anomalously high Ba (460 ppm); the nearly coincident thin black line is the median CO2/Ba ratio of 94 only from the reconstructed samples. Also plotted are CO2/Ba estimates from Michael and Graham (2015; dotted line) and Rosenthal et al. (2015; dot-dash line).

high Ba contents could indicate that Ba is slightly more incompatible than CO2, as suggested by experimental determinations of trace element partitioning (Rosenthal et al., 2015).

Following the methodology of Michael and Graham (2015) we can compute the average undegassed MORB C content from our overall median CO2/Ba ratio. Assuming a MORB Ba content of 29.2 ppm (Gale et al., 2013) and average of 32% fractional crystallization (see

Michael and Graham, 2015), average primary MORBs would have ~2000 ppm CO2. Cor-

14 respondingly, the average CO2 flux from the MORB mantle is 1.2 × 10 g/year. We may

3 9 alternatively estimate the MORB mantle CO2 flux from our median CO2/ He of 4.1 × 10 (atomic) and upper mantle 3He flux of 527 mol/year (Bianchi et al., 2010)as 0.95 × 1014 g/year, similar to the estimate based on CO2/Ba in our reconstructed and other global undegassed samples, and ~2× the value based on reconstructing C/3He ratios using an equilibrium model (Section 3.5.1).

101 3.5.4 Comparison to other estimates

The most direct comparison to our median undegassed CO2 content of 1700 ppm is to the

average initial CO2 content of 1300 ppm from Gonnermann and Mukhopadhyay (2007), who used a different disequilibrium model, different samples, and a lower C diffusivity. Ourvalue

is similar to the recent 2000 ppm estimate of Michael and Graham (2015) which was based

CO2 undersaturated samples but also included a correction for crystal fractionation. These authors also speculated that the difference between their estimate and that based on equi-

librium noble gas degassing could be due to disequilibrium. Our value is also similar to the

highest CO2 contents in Gakkel Ridge melt inclusions of 1600 ppm (Shaw et al., 2010). It is

also similar in magnitude to the estimated initial CO2 content of 1800 ppm from Cartigny et al. (2008) which was based in part on an equilibrium degassing model, although that estimate included a very large uncertainty. While the representativeness of the small number of samples used in any of these estimates may be questioned, they are all significantly higher than the 800 ppm estimate based on equilibrium noble gas degassing described in section

3.5.1.

We also note that Saal et al. (2002) and Rosenthal et al. (2015) estimated upper mantle CO2 concentrations of 72±19 and 75±25 ppm based on CO2/Nb and CO2/Ba ratios and

Hirschmann (2016) estimated 66±29 ppm based on CO2/H2O ratios. Assuming 10% melting, the CO2 content of the primary melt would be 660-750 ppm. These concentrations are more similar to those based on C/3He ratios reconstructed from equilibrium degassing models.

However, the estimate of Saal et al. (2002) is based samples from a single locality and may not be representative of the ridge system as a whole. And CO2/Ba or CO2/Nb-based estimates may suffer from significant uncertainties in average mantle Ba or Nb contents (seee.g.

Rosental et al., 2015). Another estimate lower than ours was made by Chavrit et al. (2014), although this estimate is a lower limit as it is based on MORB vesicularity measurements and does not account for CO2 that might have been lost due to open-system degassing. The convergence of multiple independent estimates strongly suggests that the average initial magmatic CO2 content is higher than 800 ppm, and may be as high as 2000 ppm. Cor-

102 13 respondingly, the upper mantle CO2 flux is likely higher than 5 × 10 g/year by a factor of 2–3×. Disequilibrium degassing therefore can resolve the apparent discrepancy between degassing-based estimates and estimates independent of degassing. We also emphasize that the ability to correct individual samples for the effects of degassing not only grants us another means to estimate the global average CO2 flux, but will also allow us access to knowledge of C contents in MORBs worldwide without the need for reliance on rare undegassed samples.

3.6 Conclusions

4 21 40 136 1. The radiogenic noble gas elemental ratios He*/ Ne*/ Ar*/ Xe*U in MORBs do not conform to an equilibrium (solubility-controlled) Rayleigh distillation or any type

of equilibrium degassing model.

2. Kinetic fractionation (disequilibrium) is capable of explaining the noble gas data, such

that He is weakly and Ne mildly affected by disequilibrium, whereas Ar and Xeare

strongly affected.

3. A new simple model of disequilibrium degassing predicts initial magmatic volatile con-

centrations commensurate with an independent estimates derived from the mantle He

flux.

4. C is likely affected by disequilibrium, but initial magmatic C contents strongly depend

on the poorly constrained total C diffusivity in basaltic melt.

5. The “canonical” mantle C/3He ratio of ~2 × 109 based on equilibrium degassing implies

an average undegassed magmatic CO2 content and mid-ocean ridge CO2 flux lower than other independent estimates. The reconstructed mantle C/3He ratios based on

disequilibrium degassing is higher, bringing degassing-based estimates of the MORB

mantle C content and flux into accord with estimates independent of degassing.

103 6. The mantle is very heterogeneous in volatile element ratios such as C/3He. It is also

quite heterogeneous is noble gas elemental ratios such as 3He/22Ne, a conclusion inde-

pendent of any degassing model.

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111 4 Using helium isotopes to constrain the amount of recycled crust in the average MORB source

Jonathan M. Tucker1, Sujoy Mukhopadhyay2 1 Harvard University

2 University of California, Davis

112 Abstract

Here we show that the helium isotope ratios in mid-ocean ridges not influenced by plumes can result from mixtures of radiogenic helium most likely derived from a recycled crustal component and an intrinsic, relatively unradiogenic depleted component. Correlations between helium and lithophile isotopes in new and literature data define the 4He/3He ratio of the depleted end-member as < 80,000 (> 9 RA) globally, less radiogenic than the typical MORB range of 80,000–100,000. We therefore conclude that normal depleted MORBs must

contain some recycled crustal material in their mantle source, a manifestation of the “marble

cake” mantle structure. The presence of an intrinsic global depleted end-member of < 80,000

implies that the average MORB value of 86,000 (8.4 RA) is not itself an end-member composition, but rather results from a multicomponent mixture. It also implies that helium in the upper mantle cannot result from a mixture of unradiogenic helium from the plume source and radiogenic helium from recycled oceanic crust, a tenet of “steady-state” mantle models.

Assuming that radiogenic helium ultimately derives from recycled oceanic crust, we estimate that average MORB source contains around 1-5% recycled oceanic crust. While the modern crustal production and resampling rates are similar today, higher crustal production rates early in Earth history could have resulted in substantial amounts of oceanic crust accumula- tion in the mantle outside the MORB source. Together, these observations demonstrate the power of helium isotopes not solely as a tracer of plume influence, but also the influence of recycled crustal materials in the MORB source mantle.

113 4.1 Introduction

The recycling of surficial material to the mantle is a natural consequence of plate tectonics.

It has long been recognized that recycled material can influence Earth’s chemical evolution

(Armstrong, 1968). Recycled materials such as oceanic crust can influence the composition of

intraplate volcanics (Hofmann and White, 1982; Weaver, 1991; Lassiter and Hauri, 1998). In

the MORB mantle, the presence of recycled oceanic crust has also been hypothesized (Kurz

et al., 1982; Zindler et al., 1984; Allegre and Turcotte, 1986). Many geochemical observa-

tions in MORBs have been attributed to the presence of a minor pyroxenite lithology (e.g.

Chabaux and Allegre, 1984; Prinzhofer et al., 1989; Hirschmann and Stolper, 1996; Salters

and Dick, 2002; Ito and Mahoney, 2005; Sobolev et al., 2007; Lambart et al., 2009; Russo

et al. 2009; Kimura and Kawabata, 2015) which is likely related to recycled oceanic crust

(e.g. Hirschmann and Stolper, 1996). However unless the pyroxenite is pure unmodified sub-

ducted oceanic crust, the relationship between pyroxenite and oceanic crust can be ambigu-

ous, and recycled materials may not even be present as a separate lithology. Consequently,

direct quantifications of the amount of recycled materials in the MORB source, asopposedto

pyroxenite generically, are scarce (Eiler et al., 2000; Sobolev et al., 2007). Here, we demon-

strate how He isotopes may be used to trace the presence of recycled materials in the MORB

source.

As in other radiogenic isotope systems, He isotopes in MORBs are generally less variable

than in OIBs. However they are far from uniform: He isotopic ratios exhibit the largest rel-

ative variability of any isotope system in MORB, ranging by a factor of 4-5 from 4He/3He =

40,000 at the Reykjanes Ridge (Hilton et al., 2000) to 188,000 in the Chile Ridge (Sturm et

−6 al., 1999) or 3.7–17.6 RA (where 1 RA = the atmospheric ratio of 1.4 × 10 ). This extreme variability is generally thought to result from large parent/daughter fractionations that can occur during degassing; He degasses to a large extent during mid-ocean ridge volcanism, such that old oceanic crust has very high (U+Th)/3He (Staudacher and Allegre, 1988; Moreira et al., 2003). Other subducted components are similarly degassed. Because of this, He iso-

114 tope ratios are extremely sensitive to the time-integrated history of degassing: a less degassed or “primitive” mantle source preserves its 3He content and consequently has low 4He/3He, whereas a more degassed source has lost its 3He such that ingrowth causes high 4He/3He (e.g.

Kurz et al. 1982). Therefore, in addition to tracing the presence of primitive material, He isotopes may also have the potential to trace subducted oceanic crust and address the efficiency of crustal recycling (e.g. Kurz et al., 1982; Graham et al., 1992a; Hanyu and Kaneoka, 1997).

4He/3He ratios in MORBs lower than the typical MORB range of ~80,000-100,000 are often thought to reflect influence of relatively undegassed material associated with plumes

(e.g. Poreda et al., 1993, 1986; Moreira et al., 1995; Kurz et al., 1998; Graham et al., 1999).

Thus He isotope variability in MORBs may reflect mixtures of low 4He/3He material brought up from the lower mantle in plumes with radiogenic 4He derived from highly degassed (and hence high U+Th/3He) recycled material. But away from plumes, 4He/3He ratios in MORBs exhibit nearly the same variability as near plumes (Pető, 2014). Thus it is possible that plume influence is not always the dominant cause of He isotope variability. An alternative explanation is similar to “marble cake” mantle models (e.g. Allegre and Turcotte, 1986), wherein slab-derived radiogenic 4He is mixed with a low 4He/3He component intrinsic to the depleted mantle (e.g. Hamelin et al., 2011), as opposed to material associated with plumes.

While plume influence is still possible in this model, it is not required to explain allHeiso- tope variations.

This type of mixing relation may be tested by examining the coupled He and lithophile isotope compositions of MORBs in regions not thought to be influenced by plumes. Using new and literature data, we will examine localities across the globe in an attempt to generalize the behavior of He in the upper mantle. We will argue that while plume influence is certainly important in some sections of mid-ocean ridge, He isotope ratios in MORBs away from known hotspots may be explained by a mixture of an intrinsic depleted component and a recycled crustal component. We will then explore the geodynamic consequences of the observed mixtures.

115 4.2 Coupled He-Pb variations in MORBs imply a ubiquitous marble cake mantle

4.2.1 Subtropical North Atlantic

In contrast to much of the Mid-Atlantic Ridge, the large region between the Kane and At- lantis Fracture Zones (23.9–30.1 ◦N) is devoid of significant geochemical anomalies and is more than 1500 km from the Azores, the nearest known hotspot. Influence of the Azores plume has not been observed south of the Hayes Fracture Zone (e.g. Schilling, 1975; Debaille et al., 2006). Therefore this region provides an excellent opportunity to study He isotope variability in the absence of known hotspots.

We analyzed 40 samples for helium isotopes primarily from between the Kane and Atlantis

Fracture Zones primarily from the recent cruise KN206-2, as well as 5 samples from the CD57 and one from OCE180 cruises. All samples were measured by step-crushing on a Nu Instru- ments Noblesse Noble Gas Mass Spectrometer at Harvard University, which moved to UC

Davis in early 2015. Between ~50–150 mg were loaded (with the exception of D19-1 where 3.3 g were loaded because of an extremely low He concentration in this sample) and pumped for at least 1–2 hours prior to He analyses. For some samples, the crushing apparatus was fitted with an activated charcoal trap cooled to liquid nitrogen temperature to prevent condensable gas (primarily CO2, Ar, and H2O) from entering the extraction line to reduce gettering and freezedown times. At least two crushing steps per sample were performed to ensure reproducibility of the measurements. Replicate analyses at Harvard and UC Davis yielded indistinguishable results. He isotope ratios were determined by normalizing to a synthetic He stan-

3 4 dard with a He/ He ratio of 8.81 RA (Gayer et al., 2008). Pb isotopic ratios in 30 of these samples were measured at the University of Bergen, Norway by Cedric Hamelin (Bergen) and

Jocelyn Fuentes (Harvard). He data are reported in Table D.1.

The He data show a distinct regional gradient ranging from more radiogenic 4He/3He ra-

4 3 tios of ~85,000 (8.5 RA) in the south near the Kane Fracture Zone to less radiogenic He/ He ratios of ~80,000 (9 RA) in the north near the Atlantis Fracture Zone (Figure 4.1a). These

116 4He/3He ratios are not atypical for normal MORBs, but are close to the low end of the range of the majority of MORBs (e.g. Pető, 2014; Graham, 2002; Moreira, 2013).

We explore the possibility that the gradient in He isotope ratios (Figure 4.1a) reflects the influence of the Azores plume. He isotopic ratios in the Azores as low as ~60,000(12RA) have been observed in Terciera (Moreira et al., 1999) so it is possible that the He isotope gradient between the Kane and Atlantis Fracture Zones is due to increasing Azores influence northward. A test of this hypothesis is that the gradient in He isotopes should continue even further to the north along the Mid-Atlantic Ridge towards the Azores platform. While little published He data exists in this region (30–39◦N), available data do not suggest a strong gradient between the Atlantis Fracture Zone and the Azores (e.g. Kurz et al., 1982; Moreira et al., 2011). For example, Moreira et al. (2011) observed He isotope ratios primarily between

◦ 85,000 and 88,000 (8.2–8.5 RA) in the Lucky Strike segment (37.2 N) and concluded that Ne isotopes suggested Azores influence but He isotopes did not. We therefore assume that the gradient in He isotopes between the Kane and Atlantis Fracture Zones is not dominantly due to Azores influence.

We also note the presence of one anomalous sample (KN207-2 D5-1 and D5-2), with

4 3 ◦ He/ He close to 65,000 (11 RA) near 29 N. Compared to the whole region between the Kane and Atlantis Fracture Zones, Pb isotopes also display a subtle geochemical anomaly between

29–30◦N (Figure 4.1b). As the origin of this anomaly is uncertain, herein we will consider data only between the Kane Fracture Zone and 29◦N (that is, excluding the two northern- most segments). Further speculations on the origin and significance of this anomaly will be discussed in the context of heavy noble gas data in Chapter 5.

Similarly to He, new Pb data (Fuentes, Hamelin, Langmuir et al., unbublished data) also demonstrate a coherent variation from more radiogenic values in the south near the Kane

Fracture Zone to more unradiogenic values in the north near the Atlantis Fracture Zone (Fig- ure 4.1b), although perhaps not as strongly as He. Because the Azores themselves are characterized by highly radiogenic Pb (e.g. Genske et al., 2016), their influence cannot be the cause of the major regional gradient between the Kane and Atlantis Fracture Zones as such

117 Figure 4.1: (a) 4He/3He and (b) 206Pb/204Pb vs. latitude for samples between Kane and Atlantis Frac- ture Zones in the subtropical north Atlantic. He data form a clear trend from more radiogenic in the south to less radiogenic in the north; Pb data for a similar trend although it is somewhat less clear. Samples north of 29◦N may be influenced by a small lengthscale anomaly. He data from this study; Pb datafrom Fuentes, Hamelin, Langmuir et al., unpublished.

118 influence would result in the opposite sense of variation. Therefore the Pb isotopes appear to indicate the increasing influence of a depleted component northward toward the Atlantis

Fracture Zone.

Together, He and Pb isotopes are positively correlated in the region between the Kane and

Atlantis Fracture Zones (Figure 4.2a). A simple explanation for this covariation is that these samples result primarily from a mixture of an enriched component with radiogenic He and Pb and a depleted component with unradiogenic He and Pb. The association of the unradiogenic

He with unradiogenic Pb seen in Figures 4.1 and 4.2a implies that the depleted mantle is

4 3 characterized by relatively unradiogenic He, with He/ He less than 80,000 (> 9 RA). Thus, such unradiogenic values are not necessarily associated with plumes.

To further assess the explanation that relatively unradiogenic He is intrinsic to the de-

pleted mantle as opposed to necessitating plume influence, we will examine He-Pb system-

atics in other regions of the mid-ocean ridges that extend to more depleted compositions than

observed in this region.

4.2.2 Equatorial Atlantic

The region of the Mid-Atlantic Ridge near the equator (approximately 8◦S to 5◦N) exhibits a wide range of trace element and isotopic compositions from extremely depleted to highly enriched (Schilling et al., 1994). The geochemical variability in this region is much more extreme than the subtropical north Atlantic, leading to a less ambiguous definition of mixing end-member compositions. Widely ranging He and Pb isotopic compositions are strongly correlated (Figure 4.2b) and can be described primarily by a mixture of two components: a highly radiogenic component characterized by 206Pb/204Pb > 20 and 4He/3He > 100,000 (<

206 204 4 3 6.8 RA), and a depleted component with Pb/ Pb < 17.7 and He/ He < 80,000 (> 9

206 204 RA). The radiogenic end-member has among the highest Pb/ Pb found in MORBs. The depleted samples are equally as extreme, having in addition to unradiogenic Pb, 87Sr/86Sr around 0.7021 and 143Nd/144Nd of 0.51330 (Schilling et al., 1994; Hoernle et al., 2011).

Therefore, the association of unradiogenic He with this highly depleted lithophile isotope

119 Figure 4.2: 4He/3He vs. 206Pb/204Pb in the (a) subtropical north Atlantic (23-29◦N), (b) equatorial At- lantic (8◦S to 5◦N), and (c) Pacific ridges ◦(14 N to 66◦S). He and Pb are positively correlated indicating that away from plumes, data represent mixtures of a depleted end-member with 4He/3He < 80,000 and a radiogenic end-member, likely deriving from recycled oceanic crust. Dashed lines are to guide the eye; the axis ranges are different in each figure indicating the composition of the end-members is not necessarily uniform. In (a), He data from this study; Pb data from Fuentes, Hamelin, Langmuir et al., unpublished. In (b), He data are from Graham et al. (1992b), Stroncik et al. (2007), Tucker et al. (2012), Kelley et al. (2013), Stroncik and Niedermann (2016) (case study); Pb data are from Schilling et al. (1994), Möller (2002), Agranier et al. (2005), and Hoernle et al. (2011). In (c), data are from Hamelin et al. (2011) and references therein; plume influenced samples are red + symbols (Hamelin et al., 2011). Garrett Fracture Zone sample (green square) data from Mahoney et al. (1994); Kurz et al. (2005).

120 composition requires that a relatively unradiogenic 4He/3He < 80,000 is intrinsic to the depleted mantle, and not associated with a plume (e.g. Tucker et al., 2012; Stroncik and Nie- dermann, 2016).

The radiogenic component has been described to have a strong HIMU-like affinity

(Schilling et al., 1994, Hannigan et al., 2001). The appellation “HIMU” or “high-µ” (Zindler and Hart, 1986) refers to highly radiogenic Pb isotopic compositions, generated over time by high U/Pb (µ) ratios. The origin of the HIMU component has been the subject of significant debate: while some studies have linked it to processes such as core involvement (e.g. Allegre,

1982), or involvement of C-rich melts (Collerson et al., 2010, Weiss et al., 2016), many studies argue that it is related in some perhaps complex way to recycled oceanic crust (e.g. Zindler et al., 1982; Hofmann, 1997; Weaver, 1991; Chauvel et al., 1992; Hauri and Hart 1993; Las- siter et al., 2003; Stracke et al., 2003; Kelley et al., 2005; Cabral et al., 2013). Radiogenic He is consistent with this hypothesis as recycled material (of any kind) should be extensively degassed of its He and therefore have high (U+Th)/He. Consequently, radiogenic He in HIMU

OIBs has been attributed to the presence of a recycled (degassed) component (e.g. Graham et al., 1992a; Hanyu and Kaneoka, 1997). In contrast to lithophile elements whose modification during subduction can be cryptic (e.g. Stracke et al., 2003), He isotopes are a less ambiguous tracer of recycled materials, although perhaps less discriminatory between different types of recycled materials.

4.2.3 Pacific ridges

Similarly to the above observation in the equatorial Atlantic, Hamelin et al. (2011) observed positively correlated He and Pb data over a very large distance of the East Pacific Rise and

Pacific-Antarctic Ridge. Whereas the correlation in the equatorial Atlantic extended over

~1500 km of ridge axis, the Pacific dataset comprises around 7000 km of ridge axis. While this broad region also includes a few distinct geochemical anomalies, the major large-scale isotopic variability was interpreted as binary mixing between intrinsic depleted and radiogenic recycled oceanic crust components (Hamelin et al., 2011). The depleted component

121 4 3 is again characterized by a He/ He ratio < 80,000 (> 9 RA) (Figure 4.2c). The depleted end-member may also be represented by a single extremely depleted sample from the Garrett

Fracture Zone with 206Pb/204Pb = 17.8 (Mahoney et al., 1994) and 4He/3He = 73,400 (9.8

RA) (Kurz et al., 2005). The Garrett Fracture Zone sample has a similar composition to the most depleted equatorial Atlantic samples, although we recognize that the true end-member composition may be more unradiogenic than the most extreme measured values and need not be identical everywhere.

4.2.4 Indian ridges

In contrast to the above examples, samples from the Southwest and Southeast Indian Ridges away from plumes require more than simple two-component mixing to explain the isotopic compositions. Gautheron et al. (2015) described the isotopic compositions of basalts from

~3500 km of the Southwest Indian Ridge as representing a mixture of three distinct compo-

4 3 nents: a depleted end-member with He/ He < 80,000 (> 9 RA), recycled oceanic crust with radiogenic Pb and He, and an additional recycled component with unradiogenic Pb but ra-

diogenic He. Graham et al. (2014) also described basalts from ~3000 km of the Southeast

Indian Ridge away from the Amsterdam–St. Paul hotspot as resulting from a mixture of a

depleted component with 4He/3He < 80,000, recycled oceanic crust, and recycled continental lithosphere.

4.2.5 Summary of He-Pb observations in MORBs

Together, these studies from geographically diverse and expansive localities demonstrate a common global feature. Outside major plume influence, MORB He comprises a mixture ofat least two distinct major components: a radiogenic component also associated with radiogenic

Pb, and a relatively unradiogenic component intrinsic to the depleted mantle. This global un-

4 3 4 3 radiogenic component has a He/ He less than 80,000 (> 9 RA), demonstrating that He/ He ratios as low as 70,000-80,000 do not necessarily represent plume influence, as they can also be associated with depleted isotopic signatures. Therefore, the distribution of He in normal

122 MORBs primarily likely does not result from a mixture of 3He fluxed from the plume source and 4He from recycled crust, a tenet of “steady-state” models, as this cannot account for the association of unradiogenic He with depleted geochemistry. Neither can He compositions result from mixtures of this intrinsic depleted component and plume-derived undegassed material, as both of these components have relatively unradiogenic He.

As the majority of MORBs have 4He/3He ratios between 80,000 and 100,000, MORBs are often represented by an average value around 85,000–90,000 (8–8.5 RA) (e.g. Kurz and Jenk- ins, 1981; Allegre et al., 1995; Graham, 2002; Moreira, 2013). As such representative values are often used as a constraint in dynamical models (e.g. Allegre et al., 1986/87; Kellogg and

Wasserburg, 1990), the above examples demonstrate that the average He isotopic composition of normal MORBs is not an end-member component, but rather results from a mixture of at least these two components. In the following sections, we will explore the consequences of this ubiquitous mixture.

4.2.6 An intrinsic unradiogenic component in the depleted mantle

While we have demonstrated that the depleted component represented by low 206Pb/204Pb and 4He/3He is distributed globally, there is no requirement that it be the same everywhere.

For example, different parts of the mantle may have experienced different histories of depletion leading to different compositions of the depleted mantle. Furthermore, the mantle end- member composition may rarely or never be sampled in a pure form so the 4He/3He ratio of the true depleted end-member composition may well be lower than the lowest measured values. It is difficult to speculate on the origin of the relatively unradiogenic depleted composition, however, one possibility is that it is the natural result of secular mantle depletion.

He, U, and Th are all highly incompatible elements, but if they have the same bulk partition coefficient during mantle melting, the time-integrated 4He/3He ratio of the depleted mantle would be the same as primitive unmelted mantle, just strongly depleted in He, U, and

Th concentrations. But if He is more incompatible, the composition will evolve to a higher

4He/3He ratio, though not nearly as high as a degassed source that is also enriched in U and

123 Th, such as recycled crust.

4.2.7 A ubiquitous recycled component in the MORB mantle

The examples shown in Figure 4.2 not only demonstrate the presence of an intrinsic depleted component in MORB, but also a ubiquitous radiogenic component. Thus He isotopes in

MORBs may be interpreted as a manifestation of the “marble cake” mantle where MORBs are sourced primarily from a mixture of depleted mantle and a recycled crustal component.

As such, He isotope variability in MORBs does not result from mixtures of radiogenic 4He derived from degassed (and hence high U+Th/3He) recycled material with low 4He/3He material brought up from the lower mantle in plumes. That type of scenario forms the basis for so-called “steady state” models where the volcanic flux of 3He from the upper mantle is balanced by input of 3He from the lower mantle (e.g. O’Nions and Oxburgh, 1983; Kellogg and

Wasserburg, 1990; O’Nions and Tolstikhin, 1994; Porcelli and Wasserburg, 1995; Tolstikhin and Hofmann, 2005). Thus the mixing systematics shown in Figure 4.2 question the funda- mental assumption of the “steady state” models.

As discussed above, there is considerable debate on the relationship between recycled materials and the composition of oceanic basalts (e.g. Stracke et al., 2003) and recycled materials display a wide array of isotopic signatures. All types of recycled material should be devoid of 3He and could hypothetically constitute a high 4He/3He component, so it is difficult to identify the nature of the recycled component on the basis of He isotopes alone.

The most significant recycled component by mass and volume is the lithospheric mantle, which comprises most of the subducting slab, however because U, Th, and He are highly incompatible elements, the concentrations in residual mantle are too low to comprise a significant high 4He/3He reservoir (Jackson et al., 2013). Recycled continental lithosphere is also an unlikely major high 4He/3He reservoir in the mantle because while it should carry high

4He/3He, its total volume in the mantle is likely to be quite small. Other recycled materials such as terrigenous or oceanic sediments may also have very high (U+Th)/He, but are also often associated with other geochemical anomalies such as radiogenic Sr isotopes, which

124 are not observed in the samples with high 4He/3He and high 206Pb/204Pb. However, oceanic crust is a ubiquitous high (U+Th)/He material, subducted to the mantle in large volumes, and has been associated with highly radiogenic He and Pb (e.g. Graham et al., 1992a; Hanyu and Kaneoka, 1997) in OIBs. Therefore, we will proceed under the assumption that radiogenic He derives from recycled oceanic crust, and explore the consequences of this assumption.

4.3 Geodynamic consequences

4.3.1 How much oceanic crust is in the mantle source of MORBs?

4 3 The vast majority (80%) of ridge segments have He/ He > 80,000 (< 9 RA; Pető, 2014). If the composition of the depleted mantle end-member is at most around 80,000, the vast majority of the MORB source mantle must contain a small amount of recycled oceanic crust.

Therefore, we estimate the proportions of recycled oceanic crust and depleted mantle in the

MORB mantle using a simple mixing calculation.

General mixing formulation

Any mixing calculation for isotope ratios of two end-members requires values for the isotopic ratios and concentrations of the end-members. If the two end-members exist as separate lithologies which melt separately, the concentrations in the end-members is divided by the average degree of melting (for a highly incompatible element).

The isotopic ratio of a mixture of recycled oceanic crust (RC) and depleted mantle (DM) is expressed as: ( ) 4 ( ) 4 − He 3 FRC 4 XRC [ He]RC + (1 XRC ) 3 [ He]DM He He FDM = DM (4.1) 3 3 FRC He (1 − XRC )[ He]DM MORB FDM which is a modification of the standard mixing equation assuming the recycled crust compo-

3 nent is devoid of He. XRC is the mass fraction of recycled crust in the mantle source of the

125 mixture. The He concentrations in the two mantle components are divided by the degree of partial melting, FRC and FDM , but these are be combined into a single relative melt productivity FRC /FDM . Equation 4.1 may be solved for XRC to find the amount of recycled crust in the mantle source of a mixture with a particular isotopic ratio.

End-member compositions

In the mixing calculations presented here, we assume the depleted end-member has a

4 3 He/ He ratio of 75,000 (9.6 RA), similar to the lowest measured values in depleted MORBs from the equatorial Atlantic and Garrett Fracture Zone. However, the 3He concentration of

the depleted end-member is significantly more uncertain. We preliminarily assume a value of

2 × 108 atoms/g but this uncertainty will be discussed later in section 4.3.2.

Instead of assuming a particular isotopic composition for recycled crust, we assume that

the crust is devoid of 3He and only delivers radiogenic 4He to the mantle. This assumption

is based on the extremely low 3He concentrations measured in old oceanic crust (Staudacher

and Allegre, 1988; Moreira et al., 2003) and the notion that subduction should strip the crust

of any remaining He. However, assuming the recycled crust contains small amounts of 3He,

such as that corresponding to a 4He/3He production ratio of ~108 where small amounts of

3He are produced from 6Li(n, α)3H→3He reactions (Andrews, 1985), the calculations are only

negligibly affected. Therefore, the 4He content of the recycled crust component may be com-

puted from U and Th contents and the age of the recycled crust. We use “post-back-arc” U

and Th contents of 47 and 92 ppb (Kelley et al., 2005) as representative of subducted slabs

beyond the magma generation depths of arcs and back-arcs, noting that these estimates are

subject to some uncertainty (Kelley et al., 2005).

Estimates of the age of oceanic crust in the mantle can potentially come from indepen-

dent estimates of the residence time of material in the MORB mantle. Models that pro-

scribe a steady state flux of noble gases through the upper mantle predict upper mantle

residence times of 1.4 Ga (Kellogg and Wasserburg, 1990; Porcelli and Wasserburg 1995),

although these models have been questioned by recent data (Mukhopadhyay, 2012). Con-

126 versely, similar models that consider radioactive and radiogenic trace element fluxes through the MORB mantle predict residence times as short as ~300–600 Myr (Galer and O’Nions,

1985; Donnelley et al., 2004). However, noble gas-based models of mantle evolution not based on the steady state requirement predict that the MORB mantle has turned over 3.5–7.5 times

(Gonnermann and Mukhopadhyay, 2009) or 4–9 times (Coltice et al., 2009), implying average residence times between a few hundred million and a billion years. Furthermore, even if the average residence time were well-defined, it would not apply uniformly to every MORB.

Therefore the age of oceanic crust in the mantle represents a significant uncertainty in this calculation.

The effect of multiple lithologies

In the simple model of Equation 1, we assume that the depleted mantle lithology and the recycled crust-bearing lithology melt separately and to different degrees, and the melts are mixed. It has been suggested that recycled crust may not necessarily exist as a separate lithology in the mantle (Stracke et al., 1999), in which case the degree of melting of this lithology is irrelevant, or FRC /FDM = 1. However, a variety of geochemical and petrological tools have inferred the presence of pyroxenite in the MORB mantle (e.g. Chabaux and

Allegre, 1984; Prinzhofer et al., 1989; Hirschmann and Stolper, 1996; Salters and Dick, 2002;

Ito and Mahoney, 2005; Sobolev et al., 2007; Lambart et al., 2009; Russo et al. 2009; Kimura

and Kawabata, 2015) which is most plausibly related to recycled oceanic crust (Hirschmann

and Stolper, 1996). If the recycled crust exists as a separate lithology such as eclogite or py-

roxenite, it would melt deeper and to a higher extent than the peridotite. Thus FRC /FDM is likely > 1.

A complication arises if deep melts from the more fertile lithology react with solid mantle peridotite, producing intermediate reaction products such as fertile peridotite (Kelemen et al., 1998) or secondary pyroxenite (Rapp et al., 1999; Sobolev et al., 2005; 2007). These secondary lithologies, along with the mantle peridotite, would then partially melt, and the primary MORB magmas are formed from mixtures of these melts, as in the model of Sobolev et

127 al. (2007). The formation of intermediate lithologies, such as secondary pyroxenite, undoubt- edly has significant petrological consequences, but actually do not affect our calculations.

Mixing calculations for highly incompatible elements do not require modeling intermediate reactions and are sensitive directly to the original amount of recycled crust even if secondary lithologies are formed (an algebraic demonstration of this is given in the supplement).

The only lithology-specific parameter that affects our mixing calculation is the ratio ofex- tent of melting of the component ultimately containing the recycled crust-derived He to that of peridotite (FRC /FDM ). While we cannot say for certain whether the lithology of this component is primary or secondary pyroxenite, eclogite, fertile peridotite, or something else, it

will likely melt to a greater extent than depleted peridotite. We therefore assume that the

lithology hosting the recycled crust-derived He melts to 3 times the extent of the depleted

mantle component, similar to the estimates of Hirschmann and Stolper (1996) and Sobolev et

al. (2007), noting that this parameter imparts some uncertainty into the mixing calculation.

Calculation result

Figure 4.3 shows He isotopic compositions resulting from mixtures of variable amounts of re-

cycled crust of variable age. The figure shows that the calculation depends strongly onthe

age of the recycled crust. For example, the majority of MORBs with 4He/3He ratios between

80,000–100,000 (7.2–9 RA) require ~1–6% recycled crust in their mantle source if the material age is large (around a billion years), higher proportions if the recycled crust is younger. 95% of all MORBs have 4/3 between 50,000 and 110,000 (6.5-14.5 RA; Peto, 2014). The low end of this range is related to plume influence but the full range implies that the amount ofcrust in the source of MORBs could vary from 0% to as high as 15% (Figure 4.3). Figure 4.3 also demonstrates that the range of He isotopic compositions in MORBs could alternatively be explained by a relatively constant amount of recycled crust but of different ages. This type of interpretation would be consistent with the notion of a continuous injection of recycled materials into the mantle over Earth history. Most likely, the distribution of He isotopic ratios in MORBs derives both from variable amounts of recycled material in the source and variable

128 Figure 4.3: Results of mixing calculation. He isotopes are assumed to result from a mixture of a depleted component with 4He/3He of 75,000 and 3He concentration of 2 × 108 atoms/g, and a recycled component providing only 4He. The 4He concentration of the recycled component is calculated from its age and U and Th content; 47 and 92 ppb (Kelley et al., 2005). The recycled component is assumed to melt to 3× the extent of the depleted component. If the recycled oceanic crust has aged for 1 Gyr, the vast majority of MORBs having 4He/3He between 80,000 and 100,000 (7.2-9.0 RA) require ~1-6% recycled oceanic crust in their source. ages of the recycled material.

4.3.2 How much crust in the source of average MORBs?

While the amount of recycled crust in the mantle source of individual MORBs may be quite variable, we can calculate a representative value by considering the composition of an average

MORB. Given a particular representative isotopic composition, Equation 1 can be rearranged to solve for the average amount of recycled crust in the MORB source.

In this calculation we only consider MORBs not likely influenced by plumes, as plumes could provide a third mixing component. The average MORB composition in depleted mid- ocean ridge segments (La/SmN ≤ 0.8) is 86,000 (8.4 RA; Pető, 2014). Alternatively, using

the “preferred N-MORB” value of 88,000 (8.2 RA; Pető, 2014) does not significantly alter the

129 calculation.

Figure 4.3 shows that for a representative 4He/3He composition of 86,000 to 88,000, the amount of recycled crust required is approximately 1-5% depending on the average age of the recycled crust, and approximately 3-4% for ages of around 1 Ga.

Because the composition of the mixture is now fixed, we may examine the effect of varying an additional parameter. Figure 4.4 demonstrates that along with the age of recycled crust, the second major uncertainty in calculating the amount of recycled oceanic crust in the average MORB source is the 3He content in the depleted end-member. It is not practical to estimate the mantle source 3He content from measurements in MORBs because degassing masks direct knowledge of initial magmatic and hence mantle compositions (see for example Chap- ter 3). However, some insight can come from the average upper mantle 3He content with the further constraint that the depleted end-member may be more gas-poor than average upper mantle. The average upper mantle 3He content may be calculated from the oceanic 3He flux of 527 mol/year (Bianchi et al., 2010) divided by the MORB mantle processing rateof

~6 × 1017 g/year derived from 21 km3/year crustal production rate (Crisp, 1983), oceanic crust density of 2900 kg/m3 (Carlson and Raskin, 1984), and 8–10% partial melting. This results in an average MORB mantle 3He concentration of 4 − 5 × 108 atoms/g, consistent with estimates reconstructed from degassed MORB compositions (see Chapter 3). It has been proposed that the deep solidus of carbonated peridotite allows deep low-degree C-rich melts to form beneath mid-ocean ridges, effectively increasing the volume out of which highly incompatible elements are extracted (Dasgupta and Hirschmann, 2006). In this case, the effective processing rate for He would be higher, and the average upper mantle 3He concentration proportionally lower.

The concentrations of highly incompatible elements such as Rb and Ba are lower in very depleted MORBs compared to average MORBs by around a factor of ~2–2.5 (Workman and

Hart, 2005, D-DMM vs. DMM; Gale et al., 2013, D-MORB vs. N-MORB). If 3He is depleted by a similar amount from the average upper mantle value, it could be ~2 × 108, the value as-

sumed in the calculations behind Figure 4.3. And while it may be impractical to attempt to

130 Figure 4.4: The amount of recycled crust in the source of average D-MORB. The 4He/3He ratio of D- MORB (average of segments with La/Sm < 0.8) is 86,000 (Pető, 2014), although using the “preferred N-MORB” value of 88,000 gives similar results. The depleted end-member 4He/3He is likely lower than the average upper mantle value of ~4 − 5 × 108 atoms/g (see text), although this along with the recycled component age represent significant uncertainties in estimating the amount of recycled crust in the average upper mantle.

131 estimate the 3He concentration of the depleted end-member from measurements in MORBs,

we note that the He concentrations in ultra-depleted MORBs from the Garrett Fracture Zone

and the equatorial Atlantic are not atypical for MORBs (around 1-10 µcc/g 4He; Kurz et al.,

2005; Tucker et al., 2012; Kelley et al., 2013). This could be an indication that the source of

ultra-depleted MORBs does not have a 3He concentration orders of magnitude different than

typical MORBs.

With the above considerations in mind, we conclude that an average of ~1–5% recycled

crust in the MORB source is a reasonable estimate based on He isotope systematics (Figures

4.3,4.4). While this estimate is subject to some uncertainties, especially in the residence time

of recycled crust and the 3He content of the depleted end-member, it is similar to other inde-

pendent estimates based on other geochemical systems (Section 4.3.3).

In summary, our simple model demonstrates the power of He isotopes to directly quantify

the amount of recycled crust in the source of MORBs. We estimate that MORBs contain

between 0 and 15% recycled oceanic crust in their source, and between 1 and 5% on average.

4.3.3 Comparison to other estimates

As stated above, a number of geochemical and petrological methodologies have been employed to infer and quantify the presence of pyroxenite in the mantle source of MORBs.

While the origin of this pyroxenite may be related to recycled oceanic crust, a quantitative relationship between recycled crust and pyroxenite, especially if it is secondary, can be challenging to establish robustly. For this reason, direct quantitative estimates of the amount of recycled crust in the MORB source, are comparatively rare.

Eiler et al. (2000) argued that O isotopes may be used a tracer of recycled oceanic crust in MORBs. Because interaction with the hydrosphere raises the 18O/16O ratio in altered

oceanic crust, positive correlations observed between MORB O isotopes and geochemical

tracers of enriched mantle sources, such as K/Ti and La/Sm ratios, are explained by mix-

tures of recycled oceanic crust and mantle peridotite. Using mass balance arguments, they es-

timated that 0–7% with an average of ~2% recycled oceanic crust could explain the O isotope

132 data. However, we also note that other explanations for anomalous O isotopes in MORBs have been argued for, including metasomatized mantle derived from altered oceanic crust melts (Cooper et al., 2004) and lower continental crust (Cooper et al., 2009).

Sobolev et al. (2005; 2007) presented a model in which melts derived from eclogitic recycled oceanic crust react with surrounding mantle peridotite to produce a secondary olivine- free pyroxenitic lithology. Within this model, the fraction of pyroxenite and ultimately eclogite comprising of the source material of mantle-derived basalts could be quantitatively estimated from Ni and Mn contents of olivines. Sobolev et al. (2007) applied this methodology to MORBs and estimated an average of ~4% recycled oceanic crust in the MORB source.

However, quantitatively, this model depends on parameters such as the degree of melting of the eclogite and pyroxenite lithologies, and the ratio of eclogitic melt to assimilated peridotite in the secondary pyroxenite, all of which are poorly constrained.

While these independent estimates as well as our own estimate are all subject to significant uncertainties, they appear to converge to around 2-5% recycled crust in the average MORB source. Next we will explore the consequences of the amount of recycled crust in the MORB source in terms of mantle dynamics.

4.4 Where does subducted oceanic crust reside?

We can use our estimate of the amount of recycled crust in the average MORB source to

address the efficiency of crustal recycling and implications for the fate of subducted oceanic

crust. The modern oceanic crustal production rate is ~6 × 1016 g/yr (the product of the vol- umetric production rate and density). Integrated over Earth history and assuming resampling and obduction rates are negligible, a total of ~3 × 1026 g of oceanic crust would have been produced, filling ~7% of the whole mantle. The average amount of oceanic crust inthe

MORB source is similar to this number, implying little or no oceanic crust has accumulated in a region of the mantle unsampled by MORBs, and that oceanic crust is dispersed relatively uniformly throughout the MORB mantle.

However, higher mantle potential temperatures in the past would have resulted in faster

133 spreading rates and higher degrees of partial melting, resulting in greater production of oceanic crust. For example, if the mantle potential temperature was 1500 ◦C at ~2.4 Ga (e.g.

Richter, 1988), the peridotite melting parameterization of Katz et al. (2003) predicts oceanic

crust ~3× thicker than the present day. Faster spreading rates would also enhance crustal

production rates even further although quantitatively, the interplay between mantle tem-

perature, spreading rate, and crustal thickness is complex (e.g. Su et al., 1994). As a simple

demonstration, assuming the production rate has decreased exponentially with time to the

present rate, reaching 3× the modern value at 2.4 Ga, the total amount of crust produced

is ~9 × 1026 g, which would fill around 23% of the mantle. While this particular exampleis

demonstrative only, it suggests that increased crustal production rate in the past could re-

sult in significant amounts of crust sequestered in the deep mantle unsampled by mid-ocean

ridges.

The presence of significant amounts of recycled oceanic crust residing outside theMORB

source would be consistent with the notion that high pressure forms of oceanic crust are

denser than the ambient mantle, allowing the crust to sink and remain in the deep mantle

(e.g. Christensen and Hofmann, 1994; Hirose et al., 1999; Aoki and Takahashi, 2004). The

notion is also consistent with the finding that the sources of some OIBs which may residein

the deep mantle contain a higher proportion of recycled crust than MORBs (e.g. Sobolev et

al., 2007).

However, the modern resampling rate of oceanic crust may not be negligible, as assumed

above. If the average MORB source contains 5% recycled oceanic crust, the crustal resam-

pling rate is within a factor of 2 of the crustal production rate. If some oceanic crust were

also resampled at subduction zones, the post-arc subduction rate could be quite similar to the

overall resampling rate. This would imply that, at least presently, crustal production and re-

sampling are in balance. If the rates were in balance through Earth history, there would be

no need to for large amounts of recycled crust to be sequestered outside the MORB mantle.

The question of whether oceanic crust has been accumulating in the deep mantle has signifi-

cant geochemical and geodynamical consequences, and should be investigated in the future.

134 Whether or not oceanic crust has been accumulating in the deep mantle, the amount of oceanic crust resampled at ridges is still significant, implying that some fraction of subducted crust is recirculated to the upper mantle. The debate on whether subducted slabs sink to the lowermost mantle or stagnate in the mid-mantle is ongoing, but the presence of recycled oceanic crust in mid-ocean ridges ridges requires that either some slabs do not sink to the lowermost mantle (e.g. Gonnermann and Mukhopadhyay, 2009; Fukao and Obayashi, 2013;

French and Romanowicz, 2015), or material pooled in the lowermost mantle can be entrained in upwellings and redispersed through the upper mantle (e.g. Phipps Morgan et al., 1995,

Yamamoto et al., 2007), or both.

4.5 Conclusions

We have presented new He data from the subtropical Mid-Atlantic Ridge which exhibit a

strong gradient with latitude, and are positively correlated with Pb isotopes. This data adds

to a global database of MORBs in which He and Pb isotopes positively correlate. Thus, glob-

ally, He isotopes in MORBs removed from plume influence may be explained by a mixture

of a relatively unradiogenic component associated with the depleted mantle and a radiogenic

component associated with recycled oceanic crust.

The correlations observed globally imply that the oft-quoted representative MORB value of

90,000 (8 RA) is not an end-member composition but rather represents a mixture of multiple components. Furthermore, the correlations define the depleted mantle 4He/3He composition as < 80,000 (> 9 RA), indicating that relatively unradiogenic He isotopic compositions do not always require plume influence. The radiogenic end-member likely derives from recycled oceanic crust, indicating that the mantle source of normal MORBs contains some amount of recycled oceanic crust.

With a simple mixing calculation, we estimate that ~1–5% recycled oceanic crust is required in the average MORB source, commensurate with other independent estimates. The modern resampling rate is similar to the modern crustal production rate, implying that at least at present oceanic crust production and resampling are close to balanced. However, if

135 the oceanic crustal production rate were significantly higher early in Earth history, substantial amounts of oceanic crust could be sequestered in the mantle outside the MORB source.

Together, these observations demonstrate the power of helium isotopes not solely as a tracer of plume influence, but also the influence of recycled high (U+Th)/3He materials such as subducted oceanic crust.

Acknowledgments

We thank Sarah Lambart and David Graham for thoughtful discussions that improved this manuscript.

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143 5 Extreme Ne, Ar, and Xe heterogeneity in depleted MORBs from the subtropical north Mid-Atlantic Ridge

Jonathan M. Tucker1, Sujoy Mukhopadhyay2, Charles H. Langmuir1, Jocelyn Fuentes1,

Cedric Hamelin3 1 Harvard University 2 University of California, Davis

3 University of Bergen

144 Abstract

We present new He, Ne, Ar, and Xe data on depleted MORBs from the subtropical north

Mid-Atlantic Ridge (23-34◦N). He data display a coherent trend with latitude, which either

indicates the strong influence of an intrinsic unradiogenic component associated with the de-

pleted mantle, or the influence of an undegassed source, or both. Mantle source 21Ne/22Ne

ratios in many samples are relatively unradiogenic for depleted MORBs, suggesting the pres-

ence of a relatively undegassed component. One sample from 29◦N has particularly unradio-

genic He and Ne isotopic compositions reminiscent of primitive plumes, despite its depleted

lithophile composition and the absence of known hotspots in the region.

Well-constrained mantle source Ar and Xe isotopic ratios extend from 40Ar/36Ar = 24,000

and 129Xe/130Xe = 7.6 to extremely low values of 40Ar/36Ar = 11,000 and 129Xe/130Xe =

6.8. These values demonstrate that the entire spectrum of Ar and Xe isotopes observed in

oceanic basalts can occur in normal depleted MORBs with no other anomalous geochemical

or geophycial attributes. This observation demonstrates the power of the noble gases to eluci-

date large-scale processes to which the lithophile isotopic systems are not sensitive.

Globally, Ar and Xe isotopes are correlated in oceanic basalts, but Ar and Xe do not corre-

late strongly with He and Ne. Along with constraints from multi-isotope Xe compositions, we

interpret these systematics to indicate that low Ar and Xe isotope ratios are in part due to

the presence of undegassed material and in part due to recycled atmospheric Ar and Xe. The

lack of correlations with He and Ne indicate that the lighter noble gases are not recycled into

the mantle in significant quantities.

145 5.1 Introduction

Noble gas compositions of oceanic basalts have long been used as a basis to discuss

large-scale convective structure of the mantle (e.g. Allegre et al., 1983; 1996; O’Nions

and Oxburgh, 1983; Kellogg and Wasserburg, 1990; Anderson, 2001; Gonnermann and

Mukhopadhyay, 2009). However, the extent of interaction between degassed and undegassed

reservoirs and between the upper and lower mantle is more complex than a simple two-

reservoir model often assumed in noble gas-based models. For example, it has been docu-

mented for decades that hotspots, which can sample primitive domains, may influence the

compositions of distant MORBs (e.g. Schilling 1973; 1975). Additionally, noble gases have

been used to identify the presence of relatively undegassed domains along certain mid-ocean

ridge segments far removed from plume influences (e.g. Moreira et al., 1995; Niedermann et

al., 1997; Sarda et al., 2000; Kurz et al., 2005). The noble gases are uniquely situated to trace

the interaction between degassed, or processed, mantle domains and undegassed, or primitive,

mantle domains. Thus, understanding their distribution in the mantle provides important

constraints on the large-scale mantle evolution.

The distribution of He isotopic compositions in MORBs is relatively well-established (e.g.

Allegre et al., 1995; Graham, 2002), with recent compilations based on around 1000 indi-

vidual analyses (Moreira, 2013; Peto, 2014). However, while analyses of heavy noble gases

(especially Ne, Ar, and Xe) in MORBs are becoming considerably more routine, ubiquitous

syn- to post-eruptive atmospheric contamination severely diminishes the number of sam-

ples for which the uncontaminated mantle source compositions can be robustly determined.

Only Ne has a sufficient number of well-determined mantle compositions such that the global

MORB distribution can be examined (Peto, 2014). The few well-determined Ar and Xe iso-

topic compositions exhibit considerable variability such that the average MORB composition,

much less the full distribution of MORB compositions, is poorly determined (e.g. Parai et al.,

2012).

The Mid-Atlantic Ridge is the ideal place to examine the distributions of noble gas com-

146 positions in MORBs and the potential for interaction between degassed and primitive reservoirs. It contains both a variety of ridge-proximal hotspots, as well as vast distal expanses far from any known hotspots. Despite being one of the most poorly sampled regions, the subtropical north Mid-Atlantic Ridge is a microcosm of the entire Mid-Atlantic Ridge. The region between the Kane and Hayes Fracture Zones (24-34◦N) lies between two large-scale geochemical and geophysical features. The first feature is centered near 14◦N, and is characterized by enriched trace element and isotopic compositions as well as a bathymetric anomaly

(Bougault et al., 1988; Dosso et al., 1991; 1993). The influence of this anomalous region ex- tends at most ~500 km (~5 degrees) to the north and does not appear to influence the ridge in the subtropics. However this region is also noteworthy as the home of the famous gas-rich

“popping rock” sample 2ΠD43 (Sarda et al., 1988; Staudacher et al., 1989; Sarda and Gra- ham, 1990; Javoy and Pineau, 1991; Burnard et al., 1997; Raquin et al., 2008), which for many years was the only oceanic basalt with well determined He, Ne, Ar, and Xe isotopic compositions (e.g. Kunz et al., 1998; Moreira et al., 1998; Kunz, 1999). The other major feature is the Azores Plateau associated with the Azores plume. Influence of the Azores plume on the Mid-Atlantic Ridge has been documented as far south as the Hayes Fracture Zone

(Schilling, 1975; White and Schilling, 1978; Dosso et al., 1999; Debaille et al., 2006) as a pro- gressive trend from more enriched compositions near the Azores to normal depleted MORBs at the Hayes Fracture Zone. Another anomaly, perhaps unrelated to the Azores plume, is located near the Oceanographer Fracture Zone at 35◦N and is superimposed on the longer- wavelength trend (White and Schilling, 1987; Shirey et al., 1987; Dosso et al., 1999).

In this study, we present new Ne, Ar, and Xe data from the region between the Kane and

Atlantis Fracture Zones. We also present new He data between the Atlantis and Hayes Frac- ture Zones as well as south of the Kane Fracture Zone, extending the dataset presented in

Chapter 4. We will discuss the new data in the regional context of the subtropical north At- lantic to address the influence of undegassed reservoirs and the Azores plume on the depleted mantle. And as the Ar and Xe data add significantly to the databases of well-determined mantle source values corrected for atmospheric contamination (e.g. Moreira et al., 1998;

147 Parai et al., 2012; Tucker et al., 2012;, Peto, 2014), we will also discuss the data in the context of the global distributions of heavy noble gas compositions.

5.2 Methods

Ne, Ar, and Xe isotopes have been measured on 10 samples from the KN207-2 cruise from

between the Kane and Atlantis Fracture Zones (24-30◦N). These data complements the He dataset described in Chapter 4. In addition, we measured He isotope ratios on 5 samples from the MARK segment just south of the Kane Fracture Zone (23◦N) and 9 samples from between the Atlantis and Hayes Fracture Zones, extending the dataset presented in Chapter 4

(Table E.1). MARK samples are from the A129-7 cruise and samples between the Atlantis to

Hayes Fracture Zones are from the OCE180 cruise. Results from our new He and heavy noble gas data will be discussed alongside the He data presented in Chapter 4. Sample locations are shown in Figure 5.1.

The procedure for measuring He isotopes is given in Chapter 4. CO2 and He abundances, along with heavy noble gas abundances and isotopic ratios, were measured on chips of fresh basaltic glass. Where necessary, minor surface alteration was removed by leaching in 5% ni- tric acid and ultrasonically cleaning in deionized water and acetone. Around ~2-4 g of fresh basalt glass were loaded for heavy gas analysis. Prior to heavy gas analyses, samples were baked under vacuum at 100 ◦C for 24 hours and pumped for approximately an additional week.

All samples were measured by step-crushing on a Nu Instruments Noblesse Noble Gas

Mass Spectrometer. He data in Chapter 4 were collected both at Harvard University and the

University of California, Davis, and all He data presented in this chapter at UC Davis. All heavy noble gas measurements except for sample D14-2 were measured at UC Davis. Dur- ing all analyses, reactive gases were pumped with hot and cold SAES getters and all noble gases were cryogenically separated and sequentially let into the mass spectrometer. Ne and

Ar isotopes were measured in full multicollection and Xe isotopes in a combination of multicollection and peak jumping. 20Ne and 22Ne were corrected for isobaric interferences from

148 Figure 5.1: Sample locations along with major fracture zones. Samples measured for He-Ne-Ar-Xe shown in yellow; samples measured for He in this study shown in orange; samples measured for He presented in Chapter 4 shown in red. One sample (OC180 D29-1) was collected slightly off-axis.

149 40 44 Ar and CO2. Procedural blanks were measured prior to step-crushing for each sample. 20Ne and 129Xe

blank volumes were typically around 1.5% that of samples, and 36Ar blanks around 0.5%.

Blanks had an isotopic composition indistinguishable from air, and because step-crushing

data represent mixtures between mantle-derived gases and atmospheric contamination, no

blank correction was applied.

He isotope ratios were determined by normalization to a synthetic standard with

3 4 He/ He = 8.81 RA. Ne, Ar, and Xe isotope ratios were determined by normalization to an air standard. Reproducibility of standards was typically better than 0.2% and 0.5% for

the 20Ne/22Ne and 21Ne/22Ne ratios, and typically better than 1% for 129Xe/130Xe and

136Xe/130Xe ratios.

5.3 Results

5.3.1 Helium

He isotope ratios of all but one sample vary between approximately 87,000 (8.2 RA) and

71,000 (10 RA), extending the range slightly from that observed just between the Kane and Atlantis Fracture Zones (Chapter 4). While mostly less radiogenic than average MORB, these samples fall well within the typical range of MORBs. There is a single anomalous sam-

4 3 ple, KN207-2 D5-1 with unradiogenic He/ He of 65,000 (11 RA). A second split of the same sample (D5-2, visually indistinguishable from D5-1) was also analyzed, which gave an identical He isotope ratio. This unique sample is discussed in detail below.

5.3.2 Neon

Heavy noble gas (Ne, Ar, Xe) analyses are typically complicated by ubiquitous syn- or post- eruptive atmospheric contamination, where the atmospheric 20Ne/22Ne is 9.8. 20Ne/22Ne ratios > 11.0 are observed on 9 of the 10 samples measured for heavy gases; on one sample

(D14-2) the maximum value is 10.76. However, excesses of 20Ne/22Ne above 12.0 are rare,

150 Table 5.1: Mantle source noble gas compositions

and only measured in samples D5-1 and D42SG.

Because step-crushing data form linear mixing arrays between the atmospheric and mantle end-members, mantle 21Ne/22Ne ratios were determined by correlation with 20Ne/22Ne

and extrapolation to the mantle 20Ne/22Ne ratio. Extrapolated mantle source isotopic com-

positions are denoted with a subscript “E”. Linear fits are performed by minimizing the total

(x and y) error-normalized distance, assuming no error correlation, and forced through the

atmospheric composition. We assume a mantle 20Ne/22Ne ratio of 12.5 (e.g. Ballentine and

Holland, 2008; Raquin et al., 2008) but note that extrapolating to different values only alters

our conclusions numerically, not conceptually.

Reasonable linear extrapolations were possible for 9 samples (Figure 5.2; Table 5.1). One sample (D38-3) has only two crushes so the fit is not well constrained and not presented. The

21 22 samples have Ne/ NeE values between 0.0513±0.001 and 0.0571±0.0003, except for sample D5-1, which has a significantly less nucleogenic value of ±0.0438 0.0004. We note that the uncertainties on some extrapolated values are relatively large compared to other data from our laboratory (e.g. Mukhopadhyay, 2012; Parai et al., 2012; Tucker et al., 2012; Peto et al.,

2013; 2014). This is due to the low number of crushes and lower 20Ne/22Ne values in these samples than sometimes observed.

151 20 22 21 22 21 22 Figure 5.2: Ne/ Ne vs. Ne/ Ne for nine samples. Mantle source ( Ne/ NeE) compositions dis- played in each panel are determined by extrapolating fits of step-crushing data to 20Ne/22Ne = 12.5. One sample (D38-3) had only two crushing steps and could not be fit well.

152 5.3.3 Argon and xenon

As heavy noble gas measurements represent mixtures of mantle gas and air contamination,

40 36 40 36 40 36 mantle values of Ar/ Ar ( Ar/ ArE) are determined by correlating Ar/ Ar with 20Ne/22Ne, and extrapolating to the mantle 20Ne/22Ne value. Mixing is hyperbolic in this

ratio-ratio space, although data often display a significant amount of scatter, indicating

the presence of multiple contaminants with atmospheric isotopic compositions but fraction-

ated Ne/Ar ratios. Therefore, a best-fit hyperbola represents an assumption of a simple 2-

component mixture, or a pseudo 2-component mixture where multiple air contaminants are

present in approximately equal proportions in each crushing step.

In general, a mixing hyperbola of this sort is represented by 4 parameters as Ax +

Bxy + Cy + D = 0 (e.g. Langmuir et al., 1978), three of which are linearly independent.

The mixing hyperbola is further constrained to pass through the atmospheric composition

(20Ne/22Ne=9.8; 40Ar/36Ar=296), and this constraint results in the elimination of an addi-

tional parameter resulting in a hyperbola defined by only two parameters. We performed fits

and estimated uncertainties using the methodology described by Parai et al. (2012). We note

that hyperbolic fits performed by this methodology often have asymmetric uncertainty distri-

butions (Parai et al., 2012).

Five samples yielded well-constrained hyperbolas where the uncertainty on the mantle

40Ar/36Ar is minimal (Figure 5.3; Table 5.1). A sixth sample (D37-1) could also be fit but yielded a larger uncertainty. Although the fit for D37-1 is mathematically robust, because it is based only on four data points and the highest measured values are considerably below the true mantle value, we have less confidence in the extrapolated value.

Mantle Xe isotope ratios are best determined by hyperbolically correlating 129Xe/130Xe

with 40Ar/36Ar rather than with 20Ne/22Ne, despite potential uncertainties in the mantle

40Ar/36Ar value. The sense of curvature in Ar-Xe mixing hyperbolas is often such that uncer-

tainty in the mantle 40Ar/36Ar does not significantly influence the extrapolated Xe isotopic

ratios (i.e. the hyperbolas are concave-down when Ar is on the x-axis), and Ar-Xe hyperbolas

are often better constrained than Ne-Xe hyperbolas. Other Xe isotopic ratios are determined

153 40 36 20 22 40 36 Figure 5.3: Ar/ Ar vs. Ne/ Ne hyperbolic fits. Mantle source Ar compositions ( Ar/ ArE) are determined by hyperbolic correlation with 20Ne/22Ne and extrapolation to 20Ne/22Ne = 12.5. Hyperbolic fits are possible for six samples although fits for D1-6 and D37-4 are less well-constrained as they arebased on only 4 data points.

154 by linear correlation with 129Xe/130Xe. Linear fits were performed in an analogous manner to

Ne-Ne linear fits. Further details of the procedures used are given in Mukhopadhyay (2012),

Parai et al. (2012), and Tucker et al. (2012).

129 130 129 130 Mantle Xe/ Xe ( Xe/ XeE) values were well determined for 4 samples (Fig- ure 5.4; Table 5.1). Sample D1-6, which only had 3 data points, has a poorly determined

129 130 40 36 Xe/ XeE. Sample 37D-1, which has a poorly defined Ar/ ArE could be fit for Xe but the fit is more uncertain and based only on 4 data points (Figure 5.4; Table 5.1).

40 36 129 130 The mantle Ar/ ArE and Xe/ XeE ratios of 24,100 and 7.59 for sample D42SG are similar to the “popping rock” sample 2ΠD43 (Moreira et al., 1998). With the possible excep-

40 36 tion of D37-1, which has poorly defined mantle values, the other samples have Ar/ ArE

129 130 between 10,000 and 17,000, and three samples have Xe/ XeE < 7.0 (Figures 5.3-5.4), extremely low values for MORBs (Parai et al., 2012; Tucker et al., 2012).

5.4 Discussion

5.4.1 Geochemical background: Kane to Oceanographer

The dominant characteristic of the subtropical north Mid-Atlantic Ridge is the Azores plateau between ~37-42 ◦N, associated with the Azores hotspot. Southward of the plateau,

Mid-Atlantic Ridge continues to be influenced by the Azores hotspot, evidenced by a steady

deepening of ridge axis depth all the way to the Kane Fracture Zone at ~24 ◦N. The geochemistry of basalts also continues to be influenced by the Azores plume as far south asthe

Hayes Fracture Zone (e.g. Schilling, 1975; Debaille et al., 2006). However the density of published geochemical data decreases significantly south of the Hayes Fracture Zone, and especially in the region between the Atlantis and Kane Fracture Zones.

The geochemical trends in lithophile isotopes and incompatible trace elements from published analyses in the region between the MARK segment south of the Kane Fracture Zone and the Oceanographer Fracture Zone are shown in Figure 5.5 (similar to Debaille et al.,

2006 Figure 2). The details of the trace element and lithophile isotope systematics are not

155 Figure 5.4: 129Xe/130Xe vs. 40Ar/36Ar hyperbolic fits. Mantle source Xe isotopic compositions 129 130 40 36 ( Xe/ XeE) are determined by hyperbolic correlation with Ar/ Ar and extrapolation to the 40 36 mantle source Ar/ ArE composition of each sample. Because of the sense of hyperbolic curvature, 129 130 40 36 Xe/ XeE compositions are not particularly sensitive to uncertainty in Ar/ ArE. Fits for samples D1-6 and D37-1 are based on 3 or 4 data points and therefore not as well-constrained.

156 the focus of this study and have been discussed elsewhere (e.g. Schilling, 1975; Dosso et al., 1993; Debaille et al., 2006), so we will only point out three salient features from these plots. The first feature is a distinct enrichment at the northern end of the region toward the Oceanographer Fracture Zone, beginning at or perhaps just south of the Hayes Fracture

Zone. The second feature is a more subtle trend from slightly more enriched to slightly more depleted compositions from the Kane Fracture Zone toward the Hayes Fracture Zone. This trend corresponds to a subtle gradient in axial depth from ~4000 m near the Kane Fracture

Zone to ~3500 m near the Hayes Fracture Zone. The third is a small geochemical anomaly just south of the Atlantis Fracture Zone, around 29-30◦N. As compositions appear to return

to depleted values north of the Atlantis Fracture Zone, it is possible this anomaly is caused

by a blob of material separated at depth in the mantle from a dispersed Azores plume. It

may alternatively be independent of the Azores plume entirely.

We note that other small-scale geochemical anomalies are seen throughout the mid-ocean

ridge system. One prominent example (because it also has He and Ne data) is located near

16-21◦S in the East Pacific Rise (EPR) just south of the Garrett Fracture Zone (Mahoney

et al., 1994). Unlike this anomaly, the EPR anomaly is also associated with a bathymetric

anomaly and may be associated with seamounts near the EPR at 16-17◦S. However, the 29-

30◦N MAR anomaly is proximal to the robust Broken Spur hydrothermal field at 29.2◦N (e.g.

Murton et al., 1995) which may indicate an increased area of magma productivity.

5.4.2 Helium

4He/3He ratios show a remarkably coherent variation with latitude, with more radiogenic ratios in the south near the Kane Fracture Zone to less radiogenic in the north near the Hayes

Fracture Zone (Figure 5.6). The origin and implications of the regional gradient between the

Kane and Atlantis Fracture Zones were discussed in depth in Chapter 4. We had previously

hypothesized (Chapter 4) that the relatively unradiogenic He and Pb isotope ratios near the

Atlantis Fracture Zone were characteristic of a depleted mantle component and that more

radiogenic compositions near the Kane Fracture Zone reflected the increased influence of

157 206 204 143 144 Figure 5.5: Pb/ Pb, Nd/ Nd, La/Sm, and K2O/TiO2 vs. Latitude for the subtropical Mid- Atlantic Ridge. K, A, H, O refer to the Kane, Atlantis, Hayes, and Oceanographer Fracture Zones. In- fluence of enriched components such as the Azores plume is observed at least as far south oftheHayes Fracture Zone. The region between the Kane and Atlantis Fracture Zones primarily displays depleted compositions, but some isotopic enrichment may be observed around 29-30◦N. Data compilation courtesy of J. Fuentes.

158 Figure 5.6: 4He/3He vs. Latitude for the subtropical Mid-Atlantic Ridge. Data between Kane (K) and At- lantis (A) Fracture Zones from Chapter 4; data south of the Kane Fracture Zone and between the Atlantis and Hayes (H) Fracture Zones from this study. The data display an overall coherent geographic trend, which could either indicate increased influece of a depleted component or relatively undegassed component near the Hayes Fracture Zone, or both. recycled oceanic crust. North of the Atlantis Fracture Zone, some He isotope compositions continue to become more unradiogenic, although the scatter is higher and sampling density lower (Figure 5.6). Pb isotopic compositions also become more variable north of the Atlantis

Fracture Zone (Figure 5.6; Debaille et al., 2006). It is therefore difficult to ascertain whether

the He and Pb systematics remain coupled north of the Atlantis Fracture Zone. The rela-

tively unradiogenic He isotope compositions between the Atlantis and Hayes Fracture Zones

could then either reflect a continuation of the trend toward depleted compositions observed

between the Kane and Atlantis Fracture Zones, or alternatively the influence of a relatively

undegassed component.

To explore whether our samples north of 29◦N, especially north of the Atlantis Fracture

Zone, are influenced by the Azores plume, we will compare these compositions to composi-

tions measured at the Azores themselves. The various volcanoes of the Azores display a wide

variety of isotopic compositions, however one end-member expressed primarily in Terceira has

very radiogenic Pb and unradiogenic He (206Pb/204Pb up to ~20; 4He/3He down to ~60,000;

159 Moreira et al., 1999). Such a component mixed with depleted mantle could potentially produce the compositions observed between the Atlantis and Hayes Fracture Zones, which extend to 4He/3He of 70,000 and 206Pb/204Pb > 19 (Figures 5.5,5.6). Therefore it is possible that the relatively unradiogenic He observed between the Atlantis and Hayes Fracture Zones is related to the Azores plume more than 1000 km away.

However, to confidently establish whether the He isotopic compositions in samples between the Atlantis and Hayes Fracture Zones are influenced by a Terceira-like Azores component, a high sampling density in He isotopes would be required all the way to the Azores platform.

The available data do not strongly suggest increasing Azores influence; for example, as far north as the Lucky Strike segment (37◦N), He isotopes vary primarily between 85,000 and

88,000 (8.2-8.5 RA; Moreira et al., 2011), more radiogenic than some of our samples which have 4He/3He lower than 80,000. The He isotopes in the Lucky Strike segment were not in-

terpreted to exhibit strong Azores influence (Moreira et al., 2011). Therefore, continuous and

gradually decreasing influence of the Azores plume on He isotope compositions southward

from the Azores Platform all the way to the Atlantis Fracture Zone is unlikely. However, it

remains unclear whether the He isotopes in the region between the Atlantis and Hayes Frac-

ture Zones reflect the influence of an undegassed component not continuously connected to

the Azores, or a continuation of the depleted trend between the Kane Fracture Zone and

29◦N.

5.4.3 Neon

Ne isotopes can provide significant insights not available from He alone as a relatively undegassed source may affect Ne isotopes more strongly than He. This is because MORBsand

OIBs with low 21Ne/22Ne do not necessarily have 4He/3He ratios much lower than average

MORBs (e.g. Moreira, 2013). While He data north of the Atlantis Fracture Zone suggested

a possible undegassed component, this component is speculative and ultimately not our pre-

ferred explanation for the He compositions between the Kane and Atlantis Fracture Zones.

Extrapolated (mantle) Ne isotopic compositions are plotted against latitude in Figure 5.7.

160 21 22 Figure 5.7: Ne/ NeE vs. Latitude for the subtropical Mid-Atlantic Ridge. Some lower values near 21 22 0.05 are rare for depleted MORBs. One exceptional sample has extremely low “plume-like” Ne/ NeE of 0.044. Filled symbols from this study. Open symbols are fits to data from Sarda et al. (1988), Marty (1989), and Moreira and Allegre (2002). Dashed line and grey bar are an estimate of average MORB (Peto, 2014).

21 22 The first apparent feature from this figure is that the Ne/ NeE values are relatively low compared to average MORB, even excluding the obviously exceptional sample D5-1 (Figures

5.2,5.7; Table 5.1). Aside from that sample, the values range from 0.051 to 0.057. The av-

21 22 erage depleted mantle is often thought to be represented by a Ne/ NeE value of around 0.06 (extrapolated to 12.5; e.g. Sarda et al., 1988; Hiyagon et al., 1992; Moreira et al., 1998;

Ballentine and Holland, 2008), with extremely depleted samples as high as 0.066 (Tucker et

21 22 al., 2012; Stroncik and Niedermann 2016). Lower Ne/ NeE values are observed in areas of plume-ridge interaction (e.g. Moreira et al., 2011; Parai et al., 2012) but low values are also often attributed to plume influence even in the absence of a known hotspot (e.g. Moreira et al., 1995; Niedermann et al., 1997; Tucker et al., 2012). In these cases, some other geochemical feature, such as isotopic enrichment, or geophysical feature, such as a bathymetric anomaly or nearby seamounts, is usually present.

The samples between the Kane and Atlantis Fracture Zones show none of these anomalous features, with the possible exception of a small geochemical anomaly at 29-30◦N. The ridge

161 axis depth varies gently from approximately 4000 m near the Kane Fracture Zone to 3500 m near the Atlantis Fracture Zone; εNd varies between +8 and +12 (n=89; with one exception:

KN207-2 RC117 has εNd = +6.5) and 206Pb/204Pb varies between 18.1 and 18.8 (n=82) with most samples lower than 18.5 (Fuentes et al., unpublished data). The region between the

Kane and Atlantis Fracture Zones strongly appears to be 800 km of normal depleted mid-

21 22 ocean ridge, and normal mid-ocean ridge segments with Ne/ NeE < 0.056 are particularly rare (Peto, 2014).

To explain He and Pb variations, we hypothesized that the region near the Atlantis Frac- ture Zone (especially up to 29◦N) is sampling an intrinsic depleted component with relatively unradiogenic He while the region near the Kane Fracture Zone sampled a degassed component with radiogenic He and Pb derived from recycled oceanic crust. However, in contrast to relatively unradiogenic He, the depleted end-member is characterized by extremely nucleogenic 21Ne/22Ne (Tucker et al., 2012; Stroncik and Niedermann, 2016). Hence, the low values observed here are likely not reflective of a depleted mantle component. Like 4He/3He

21 22 and other chemical systems, Ne/ NeE may display a gradient with latitude (Figure 5.7), although this may be obscured by large error bars. Additional high-precision work would be required to robustly uncover an underlying gradient. However, the lack of a strong gradient could indicate that from south to north there is an increasing influence of both a depleted component with high 21Ne/22Ne and an undegassed component with low 21Ne/22Ne, which counter each other producing no overall coherent variation. Whereas a plume-like component has not been hypothesized in Pb south of the Hayes Fracture Zone, a relatively undegassed component is perhaps observed in He isotopes at least as far south as the Atlantis Fracture

Zone, and observed in Ne south of the Atlantis Fracture Zone toward the Kane Fracture

Zone.

21 22 The observation of low Ne/ NeE between the Kane and Atlantis Fracture Zones has the important implication that a region of mid-ocean ridge with normal depleted isotopic and trace element signatures can still be influenced by a relatively undegassed or plume-like component. If these samples indeed experience Azores influence expressed in Ne isotopes, that

162 influence is being felt more than a staggering 2000 km away. And furthermore the southwest- ward transport of Azores plume material must be extremely rapid so as to avoid significant nucleogenic ingrowth. It is also possible that the undegassed noble gas signature derives from a geophysical entity distinct from the Azores. One highly speculative possibility is that this component is related to the New England/Great Meteor/Seewarte Seamount Chains that straddle the Mid-Atlantic Ridge south of the Azores. But even if it is unrelated, the presence of these seamounts raise possibility of other geophysical anomalies in the north Atlantic unrelated to known hotspots.

5.4.4 The geochemical anomaly at 29◦N

In the above discussions of He and Ne isotopic compositions, we have excluded discussion of the geochemical anomaly between 29-30◦N, which contains the sample 5D-1. This sam-

4 3 21 22 4 3 ple has exceptionally low He/ He and Ne/ NeE for a MORB. At 65,000, the He/ He of this sample is indistinguishable from the lowest 4He/3He from Terceira (Azores), and its slope in Ne 3-isotope space is identical to the regression line through the most uncontaminated Terceira sample, passing through 21Ne/22Ne = 0.044 at 20Ne/22Ne = 12.5 (Madureira et al., 2005). But more strikingly, the lithophile isotope systems are similar to other depleted samples from this region (εNd = 10.6; 206Pb/204Pb = 18.3; Fuentes et al., unpublished data).

Therefore this sample is unusual among MORBs in its unradiogenic He and Ne isotopic compositions but normal depleted lithophile isotopes.

Could this be a detached part of the Azores plume? In one possible scenario, a rising

Azores plume could encounter a discontinuity in the mantle and break into smaller plumelets or rising blobs that are sampled discontinuously along the Mid-Atlantic Ridge. In contrast to the similarity in noble gases, nearly all Terceira samples have εNd between +6 and +6.5,

and 206Pb/204Pb between 19.5 and 20 (Georoc database), significantly more enriched than

this sample. So if this sample is indeed sampling noble gases from the Terceira end-member,

that end-member would need to be extremely gas-rich compared to the depleted mantle, so

as to influence the noble gas compositions but maintain a depleted lithophile isotopic com-

163 position. If the Terciera end-member composition were more unradiogenic than the most extreme measured samples, perhaps similar to plumes like Iceland, Hawaii, or the Galapagos, it would not need to be as gas-rich. However, such an unradiogenic end-member in the Azores is speculative as it has not been observed. Furthermore, the Tercira component would need to be sampled only at this specific location, more than 1800 km away from the Azores, without significantly influencing the noble gas compositions of other samples from thesameand adjacent segments, less than 30 km away.

More likely, the low He and Ne isotopes of this sample may be sampling a mantle anomaly independent of the Azores. In that case, this sample demonstrates the preservation and sampling of an extremely small mantle domain with undegassed noble gas compositions. This domain then only influences MORBs compositions over 10s of km as the other samples from the same 50 km long segment have 4He/3He between 78,000 and 79,000 (D3-1, D4-1, D63-2;

~9.2 RA). But its presence also strengthens the argument that the other samples from this area may be influenced by the presence of a relatively undegassed component, as discussed

above with Ne isotopes.

5.4.5 Argon

40 36 While there are not enough samples with well determined mantle source Ar/ ArE ratios to examine regional trends, two groupings are apparent. Samples near the Kane Fracture Zone

◦ 40 36 ◦ at 24 N have Ar/ ArE > 24,000, and samples near the Atlantis Fracture Zone at 30 N

40 36 have Ar/ ArE < 17,000 (Figure 5.8a).

40 36 The mantle source Ar/ ArE ratio for D42SG is quite close to the value of the E- MORB popping rock 2ΠD43 of ~24,000 (Moreira et al., 1998; Raquin et al., 2008; Figure

5.3; Table 5.1) but significantly less than ~40,000 from depleted MORBs in the equato-

rial Atlantic (Tucker et al., 2012; Stroncik and Niedermann, 2016) and Bravo Dome (Hol-

land and Ballentine, 2006) and toward the low end of the range of non plume-influenced

SWIR MORBs (Parai et al., 2012). However, 2ΠD43 is relatively enriched isotopically, with

206Pb/204Pb=19.02; 87Sr/86Sr=0.7027; 143Nd/144Nd=0.51305; and extremely enriched in

164 40 36 129 130 Figure 5.8: (a) Ar/ ArE and (b) Xe/ XeE vs. Latitude. The samples appear to form two clusters with more radiogenic values near the Kane Fracture Zone and less radiogenic values near the Atlantis Fracture Zone. terms of trace elements, with La/Sm=3.0; Ba=150 ppm (Dosso et al., 1991, 1993). 2ΠD43 is

furthermore associated with a strong geochemical and bathymetric anomaly centered around

14◦N, and is proximal to a chain of seamounts termed the Researcher Ridge just west of the

Mid-Atlantic Ridge axis. This region has also been hypothesized as the location of the triple

junction between the African, North American, and South American plates. In contrast, sam-

ple D42SG is typical of normal depleted MORBs with 206Pb/204Pb=18.5, 87Sr/86Sr=0.7025,

143Nd/144Nd=0.51315; La/Sm=0.92; Ba=12.5 ppm (Fuentes et al., unpublished data), and

not associated with any known geophysical or geochemical anomalies. The comparison of this

sample to 2ΠD43 alone demonstrates that large variations in lithophile chemistry are possible

with little variation in heavy noble gas compositions. While we note that our D42SG sample

is station glass, and it cannot be guaranteed that all splits are identical material, a second

piece of station glass from this dredge yielded identical Ne-Ar-Xe composition (Mukhopad-

hyay et al., unpublished data).

40 36 The mantle source Ar/ ArE ratios for the other samples are all extremely low for

40 36 MORBs (Figures 5.3,5.8; Table 5.1). The Ar/ ArE ratios of 10,000-11,000 observed in D5- 1 and D2-4 represent the lowest ever determined for the mantle source of MORBs. D11-4 and

165 40 36 D1-6 also have low Ar/ ArE, around 16,000. The Ar compositions of these four MORB samples are very similar to the values determined for the Iceland and Galapagos plumes of

~10,000 (Mukhopadhyay, 2012; Péron et al., 2016), and the Rochambeau Rift sampling the

Samoan plume of ~16,000 (Peto et al., 2013). Therefore one explanation for these exception-

ally low MORB values is the strong involvement of a plume-like component.

An alternative explanation for low mantle 40Ar/36Ar is the involvement of recycled atmo-

spheric Ar, which carries a very low 40Ar/36Ar ratio (e.g. Sarda et al., 1999). As the atmo-

spheric 40Ar/36Ar ratio is ~100× lower than the depleted mantle, a gas-poor depleted mantle

might be particularly susceptible to overprinting from recycled air. But without strong evi-

dence for other significant recycled components, it is difficult to assess this possibility. And

with 40Ar/36Ar ratios alone, it is impossible to distinguish between the involvement of recy-

cled air and a plume-like component.

40 36 Regardless of the explanation for the wide range of Ar/ ArE ratios observed in these MORBs, the entire range, including the extreme low values in samples from near the Atlantis

Fracture Zone, occurs with lithophile isotopic compositions typical of MORBs. Among these

samples, 206Pb/204Pb varies between 18.3 and 18.7, and εNd varies between +9.6 and +10.6

(Fuentes et al., unpublished data). Also considering the depleted MORBs from the equato-

40 36 rial Atlantic (Tucker et al., 2012), the entire range of MORB Ar/ ArE, from ~10,000 to ~40,000, is observed in samples with little variation in lithophile chemistry.

This study significantly adds to the database of MORBs with well-defined mantle source

values. Acknowledging the small number of MORBs with well-defined mantle source values,

and the very large range of variation between them, it is possible that the average MORB

40Ar/36Ar composition is not as high as 40,000 as observed in depleted MORBs and the

Bravo Dome well gases, but rather lies between 20,000 and 30,000. Such values are only fac-

tors of ~2-3× higher than primitive plume values of ~10,000-15,000. This difference is much

smaller than factors of >5 sometimes used in dynamical models of terrestrial noble gas distri-

butions (e.g. upper mantle 40Ar/36Ar of 30,000-40,000; lower mantle 40Ar/36Ar of ~5,000;

O’Nions and Tolstikhin, 1994; Tolstikhin and Marty, 1998). These types of models, con-

166 strained by large noble gas isotopic differences between MORBs and OIBs, strengthened the notion of convectively isolated upper and lower mantle reservoirs (see e.g. Porcelli and

Ballentine, 2002). However, a much smaller difference between MORBs and OIBs and over- lapping ranges implies a larger degree of interaction between the two reservoirs than is often assumed to be possible.

5.4.6 Xenon

129 130 Similarly to Ar isotopes, mantle source Xe/ XeE ratios also form two clusters, with more radiogenic values near the Kane Fracture Zone and less radiogenic values near the Atlantis

129 130 Fracture Zone (Figure 5.8). The Xe/ XeE ratio of D42SG of 7.59 is similar to the 2ΠD43 value of 7.6 (Moreira et al., 1998). And because its Ne and Ar compositions are also com-

parable, the two samples might be considered similar in their heavy noble gas compositions.

129 130 The samples from near the Atlantis Fracture Zone have very low Xe/ XeE, ranging between 6.8-7.1. As with Ar, these low values could indicate plume involvement, as plumes have

129 130 low Xe/ XeE close to 7 (Mukhopadhyay, 2012; Peto et al., 2013) or the involvement of recycled air, which carries 129Xe/130Xe of 6.5, or both.

The potential involvement of recycled air can be examined by plotting 130Xe/136Xe vs.

129Xe/136Xe (Figure 5.9). In this space, compositions would evolve starting from the primori- dal composition, which has 130Xe/136Xe > 0.5 and 129Xe/136Xe > 3.3 regardless of the source

(e.g. chondritic, solar, U-Xe, etc.). It is also not guaranteed that the whole mantle begins

with the same initial composition. The compositions then evolve vertically due to the de-

cay of short-lived 129I producing 129Xe. An early degassed reservoir which has lost Xe would

evolve vertically more quickly than an undegassed reservoir due to its higher 129I/Xe ratio.

After ~100 Myr, compositions evolve toward the origin due to decay of 238U and 244Pu producing 136Xe through spontaneous fission. A degassed reservoir will lose its Xe isotopes and thus have low (129Xe,130Xe)/(244Pu+238U) and its composition will evolve toward the origin faster than less degassed reservoir which retains its Xe complement. Recycling of atmospheric

Xe moves compositions toward the atmospheric composition (open diamond in Figure 5.9).

167 Figure 5.9: 129Xe/136Xe vs. 130Xe/136Xe. Error-weighted mean compositions of two pooled groups of samples are shown along with literature data. Atmospheric composition is the open diamond. Filled stars are pooled Xe compositions of samples from this study; group 1 are the more radiogenic samples from near the Kane Fracture Zone and group 2 are the less radiogenic samples from near the Atlantis Fracture Zone. The two groups cannot be related to each other or related to the composition of depleted equatorial At- lantic MORBs solely by the addition of recycled atmospheric Xe. However the cause of the Xe isotopic differences cannot be uniquely determined from this plot. Equatorial Atlantic data from Tucker et al. (2012); 2ΠD43 data from Moreira et al. (1998) and Kunz et al. (1998); Iceland data from Mukhopadhyay (2012).

Therefore any location on this plot can be reached through non-unique combinations of variable initial Xe isotopic composition, initial 129I-244Pu-238U compositions, extent of early degassing, extent of long-term degassing, and history of atmospheric recycling.

But while evolution on this diagram can be complicated and highly non-unique, the diagram can discriminate whether different measured compositions can be related solely through

differences in the amount of recycled atmospheric Xe. This is because two such related sam-

ples would be collinear with the atmospheric composition. We can therefore test whether the

129 130 extremely low Xe/ XeE ratios in samples from near the Atlantis Fracture Zone are re-

129 130 lated to the moderate Xe/ XeE ratios in samples from near the Kane Fracture Zone, or

129 130 the high Xe/ XeE ratios in samples from the equatorial Atlantic by the addition of recycled atmospheric Xe. To that end, we have combined our samples into two groups on the

basis of Ar and Xe isotopic compositions and geography (e.g. Figure 5.8); D42SG and D37-

1 with moderate 40Ar/36Ar and 129Xe/130Xe in “group 1” and D1-6, D2-4, D5-1, and D11-

168 4 with low 40Ar/36Ar and 129Xe/130Xe in “group 2”). Plotted in Figure 5.9 are the error- weighted mean compositions of all crushing steps from these two group. Because the compositions shown here have not been corrected for post-eruptive air contamination, the true mantle source composition lies further along the mixing line with the atmospheric composition. But because recycled atmospheric Xe would move a composition along the same mixing line, the contamination correction is not necessary to address whether samples can be related solely by addition of recycled atmospheric Xe. The mean compositions of the two groups plot on distinct mixing lines with air, implying that the unradiogenic Xe isotopic compositions, and by inference unradiogenic Ar compositions, of group 2 cannot be related to the more radiogenic values of group 1 solely by addition of recycled atmospheric Xe. Further- more, neither group can be related to the equatorial Atlantic MORBs with highly radiogenic

129 130 Xe/ XeE solely by addition of recycled atmospheric Xe. But because of the variety of processes by which a composition may evolve in Figure 5.9, we cannot say with certainty which combination of processes generated any particular composition. For example, the apparent coincidence of the group 1 samples with the composition of the Iceland plume should not be interpreted to mean that the group 1 samples derive from an undegassed Iceland-like source save for differences in the amounts of recycled air. Thisis because of the non-unique ways to arrive at any composition. Thus the origin of the composi-

129 130 tions of the MORBs in this study, including the unusually unradiogenic Xe/ XeE ratios in some samples, cannot be fully addressed with this analysis alone. Such questions on the origin of a particular Xe composition can be addressed with a full deconvolution of the Xe isotopes to calculate the relative proportions of I-derived, U-derived, Pu-derived, primordial, and recycled atmospheric Xe. Such calculations will be presented in a later contribution.

Regardless of the cause of the Xe isotope variations, these samples display a wide range

129 130 in Xe/ XeE ratios, extending the MORB range to values lower than observed in some

129 130 plumes. Including the depleted equatorial Atlantic MORBs, the entire range of Xe/ XeE ratios from ~6.8 to ~7.8 occurs in samples with little variation in lithophile chemistry. To-

gether with the similar observation in Ar isotopes, these observations demonstrate that heavy

169 noble gases can be sensitive to, and therefore diagnostic of, geological processes that do not strongly affect lithophile chemistry.

5.5 Global variations in heavy noble gases

The global coverage of He and Ne isotopes in oceanic basalts has increased significantly in

the past few decades (for example, see reviews by Graham, 2002; Moreira, 2013; and a recent

global compilation by Peto, 2014). However, the corresponding database of well-defined man-

40 36 129 130 tle source Ar/ ArE and Xe/ XeE values remains quite small such that the samples presented in this study significantly add to that count. Despite the paucity of data, wecan begin to examine global systematics of Ar and Xe isotopes and compare them to the better understood global He-Ne systematics.

Figure 5.10 shows covariations of He, Ne, Ar, and Xe isotopes in the samples where the extrapolated mantle source values are deemed to be best determined (grey squares are samples from this study; white squares from the literature). The MORBs with He-Ne-Ar-Xe data include samples from the Mid-Atlantic Ridge (Tucker et al., 2012; this study) as well as the popping rock 2ΠD43 (Stuadacher et al. 1989; Moreira et al., 1998); the Southwest Indian

Ridge (Parai et al., 2012); and the Gakkel Ridge (Peto, 2014). We also include Ne-Ar-Xe data from the Bravo Dome well gas (Holland and Ballentine, 2006) and He-Ne-Ar data for one sample each from the Mid-Atlantic Ridge and the Southeast Indian Ridge (Peto, 2014).

The three plume samples shown are DICE 10 from Iceland (Trieloff et al., 2000; Mukhopad- hyay, 2012), NLD-27 from the Lau backarc basin sampling the Samoan plume (Peto et al.,

2013), and AHA-NEMO2-D22 from Fernandina in the Galapagos (Kurz et al., 2009; Peron et al., 2016; He-Ne-Ar data only).

Figures 5.10a-b show good correlations between He and Ne and between Ar and Xe iso-

topes. On the other hand, Figures 5.10c-f show relatively low Ar and Xe isotopic variability in samples with unradiogenic He and Ne but a high degree of variability in samples with radiogenic He and Ne. Together, these plots demonstrate a contrasting behavior between the lighter noble gases (He and Ne) and the heavier noble gases (Ar and Xe).

170 Figure 5.10: Cross plots of mantle source He, Ne, Ar, and Xe isotopic compositions in oceanic basalts with well-determined Ar and Xe compositions. MORBs from this study are filled grey squares; MORBs from the literature are open squares; OIBs from the literature are filled black squares. Panels (a) and (b) show correlations between He and Ne and between Ar and Xe isotopic compositions, but significant scatter in Ar and Xe compositions is observed in samples with radiogenic He and Ne (panels c-f). Unradiogenic Ar and Xe isotopic compositions may be influenced by a combination of recycled atmosphere and undegassed components, both of which carry low 40Ar/36Ar and 129Xe/130Xe, preserving the correlation in panel (b). But the lack of strong correlations in panels c-f could indicate that Ar and Xe compositions are in part influenced by recycled atmosphere whereas He and Ne are not recycled in significant quantities.

171 Globally, He and Ne isotope ratios appear to represent a mixture between relatively degassed reservoirs with high 4He/3He and 21Ne/22Ne and undegassed reservoirs with low

4He/3He and 21Ne/22Ne (Figure 5.10a) which has been observed often in the literature.

We note that this mixture need not be linear as undegassed reservoirs tend to have lower

3He/22Ne than degassed reservoirs (e.g. Honda and Patterson, 1999; Moreira and Sarda,

2000; Moreira, 2013). We also note that the samples plotted here are only those that also have well-determined Ar and/or Xe isotopic ratios so while the general scope of the global systematics are captured, local trends may differ from this broader global trend (e.g. Shaw et al., 2001; Tucker et al., 2012; Moreira, 2013). As the origins and consequences of this two- component mixture have been examined in detail (e.g. Graham, 2002; Moreira, 2013), they will not be discussed here further.

Ar and Xe isotope ratios broadly appear to represent a mixture between a component with high 40Ar/36Ar and 129Xe/130Xe and a component with low 40Ar/36Ar and 129Xe/130Xe

(Figure 5.10b) although the origin of these components is more complex than in the case of

He-Ne. High 40Ar/36Ar and 129Xe/130Xe are created by ingrowth of 40Ar and 129Xe in a degassed (high 40K/36Ar, 129I/130Xe) reservoir. Therefore, the radiogenic end of the correlation in Figure 5.10b likely represents reservoirs with extensive histories of early and/or long-term degassing. On the other hand, low 40Ar/36Ar and 129Xe/130Xe may represent either a rela-

tively undegassed reservoir or the addition of recycled atmospheric Ar and Xe. Because both

of these effects result in lower 40Ar/36Ar and 129Xe/130Xe, the overall correlation between Ar

and Xe isotopes could be preserved regardless of the cause.

In contrast, Figures 5.10c-f show a very different behavior: MORBs and OIBs with unradiogenic He and Ne tend to also have unradiogenic Ar and Xe, but MORBs with more radiogenic He and Ne have highly variable Ar and Xe compositions. We interpret this as evidence that the Ar and Xe compositions do not solely result from mixing degassed and undegassed reservoirs, as this would also result in correlations between He or Ne and Ar or Xe, which are not observed. If, however, some of the Ar and Xe variation were due to the incorporation of subducted atmospheric Ar and Xe, but He and Ne were not recycled in significant quantities,

172 correlations between He or Ne and Ar or Xe would be broken but preserved between Ar and

Xe. Indeed, recycled atmosphere has been argued to comprise a large proportion of mantle

Ar and Xe budgets (e.g. Sarda et al., 1999; Holland and Ballentine, 2006; Mukhopadhyay,

2012; Tucker et al., 2012; Parai and Mukhopadhyay, 2015). However, Figure 5.9 demonstrates the variability in Xe isotopic compositions in oceanic basalts cannot result solely from the

mixture of a common composition such as that of depleted MORBs or 2ΠD43 with various

degrees of recycled air. Therefore we conclude the correlation between Ar and Xe isotopes

observed in Figure 5.10b likely results from the combined effects of involvement of a rela-

tively undegassed source and recycled atmospheric Ar and Xe.

The observation that the entire range of Ar and Xe isotopic compositions can occur in

MORBs with restricted ranges in He and Ne isotopic compositions (Figure 5.10c-f) could indicate that recycled slabs contain variable amounts atmospheric Ar and Xe. We have argued

(Chapter 4) that He isotope compositions can be sensitive to the amount of recycled material in the mantle source of MORBs, so MORBs with similar He isotopic compositions could have similar amounts of recycled materials in their mantle source. Therefore, the high degree of Ar and Xe isotopic variability at a relatively constant He isotopic composition could result from variable amounts of atmospheric Ar and Xe in subducting slabs, rather than variable amounts of recycled material in the source. Such an explanation is consistent with the notion that subducting slabs exhibit a wide range in thermal structures and can retain variable amounts of volatiles during subduction (e.g. van Keken et al., 2011). A thorough evaluation of this hypothesis would require examining the joint systematics of the noble gases with other systems such as lithophile isotopes, trace elements, and water contents.

5.6 Summary and conclusions

This study presents new He, Ne, Ar, and Xe data on depleted MORBs from the subtropical

north Mid-Atlantic ridge (23-34◦N). The He and Ne data extend coverage in a poorly sampled region, and the Ar and Xe data significantly increase the number of MORBs for which mantle source Ar and Xe ratios can be robustly determined.

173 He data display a coherent trend with latitude between the Kane and Hayes Fracture

Zones, extending as low as 4He/3He = 70,000 near the Hayes Fracture Zone. This could ei-

ther indicate the strong influence of an intrinsic unradiogenic component associated with the

depleted mantle, or the influence of an undegassed source, or both.

Ne data between the Kane and Atlantis Fracture Zones reveal a mantle source with

21Ne/22Ne of around 0.051-0.057, quite unradiogenic for depleted MORBs. A geochemi-

cal anomaly is also present around 29◦N with very unradiogenic 4He/3He of 65,000 and

21 22 Ne/ NeE of 0.044. This composition could indicate the presence of very small plume-like component among normal, depleted MORBs. Together, the data demonstrate the power of

Ne isotopes to trace the presence of undegassed material in the absence of any other geochemical anomalies.

Mantle source Ar and Xe isotopic ratios span the range from values typical of MORBs

40 36 129 130 ( Ar/ ArE = 24,000; Xe/ XeE = 7.6) to values as unradiogenic as observed in some

40 36 129 130 plumes ( Ar/ ArE = 11,000; Xe/ XeE = 6.8). These values expand the ranges of Ar and Xe isotope ratios observed in MORBs and demonstrate that the entire range of Ar and

Xe isotope ratios is observed in normal, depleted MORBs. The observation that noble gas compositions can vary widely with little variation in lithophile geochemistry demonstrates the power of the noble gases to elucidate large-scale processes to which the lithophile isotopic systems are not sensitive.

Globally, Ar and Xe isotopes are correlated in oceanic basalts, but Ar and Xe do not correlate strongly with He and Ne. While Xe isotopes appear to require the presence of an undegassed component, the lack of correlation with He and Ne isotopes indicates that low

40 36 129 130 Ar/ ArE and Xe/ XeE ratios are not solely due to the presence of an undegassed component. Rather, we conclude that low Ar and Xe isotope ratios are in part due to the presence of undegassed material and in part due to recycled atmospheric Ar and Xe. The lack of correlations with He and Ne indicate that the lighter noble gases are not recycled into the mantle in significant quantities.

174 Acknowledgments

We thank Jennifer Middleton and Rita Parai who were instrumental in sample collection during the KN207-2 cruise. We are indebted to Charlie Langmuir for inviting us to collect these samples specifically for heavy noble gas analysis.

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179 A Supplemental material for Chapter 1

180 A.1 Data tables

Table A.1: C, He, Ne, Ar abundances and isotope ratios

181 Table A.1 (Continued)

182 Table A.1 (Continued)

183 Table A.2: Xe abundances and isotope ratios

184 Table A.2 (Continued)

185 A.2 Supplementary figures

Figure A.1: Determination of 129Xe/132Xe from (a) all depleted MORB crushing steps and (b) all HIMU- type MORB crushing steps from Ar-Xe mixing systematics. Hyperbolas are extrapolated to 40Ar/36Ar = 41,500 for depleted MORB and 18,100 for HIMU-type MORB, and are not particularly sensitive to uncertainty in the mantle 40Ar/36Ar ratio.

87 86 4 3 21 22 Figure A.2: Relationship between Sr/ Sr and (a) He/ He and (b) Ne/ NeE. The solid lines are illustrative two-component mixture calculations between a depleted (D-DMM) and HIMU plume component. The 87Sr/86Sr ratio of D-DMM and HIMU are 0.70219 and 0.7045 respectively. He and Ne isotopic compositions are as in Figures 3 & 4. The curvature of the hyperbola is controlled by the parameter r, defined 3 86 3 86 as, e.g., ( He/ Sr)D-DMM/( He/ Sr)HIMU

186 Figure A.3: Error-weighted means of the measured fissiogenic Xe isotopes for the depleted MORBs (filled circles) and the HIMU-type MORBs (open circles). The solid lines show Pu- and U-derived fission Xe addition to chondritic (AVCC) Xe. The two groups of MORBs are not co-linear with air, demonstrating that these groups have different proportions of Pu- to U-derived Xe. A similar set of lines can be constructed for a solar starting composition for the mantle. Note that based on the primordial Xe isotopes (e.g., Caffee et al., 1999; Holland and Ballentine, 2006) and the composition of the Archean atmosphere (Pujol et al., 2011), present day atmospheric Xe cannot represent the initial composition of the mantle. In panel (B) the measured compositions lie outside the region defined by addition of fissiogenic Xe to AVCC. This is dueto syn-to post-eruptive atmospheric contamination and recycling of atmospheric Xe to the mantle source.

187 B Supplemental material for Chapter 2

188 3 22 B.1 Calculation of He/ Nem by correcting for air contamination and degassing (Method 2)

3 22 3 22 In this method, we use measured He/ Ne elemental ratios to calculate the He/ Nem ratio. We correct 3He/22Ne ratios for syn- to post-eruptive air contamination by correlating mea-

sured 3He/22Ne with 20Ne/22Ne and extrapolating 3He/22Ne to a mantle 20Ne/22Ne ratio of

3 22 3 22 12.5 ( He/ NeE; Fig. 2.1a). He/ NeE is corrected for magmatic degassing by the degree to which the sample’s (4He/21Ne)* ratio is fractionated from the expected production ratio (e.g.,

Graham, 2002). We correct the measured 4He/21Ne ratio for syn- to post-eruptive air contamination by correlating measured 4He/21Ne with 22Ne/21Ne and extrapolating 4He/21Ne to

22 21 22 21 the mantle Ne/ NeE ratio ( Ne/ NeE; Fig. 2.1b). Such an approach is analogous to the 3He/22Ne correction for air contamination. We then compute the sample’s (4He/21Ne)* ratio

through the following relationships:

( ) ( ) 4 ∗ 4 He He × fHe 21 = 21 (B.1) Ne sample Ne E fNe

4 21 where fHe and fNe are the fractions of mantle He and Ne that are radiogenic and nucleogenic, respectively: ( ) ( ) 4He 4He 3 − 3 He (meas) He i fHe = (B.2) 4He 3 He meas and ( ) ( ) 21Ne 21Ne 22 − 22 Ne( E ) Ne i fNe = (B.3) 21Ne 22 Ne E The undegassed (mantle source) 3He/22Ne ratio is then determined from:

( )∗ ( ) ( ) 4He 3 3 21 He He Ne production = × ( )∗ (B.4) 22Ne 22Ne 4He mantle E 21 Ne sample

189 Table B.1: Concentrations

Depleted mantle Recycled oceanic crust Primitive mantle 3He (atoms/g) 1 × 109 1 × 107 1 × 1010 22Ne (atoms/g) 8.3 × 107 3.3 × 107 4.3 × 109 Pb (ppm) 0.014 0.23 0.150 Sr (ppm) 6.092 94.3 19.9 Nd (ppm) 0.483 9.32 1.25

B.2 Three-component mixing model

Multi-component mixing has been used to explain the variations in Sr, Nd, and Pb isotope ratios (Schilling et al., 1994), trace elements (Hannigan et al., 2001) and noble gas isotope ratios (Tucker et al., 2012) in equatorial Atlantic MORBs. We extend this idea to quantitatively model the He-Ne-Pb-Sr-Nd compositions as a mixture of a depleted mantle component, a recycled component, and primitive mantle. This simple mixing model demonstrates the coupled nature of the noble gas and lithophile isotope systematics; it is not meant to constrain the actual end-member compositions and mixing proportions. The compositions of the three end-members used are given in Tables B.1 and B.2.

The He concentration in depleted mantle is from Gonnermann and Mukhopadhyay (2009) and we assume a 100× depletion in recycled crust and 10× enrichment in primitive mantle.

Ne concentrations assume a 3He/22Ne (atomic) ratio of 12 in depleted mantle (slightly higher

than the highest measured value in our most depleted MORB sample—see text), 0.3 in re-

cycled crust, and 2.3 in primitive mantle (similar to primitive OIBs—see text). Pb, Sr, Nd

concentrations in the depleted mantle, recycled crust, and undegassed mantle are from Work-

man and Hart (2005) “D-DMM”, Chauvel et al. (1992) “Altered N-MORB (2 Ga old)”, and

McDonough and Sun (1995) “Pyrolite”.

Depleted mantle isotope ratios are slightly more extreme than our most depleted sample

(lower for 4He/3He, 206Pb/204Pb, and 87Sr/86Sr; higher for 21Ne/22Ne and 143Nd/144Nd). Re-

cycled crust He and Ne isotope ratios are similar to crustal production ratios; Pb, Sr, and

Nd isotope ratios are similar to the most extreme Cook-Austral HIMU OIBs (e.g. Chau-

vel et al., 1992). The primitive mantle 4He/3He ratio is similar to the Baffin Island source

190 Table B.2: Isotope ratios

Depleted mantle Recycled oceanic crust Primitive mantle 4 3 7 He/ He 80,000 (9 RA) 7.0 × 10 (0.01 RA) 14,400 (50 RA) 21Ne/22Ne 0.065 0.8 0.034 206Pb/204Pb 17.5 22.0 18.0 87Sr/86Sr 0.7021 0.7035 0.7048 143Nd/144Nd 0.5133 0.5128 0.5126 with the least radiogenic He isotopic ratio (Stuart et al., 2003); 21Ne/22Ne is computed from

4He/3He by closed system evolution from a solar 21Ne/22Ne of 0.0328 assuming 3He/22Ne =

2.3; 206Pb/204Pb, 87Sr/86Sr, and 143Nd/144Nd are computed from initial solar system values

assuming the bulk silicate Earth “pyrolite” composition (McDonough and Sun, 1995).

The model fits the fraction of each component (depleted mantle, recycled crust, and primi-

tive mantle) in a given sample and computes the sample’s isotope ratios based on the fit. Fits

are performed to minimize the sum of squared normalized residuals. The residuals are nor-

malized by the variance in measurements of the isotope ratio to proportionally weight each

isotope ratio. Model results are shown in Figure B.1 along with 1:1 lines. He and Ne isotope ratios are from Tucker et al. (2012) and Pb, Sr, and Nd isotope ratios are from Schilling et al. (1994) and Agranier et al. (2005). Overall, using literature estimates of end-member compositions, all of the samples are well fit using the 3-component mixing model (Figure B.1).

However we emphasize again that this calculation does not constrain the end-member compositions, as other compositions may work equally well. The calculation is meant only to demonstrate that the isotopic compositions of our samples can be explained by simple multicomponent mixing.

B.3 Calculation of 3He/22Ne ratios in primordial and modern terrestrial reservoirs

3 22 Here we describe the specific methods we used to compute He/ Nem ratios mentioned in the text and Figure 2.3.

191 Figure B.1: Fitted vs. measured compositions of the 9 samples in the 3-component mixing model. 4He/3He is fitted to an average accuracy of 1.4%, 21Ne/22Ne to 0.5%, 206Pb/204Pb to 0.7%, 87Sr/86Sr to 0.01%, and 143Nd/144Nd to 0.006%.

192 B.3.1 MORB average (H&M)

Honda and McDougall (1998) report a weighted average and standard deviation of MORB

3 22 20 22 21 22 4 3 He/ Nem = 10.2 ± 1.6 (n = 20) assuming Ne/ Ne = 13.8, Ne/ Nei = 0.033, He/ Hei

20 22 = 2174 (330 RA). Subsequent research however indicates a Ne/ Ne ratio of 12.5 for the MORB source (Ballentine et al., 2005; Holland and Ballentine, 2006; Raquin and Moreira,

2009). For direct comparison to our data, we adjusted Honda and McDougall’s value to a

20 22 21 22 4 3 Ne/ Ne = 12.5, Ne/ Nei = 0.03129, and He/ Hei = 6024. We also assumed a global

MORB average value of 83300 (8.6 RA) (Honda and McDougall, 1998).

21 22 21 22 We first computed the Ne/ NeE ( Ne/ Ne13.8) corresponding to the reported

3 22 3 22 4 3 He/ Nem ( He/ Ne13.8) and He/ He by: ( ) ( ) 3He ( ) 21 22 4 Ne Ne 13.8 He = ( )∗ − 2174 + 0.033 (B.5) 22Ne 4He 3He 13.8 21 Ne production

21Ne/22Ne was then recomputed to 20Ne/22Ne = 12.5 assuming binary mixing with air: ( ) ( ) 21Ne − 21Ne 22Ne 0.029 = 13.8 (12.5 − 9.8) + 0.029 (B.6) 22 − Ne 12.5 13.8 9.8

3He/22Ne was then calculated as in Method 1: ( ) ( ) 21Ne − ( )∗ 3He 22Ne 0.03129 4He = 12.5 (B.7) 22Ne 4He − 21Ne 12.5 3He 6024 production

3 22 We propagated the uncertainty through these equations to compute a He/ Nem ratio of 7.35 ± 1.13.

We additionally recomputed an average value from the same original data (Hiyagon et al., 1992; Moreira et al., 1998; Sarda et al., 1988) under assumptions consistent with the

20 22 21 22 4 3 rest of our analysis ( Ne/ Ne = 12.5, Ne/ Nei = 0.03129, He/ Hei = 6024). Heating and crushing steps within 2σ of air were excluded, as in Honda and McDougall (1998). The

193 4He/3He ratios used were the reported totals, except for the data of Moreira et al. (1998)

3 22 where we used the average and standard deviation of all crushing steps. He/ Nem and its associated uncertainty were determined for each sample as described in Method 1 (see text). For the 20 samples, we computed the error-weighted mean and the 1 uncertainty on the error-weighted mean as 7.62 ± 0.15.

B.3.2 MORB average (Graham)

3 22 Graham (2002) compiled a large data set of MORB He/ Nem (n = 85) and reported the

20 22 21 22 4 3 average and standard deviation assuming Ne/ Ne = 13.8, Ne/ Nei = 0.0328, He/ Hei

20 22 = 4800 (150 RA). For direct comparison to our data, we adjusted this value to a Ne/ Ne

21 22 4 3 = 12.5, Ne/ Nei = 0.03129, and He/ Hei = 6024 by a method analogous to that for the average from Honda and McDougall (1998) (Section B.3.1). We assumed a global MORB average value of 82220 ± 20000 (8.75 RRA) as reported in Graham (2002). We propagated the

3 22 uncertainty through the calculations and computed a He/ Nem ratio of 6.12 ± 2.40.

B.3.3 HIMU OIBs (Mangaia and Cameroon line; sample recycled oceanic crust)

3 22 A He/ Nem ratio for Mangaia (HIMU locality in the Cook-Australs) was computed from

3 22 data from Parai et al. (2009) by Method 1 as 4.63 ± 0.29.A He/ Nem ratio was also computed by Method 1 for the Cameroon line from data from Barfod et al. (1999). We only used data from the Biu V and R56 xenoliths (taken together) because the Ne data from the other xenoliths and lavas are atmospheric with large errors, and the CO2 gas Ne data does not pass through the atmospheric composition. The 4He/3He ratio used was the average and standard

deviation of the steps also used for Ne. We computed a value of 4.85 ± 1.08 for the Cameroon

line. Because HIMU OIBs have MORB-like 21Ne/22Ne, we assumed 20Ne/22Ne = 12.5 and

21 22 Ne/ Nei = 0.03129.

194 B.3.4 Samoa

3 22 3 4 A He/ Nem ratio for the Samoan plume was computed for three individual high He/ He samples from Ta’u and Ofu Islands T25, Ofu-04-03, and Ofu-04-06 from data from Jackson et

3 22 20 22 al. (2009). We computed the He/ Nem ratio by Method 1 assuming Ne/ Ne = 13.8 and

21 22 Ne/ Nei = 0.0328. The choice of solar initial Ne isotopic composition for Samoa, Iceland and Galapagos (Sections B.3.5 and B.3.6 below) is based on the observations of 20Ne/22Ne

= 12.9 in the Iceland and Kola mantle plumes (Mukhopadhyay, 2012; Yokochi and Marty,

2004). For the 3 samples, we computed the error-weighted mean and the 1σ uncertainty on

the error-weighted mean as 4.64 ± 0.44.

B.3.5 Iceland

3 22 A He/ Nem ratio for the Iceland plume was computed from data presented in Mukhopad- hyay (2012) by Method 1 as 2.86 ± 0.07 assuming 20Ne/22Ne = 13.8 and 21Ne/22Nei =

0.0328. The DICE 10 sample from Iceland is undegassed and 3He/22Ne corrected for air con-

3 22 tamination yields He/ Nem = 2.97 ± 0.15 (Mukhopadhyay, 2012), similar to that computed from Method 1 above.

B.3.6 Galapagos

3 22 A He/ Nem ratio for the Galapagos plume was computed from Fernandina data presented

3 22 in Kurz et al. (2009) and Raquin and Moreira (2009). A He/ Nem ratio was computed for

20 22 21 22 each individual sample by Method 1 assuming Ne/ Ne = 13.8 and Ne/ Nei = 0.0328. The error-weighted mean and standard error of the weighted mean of 10 samples is 2.28 ±

0.13.

B.3.7 Solar nebula

Because deuterium burning in the Sun has produced 3He, the 3He/22Ne of the solar nebula cannot be determined by present-day measurements of the solar wind. The 3He/22Ne ratio of

195 the solar nebula can be computed from 4He/20Ne, 20Ne/22Ne, and 4He/3He ratios. We used the Jovian atmosphere 3He/4He ratio of 1.66 ± 0.05 × 10−4 as the value for the solar nebula

(Mahaffy et al., 1998). We used 4He/20Ne = 641 ± 15 (Pepin et al., 2012) and 20Ne/22Ne =

13.75 ± 0.025 (Grimberg et al., 2006) determined for the solar wind from the Genesis mission.

Our computed value of 1.46 ± 0.06 is similar to the value of 1.5 computed in Yokochi and

Marty (2004). The previously used solar 3He/22Ne ratio of 3.8 in some studies is therefore not an accurate estimate of the nebular value.

B.3.8 Implanted solar wind (Ne-B)

The 3He/22Ne ratio of implanted solar wind (Ne-B) is taken from Raquin and Moreira (2009)

as 0.9 ± 0.1; the average 3He/22Ne ratio of meteorites with 20Ne/22Ne > 11.5.

B.3.9 Chondrite

The 3He/22Ne ratio of chondrites is taken as the trapped HL component. We compute a

value of 0.89 ± 0.11 from 4He/132Xe = 300, 000 ± 30, 000, 20Ne/132Xe = 485 ± 26, 20Ne/22Ne

= 8.500 ± 0.057, and 3He/4He = 1.7 ± 0.1 × 10−4 (Ott, 2002). Because the 3He/4He ratio is a maximum value (Ott, 2002), our computed 3He/22Ne ratio is also a maximum value.

B.3.10 Iron

The 3He/22Ne ratio of the Washington County iron meteorite (ungrouped) is computed from

the average 3He/22Ne of the two analyses in Becker and Pepin (1984). Although they re-

port trapped 3He abundances, the uncertainties are ~100–300%; so we used the trapped 4He

abundance and a solar nebular 4He/3He ratio of 6024. We used the reported trapped 22Ne abundances and trapped 20Ne/22Ne ratio of 13.3 ± 0.5 and compute a trapped 3He/22Ne of

1.44 ± 0.11.

196 B.3.11 Pallasite

The 3He/22Ne ratio of Brenham pallasite olivines is computed from Mathew and Begemann

(1997). We used the reported trapped 20Ne/22Ne ratio of 12.9 ± 0.3 and a solar nebular

4He/3He ratio of 6024. Because some (or all) 4He may be radiogenic, they report a maximum trapped 4He/20Ne ratio of 100, so our computed 3He/22Ne ratio of 0.21 ± 0.01 is a maximum value.

B.3.12 Howardite

The 3He/22Ne ratio of howardites is computed as the average 3He/22Ne ratio of the analy-

ses of Kapoeta and Jodzie from Mazor and Anders (1967). We used the reported trapped

20Ne/22Ne ratios of 13.3 and 12.7, respectively, and a solar nebular 4He/3He ratio of 6024.

Because some 4He may be radiogenic, they report a maximum trapped 4He/20Ne ratio of 100, so our computed 3He/22Ne ratio of 0.22 ± 0.01 is a maximum value.

B.3.13 Aubrite

The 3He/22Ne ratios of aubrites is computed as the average and standard deviation of the

3He/22Ne ratios computed for the 7 analyses from Lorenzetti et al. (2003). We use the re-

ported trapped 20Ne/22Ne ratio of 12.1 ± 0.2, individual trapped 4He and 20Ne abundances,

and a solar nebular 4He/3He ratio of 6024 and compute a 3He/22Ne ratio of 0.62 ± 0.29.

B.3.14 Angrite

The 3He/22Ne ratio of angrites is computed as the average 3He/22Ne ratio of the two analysis

of D’Obrigny glass samples from Busemann et al. (2006). We use the trapped 20Ne/22Ne ra-

tio of 11.9 ± 0.3 and reported trapped 20Ne abundances. They report that <30% of the 4He

is trapped, so we use 30% of the total reported 4He abundances and a solar nebular 4He/3He

ratio of 6024. Our computed 3He/22Ne ratio of 0.14 ± 0.02 is therefore a maximum value.

197 B.4 Coupled hydrodynamic escape/magma ocean outgassing model

In the coupled hydrodynamic escape/magma ocean outgassing model, EUV flux from the young Sun drives H2 loss that in turn lifts He and Ne from the atmosphere. Because the atmosphere and magma ocean remain in equilibrium, atmosphere loss leads to outgassing from the magma ocean. The coupled hydrodynamic escape/magma ocean outgassing model numerically solves the equations for H2, He and Ne evolution during hydrodynamic escape where a compositionally homogeneous atmosphere is continuously in equilibrium with a magma

ocean. For simplicity, we assume the magma ocean comprises two-thirds the mass of the

proto-Earth, corresponding to a whole mantle magma ocean. From a specified initial total

(H2) surface pressure, planet size, and magma ocean temperature, the initial dissolved H2, 3He, and 22Ne are computed assuming solar system relative abundances (Lodders, 2003). Sol-

ubility of pure molecular H2 in peridotite magma is taken from Hirschmann et al. (2012), and He and Ne solubilities from Iacono-Marziano et al. (2010). For simplicity, we assume all the

dissolved hydrogen is H2.

The initial atmospheric H2 column number density is:

psurf NH2 = (B.8) g mH2

where psurf is the initial surface pressure, g is the gravitational acceleration, and mH2 is the mass of a hydrogen molecule. At each time step, the atmospheric column density is reduced

dNH2 by the outgoing hydrogen flux. The equation for outgoing hydrogen flux FH2 (= dt ) during energy-limited escape with decay timescale τ is:

0 −t/τ FH2 (t) = FH2 e (B.9) with initial hydrogen flux:

0 r ϕ ε FH2 = (B.10) G mH2 Mplanet where ϕ is the EUV flux, assumed to be 100× the present value of 3.05 ergs s-1 cm-2 (Ribas

198 et al. 2005), and ε is the fraction of incident EUV flux converted to thermal escape energy of

H2. r is the exobase height computed as the height in the atmosphere where the mean free path of H2 equals the atmosphere scale height. The equation for evolution of trace constituent N (in this case 3He or 22Ne) during hydrodynamic escape is from Hunten et al. (1987) and Pepin (1991): ( ) dN F 0 m − m = −N H2 e−t/τ − N H2 (B.11) 0 − dt NH2 mc,N mH2

0 where mc,N is the initial critical or “crossover” mass for constituent N defined as:

k T F 0 0 H2 mc,N = mH2 + (B.12) bN g

with exobase temperature T from Pepin (1991) and diffusion parameters bN from Zahnle and Kasting (1986).

After each time step of hydrodynamic escape, the equilibrium for each species is computed by simultaneously solving Henry’s Law and mass conservation for the dissolved and atmospheric gas contents. The calculation ceases when the atmospheric H2 abundance reaches zero.

In the model shown in Figure 2.7, we have assumed a planet mass of 0.3 × MEarth, initial surface pressure of 30 bar and temperature of 2000 K. The decay timescale τ is 90 Myr and

the temperature at the top of the atmosphere is 270 K, as in Pepin (1991). The correspond-

ing initial Ne and He crossover masses are 762 and 541 amu. We find that in general, mag-

matic He/Ne fractionation is muted for the majority of the duration of hydrodynamic escape,

with significant fractionation occurring only when atmospheric H2 is nearly depleted (cf. Fig. 2.7). An extensive parameter search reveals no combination of parameters that results in an

increase in the magmatic He/Ne ratio. We conclude that hydrodynamic escape coupled with

magma ocean outgassing is unlikely to raise the magmatic 3He/22Ne ratio, despite the open system-like nature of outgassing.

199 B.5 Terrestrial noble gas abundances

The large uncertainty in 3He concentrations in the mantle, particularly for the primitive OIB

mantle, precludes definitive statements as to how present-day mantle concentrations may

have been generated. Additionally, the initial mantle concentrations acquired during accre-

tion, and the efficiency of gas loss via magma ocean outgassing and plate tectonic processing

introduce further uncertainty on the evolution of mantle noble gas concentrations. There-

fore, we simply note that multiple atmospheric loss and magma ocean outgassing episodes

can yield He and Ne concentrations that are compatible with concentrations inferred for the

present-day mantle.

The present-day MORB mantle source is estimated to have 3 × 108 − 1.2 × 109 atoms/g 3He

(Bianchi et al., 2010; Moreira and Kurz, 2013; Porcelli and Wasserburg, 1995). Solar wind implantation on dust grains is often invoked as the source of He and Ne in MORB mantle.

Meteorites preserving implanted solar gas, such as the CV3 carbonaceous chondrite Mokoia,

3 13 have He contents of 10 atoms/g (Mazor et al., 1970). If SHe/SNe in the magma ocean is 2 and the magma ocean degasses in equilibrium with the atmosphere, when the He/Ne fractionation reaches a factor of 1.9, 10% of the initial 3He would be retained. Thus, two episodes of atmospheric loss and magma ocean outgassing would decrease 3He concentrations by a factor of 100. Plate tectonic outgassing has further decreased 3He concentrations by a factor of

20–1000 (e.g., Gonnermann and Mukhopadhyay, 2009; Porcelli and Wasserburg, 1995). Con- sequently, MORB source 3He concentrations would be between 1 × 108 − 5 × 109 atoms/g, which compares well with the present day estimates given above (Bianchi et al., 2010; Mor- eira and Kurz, 2013; Porcelli and Wasserburg, 1995).

OIB mantle source 3He concentrations are significantly more uncertain than the MORB mantle. The 3He concentration in the OIB mantle source may be similar to or more than an order of magnitude higher than the MORB source. Recent estimates are 4 × 108 (e.g., Füri et al., 2010), > 4 × 109 (Moreira and Kurz, 2013) and 3 × 1010 atoms/g (Gonnermann and

Mukhopadhyay, 2007). OIBs are thought to be primarily comprised of recycled material with

200 ~1–10% primitive material (Coltice et al., 2011; Gonnermann and Mukhopadhyay, 2009; Tol- stikhin and Hofmann, 2005). Because recycled material would have negligible 3He (main text,

Section 2.5.2), the 3He concentration of the primitive material (the material with 3He/22Ne of 2.3–3) would be between 4 × 109 and 3 × 1012 atoms/g. 3He concentrations of 3 × 1012 atoms/g can be produced by ingassing of a 10–100 bar nebular atmosphere (Harper and Ja- cobsen, Porcelli et al., 2001; Yokochi and Marty, 2004) followed by a factor of a few decrease associated with plate tectonic processing (e.g., Gonnermann and Mukhopadyay, 2009). The lower end of possible primitive 3He concentrations (4 × 109 atoms/g) could also be produced by ingassing, but would require subsequent degassing before the end of accretion through a process that does not increase its He/Ne ratio significantly. For example, after the solar nebula dissipated, hydrodynamic escape of a nebular atmosphere overlaying a magma ocean could have decreased 3He and 22Ne concentrations in the magma ocean dramatically but left the He/Ne ratio largely unchanged (Fig. 2.7; Section B.4). Subsequent accretion during the giant impact phase of terrestrial accretion delivered He, Ne, and other volatiles to the shallow mantle. We note that there is no reason the initial volatile contents in the shallow and deep mantle sources should be the same; different 20Ne/22Ne ratios in MORBs and OIBs point to different provenance of light noble gases in the different mantle domains and itispossi- ble that the deeper mantle may have had a lower initial 3He concentration compared to the

shallower mantle at the end of the giant impact phase of terrestrial accretion.

201 B.6 21Ne*/40Ar* vs. 4He*/40Ar*

Figure B.2: (21Ne/40Ar)* vs (4He/40Ar)* for each of the 9 equatorial Atlantic MORB samples. The grey box indicates the range in estimated mantle (21Ne/40Ar)* and (4He/40Ar)* production ratios and our samples define a trend similar to previous observations (e.g., Honda and Patterson, 1999). Because thesamples have been clearly degassed upon eruption onto the seafloor, we used two separate methods to compute the mantle 3He/22Ne ratios. The first method (Honda and McDougall, 1998) relies only on the isotopic ratios and not the elemental ratios. In the second method we explicitly correct for magmatic degassing (Section B.1). Since both methods give identical 3He/22Ne ratios (Table 2.1), the computed mantle 3He/22Ne ratios are robust.

202 Supplemental references

Bianchi, D., Sarmiento, J.L., Gnanadesikan, A., Key, R.M., Schlosser, P., Newton, R., 2010. Low helium flux from the mantle inferred from simulations of oceanic helium isotope data. Earth Planet. Sci. Lett. 297, 379–386.

Chauvel, C., Hofmann, A.W., Vidal, P., 1992. HIMU-EM: the French Polynesian connection. Earth Planet. Sci. Lett. 100, 99–119.

Hirschmann, M.M., Withers, A.C., Ardia, P., Foley, N.T., 2012. Solubility of molecular hydrogen in silicate melts and consequences for volatile evolution of terrestrial planets. Earth Planet. Sci. Lett. 345–348, 38–48.

Hiyagon, H., Ozima, M., Marty, B., Zashu, S., Sakai, H., 1992. Noble gases in submarine glasses from mid-oceanic ridges and Loihi seamount: constraints on the early history of the Earth. Geochim. Cosmochim. Acta 56, 1301–1316.

Honda, M., Patterson, D.B., 1999. Systematic elemental fractionation of mantle-derived helium, neon, and argon in mid-oceanic ridge glasses. Geochim. Cosmochim. Acta 63, 2863–2874.

Hunten, D.M., Pepin, R.O., Walker, J.C.G. 1987. Mass fractionation in hydrodynamic escape. Icarus 69, 532–549.

Mazor, E., Heymann, D., Anders, E., 1970. Noble gases in carbonaceous chondrites. Geochim. Cosmochim. Acta 34, 781–824.

Moreira, M.A., Kurz, M.D. 2013. Noble gases as tracers of mantle processes and magmatic degassing. In: Burnard, P. (Ed.), The noble gases as geochemical tracers, Springer, Heidel- berg, pp. 371–391.

Moreira, M., Kunz, J., Allègre, C., 1998. Rare gas systematics in popping rock: isotopic and elemental compositions in the upper mantle. Science 279, 1178–1181.

Porcelli, D., Wasserburg, G.J., 1995. Mass transfer of helium, neon, argon, and xenon through a steady-state upper mantle. Geochim. Cosmochim. Acta 23, 4921–4937.

Sarda, P., Staudacher, T., Allègre, C.J., 1988. Neon isotopes in submarine basalts. Earth Planet. Sci. Lett. 91, 73–88.

Stuart, F.M., Lass-Evans, S., Fitton, J.G., Ellam, R.M., 2003. High 3He/4He ratios in picritic basalts from Baffin Island and the role of a mixed reservoir in mantle plumes. Na- ture 424, 57–59.

203 Tolstikhin, I., Hofmann, A.W., 2005. Early crust on top of the Earth’s core. Phys. Earth Planet. Int. 148, 109–130.

Workman, R.K., Hart, S. R., 2005. Major and trace element composition of the depleted MORB mantle (DMM). Earth Planet. Sci. Lett. 231, 53–72.

Zahnle, K.J., Kasting, J.F., 1986. Mass fractionation during transonic escape and implications for loss of water from Mars and Venus. Icarus 68, 462–480.

204 C Supplemental material for Chapter 3

205 C.1 Calculation of radiogenic noble gas abundances

The abundances of radiogenic 4He* is calculated as:

4 ∗ 3 4 3 4 3 He = Hemeas × ( He/ Hemeas − He/ Hei)

4 3 where He/ Hei is the solar system initial of 6024 (e.g. Mahaffey et al., 1998). Because MORBs have high 4He/3He relative to the solar system initial, this correction is usually a

few %, and often neglected in the literature.

The abundance of radiogenic 21Ne* assumes that measured 21Ne is a combination of pri-

mordial 21Ne, radiogenic 21Ne, and atmospheric contamination. Following the summaries in

Graham (2002):

21 ∗ 22 21 22 21 22 Ne = Nemeas × f22 × ( Ne/ NeE − Ne/ Nei)

where 20 22 20 22 Ne/ Nemeas − Ne/ Neair f22 = 20 22 20 22 Ne/ Nei − Ne/ Neair

21 22 21 22 and Ne/ NeE is the ratio corrected for atmospheric contamination and Ne/ Nei is assumed to be 0.0313, the solar composition mass fractionated to 20Ne/22Ne = 12.5.

The calculation of 40Ar* assumes negligible primordial Ar, and assumes all measured 36Ar

is atmospheric, summarized in Graham (2002):

40 ∗ 36 40 36 40 36 Ar = Armeas × ( Ar/ Armeas − Ar/ Arair)

As long as measured 40Ar/36Ar ratios are more than a few thousand, these assumptions are valid to within a few %.

206 C.2 Derivation of Rayleigh-like degassing formulation

The mass balance equation (equation 4 of Jambon et al., 1986) is:

∗ 0 PiV · T0 Ci = Ci + (C.1) P0ρ Tc

0 where Ci is the abundance before vesiculation, Ci is the residual dissolved content and the

rest is the vesicle content. Pi is the partial pressure of the species i in the gas phase (at Tc), ∗ V is the vesicularity, ρ is the melt density, and P0 and T0 are 1 bar and 273 K. For simplic-

ity we will call vesicularity V and P0ρTc/T0 = A. In the rest of this we will call the dissolved concentration Cd. Eq. 1 applies generally, whether at equilibrium or disequilibrium.

Crank (1975) (their equation 4.23) derived the disequilibrium condition

∞ M 8 ∑ 1 t = 1 − exp[−D(2j + 1)2π2(t/4a2)] (C.2) M∞ π2 (2j + 1)2 j=0 where “Mt denotes the total amount of diffusing substance which enters the sheet during time t, and M∞ the corresponding amount during infinite time”. In other words, M∞ is the

equilibrium exsolved concentration and Mt/M∞ is the fractional amount of degassing from zero (full disequilibrium) to full equilibrium.

Gonnermann and Mukhopadhyay (2007) (“GM07”, their supplement equation 3) used

∞ 8 ∑ 1 θ = exp[−D(2j + 1)2π2(t/4a2)] (C.3) π2 (2j + 1)2 n=0

The GM07 θ is equivalent to the Crank (1975) 1 − Mt/M∞. So θ is the fractional amount of

disequilibrium and (1 − θ) = Mt/M∞ is the fractional amount of equilibrium. (Note GM07 supplement equation 3 used a finite series but the series usually converges after just afew

terms. GM07 also recast time in terms of the Ar diffusivity and assumed lengthscale.) See

main text Equation 3.1.

During disequilibrium some gas does not diffuse into vesicles so the vesicle concentration is

207 less than the equilibrium vesicle concentration. Since

v Mt Cdiseq = v (C.4) M∞ Ceq

v and because Mt/M∞ = (1 − θ), the equilibrium and disequilibrium vesicle concentrations C are related by v v − Cdiseq = Ceq(1 θ) (C.5)

At equilibrium, the vesicle partial pressure of a species is governed by Henry’s law: Pi =

d Ci /S. At disequilibrium, the vesicle concentration becomes:

d − Pi = Ci (1 θ)/S (C.6)

This equation implies that at equilibrium (θ = 0), the distribution between gas and magma is

the solubility, and at full disequilibrium (θ = 1) the partial pressure of the gas in the vesicles

is 0. It can be seen immediately that the rest of this derivation can proceed exactly like an

equilibrium calculation but instead of using solubility S, it uses a “modified solubility” of

S/(1 − θ). I will then use the symbol S′ to represent S/(1 − θ).

Following Jambon et al. (1986), the residual dissolved concentration Cd and exsolved concentrations Cv can be related to the initial dissolved concentration C0 by applying the “modified” Henry’s law (Eq. C.6) to Eq. C.1 (Jambon equations 5and6):

Cd S′A = (C.7) C0 S′A + V

Cv V = (C.8) C0 S′A + V

In an open system, the initial concentration at step n is the dissolved concentration at step n − 1, so Eq. 7 can be written as

S′A Cd = Cd (C.9) n+1 n S′A + V

208 This equation implies that the dissolved concentration decreases by a constant fraction,

S′A/(S′A + V ). We will refer to this quantity as X.

The fractional change in vesicular concentration is also X:

v d V d C C ′ C n+1 = n S A+V = n = X (C.10) Cv d V d n Cn−1 S′A+V Cn−1

Because the change in composition at each step is fractional, the overall evolution is exponential:

d d n v v n Cn = C0 X and Cn = C0 X (C.11)

d v where C0 is the initial dissolved concentration and C0 is the first vesicle composition, which can be computed from Eq. C.8.

For a pair of elements a and b, equations of the form of Eq. C.11 (regardless of whether

talking about dissolved or vesicular concentration) can be solved for n and equated:

ln(a/a ) ln(b/b ) n = 0 = 0 (C.12) Xa Xb

′ SaA ln ′ ln Xa SaA+V ln(a/a0) = ln(b/b0) = ln(b/b0) ′ (C.13) ln X SbA b ln ′ SbA+V Now consider the limit where vesicles are created and instantaneously lost, i.e. Rayleigh fractionation. Such a system is equivalent to this open-system formulation in the limit as vesicularity goes to zero. In this limit, the part of Eq. 13 with X is:

′ SaA ′ ln ′ ln Xa SaA+V Sb lim = lim ′ = ′ (C.14) V →0 ln X V →0 SbA S b ln ′ a SbA+V

The result for infinitesimal V is:

′ Sb ln(a/a0) = ln(b/b0) ′ (C.15) Sa

Equation C.15 can be rearranged to a more familiar form of Rayleigh distillation found in the

209 literature (e.g. Marty and Jambon, 1987), noting that here w use S′ for the general disequi-

librium case instead of the solubility S, sometimes called K or k:

(1−S′ /S′ ) (a/b) = (a/b)0(a/a0) a b (C.16)

This equation is often written using for example fa = (a/a0), the fraction of species a remaining.

Furthermore, the equilibrium and disequilibrium cases are identical with the adjustment that S′ = S/(1 − θ). In other words, disequilibrium degassing uses the equivalent math as equilibrium degassing, just replacing the solubility S with S/(1 − θ).

Application to ratio-ratio plots

An equation analogous to equation C.16 may be written for two additional elements c and ′ ′ Sa/Sc d in terms of fc. fc is related to fa by fc = fa (equation C.15; main text equation 3.6).

Equation C.16 and the analogous equation for c and d can be solved for fa and equated, resulting in: S′ /S′ − S′ /S′ a c a d − log(c/d) = − ′ ′ [log(a/b) log(a/b)0] + log(c/d)0 (C.17) 1 Sa/Sb

Thus the slope is a function only of modified solubility ratios. Because the fractional change in concentration X is the same for vesicles as residual magma, the equation applies

to both. The compositional evolution path for the magma and vesicles will be parallel, but

will have different initial points. The initial point of the magma (a/b)0, (c/d)0 is generally from the production ratios, whereas for the vesicles it can be computed from Eq. 8. In the

case of infinitesimal (Rayleigh-like) degassing, the initial ratio of two elements in the vesicles

is: ( ) ( ) V ( ) ′ ( ) a v a ′ a S a (1 − θ ) S lim = lim SaA+V = b = a b (C.18) → → V ′ − V 0 b 0 V 0 b 0 ′ b 0 Sa b 0 Sa (1 θb) SbA+V where (a/b)0 is for example the production ratio.

210 C.3 Data tables

Table C.1: Measured and reconstructed initial gas contents

211 D Supplemental material for Chapter 4

212 D.1 The effect of intermediate reactions on mixed lithology mixing calculation

For the purpose of demonstration and the simplicity of nomenclature, we assume recycled crust exists as an eclogitic lithology, and the depleted mantle component is a peridotite lithology. The eclogite melts to a particular extent Fec, creating eclogitic (adikitic) melt and residue. The residue does not participate further except in the total mass balance. The melt reacts with the depleted mantle peridotite component forming pyroxenite. The pyroxenite

px px is comprised of some proportion of eclogitic melt fec and reacted peridotite (1 − fec ). The remaining peridotite is the rest of the depleted mantle component.

The general mixing equation for an isotope ratio between the ultimate pyroxenite and peridotite components is:

xpx rpx cpx + xpd rpd cpd rmix = xpx cpx + xpd cpd

In the main text we assumed the recycled component contained no 3He but this detail is not important here. The components of this equation are:

xpx, the fraction or mass of pyroxenite component is equal to the mass of eclogitic melt

melt melt px xec divided by the fraction of pyroxenite comprised of eclogitic melt: xpx = xec /fec = px xec Fec/fec .

3 rpx and cpx are the isotopic ratio and He content of the pyroxenite which is just a mixture of the eclogitic melt and depleted mantle. Their product is the 4He content of the pyroxenite

px px 3 which is: rpx cpx = fec rec cec/Fec + (1 − fec ) rdm cdm where cec/Fec is the He content of the eclogitic melt.

xpd is the mass of peridotite in the final mixture which is the original amount of depleted mantle component minus the amount that reacted with eclogitic melt to form pyroxenite.

The mass of reacted peridotite is the mass of pyroxenite minus the mass of eclogitic melt, so: − − melt − px xpd = xdm (xpx xec ) = xdm xec Fec/fec + xec F . 3 The final peridotite component isotope ratio rpd and He content are equal to those of the

213 original depleted mantle component: rpd = rdm; cpd = cdm. Inserting these values into the first equation, the RHS becomes:

xec Fec px cec px xec Fec px (fec rec + (1 − fec ) rdm cdm) + (xdm − px + xec Fec) rdm cdm fec Fec fec xec Fec px cec px xec Fec px (fec + (1 − fec ) cdm) + (xdm − px + xec Fec) cdm fec Fec fec

px Many of the terms cancel out, including importantly fec and Fec, leaving:

xec rec cec + xdm rdm cdm rmix = xec cec + xdm cdm

If the pyroxenite melts more than peridotite, cpx is divided by the relative factor; this fac-

tor follows through to the end, modifying cec. Therefore the only important factor is the degree of melting of the component ultimately containing recycled crust-derived He, whether

eclogite or pyroxenite, not the mechanism or details of transfer to any intermediate compo-

nent.

214 D.2 Data tables

Table D.1: He isotope compositions for samples between the Kane and Atlantis Fracture Zones and dredge locations of KN207-2 samples

215 E Supplemental material for Chapter 5

216 E.1 Data tables

Table E.1: He isotope composition of samples south of Kane and between Atlantis and Hayes Fracture Zones

217 Table E.2: Ne, Ar, Xe abundances and isotopic ratios and CO2, He abundances

218 Table E.2 (Continued)

219 Table E.2 (Continued)

220