# The origin of Earth’s mantle nitrogen: primordial or early biogeochemical
cycling?

###### Abstract

Earth’s mantle nitrogen (N) content is comparable to that found in its N-rich
atmosphere. Mantle N has been proposed to be primordial or sourced by later
subduction, yet its origin has not been elucidated. Here we model N
partitioning during the magma ocean stage following planet formation and the
subsequent cycling between the surface and mantle over Earth history using
argon (Ar) and N isotopes as tracers. The partitioning model, constrained by
Ar, shows that only about 10% of the total N content can be trapped in the
solidified mantle due to N’s low solubility in magma and low partitioning
coefficients in minerals in oxidized conditions supported from geophysical and
geochemical studies. A possible solution for the primordial origin is that
Earth had about 10 times more N at the time of magma ocean solidification. We
show that the excess N could be removed by impact erosion during late
accretion. The cycling model, constrained by N isotopes, shows that mantle N
can originate from efficient N subduction, if the sedimentary N burial rate on
early Earth is comparable to that of modern Earth. Such a high N burial rate
requires biotic processing. Finally, our model provides a methodology to
distinguish the two possible origins with future analysis of the surface and
mantle N isotope record.

Geochemistry, Geophysics, Geosystems

Earth-Life Science Institute, Tokyo Institute of Technology Division of
Science, National Astronomical Observatory of Japan Department of Earth and
Planetary Sciences, Tokyo Institute of Technology Blue Marble Space Institute
of Science Earth and Planets Laboratory, Carnegie Institution of Washington

H<EMAIL_ADDRESS>
We studied two possible origins for mantle nitrogen: the primordial and
recycling scenarios.

The primordial scenario requires accretion of excess nitrogen and impact
erosion during late accretion.

The recycling scenario needs efficient N fixation and biotic processing on
early Earth.

## Plain Language Summary

Nitrogen (N) is the main component of Earth’s atmosphere, and essential for
life. The atmospheric N content influences Earth’s climate and capability to
retain its surface water. Primary biological production is limited by bio-
available N as well as phosphorous on modern Earth. It has been recently
recognized that Earth’s interior contains N comparable to that found in its
atmosphere, and thus its origin is important for our understanding of Earth-
life co-evolution. We modeled N partitioning in Earth’s molten stage and long-
term cycling after Earth’s solidification. Two scenarios are proposed from our
modeling. One is that Earth’s mantle acquired its modern N content in the
earlier stage due to an excess amount of N Earth accreted, which was later
lost to space following asteroid impacts. Another is that Earth’s mantle
acquired N via subduction of N-rich sediments, which requires the sedimentary
N burial rate on early Earth comparable to the modern value sustained by
biological activity. The two scenarios can be tested with future analysis of
the geochemical record of surface and mantle N.

##  1 Introduction

Nitrogen (N) is the main component of Earth’s atmosphere and essential for the
biosphere as it is an integral part of the building blocks of life. Though
molecular nitrogen (N2) is transparent in the infrared, its presence in the
atmosphere increases the warming effect of existing greenhouse gases by
pressure broadening of their absorption lines [Goldblatt . (2009)]. The N
inventory in the atmosphere is also important for sustaining water on planets
by the cold-trap mechanism [Wordsworth Pierrehumbert (2014)]. Primary
biological production in modern aquatic environments is mostly limited by
either fixed N or phosphorus [Zerkle (2018)]. Though deficits in biologically-
available N can be mitigated by microbial N fixation on modern Earth, it might
have been a limiting factor for early life on Earth.

Though N was once thought to predominantly reside in the atmosphere and
biosphere, it can indeed become incorporated into the geosphere: minerals and
rocks [<]e.g,¿[]Johnson+Goldblatt2015. Combined sample analyses with N-40Argon
(Ar) geochemistry [Marty (1995)] suggest that present Earth’s mantle contains
a comparable mass of N as the atmosphere [Marty Dauphas (2003), Halliday
(2013), Bergin . (2015), Johnson Goldblatt (2015)]. A mantle which hosts N at
a similar level as found in the atmosphere has great potential for influencing
the surface environment through ingassing and outgassing of this mantle
reservoir. Determining whether mantle N is a primordial feature set during the
magma ocean stage or evolved with the subduction of sediments by plate
tectonics is essential to our understanding of Earth’s formation and early
biogeochemical cycling.

Mantle N has been proposed to be sourced by subduction of N-bearing sediments
and the altered oceanic lithosphere [Marty Dauphas (2003), Barry Hilton
(2016), Johnson Goldblatt (2018), Stüeken . (2021)], which would also lead to
secular evolution of atmospheric N partial pressure ($p_{\rm N_{2}}$) [Zerkle
Mikhail (2017), Laneuville . (2018)]. Notably, such subducting N on modern
Earth has ${\rm\delta^{15}N\sim+6}$‰ [Cartigny Marty (2013), Halama . (2014),
Johnson Goldblatt (2018)], where
${\rm\delta^{15}N=[(^{15}N/^{14}N)_{sample}/(^{15}N/^{14}N)_{standard}}-1]\times
1000$. Thus, efficient subduction should lead to 15N enrichment in the mantle.
Carbon-bearing deep mantle diamonds have been found to host N with almost
exclusively positive ${\rm\delta}^{15}$N values [Regier . (2020)], which might
be consistent with an origin from subducted oceanic sediments.

However, mantle N sampled from mid-ocean ridge basalt (MORB) is rather
depleted in 15N (${\rm\delta^{15}N}\sim-5$‰), which is known as N isotopic
disequilibrium [Marty (1995), Cartigny Marty (2013)]. In this regard, several
previous studies hypothesized that mantle N is predominantly a remnant of
planet formation [Cartigny Marty (2013), Mallik . (2018), Labidi . (2020)]. In
this primordial origin scenario, the isotopic disequilibrium is attributed to
atmospheric escape, which enriches the residual atmosphere in 15N. Another
study focusing on N isotopes proposed a recycling origin scenario in which the
N isotope composition of sediments has changed over time [Marty Dauphas
(2003)]. We note that here the prefix “re” is given because, in this scenario,
the modern mantle N is a component once degassed to the atmosphere in the
magma ocean stage.

Ar is another tracer of N partitioning and cycling [Marty (1995)]. In oxidized
magma, where N exists in the form of N2, N and Ar behave similarly
[<]e.g.,¿[]Marty+Dauphas2003. However, under reducing conditions N exists as
NH${}_{4}^{+}$, which can substitute for K+ in mineral phases, allowing for
more efficient recycling of N than Ar. The large difference in 40Ar/36Ar
ratios between the modern atmosphere and mantle implies that the two
reservoirs have largely stopped exchanging Ar with each other since early
catastrophic degassing, and radiogenic 40Ar derived from 40K has continued to
accumulate in the mantle [<]¿[and references therein]Ozima+Podosek2002.

Previous studies which argued either primordial or recycling scenarios have
greatly contributed to our understanding of the origin of mantle N, but they
have missed some important behavior. N partitioning between the atmosphere and
magma ocean has been experimentally investigated by several studies [Libourel
. (2003), Boulliung . (2020)], which concluded that mantle N could be
primordial. However, these studies have not considered N degassing upon magma
ocean solidification, which might limit N partitioning into the solidified
magma significantly [Hier-Majumder Hirschmann (2017)]. Models which treated
long-term N cycling after the magma ocean solidification did not trace N
isotopic exchange between different reservoirs [Stüeken, Kipp, Koehler,
Schwieterman . (2016), Johnson Goldblatt (2018)] or introduced a simplified
assumption on the N isotopic ratio of the upper mantle [Tolstikhin Marty
(1998)] or sediments [Labidi . (2020)]. These points are covered by this study
to further test the two scenarios (see Section 4.4 for more detailed
comparison with these previous studies).

Here we test the primordial and recycling origin scenarios using numerical
models for N partitioning and cycling coupled with Ar and N isotopes. Section
2 presents our models. Section 3 shows the model results. We discuss the
origin of N in the mantle and the implications for the future analysis of N
isotope record of early Earth and for other rocky planets in Section 4, and
conclude in Section 5.

##  2 Methods

Figure 1: Schematic view of our models. Reservoirs and exchange fluxes are written in yellow and black, respectively. Reservoir | N content [PAN] |  ${\rm\delta^{15}N}$ [‰] |  36Ar content [PA36Ar]
---|---|---|---
Atmosphere | 1 | 0 | 1
Mantle | 0.41–2.53a | -10 to -2b | 2.8–5.7$\times 10^{-3}$ c
Continental crust | 0.25–0.43d | +1 to +10e | –
Oceanic crust | 0.038–0.15f | +4 to +10g | –
Table 1: Constraints on our model results. 1 present atmospheric N (PAN) =
$4.0\times 10^{18}$ kg. 1 PA36Ar = $2.1\times 10^{14}$ kg. a:
Marty+Dauphas2003,Halliday2013,Bergin+2015. b: Marty+Dauphas2003. c:
Bekaert+2020. d: Rudnick+Gao2003,Johnson+Goldblatt2015,Johnson+Goldblatt2017.
e: Busigny+Bebout2013. f: Johnson+Goldblatt2015. g: Cartigny+Marty2013.

###  2.1 Model overview and constraints

We modeled N partitioning in the magma ocean stage and N cycling after magma
ocean solidification separately (Figure 1). Our first model tested whether N
in the modern mantle could be primordial by computing the N content trapped in
the mantle upon solidification. Partitioning was also computed for 36Ar
because the discrepancy in N/36Ar ratios between the present atmosphere and
mantle has been used to discuss the origin of mantle N [Marty Dauphas (2003)].
Our second model tested whether mantle N can originate from secular
subduction. This cycling model explicitly calculates 15N/14N ratios in the
surface reservoirs (the atmosphere and continental and oceanic crust) and
mantle, which can be used as another constraint.

Table 1 summarizes the constraints on model results: N contents,
$\delta^{15}$N values, and 36Ar contents in the four largest reservoirs: the
atmosphere, continental and oceanic crust, and mantle. We adapted a N content
estimate for the modern mantle derived from N-40Ar geochemistry by
Bergin+2015: $0.41$–$2.53$ times present atmospheric N $4.0\times 10^{18}$ kg
[<]hereafter PAN,¿[]Johnson+Goldblatt2015. This range brackets independent
estimates by Marty+Dauphas2003 ($0.41$–$1.27$ PAN) and Halliday2013
($0.42$–$1.12$ PAN). We adapted the N isotopic composition of the modern
mantle of ${\rm\delta^{15}N}=-10$ to $-2$‰ as informed from MORB [Marty
Dauphas (2003)]. We note that Johnson+Goldblatt2015 derived a higher estimate
($2$–$10$ PAN) by assuming the existence of the “high-N mantle,” which is
associated with some oceanic island basalts (OIB) and OIB-related xenoliths.
This proposed component is isotopically distinct [<]$\delta^{15}$N =
+5‰,¿[]Johnson+Goldblatt2015. The high-N estimate was not used in our main
results as its presence is not assumed in the other studies, but we discuss it
further in Section 4.3. The 36Ar amounts of modern atmosphere and mantle were
adapted from the estimate of Bekaert+2020.

###  2.2 Partitioning model

density | $\rho$ | PREM a
---|---|---
difference between solidus and liquidus | $\Delta T$ | F-peridotitic model b
heat capacity | $C_{p}$ | 1000 [${\rm J\ kg^{-1}\ K^{-1}}$] c
entropy change on melting | $\Delta S$ | 300 [${\rm J\ kg^{-1}\ K^{-1}}$] c
disaggregation melt fraction | $\phi_{\rm c}$ | 0.3 c
compaction time | $\tau$ | 4.35 Myr c
solidification time | $t_{\rm s}$ | 0.2–7 Myr d
solubility of N | $S_{\rm N}$ | Equation 16 e
partitioning coefficient of N | $D_{\rm N}$ | 0.0073, 0.020, 0.0030 f
solubility of Ar | $S_{\rm Ar}$ | 0.2 [ppm/MPa] g
partitioning coefficient of Ar | $D_{\rm Ar}$ | 0.0011 h
Table 2: Parameter values used in our partitioning model. a:
Dziewonski+Anderson1981. b: Monteux+2016. c: Hier-Majumder+Hirschmann2017. d:
Hamano+2013,Salvador+2017,Nikolaou+2019. e: Used Boulliung+2020 data (see A).
f: For upper mantle, transition zone, and lower mantle from Yoshioka+2018. g:
Model of Iacono+2010, assuming a bulk silicate Earth (pyrolite) magma
composition [McDonough Sun (1995)] and 1,700 K. h: Heber+2007.

Our partitioning model calculated the N and 36Ar amounts trapped in the
solidified mantle upon magma ocean cooling after core-mantle separation
(Figure 1). Our model assumes bottom-up solidification, but the case for a
basal magma ocean is discussed in Section 4.3. In contrast to previous studies
which modeled N partitioning [Libourel . (2003), Boulliung . (2020), Gaillard
. (2022)], degassing caused by magma solidification, which limits N trapping
into the mantle, was considered. We did not calculate N isotopes in this first
model. Equilibrium degassing enriches the residual melt in 15N by $\sim$+1‰
[<]e.g.,¿[]Dalou+2019. As we discuss quantitatively in Section 4.1, however,
atmospheric escape processes enrich atmospheric 15N easily and should be
responsible for the observed isotopic disequilibrium between the current
atmosphere and mantle in the primordial origin scenario.

####  2.2.1 N partitioning between reservoirs

Our method is based on the melt-trapping model of Hier-
Majumder+Hirschmann2017. The relevant parameters are summarized in Table 2.
Dissolution equilibrium was assumed between the atmosphere and magma ocean for
each time step, given as (see B for derivation),

$M^{i}_{\rm atm}=\frac{M^{i}_{\rm atm+mo}}{1+{(\bar{m}/m_{i})\cdot}S_{i}M_{\rm
mo}g/A_{\rm E}},$ (1) $M^{i}_{\rm mo}=M^{i}_{\rm atm+mo}-M^{i}_{\rm atm},$ (2)

where $M^{i}_{\rm j}$ is the mass of element $i$ (N or 36Ar) in the reservoir
$j$ (atm = atmosphere, mo = magma ocean, and sm = solidified mantle), $m_{i}$
is the molecular mass in the atmosphere (28 and 36 amu for N2 and 36Ar),
$\bar{m}$ is the mean molecular mass of atmospheric gases, $S_{i}$ is the
solubility, $g$ is the gravitational acceleration at the surface, and $A_{\rm
E}$ is the total surface area of Earth. The value without a superscript $i$ to
identify an element is the mass of the reservoir itself (e.g., the mass of
magma ocean $M_{\rm mo}$). Here we assumed that the volatile abundances in the
magma ocean are constant in depth to derive Equation 1. This assumption is
justified because the viscosity of the magma ocean is so low that the mixing
time scale is much shorter than the cooling timescale [<]the orders of days to
weeks vs. Myrs,¿[]Solomatov2015,Nikolaou+2019,Sossi+2020. The mean molecular
mass $\bar{m}$ was assumed to be 28 amu, assuming CO as the dominant gas. This
assumption is valid for Earth’s magma ocean [Sossi . (2020)]. While
$S_{\rm{}^{36}Ar}$ was assumed to be constant, $S_{\rm N}$ is dependent on N
partial pressure, $p_{\rm N_{2}}$ ($=(\bar{m}/m_{\rm N_{2}})\cdot M_{\rm
atm}^{\rm N}g/A_{\rm E}$, Equation 16). Thus, Equations 1 and 16 were
iteratively solved to obtain $S_{\rm N}$ and $M_{\rm atm}^{\rm N}$. Our N
solubility model, based on Boulliung+2020, assumed atmospheric N is in the
form of N2 (A), which is expected for the oxygen fugacity range considered
here [<]e.g., that of¿[]Schaefer+Fegley2017. As magma solidifies at the bottom
of magma ocean, the volatile content in the solidified mantle increases as,

$\frac{dM^{i}_{\rm sm}}{dt}=[F_{\rm tl}+D_{i}(1-F_{\rm tl})]C_{i}\frac{dM_{\rm
sm}}{dt},$ (3)

where $t$ is the time, $F_{\rm tl}$ is the trapped melt fraction, $D_{i}$ is
the partitioning coefficient between minerals and silicate melt, and $C_{i}$
is the concentration of the element $i$ in the magma ocean ($C_{i}\equiv
M^{i}_{\rm mo}/M_{\rm mo}$). The first and second terms in the bracket of
Equation 3 correspond to melt trapping and partitioning into minerals,
respectively. The trapped mass is subtracted from the rest of the system, as,

$\frac{dM^{i}_{\rm atm+mo}}{dt}=-\frac{dM^{i}_{\rm sm}}{dt}.$ (4)

The trapped melt fraction as a function of cooling rate is defined as the
fraction of the solidified mass trapped as interstitial melt relative to the
total solidified mass (solidified interstitial melt plus crystallized
minerals), and given by [Hier-Majumder Hirschmann (2017)],

$F_{\rm tl}=-\frac{\phi_{\rm c}\tau}{\Delta T}\frac{dT_{\rm p}}{dt},$ (5)

where $\phi_{\rm c}$ is the disaggregation melt fraction, $T_{\rm p}$ is the
mantle potential temperature, $\Delta T$ is the difference between the solidus
and the liquidus temperatures at the bottom of magma ocean, and $\tau$ is the
compaction time of the mushy layer at the bottom of magma ocean. The upper
limit of $F_{\rm tl}=0.3$ is given by the melt fraction for rheological
transition [Hier-Majumder Hirschmann (2017)].

####  2.2.2 Thermal evolution

The thermal evolution of Earth was solved to compute $dT_{\rm p}/dt$ in
Equation 5, as given by [Hier-Majumder Hirschmann (2017)],

$\frac{dT_{\rm p}}{dt}=-L_{\rm int}\biggl{[}C_{p}(M_{\rm E}-M_{r}(a))-4\pi\rho
T_{\rm p}\Delta Sa^{2}\frac{da}{dt}\biggr{]}^{-1},$ (6)

where $L_{\rm int}$ is the intrinsic luminosity, $M_{\rm E}$ is Earth’s mass,
$M_{r}$ is the enclosed mass, $\rho$ and $C_{p}$ are the density and the heat
capacity of the magma, and $a$ is the radius of the solidification front. We
derived a fitting formula for $a$ to reproduce Figure 2 of Hier-
Majumder+Hirschmann2017 as,

$a(T_{\rm p})=\begin{cases}R_{\rm E}\ (T_{\rm p}<1810\ {\rm K}),\\\
-1.587\times 10^{-1}T_{\rm p}^{3}+8.83571\times 10^{2}T_{\rm
p}^{2}-1.641\times 10^{6}T_{\rm p}+1.0234\times 10^{9}\ [{\rm m}]\ \\\ (1810\
{\rm K}<T_{\rm p}<2100\ {\rm K}),\\\ R_{\rm core}(2100\ {\rm K}<T_{\rm
p}),\end{cases}$

where $R_{\rm E}$ and $R_{\rm core}$ are the radii of Earth and the core,
respectively. Computing the intrinsic luminosity $L_{\rm int}$ requires a
radiative-convective model for the atmospheric structure with complete
description of molecular composition, cloud properties, etc.
[<]e.g.,¿[]Salvador+2017,Nikolaou+2019. Instead, we assumed a constant value
for $L_{\rm int}$ estimated from the given solidification time $t_{\rm s}$.

####  2.2.3 Initial conditions and parameters

The redox state of the mantle influences N solubility and, consequently, the
trapped N content. Earth’s magma ocean in its final stage is thought to be
more oxidized than $\log_{10}f_{\rm O_{2},\Delta{\rm IW}}=-1$ [Badro . (2015),
Armstrong . (2019), Sossi . (2020)], where $f_{\rm O_{2},\Delta{\rm IW}}$ is
the oxygen fugacity relative to that of the iron-wüstite buffer. Following
Dalou+2017, we considered three cases – oxidized ($\log_{10}f_{\rm
O_{2},\Delta{\rm IW}}=-1$), intermediate ($\log_{10}f_{\rm O_{2},\Delta{\rm
IW}}=-2$), and reduced ($\log_{10}f_{\rm O_{2},\Delta{\rm IW}}=-3.5$) cases
(Table 2), where the latter two are shown for comparison with the realistic,
oxidized model.

We considered $t_{\rm s}=0.2$–$7$ Myrs, which covers the range of estimates in
previous studies which simulated the magma ocean solidification [Hamano .
(2013), Salvador . (2017), Nikolaou . (2019)].

A fully molten magma ocean ($T_{\rm p}=2100$ K) was assumed for the initial
condition. The assumption maximizes the amount of trapped N. Initially the
total N content (Table 1) was assumed to be in the atmosphere and magma ocean
with the dissolution equilibrium. As we focus on the evolution after the major
accretion and core-mantle separation, we did not model partitioning into alloy
which would determine the total N content in concert with atmospheric loss
during the major accretion stage [Hirschmann (2016), Grewal . (2019), Grewal .
(2021), Sakuraba . (2021)] before the magma ocean solidification stage we
considered here.

###  2.3 Cycling model

Figure 2: A schematic image of our N cycling model.

To test the recycling origin scenario, our N cycling model simulated the
secular evolution of N masses and isotope ratios in the four major reservoirs:
the atmosphere, continental and oceanic crust, and mantle (Figure 2). Our
model explicitly treats more reservoirs than a recent study considering
isotopic evolution [Labidi . (2020)] but is simplified compared to the N
cycling models that were developed based on geophysics and (bio-)geochemistry
[Stüeken, Kipp, Koehler Buick (2016), Laneuville . (2018), Johnson Goldblatt
(2018)]. Our model was designed to understand i) the requirement for realizing
the recycling origin, and ii) its isotopic signatures as explained below.

Evolution of N masses and isotopic ratios (15N/14N) in the reservoirs was
calculated by using the following equations [Kurokawa, Foriel . (2018)],

$\frac{dM_{i}}{dt}=\sum_{\rm sources}F_{k}-\sum_{\rm sinks}F_{k},$ (7)
$\frac{d}{dt}(M_{i}I_{i})=\sum_{\rm
sources}(F_{k}\alpha_{k}I_{i^{\prime}})-\sum_{\rm
sinks}(F_{k}\alpha_{k}I_{i}),$ (8)

where $M_{i}$ and $I_{i}$ are the mass and isotopic ratio of N in the
reservoir $i$ (atm: atmosphere, cc: continental crust, oc: oceanic crust, and
ma: mantle), and $F_{k}$ and $\alpha_{k}$ are the flux of the process $k$ and
its isotopic fractionation factor. We considered net isotopic fractionation in
sediment deposition (the atmosphere to sediments on the crust, through fixed N
in the oceans). The other processes are known to induce relatively small
isotopic fractionation only [<]typically
$\simeq$1‰,¿[]Busigny+Bebout2013,Cartigny+Marty2013. A potential caveat here
is that N isotopic fractionation in the subduction zones and in the mantle has
not been fully understood, which is discussed in Section 4.3.

####  2.3.1 Sediment burial

Surface N cycling evolved through time
[<]e.g.,¿[]Shen+2006,Stueken+2016,Ader+2016. On modern Earth, biology mediates
primary N fixation from N2, and dissolved nitrate in the ocean is the main
form of bio-available N. In contrast, abiotic N fixation might have been a
dominant source of fixed N on early Earth [Navarro-González . (2001)],
especially before the development of biological N fixation [Stüeken . (2015)],
and nitrate would be limited because of limited biological oxidative
nitrification in anaerobic environments. A fraction of fixed N is continuously
removed from the N pool as sedimentary deposits, which is ultimately
transported to the mantle via subduction through time (Figure 2).

Because how the sedimentary N deposition rate changed through time is poorly
constrained, we simply parameterized the flux as,

$F_{\rm sed}(t)=F_{{\rm sed},0}\times 10^{C_{\rm sed}(t_{0}-t)/t_{0}},$ (9)

where $t_{0}$ = 4.5 Gyr, $F_{0}$ is the sediment deposition (N burial) flux on
modern Earth [<]0.455 PAN/Gyr,¿[]Stueken+2016ABb and $C_{\rm sed}$ is the
power-law parameter and can be either positive or negative. This
parameterization does not require explicit modeling of the size of biosphere,
which influences surficial N cycling, but we discuss the implications for the
early biosphere by utilizing the obtained values of $C_{\rm sed}$ (Section
4.2). The majority of sediments is deposited onto continental shelves (modeled
as a part of the continental crust), and the rest onto the oceanic crust as
pelagic sediments. We assumed the fraction of pelagic sediments, $f_{\rm
pel}$, to be 0.038 [Berner (1982), Stüeken, Kipp, Koehler, Schwieterman .
(2016)].

Sedimentary N can be incorporated into rocks after deposition. This process
was not explicitly included in our model as the crust and overlying sediments
are treated as a single reservoir, but it was implicitly considered as an
internal process.

Because there exists an isotopic disequilibrium within the N cycle [Cartigny
Marty (2013)], a successful recycling model should take into account the
evolution of the surficial N cycle which controls the net fractionation factor
between atmospheric and sedimentary N. The net isotopic fractionation factor
from the atmosphere to the sediments was modeled as occurring over four
stages.

In Period 1 ($>$3.2 Ga), $\Delta{\rm{}^{15}N}=-9$‰ was assumed (by definition,
$10^{3}\ln\alpha_{\rm sed}=\Delta{\rm{}^{15}N}$). This was motivated by lower
mean ${\rm\delta^{15}N}$ values ($-3.6$‰) of organic matter in the Eo-
paleoarchean [<]e.g.,¿[]Marty+Dauphas2003,Shen+2006. The adapted factor
($\sim-9$‰) is the lowest value of the sedimentary record (assuming
${\rm\delta^{15}N}=0$‰ for the atmosphere) as well as the value typically
expected for abiotic N-fixation via lightning or photochemistry [Moore (1977),
Navarro-González . (2001), Kuga . (2014), Stüeken . (2021)]. Anaerobic
processing after N fixation (and thus absence of nitrate) was implicitly
assumed in this stage, as we did not consider 15N enrichment due to
denitrification. Abiotically-fixed, 15N-depleted ammonia [Moore (1977),
Navarro-González . (2001)] would have been consumed by chemosynthetic bacteria
in hydrothermal systems under anaerobic conditions in this period [Shen .
(2006)].

In Period 2 (3.2–2.75 Ga), $\Delta{\rm{}^{15}N}=0$‰. The environment is still
anaerobic, but biotic N fixation (diazotrophy) began and became the major
source of bio available N in this period [Stüeken . (2015)].

During Period 3 (2.75–2.4 Ga), $\Delta{\rm{}^{15}N}=+10.8$‰. Aerobic N cycling
(coupled nitrification, denitrification, and assimilation) started in this
period [Garvin . (2009)]. Dissimilatory denitrification leads to residual
nitrate being kinetically enriched in 15N, and the isotopically enriched
nitrate is then reduced to ammonium and converted to organic matter and
finally trapped in sediments [<]e.g.,¿[]Stueken+2016. Larger N fractionation
as recorded in organic matter compared to the modern value can be explained by
limited amounts of nitrate [Shen . (2006)].

In Period 4 ($<$2.4 Ga), $\Delta{\rm{}^{15}N}=+6$‰. The isotopic shift during
nitrification-denitrification-assimilation would have decreased to the modern
average value due to the formation of a sizable global nitrate pool [Shen .
(2006)].

####  2.3.2 Continental weathering

Continental N is gradually transported to the oceanic crust via weathering.
The weathering flux is assumed to be proportional to $M_{\rm cc}$ as,

$F_{\rm wea}=\frac{M_{\rm cc}}{\tau_{\rm wea}},$ (10)

where $\tau_{\rm wea}$ is the timescale of weathering. The timescale depends
on atmospheric O2 partial pressure, and here modeled as [Johnson Goldblatt
(2018)],

$\tau_{\rm wea}=\tau_{{\rm wea},0}\cdot\biggl{[}a_{\rm wea}+(1-a_{\rm
wea})\frac{PAL_{\rm O_{2}}}{PAL_{\rm O_{2}}+k_{\rm wea}}\biggr{]}^{-1},$ (11)

where $\tau_{{\rm wea},0}$ is the weathering timescale on modern Earth
($\tau_{{\rm wea},0}=0.3\ {\rm Gyr}$), $PAL_{\rm O_{2}}$ is the atmospheric O2
partial pressure scaled to present atmospheric levels for which we used the
model of Johnson+Goldblatt2018 developed based on geochemical reconstruction
[<]e.g.,¿[]Lyons+2014, $a_{\rm wea}$ is the fraction of available material
weathered under anoxic conditions ($a_{\rm wea}=0.1$), and $k_{\rm wea}$ is
the weathering constant ($k_{\rm wea}=10^{-3}$), respectively [Johnson
Goldblatt (2018)]. The dependence on $PAL_{\rm O_{2}}$ is not critical for the
surface-mantle N exchange, but it is important to reproduce the Archean low
$p_{\rm N_{2}}$ record [<]¿[see Section 3.2]Marty+2013,Som+2012,Som+2016.

####  2.3.3 Subduction, arc volcanism, and continental growth

Sedimentary N on the oceanic crust is eventually conveyed to subduction zones.
N is then either returned to the atmosphere via arc volcanism ($F_{\rm arc}$),
incorporated into the continental crust ($F_{\rm ccg}$), or transported to the
mantle ($F_{\rm sub}$). We modeled these fluxes as,

$F_{\rm sub,tot}\equiv F_{\rm sub}+F_{\rm arc}+F_{\rm ccg}=\frac{M_{\rm
oc}}{\tau_{\rm sub}},$ (12)

where $\tau_{\rm sub}$ is the subduction timescale. We assumed $\tau_{\rm
sub}=0.1\ {\rm Gyr}$, following Stueken+2016ABb. Fast plate tectonics on early
Earth, which leads to the short $\tau_{\rm sub}$, was assumed in the past, but
recent studies suggest that the plate speed is nearly constant through time
[Korenaga (2003), Bradley (2008), Condie . (2015), Pehrsson . (2016), Korenaga
(2018)].

We note that hydrothermal addition of N to the oceanic crust is not explicitly
included in our cycling model. In reality, N in the altered crust can also
transport N to the mantle [Mitchell . (2010), Halama . (2014), Johnson
Goldblatt (2018)]. However, this N in the altered crust is likely sourced from
sedimentary organic material deposited to the crust [Halama . (2014)], and
thus the conversion does not change the global N balance.

The ratio $F_{\rm sub}$:$F_{\rm arc}$:$F_{\rm ccg}$ ($\equiv 1-f_{\rm
arc}-f_{\rm ccg}$:$f_{\rm arc}$:$f_{\rm ccg}$) is highly uncertain [Johnson
Goldblatt (2018), Catling Zahnle (2020)]. We evaluated $f_{\rm arc}$ and
$f_{\rm ccg}$ as follows. First, we assumed $f_{\rm arc}=f_{\rm ccg}$,
following Johnson+Goldblatt2018. Then, We evaluated $f_{\rm ccg}$ by
considering the mass balance. Assuming a steady state for $M_{\rm cc}$ and
$M_{\rm oc}$ leads to,

$M_{\rm cc}=F_{\rm sed}\tau_{\rm wea}\biggl{(}\frac{1}{1-f_{\rm ccg}}-f_{\rm
pel}\biggr{)},\ M_{\rm oc}=\frac{F_{\rm sed}\tau_{\rm sub}}{1-f_{\rm ccg}}.$
(13)

Provided the short $\tau_{\rm wea}$ after the GOE and $\tau_{\rm sub}$, the
steady state assumed here to evaluate $f_{\rm ccg}$ is shown to be valid with
our cycling model where the time evolution is explicitly solved (Section 3.2).
In order to reproduce the modern $M_{\rm cc}$ and $M_{\rm oc}$ (Table 1) with
Equation 13, $f_{\rm ccg}$ needs to be $\simeq 0.5$. Thus, we assumed $f_{\rm
ccg}=f_{\rm arc}=0.45$, and the rest, $1-f_{\rm ccg}-f_{\rm arc}=0.1$, is
transported to the mantle.

####  2.3.4 Mantle degassing

The flux of volcanic N degassing from the mantle with time depends on the
mantle N content, $M_{\rm ma}$, the thermal evolution [Keller Schoene (2018),
Korenaga (2018)], and the redox state [Mikhail Sverjensky (2014), Zerkle
Mikhail (2017)] which might have become oxidized over time [Aulbach Stagno
(2016), Nicklas . (2018), Nicklas . (2019), Aulbach . (2019)].

We parameterized the volcanic degassing flux from the mantle as,

$F_{\rm vol}=\frac{M_{\rm ma}}{\tau_{\rm vol}},$ (14)

where $\tau_{\rm vol}$ is the degassing timescale, which was parameterized as,

$\tau_{\rm vol}=\tau_{{\rm vol},0}\times 10^{C_{\rm vol}(t_{0}-t)/t_{0}}.$
(15)

The power-law parameter, $C_{\rm vol}$, can be either positive or negative.
The mantle N degassing timescale, $\tau_{\rm vol,0}$, on modern Earth was
estimated from the mean value of the estimates of modern mantle N content 1.47
PAN (Table 1) divided by the modern N degassing flux [<]0.018
PAN/Gyr,¿[]Busigny+2011.

####  2.3.5 Initial conditions, parameters, and classification of results

We performed Monte Carlo simulations to find parameter sets which satisfy the
constraints on N masses and isotopic compositions of present reservoirs (Table
1). The model runs which are consistent with these observations are hereafter
called “accepted runs.” The Monte Carlo simulations were repeated until 100
accepted runs were found; this typically required 106 trials. In accepted
runs, we classified those with $M_{\rm ma}(t=0\ {\rm Ga})\times 0.5>M_{\rm
ma}(t=4.5\ {\rm Ga})$ as “accepted recycling-origin runs,” and the others as
“accepted primordial-origin runs.”

There are five Monte Carlo parameters. The total N content is varied from
1.844 to 3.964 PAN (Table 1). The initial mantle N content is from 0 PAN to
the total N content. The N isotopic ratio of initial mantle is from $-$40 to
0‰ as found in enstatite chondrites [<]¿[and references therein]Piani+2020. We
note that such low $\delta^{15}$N values have been reported for some rare
diamonds from Earth’s mantle, which possibly record the signature of Earth’s N
source [Palot . (2012)]. The subduction and degassing parameters $C_{\rm sub}$
and $C_{\rm vol}$ are both from $-$5 to 5.

The other parameters were fixed during the Monte Carlo simulations, but their
influences were investigated separately. i) The onset time of biological N
fixation. Our nominal case assumed that biological N fixation (Phase 2)
started at 3.2 Ga. This is based on the N isotope record which suggests that
biological N fixation had already started by that time [Stüeken . (2015)].
Phylogenetic data also suggests that the last universal common ancestor (LUCA)
had this function [Weiss . (2016)]. Thus, we tested the case where Period 2
started 4.5 Ga as another endmember. ii) The onset time of the plate
tectonics. The onset time of the plate tectonics on Earth is controversial
[Korenaga (2013)]. In the nominal case, we assumed the initiation time for
plate tectonics, $t_{\rm pt,init}$, to be 3.5 Ga, following
Johnson+Goldblatt2018. We also tested $t_{\rm pt,init}$ = 4.5 Ga. iii) The
onset time of N subduction. Our nominal case assumed $f_{\rm ccg}=f_{\rm
arc}=0.45$ and, thus, 10% of N conveyed to subduction zones is transported to
the mantle. Because a hot mantle might have inhibited N subduction prior to
2.5 Ga [Johnson Goldblatt (2018)], we also tested a model where $f_{\rm
ccg}=f_{\rm arc}=0.5$ and $f_{\rm ccg}=f_{\rm arc}=0.45$ before and after 2.5
Ga, respectively. However, we find that these model variants do not differ
significantly (Section 3.2).

Paleo-atmospheric pressure and N2 partial pressure, $p_{\rm N_{2}}$, have been
constrained from geochemical and geological record [Marty . (2013), Som .
(2012), Som . (2016)]. These studies suggest low $p_{\rm N_{2}}$ values in the
Archean, which corresponds to 0.64–1.4 PAN at 3.5-3.0 Ga [Marty . (2013)] and
$<$0.64 PAN (assuming that N2 is the dominant atmospheric gas) at 2.7 Ga [Som
. (2012), Som . (2016)]. Our model did not adapt these constraints explicitly,
but we compared the accepted runs with them. Overall, we find that these low
$p_{\rm N_{2}}$ values are satisfied in many, but not all, accepted runs by N
sequestration in the crust [<]as proposed by¿[]Stueken+2016ABb.

##  3 Results

###  3.1 Partitioning model

Figure 3: Evolution of the N content in each reservoir in our partitioning
model. Blue line: atmosphere. Red line: magma ocean. Green lines: solidified
mantle (dashed: trapped melt and minerals, dotted: minerals only). The result
for the oxidized case with $t_{\rm s}=0.2$ Myrs and the total content = 2 PAN
is shown. Figure 4: N partitioning between the atmosphere and mantle at the
time of magma ocean solidification. The result of one simulation run
corresponds to a single point in the figure, and changing two parameters (the
solidification time $t_{\rm s}$ and the total N content in the system $M^{\rm
N}_{\rm atm+mo+sm}$) draws a green patch of solutions. Results are shown for
the oxidized, intermediate, and reduced cases (see text) with increasing
transparency. Dashed curves show constant total-N (1.698 and 4.110 PAN). The
shaded areas are the N amounts in the modern surface (the atmosphere plus
continental and oceanic crust, blue) and mantle (red). Figure 5: 36Ar
partitioning between the atmosphere and mantle at the time of magma ocean
solidification. Dashed curves show constant total-36Ar (1.0028 and 1.0057
PA36Ar). The shaded areas are the 36Ar amounts in the modern atmosphere (blue)
and mantle (red). Figure 6: N partitioning between the atmosphere and mantle
at the time of magma ocean solidification in the cases where we assumed larger
amounts of total N to reproduce the modern mantle N content with the oxidized
magma ocean model. Results are shown for the oxidized, intermediate, and
reduced cases (see text) with increasing transparency. Dashed curves show
constant total-N (8.11 and 152.53 PAN). The shaded areas are the N amounts in
the modern surface (the atmosphere plus continental and oceanic crust, blue)
and mantle (red).

First, we studied N partitioning in the magma ocean stage to test the
primordial-origin scenario. Time evolution with $t_{\rm s}$ = 0.2 Myrs and the
total N content = 2 PAN in the oxidized case is shown in Figure 3. N was
chiefly partitioned into the atmosphere owing to its low solubility (Equation
16 in A). As the magma ocean solidified, a fraction of N in the magma ocean
partitioned into the solidified mantle chiefly in the form of N in the trapped
melt. Because of its incompatibility (low mineral-melt partitioning
coefficients, $D_{\rm N}$, Table 2), the contribution of N partitioned into
minerals was small. As a consequence, the mantle right after magma ocean
solidification is depleted in N (the mantle N content is only $\sim$0.1 PAN).
We note that the final mantle N content in this low solubility limit is well
approximated by $M^{\rm N}_{\rm mantle}/M_{\rm mantle}\simeq p_{\rm
N_{2}}S_{\rm N}F_{\rm tl}$ [<]Equation 11 of ¿[]Kurokawa+2021 with $F_{\rm
tl}=0.3$ in this rapid solidification case.

Figure 4 shows the atmospheric and mantle N contents after magma ocean
solidification for a range of total N content and solidification times $t_{\rm
s}$ in the oxidized, intermediate, and reduced cases. For a given redox state,
increasing the total N content leads the results to move to the upper right
perpendicular to the constant total-N curves, while increasing $t_{\rm s}$ to
the upper left parallel to the curves. If the atmospheric and mantle N
contents obtained in the model match those of the modern surface (N in the
atmosphere plus continental and oceanic crust which is thought to be in the
atmosphere when the magma ocean solidified) and mantle, the results suggest a
primordial origin for mantle N. However, in both oxidized and intermediate
cases, the model mantle N content was lower than the modern value. Only the
reduced case reproduced the lower estimate ($\lesssim$1 PAN) of the modern
mantle N content. This is caused by higher N solubilities in reduced
conditions due to chemically-bound N in the magma [Libourel . (2003)]. The
mantle N amounts in all cases were mainly attributed to trapped interstitial
melt (Figure 3). The contribution of N in minerals was smaller by an order of
magnitude. A shorter solidification time $t_{\rm s}$ leads to a higher trapped
melt fraction $F_{\rm tl}$ and thus more N in the solidified mantle. However,
our result with the shortest solidification time ($t_{\rm s}=0.2$ Myrs)
already reached the maximum value ($F_{\rm tl}=0.3$).

In contrast, the partitioning model reproduced the 36Ar content of the modern
mantle as well as the atmosphere (Figure 5). Ar behaves similarly to N in the
oxidized magma [<]e.g.,¿[]Marty+Dauphas2003, and ends up with a similar degree
of depletion in the mantle. The agreement between the model and observations
is due to the fact that the modern mantle is depleted in 36Ar by two orders of
magnitude with respect to N/36Ar ratios compared to the current atmosphere.

To summarize, our partitioning model suggests that the mantle received only
$\sim$10% of the total N when the magma ocean fully solidified, unless the
magma was reducing. The reduced magma ocean at the time of solidification is
not supported from geophysical and geochemical studies [Badro . (2015),
Armstrong . (2019), Sossi . (2020)].

We also performed model calculations with increased total N content and found
that putting the modern N content into the solidified mantle in the oxidized
case ended up with 7.7–150 PAN in the atmosphere (Figure 6). The range was
derived from uncertainties in the modern mantle N content $M^{\rm N}_{\rm
mantle}$ and the magma ocean solidification time $t_{\rm s}$. In Section 4.1,
we discuss a primordial-origin scenario for the mantle N by considering the
excess amount of total N, which could have been removed later by atmospheric
escape processes.

###  3.2 Cycling model

Figure 7: Cycling model results for the nominal case where we assumed the
onset times of biological N fixation, plate tectonics, and N subduction to be
3.2, 3.5. and 3.5 Ga, respectively (see Section 2.3.5 for details). Top:
Evolution of masses (left) and 15N/14N ratios (right) in the atmosphere
(blue), continental and oceanic crust (purple and green), and mantle (red).
Curves show accepted runs whose outcomes are consistent with modern values
(shown along the right y-axis). Thick and thin curves denote accepted
recycling- and primordial-origin runs, respectively. Gray boxes indicate
$p_{\rm N_{2}}$ constraints from Som+2016 and Marty+2013. Bottom: Histograms
of Monte Carlo parameters of all accepted runs. Recycling- and primordial-
origin runs are shown in red and blue, respectively. Figure 8: Cycling model
results for the case where we assumed Phase 2 (biological N fixation) started
4.5 Ga, while the other settings are the same as in the nominal case (Figure
7). See Figure 7 caption for details.

####  3.2.1 Evolution of N contents in reservoirs

Next, we tested the recycling origin for mantle N with our cycling model. We
note that, unless otherwise stated, we refer to the results of the nominal
case where we assumed the onset times of biological N fixation, plate
tectonics, and N subduction to be 3.2, 3.5. and 3.5 Ga, respectively (see
Section 2.3.5 for details). The evolution of N masses and isotopic ratios in
the atmosphere, continental and oceanic crust, and mantle after the
solidification of magma ocean was simulated with the nominal parameter set
(Figure 7). Rather than directly adopting the results of the magma-ocean
partitioning model, initial conditions of the cycling model were treated as
Monte Carlo parameters, and we looked for parameter sets which reproduce the
modern N contents and isotopic ratios in the four reservoirs. We compare the
results of the two models to discuss possible scenarios for N partitioning and
cycling in Section 4.

The atmospheric N contents in the runs which started from a few PAN show
decline with time to reach a minimum at 2.4 Ga (the top-left panel of Figure
7). The decline is caused by sediment deposition and sequestration in the
continental and oceanic crust. Notably, the constraints on $p_{\rm N_{2}}$
[Marty . (2013), Som . (2012), Som . (2016)] can be satisfied by many, but not
all, accepted runs. The modeled evolution curves also agree with evidence for
a stable atmospheric $p_{\rm N_{2}}$ reservoir over the Phanerozoic [Berner
(2006)]. The initiation of plate tectonics can be seen as the decline of N
contents in the oceanic crust after 3.5 Ga. In contrast, the influence of
subduction on the mantle N contents in the recycling-origin runs is limited
before 2.4 Ga. In some primordial-origin runs, the mantle N contents even
decreased in this period due to degassing.

At 2.4 Ga, which corresponds to the GOE, the rate of continental weathering
increased drastically, leading to the decline of N content in the continental
crust. The continental N was first transported to the oceanic crust as
sediments, and then to the mantle via subduction. Owing to the return N flux
via arc volcanism, the atmospheric N contents start to increase with time
after the GOE.

####  3.2.2 Evolution of N isotopic ratios in reservoirs

N cycling between the reservoirs is reflected to the evolution of isotopic
ratio (the top-right panel of Figure 7). In the recycling-origin runs, the
atmospheric $\delta^{15}$N values increase by $\sim$+5‰ with time prior to 3.2
Ga. This is caused by deposition of 15N-depleted sediments in Period 1 ($>$3.2
Ga, Section 2.3). As the net fractionation factor between the atmosphere and
sediments became zero (Period 2, 3.2–2.75 Ga) to positive (Periods 2 and 3,
$<$2.75 Ga), the atmospheric $\delta^{15}$N values change their trend to
decline with time. The minimum values at 2.4 Ga correlate with the atmospheric
N contents at that time. Following the recovery of $p_{\rm N_{2}}$ after 2.4
Ga, the atmospheric $\delta^{15}$N values approach asymptote of 0‰.

The $\delta^{15}$N values of the continental and oceanic crust showed secular
increase as a result of the change in $\Delta^{15}$N between the atmosphere
and sediments deposited. The rate-determining process of the continental
$\delta^{15}$N evolution is continental weathering whose timescale is 3 Gyrs
and 0.3 Gyrs before the GOE and at present, respectively (Equation 11). The
timescale of the evolution of the oceanic crust $\delta^{15}$N values is
determined by the subduction (0.1 Gyrs) after the onset of the plate
tectonics. Because this is much shorter than the timescale of continental
weathering, the oceanic crust follows the continents in terms of
$\delta^{15}$N evolution.

Mantle $\delta^{15}$N stays constant before 3.5 Ga because no subduction is
assumed in the nominal case. After the onset of the plate tectonics, these
values start to increase due to subduction of relatively-15N-rich surface N.
The rate of change increases after 2.4 Ga. This is caused by enhanced
continental weathering after the GOE, which leads to more N transported onto
the oceanic crust, and consequently, to the mantle.

We note that several primordial origin runs showed high $\delta^{15}$N values
for the atmosphere and crust initially. These are runs where the Monte Carlo
code chose high initial mantle N contents, so that the mass balance led to
high atmospheric $\delta^{15}$N values to keep the bulk $\delta^{15}$N
consistent with the modern value. Because the continental and oceanic crust
receives atmospheric N as sediments, their $\delta^{15}$N values were also
high earlier on. The record of the initial state is eventually lost after
$\sim$1 Gyr.

####  3.2.3 Monte Carlo parameters in accepted runs

Histograms of Monte Carlo parameters in accepted runs are shown in the bottom
panels in Figure 7. Because our model is not fully physics-based but rather
conceptual, all results should not necessarily be treated as realistic without
discussion, but these should be considered as requirements to reproduce the N
contents and isotopic ratios in the modern reservoirs (see Section 4.2 for
discussion on possible scenarios).

In comparing the recycling- and primordial-origin runs, the former show lower
total N masses and lower initial mantle $\delta^{15}$N values than the latter.
This is caused by the finite ability of the system to transport surface N
without increasing the mantle 15N value too much. The low initial mantle
$\delta^{15}$N values in the recycling runs (typically $-40$ to $-20$‰) mean
that, even they were classified as the recycling origin, the initial mantle
condition matters - in terms of the isotopic composition, mantle N cannot be
fully of recycling origin.

The sediment deposition parameter, $C_{\rm sed}$ (positive and negative values
mean higher and lower fluxes in earlier time, respectively), was constrained
around zero, which means that sediment N burial has been nearly constant, for
both recycling- and primordial-origin runs. This is reasonable for the former.
Given the modern N subduction flux, $\sim$0.1 PAN/Gyr assumed in our model, it
takes $\sim$4 Gyrs to transport $\sim$0.4 PAN (the lowest estimate for the
modern mantle N mass) to the mantle. Lower sediment N deposition flux on early
Earth (negative $C_{\rm sed}$) would lead to less N subduction, which would
not satisfy the constraints of modern mantle N content.

Why $C_{\rm sed}$ is highly constrained even for the primordial-origin runs is
not so intuitive. In order to understand this behavior, we tested an
additional case where we omitted the constraints on the N masses and
$\delta^{15}$N values for the modern continental and oceanic crust (Figure
12). In this case, accepted primordial-origin runs include lower $C_{\rm sed}$
values down to $-$5, but these runs show lower N contents in the continental
and oceanic crust. This result indicates that modern crustal N masses rule out
low $C_{\rm sed}$ values from the primordial-origin runs. Importantly, even in
this case where the constraints on crustal N masses are relaxed, the
recycling-origin runs showed their $C_{\rm sed}$ values constrained to be
around zero, indicating that sediment N deposition flux on early Earth
comparable to the modern value is a robust requirement for the recycling-
origin scenario.

In contrast to $C_{\rm sed}$, the accepted degassing parameter values, $C_{\rm
vol}$ (positive and negative values mean longer and shorter earlier degassing
timescale, respectively), were distributed over a wider range. This is likely
because mantle degassing has a relatively minor effect on overall N cycling.
The modern degassing flux of mantle N was assumed to be 0.018 PAN/Gyr [Busigny
. (2011)], which is an order of magnitude lower than the N subduction flux.

####  3.2.4 Effects of the onset time of biological N fixation, plate
tectonics, and N subduction

The case where we assumed the onset of biological N fixation (Phase 2) at 4.5
Ga is shown in Figure 8. There was no significant difference with the nominal
case (Figure 7) in the accepted Monte Carlo parameters. However, the
difference of the evolution of $\delta^{15}$N values is notable. In contrast
to the nominal case showing atmospheric $\delta^{15}$N values to be $\sim$+5‰
prior to 2.4 Ga in the recycling-origin runs, the atmospheric $\delta^{15}$N
values stayed nearly constant at 1–4‰ in the early biological-N-fixation case.
Because there is no net-fractionation between the atmosphere and sediments,
the crustal $\delta^{15}$N values stayed equal to the atmospheric values
before 2.75 Ga.

Finally, we tested two cases where we assumed the onset of plate tectonics at
4.5 Ga (Figure 13) and all subducted N was returned to the atmosphere and
continental crust before 2.5 Ga due to the hotter mantle of early Earth
(Figure 14). Although there were differences in the evolution of N contents in
the oceanic crust and mantle, no significant difference was found in the
accepted Monte Carlo parameters. This is because the most important mechanisms
to determine N cycling are N storage in the crust and efficient continetal
weathering to cause N subduction before and after the GOE, respectively, both
of which were satisfied in these variants of the nominal case.

##  4 Discussion

###  4.1 The origin of mantle N: the primordial excess-N scenario

Figure 9: The amount of escaped N required to enrich the remnant atmosphere (1
PAN) in 15N by $+6$‰ as a function of isotopic fractionation factor. Blue
circles and a red square are estimates for EUV-driven hydrodynamic escape and
solar wind-induced ion pickup, respectively. Figure 10: Evolution of
atmospheric N content during the late accretion in the primordial N-excess
scenario. Green: Enstatite chondrite-like impactors. Yellow: N-depleted “dry”
impactors. Initial N contents are 7.7 PAN (thin curves) and 150 PAN (thick
curves), which corresponds to the atmospheric N content required to put N into
the mantle comparable to the current mantle in the oxidized magma-ocean
scenario (Section 3.1 and Figure 6). The horizontal blue line is the modern
surface N content (the atmosphere and crust). The vertical dashed line is the
minimum estimate for the cumulative mass of the late accretion. Note that the
thick green and yellow curves are largely overlapping.

In Section 3.1, we suggests that magma ocean solidification led to depletion
of N in the mantle, unless the magma ocean was reducing (Figure 4). Both high
pressure experiments [Armstrong . (2019), Sossi . (2020)] and coupled
geochemical and geophysical constraints [Badro . (2015)] point to Earth’s
magma ocean at the time of solidification being close to or more oxidizing
than IW-1. Therefore, we rule out a scenario that reducing conditions led to
the primordial origin of N in the mantle, and focus on the oxidized magma
ocean condition.

A possibility we should consider is that primitive Earth right after core-
mantle separation might have a higher bulk N content than it currently does,
and thus even preferential partitioning into the atmosphere in the oxidized
magma ocean condition could end up with an amount of N remaining in the mantle
sufficient to match modern observed values. If this were the case, the early
atmosphere would have an excess amount of N of 7.7–150 PAN in the oxidized
case (Section 3.1 and Figure 6). We name this case the primordial “excess-N”
scenario as a variant of the primordial origin and test whether atmospheric
escape processes can remove the excess N in the atmosphere.

We estimated the 15N-enrichment effect due to extreme ultraviolet (EUV)-driven
escape and solar wind-induced ion pickup to see how much atmospheric N should
be removed to end up with $\sim+$6‰ 15N-enrichment in the remnant 1 PAN
atmosphere (Figure 9, see D for model details). We found that these processes
can remove only 0.5 PAN at most even assuming an EUV level 500 times higher
than at present, which is significantly smaller than the excess atmospheric N
estimated above. This level of EUV corresponds to so-called fast-rotating
young Sun model, but previous studies focusing on volatile contents on Venus
[Lammer, Leitzinger . (2020), Lammer, Scherf . (2020)] and the Moon [Saxena .
(2019)] concluded that the EUV level of the young Sun is likely to be less
active than a moderate rotator, whose EUV level was $\simeq$100 times that of
the current Sun. For this EUV level, neither 14N nor 15N can be removed by
EUV-driven escape. Moreover, the contribution of solar wind-induced ion pickup
should be limited to 0.01 PAN, otherwise the atmosphere would have excess 15N.

Next we estimated how much N can be removed by atmospheric erosion due to late
accretion impacts, using the model of Sakuraba+2019 (Figure 10, see E for
model details). Impact erosion does not fractionate isotopes, as it removes
the bulk atmosphere well below the homopause. However, we found that impact
erosion cannot remove the excess N (7.7–150 PAN) with the minimum estimate of
the late accretion mass (0.5 wt.% of Earth’s total mass) and N-containing
impactors (such as enstatite chondrites) that have been suggested from the
isotopic analysis of siderophile elements in Earth and the Moon [Dalou .
(2017), Fischer-Gödde Kleine (2017), Fischer-Gödde . (2020), Worsham Kleine
(2021)]. The excess N can be removed by completely N-depleted impactors or by
a higher cumulative mass of late accreting material [Marchi . (2018)]. We note
that here we assumed asteroid-belt-like impactor-size distribution which leads
to efficient impact erosion. Assuming shallower size distribution [<]more
large impactors, as proposed by¿[]Bottke+2010 does not yield sufficient
atmospheric loss [Sakuraba . (2019), Sakuraba . (2021)].

From these results shown above, we conclude that the primordial origin
scenario for the mantle N is possible only if Earth at the time of magma ocean
solidification had an excess amount of N ($>$7.7 PAN in the atmosphere), and
if the N content, size distribution, and total mass of late accretion
impactors allowed efficient loss of the excess N in the atmosphere to space by
impact erosion. The feasibility of this model also depends on primitive
Earth’s total N content after major accretion and core-mantle separation.
Grewal+2021 modeled Earth’s accretion and argued that the N content of the
bulk silicate Earth (Earth minus the core, hereafter BSE) was determined by
partitioning into the core and atmospheric loss during major accretion, which
is incompatible with the excess-N scenario proposed here. In their model, the
atmospheres on planetesimals in each stage of accretion were assumed to be
lost completely. In contrast, Sakuraba+2021 simulated Earth’s accretion with
an impact erosion model [Sakuraba . (2019)]. They showed that atmospheric loss
in the main accretion stage before the late accretion is significant but not
complete, and thus Earth formed with excess N, which was removed by late
accretion impacts.

The excess-N and impact erosion scenario need to reproduce 36Ar/N ratios in
Earth’s atmosphere and mantle. The agreement of the 36Ar partitioning model
results with 36Ar in the modern atmosphere and mantle (Figure 5) suggests
that, in contrast to N, there was no significant excess atmospheric36Ar at the
time of solidification, requiring preferential N removal. However, impact
erosion itself is not a fractionation process. A possibility to reconcile the
excess-N scenario with the observed 36Ar/N ratios is late accretion of bodies
having a high 36Ar/N ratio on average, as proposed for the cometary
contribution to Earth’s atmospheric noble gases [<]but not to major volatile
elements: H, C, and N,¿[]Marty+2016,Marty+2017, while the majority of
impactors would be chondritic or more dry bodies. If this was the case, even
though impact atmospheric erosion itself is not a selective process, the
erosion combined with the replenishment of Ar would lead to a net loss of N
preferentially to Ar. This gives another constraint on the impactor
composition in the primordial scenario.

###  4.2 The origin of mantle N: the early biogeochemical cycling scenario

In Section 3.2, we showed that the recycling origin scenario requires sediment
N deposition rates on early Earth being comparable to that of modern Earth.
The high sediment N deposition flux is, as discussed below, likely to be
sustained by biotic activity.

A simple solution is that high sediment deposition flux at earlier times has
been sustained by biological N fixation similar to as on modern Earth (as
assumed in Figure 8). This scenario might be consistent with the phylogenetic
study which suggests that LUCA was able to fix N [Weiss . (2016)].

Alternatively, even if N fixation on early Earth was being sustained by
abiotic processes (as assumed in the nominal case, Figure 7), biotic activity
is needed to keep high N concentration in sediments. Considering the
reasonable range of abiotic N fixation fluxes, adsorbed N content in sediments
was estimated to be smaller by more than an order of magnitude in abiotic
conditions than in modern Earth condition [<]$\sim$10 ppm vs. $\sim$400
ppm,¿[]Stueken2016AB,Busigny+2011. This is the maximum estimate as it assumes
that all NOx is reduced to NH${}_{4}^{+}$ during hydrothermal circulation or
by reaction with ferrous iron. Another study found that abiotic chemistry
significantly limits the NOx abundance in the oceans [Hu Diaz (2019)] and thus
NH${}_{4}^{+}$ as well. On modern Earth, the efficient NH${}_{4}^{+}$
adsorption is caused by a high NH${}_{4}^{+}$ concentration in pore water of
anoxic sediments due to the degradation of organic matter
[<]e.g.,¿[]Stueken2016AB. Therefore, here we suggest a scenario that the same
mechanism also contributed to the high NH${}_{4}^{+}$ abundance in sediments
and thus efficient cycling, and that the modern mantle N was sourced by
biogeochemical cycling (either biotic or abiotic N fixation and subsequent
biotic processing) developed on early Earth.

###  4.3 Model uncertainties and limitation

As discussed in Section 2, Johnson+Goldblatt2015 estimated a higher modern
mantle N content (2–10 PAN) than the range assumed in our study (0.41–2.53
PAN). The higher N content is more difficult to reconcile with partitioning in
the magma ocean stage. In contrast, because the proposed high-N mantle has
high $\delta^{15}$N values ($\sim$+5‰) comparable to modern sediments [Johnson
Goldblatt (2015)], it can be sourced by subduction of sediments after the
development of the modern aerobic N cycle, if high sedimentary deposition flux
is considered [<]as modeled by¿[]Johnson+Goldblatt2018. Therefore, the high-N
mantle component, if confirmed, supports the recycling origin for mantle N.

Our cycling model assumes monotonic increase or decrease for the sediment
deposition flux and the mantle degassing timescale for simplicity, but Earth
might have experienced continuous inversions of N subduction and degassing
fluxes [Zerkle Mikhail (2017)]. For instance, the N subduction flux has likely
been lower and higher before and after the emergence of life as it enhances
NH${}_{4}^{+}$ adsorption efficiency (Section 4.2). Nevertheless, our
conclusion for the requirement for the high sediment N burial rate would be
valid as an averaged condition before the onset of aerobic N cycling.

Following Stueken+2016ABb, we assumed that the effects of continental growth
[<]e.g.,¿[]Korenaga2018 on the offshore to onshore ratio of sediment burial
($f_{\rm pel}/(1-f_{\rm pel})$) and on the continental weathering timescale
($\tau_{\rm wea}$) were minor. The reader is referred to Stueken+2016ABb for
detailed discussion. Key assumptions of our model were that sediments are
mainly deposited to the continental crust (shelves) through Earth’s history
($f_{\rm pel}\ll 1$ and is assumed to be constant through time) and the long
residence time of sediments on the continental crust before the GOE
($\tau_{\rm wea}\sim$1 Gyr). Thus, unless the continental fraction was
extremely small in the Archean to lead $f_{\rm pel}\sim 1$, the continental
growth curve would not influence our model results and conclusions
significantly. If these assumptions did not hold, the low $p_{{\rm N}_{2}}$
constraints might not be satisfied in the recycling scenario.

Our modeling followed the generally-accepted inference that 15N-enriched
sedimentary rocks are dominant in subduction flux of N
[<]e.g.,¿[]Bekaert+2020, and thus there exists N isotopic disequilibrium
between the atmosphere and mantle [Marty Dauphas (2003)]. However,
Mitchell+2010 argued that hydrothermally-altered oceanic crust is the dominant
cause of this, and it has a negative ${\rm\delta^{15}}$N value (-1.8‰) on
average. The negative ${\rm\delta^{15}}$N value assumed is the case for
Mariana trench [Li . (2007)], and may not necessarily represent the mean value
of the whole oceanic crust. Estimates in other studies have shown positive
${\rm\delta^{15}}$N values for the average oceanic crust [Busigny . (2011),
Bekaert . (2021)].

N isotopic fractionation in the subduction zones and in the mantle has not
been fully understood, and thus not considered in our cycling model.
Devolatilization during subduction leads to an increase in residual 15N of
metamorphic rocks [Haendel . (1986)]. The effect is limited on present-day
Earth [Cartigny Marty (2013)], yet its influence on N cycling through Earth’s
history remains to be resolved. Additionally, it is not yet known whether N
isotopes are fractionated during partial melting reactions in the mantle
[Busigny Bebout (2013)]. Better understanding of N isotopic fractionation in
these processes is needed to further test the recycling scenario.

Atmospheric loss processes (EUV-driven escape, ion pickup, and impact erosion)
and replenishment by impactors were not coupled in our model. This would
require complete modeling of atmospheric composition and of how escape rates
are dependent on it, the latter of which is not available for ion pickup. A
possible scenario to support the primordial origin scenario by combining those
processes is that, EUV-driven escape or ion pickup first removed the large
amount of excess N in the atmosphere, and then impact erosion and
replenishment later erased the excess 15N signature. Though the comparable
timescales of those processes ($\simeq$100 Myrs) implies that this is not the
case, a future modeling study is needed to fully test this scenario.

Mineral-melt partitioning of N in the magma ocean solidification stage has not
been fully understood. We used the partitioning coefficients estimated by
Yoshioka+2018. This estimation was based on solubility experiments involving
minerals and melts coexisting with a discrete fluid phase, and it is not
guaranteed whether the partitioning coefficients are applicable for lower
levels of N concentration. However, our partitioning model showed that the
contribution of minerals as N hosts is smaller than that of melt trapping in
the cumulate by two orders of magnitude (Figure 3). Thus, unless the actual
mineral-melt partitioning coefficients were more than two orders of magnitude
higher, the influence of their uncertainties would be minor.

Our cycling model does not consider possible N supply from the core, but its
contribution for the mantle N content seems to be limited from the following
reasons. First, the N abundance in the core is too low to cause N exsolution
from the outer core due to N saturation induced by cooling and inner core
solidification. The N solubility in the core condition is the order of
$\sim$10 wt.% [Speelmanns . (2018)]. In contrast, geophysical constraints
limit the N abundance in the core to be $\ll$ 2.0 wt.% [Bajgain . (2019)] and
modeling of Earth’s accretion and volatile partitioning has estimated the core
N abundance to be $\sim$10–100 ppm [Sakuraba . (2021)], both of which are much
smaller than the saturation level. Second, the N exchange at the core-mantle
boundary (CMB) would be insufficient to supply N from the core to explain the
modern mantle N abundance. Occasional observations of core signatures in
surface lavas suggest the fraction of silicate Earth which interacted with the
core at the CMB may be the order of $\sim$1 wt.% [Hernlund . (2015), Lim .
(2021)]. In order to estimate the maximum contribution of the core, here we
assume that this fraction of silicate Earth received core N through the
interaction at the CMB and released all N to the entire mantle. To explain the
modern mantle N abundance ($\sim$1 ppm), the mantle portion which interacted
with the core needs to contain $\sim$100 ppm of N. Although mantle mineral-
metal melt partition coefficients have not been directly measured, adapting an
estimated value [<]$\sim$100,¿[]Speelmanns+2018 leads to the required N
abundance in the core side to be $\sim$1 wt.%, which is much higher than the
above-mentioned estimates [Bajgain . (2019), Sakuraba . (2021)].

Our partitioning model assumed bottom-up solidification of an initially-fully-
molten magma ocean, but Earth might have had a long-lived (the order of
$\sim$1 Gyr) basal magma ocean [Labrosse . (2007)], which could affect N
partitioning and trapping in the mantle. Although quantitative modeling of the
influence of the basal magma ocean is beyond the scope of our study, we expect
that, because of the two-step processes discussed below, its primary effect is
to reduce the amount of N trapped in the bulk mantle and, consequently, limit
the possibility of the primordial scenario. First, the lower cooling rate of
the basal magma ocean compared to that of the surficial magma ocean (the
orders of Gyrs vs. Myrs) would reduce the trapped melt fraction $F_{\rm tl}$
(Equation 5) significantly. This effect would limit the trapped N content in
the solidified mantle above the basal magma (We note that for the basal magma
ocean its solidification proceeds in a top-down fashion) and the majority of N
which was initially in the magma just solidified would be released into the
residual basal magma ocean. In the slow-cooling limit, the trapped N content,
which is determined by N partitioning into crystallized minerals, would be
smaller than that in the fast-cooling limit by two orders of magnitude (see
Figure 3 for comparison of N contents in minerals and in trapped melt).
Second, N which concentrated in the residual basal magma ocean would
ultimately be lost to the underlying core. Recent high-pressure experiments
performed in graphite-undersaturated conditions [Grewal . (2021)] have shown
that the metal-silicate melt partitioning coefficient of N is $\sim$20–30 for
$\log_{10}f_{\rm O_{2},\Delta{\rm IW}}=-2$ [<]the oxygen fugacity expected for
the core-magma ocean boundary,¿[]Armstrong+2019. As a result, the trapped N
content in the bulk mantle would become smaller than that in the case of
bottom-up solidification without the basal magma ocean.

###  4.4 Comparison with previous studies

Several studies on N partitioning in the magma ocean stage have concluded that
Earth’s mantle N is primordial [Libourel . (2003), Boulliung . (2020)], but
these studies did not consider degassing upon solidification. The degassing
process significantly limits N in the solidified mantle (Section 3.1), which
led us to conclude that the primordial origin scenario is only possible if
Earth had an excess amount of N (Section 4.1).

Labidi+2020 simulated the evolution of N masses and isotopic ratios by using a
two-reservoir model (the surface and mantle) where the atmosphere-sediment N
isotopic fractionation factor was assumed to be constant through time. Their
preferred model supported the primordial origin for mantle N. In contrast, our
cycling model uses four reservoirs (the atmosphere, continental and oceanic
crust, and mantle) and the isotopic fractionation factor varied with time
following the evolution of surface N biogeochemical cycling, and found that
the recycling origin was possible with high sedimentary N deposition rates on
early Earth.

Although our N cycling model is simple compared to the two recent models
[Stüeken, Kipp, Koehler, Schwieterman . (2016), Johnson Goldblatt (2018)],
those most important results were reproduced: sequestration of N in the
continental crust in the Archean [Stüeken, Kipp, Koehler, Schwieterman .
(2016)] and efficient N subduction after the GOE [Johnson Goldblatt (2018)].
We note that the mechanisms are slightly different. In contrast to
Stueken+2016ABb which modeled enhanced crustal weathering after the GOE as the
release of N to the atmosphere, our model assumed the weathering as
N-containing sediment transport to the oceanic crust, following
Johnson+Goldblatt2018. The latter treatment seems to be more consistent with
the picture of global N balance which suggests high N flux from crustal rocks
to sediments [Houlton . (2018)]. As a consequence, whereas weathering mainly
led to increase of $p_{\rm N_{2}}$ in Stueken+2016ABb, our model showed
efficient N subduction after the GOE. Moreover, efficient N subduction after
the GOE in Johnson+Goldblatt2018 was caused by an increase in primary
biological production at the time, but in our case N transport to the mantle
was the result of the release of the continental crust N, which was a product
of N fixation before the GOE. This difference in the model assumption allowed
our model to meet the low $p_{\rm N_{2}}$ constraints [Som . (2012), Som .
(2016), Marty . (2013)] in the Archean, while it was difficult with the
nominal model of Johnson+Goldblatt2018.

###  4.5 Implications for sample analysis

Our modeling of N isotopic exchange provides a methodology to distinguish
primordial and recycling origins for mantle N. The recycling origin is
characterized by large increase ($\gtrsim$+10‰) in the mantle $\delta^{15}$N
values with time, while the primordial origin model showed more limited change
(Figures 7, 8, 12, 13, and 14). The surface (the atmosphere and crust)
$\delta^{15}$N record is more complicated because they can vary owing also to
N exchange between the surficial reservoirs, but combining them with the
mantle trend would help constrain deep N cycling. Moreover, if the surface N
cycle had already become slightly aerobic as assumed in our model (Period 3,
Section 2.3), the possible minimum in $p_{\rm N_{2}}$ around the time of the
GOE can be informed from a kink in the surface $\delta^{15}$N values.

Given these results, constraining mantle isotopic evolution informed for
example from diamonds [<]e.g.,¿[]Cartigny+Marty2013 would offer a more global
picture of Earth’s N cycling and the origin of mantle N. In addition, better
determination of the surface N isotopic composition and particularly more data
around the time of the GOE will be useful.

###  4.6 Constraints from other volatile elements and isotopes

Comparison to cycling of other volatile elements is potentially useful, but
care should be taken to the importance of redox control on N. Xenon (Xe)
isotope studies suggest limited subduction before 2.5 Ga [Parai Mukhopadhyay
(2018)] and a higher degassing rate at the time [Marty . (2019)]. If N behaved
similarly to Xe, these conditions might rule out the recycling-origin
scenario. However, the crust is an additional reservoir for N to cause
different evolution. Furthermore, because both the surficial and mantle redox
states chiefly influence N (but not noble gases), the redox control, in
addition to the different stability in their host phases, can lead decoupling
of N from noble gases. Such decoupling between volatile elements has already
been suggested for sulfur (S) and Xe [Bekaert . (2021)]. Mass-independent S
isotope signatures in the source of various hotspots indicate significant
recycling occurred prior to 2.5 Ga [Cabral . (2013), Dottin III . (2020),
Bekaert . (2021)].

A classical interpretation for elementally-depleted and isotopically-
fractionated Xe in Earth’s atmosphere as a result of early hydrodynamic escape
[<]e.g.,¿[]Pepin1991 might suggest significant N loss due to the same process
and support the presence of excess N. However, this interpretation is not
supported by recent measurements of paleo-atmospheric Xe which revealed that
Xe isotopic fractionation was progressive through time [Pujol . (2011), Avice
. (2017), Avice . (2018), Bekaert . (2018), Bekaert . (2020)]. Rather, Xe
fractionation was likely due to selective loss of Xe+ ions caused by strong
coupling with escaping H+ ions with time [Zahnle . (2019), Avice Marty
(2020)].

The 40K-40Ar decay system gives another constraints on degassing history as
well as continental growth [Ozima Podosek (2002), Pujol . (2013), Johnson
Goldblatt (2018), Guo Korenaga (2020)]. Our cycling model showed that N masses
and isotopic ratios in different major reservoirs on modern Earth can be
reproduced with a wide range of the degassing parameter, $C_{\rm vol}$
(Section 3.2), but it can be constrained by 40Ar data. Combining these
volatile elements and their isotopes in a single model would be important for
future studies.

###  4.7 Implications for Venus, Mars, and exoplanets

Venus’ atmosphere has about 3 PAN [Johnson Goldblatt (2015)], which is
comparable to BSE N content (Table 1). Whether Venus once possessed an
habitable condition and an Earth-like volatile cycle is controversial
[<]e.g.,¿[]Way+2020,Krissansen+2021, but recent three-dimensional atmospheric
simulations [Turbet . (2021)] and accretion modeling focusing on the
difference in hydrogen to carbon ratios between Earth and Venus [Sakuraba .
(2021)] suggest Venus never possessed oceans. This lack of oceans would lead
to no N cycling between the surface and mantle. Because Venus’ magma ocean was
likely more oxidized than Earth’s due to hydrogen loss to space [Wordsworth
(2016)], we predict that its mantle right after magma ocean solidification was
depleted in N similarly to Earth (Section 3.1). Provided that Venus and Earth
have similar bulk N contents (namely that the atmosphere is the major
reservoir of N for Venus), the comparison with Venus may suggest that N
recycling operating only on Earth differed the distribution of N on the two
planets. Alternatively, the different distribution might be caused by the
cumulative effect of possible active volcanism on Venus. Constraining Venus’
volcanic activity with future missions [<]e.g., ESA’s EnVision and NASA’s
VERITAS and DAVINCI+,¿[]DIncecco2021 may provide better understanding of the
partitioning and cycling of N on Venus.

Prolonged N degassing on Mars has been suggested from the atmospheric 15N/14N
ratio being close to the steady state between atmospheric escape and degassing
[Kurokawa, Kurosawa Usui (2018), Lammer, Scherf . (2020)]. Mars’ small size
might have led to a more reducing condition than Earth during its magma ocean
stage [Armstrong . (2019)]. Our partitioning model predicted $\gtrsim$10% of
bulk N can be partitioned into the mantle in the reduced case (Section 3.1).
While N recycling driven by plate tectonics has been absent at least since
$\sim$4 Ga on Mars [<]e.g.,¿[]Grott+2013, the N-rich mantle might have
contributed to prolonged degassing. The atmospheric neon abundance which is
likely in balance between atmospheric escape and mantle degassing also
suggests abundant volatile elements in Mars’ mantle [Kurokawa . (2021)].

Our study suggests that the $p_{\rm N_{2}}$ of extrasolar rocky planets in
habitable zones may provide useful constraints not only on present climate
[Vladilo . (2013), Wordsworth Pierrehumbert (2014)] but also on the
biogeochemical processes that have acted on such planets. The $p_{\rm N_{2}}$
of extrasolar rocky planets can in principle be constrained from future
observations [<]e.g.,¿[]Schwieterman+2015,Stueken+2016ABb through e.g., N2-N2
dimer absorption, collision-induced absorption involving N2, and/or Rayleigh
scattering slope, although the last measurement is prone to the degeneracy
with other parameters. Combined with the estimates for the amount of N that a
planet initially accreted and the amount that has escaped to space, a low
$p_{\rm N_{2}}$ value may indicate efficient subduction of N, which may be
attributed to active tectonics (which may not necessarily Earth-like plate
tectonics but can be mobile lid and episodic resurfacing for example) with
liquid water and perhaps biological N cycling. It would be interesting to look
at the $p_{\rm N_{2}}$ of multiple rocky planets in the same system whose
building blocks can be reasonably considered to be similar; they may show
interesting diversity in the $p_{\rm N_{2}}$ depending on their evolution,
similar to the case of Venus, Earth and Mars. Our model for the recycling
origin scenario for mantle N implies that the $p_{\rm N_{2}}$ of planets with
active tectonics and an anoxic atmosphere anti-correlates with their age,
which can be tested with future observations. In this manner, understanding
the origin of Earth’s mantle N and the surface environments of extrasolar
rocky planets is linked with each other.

##  5 Conclusions

Two hypotheses for the origin of N in Earth’s mantle were tested with
numerical models constrained by Ar and N isotopes. Our model results for N
partitioning in the magma ocean stage constrained by Ar showed that low
solubility and low partition coefficients between minerals and silicate melts
leads to N depletion in the solidified mantle unless the magma ocean was
reducing. The highly reducing magma ocean model may be relevant to Mars which
shows indirect evidence of prolonged degassing of N, but it is not favored for
Earth from high pressure experiments or geochemical and geophysical
constraints. Modeling of impact erosion and isotopic fractionation via EUV-
driven escape and ion pick up suggests that the excess atmospheric N, which is
required to put sufficient N into the mantle as comparable as the minimum
estimate for the modern mantle, can be removed only when efficient net removal
is assumed. Our model results for N cycling between surface reservoirs and
mantle constrained by N isotopes showed that sequestration of N into the crust
before the GOE and subsequent efficient weathering and subduction after the
period could have sourced N to the modern mantle. This recycling origin
scenario requires high sedimentary N burial flux on early Earth, which was
likely sustained by biotic N utilization. The two hypotheses can be tested by
analyzing the surface and mantle N isotope record. Unveiling the origin of
Earth’s mantle N is linked with understanding the difference in N contents
with Venus and the evolution of surface environments of extrasolar rocky
planets.

##  Appendix A N solubility model

Figure 11: N solubility model used in this study (Equation 16, purple curve).
Two terms in the fitting formula are also shown (fitting curves 1 and 2, red
and yellow lines). Original data are from Boulliung+2020 (Blue points).

We developed a model for N solubility as a function of the oxygen fugacity and
the N partial pressure. Solubility data measured by Boulliung+2020 for the
terrestrial magma ocean-like composition (MO2) were fitted by the sum of two
terms following Libourel+2003 as (Figure 11),

$S_{\rm N}{\rm[ppm\cdot atm^{-1}]}=10^{-0.6934{\log_{10}f_{\rm
O_{2},\Delta{\rm IW}}}-1.7002}\cdot\biggl{(}\frac{p_{\rm N_{2}}}{\rm 1\
atm}\biggr{)}^{-\frac{1}{2}}+0.2.$ (16)

The first and second terms denote chemical and physical solubilities dominant
under reducing and oxidizing conditions, respectively [Libourel . (2003),
Bernadou . (2021)]. The first term was given with the least squares method for
$\log_{10}f_{\rm O_{2},\Delta{\rm IW}}<-1.5$ data, assuming $p_{\rm
N_{2}}^{1/2}$ dependence [Boulliung . (2020)]. The second term was given to
much the data point for the oxidized limit ($\log_{10}f_{\rm O_{2},\Delta{\rm
IW}}=+4$).

##  Appendix B Derivation of Equation 1

The equation for the solubility equilibrium between the atmosphere and the
magma ocean (Equation 1) is derived from those for hydrostatic equilibrium,
the ideal gas, and the definition of solubility, which are given by,

$\frac{dp}{dz}=-\rho_{\rm atm}g,$ (17) $p_{i}=n_{i}k_{\rm B}T=\rho_{i}k_{\rm
B}T/m_{i},$ (18)

and,

$p_{i}=\frac{x_{i}}{S_{i}},$ (19)

where $z$, $\rho_{\rm atm}$, $n_{i}$ and, $x_{i}$ are the height from the
surface, the density of atmospheric gas, the number density of species $i$,
and the mass fraction of species $i$ in the magma ocean, respectively. From
Equations 17 and 18, we obtain,

$\frac{d}{dz}\biggl{(}\frac{n}{n_{i}}p_{i}\biggr{)}=-\frac{n}{n_{i}}\frac{\bar{m}}{m_{i}}\rho_{i}g.$
(20)

Assuming the mixing ratio $n_{i}/n$ to be constant in the atmosphere, Equation
20 can be integrated analytically to lead,

$p_{i}(z=0)=\frac{\bar{m}}{m_{i}}\frac{M_{{\rm atm},i}}{A}g.$ (21)

We can rewrite $M_{{\rm mo},i}$ using Equations 19 and 21 and obtain,

$M_{{\rm mo},i}=x_{i}M_{\rm mo}=\frac{\bar{m}}{m_{i}}\frac{M_{{\rm
atm},i}}{A}g\cdot S_{i}\cdot M_{\rm mo}.$ (22)

Finally, substituting Equation 22 into Equation 2 leads to Equation 1.

##  Appendix C Supplementary results of the cycling model

Figure 12 shows the result of the nominal model runs without the constraints
on the crustal N masses and isotopic ratios. Figures 13 and 14 show the
variants of the nominal model, where we assumed the onset time of plate
tectonics to be 4.5 Ga (Figure 13) and the initiation of N subduction at 2.5
Ga (Figure 14), respectively.

Figure 12: Cycling model results for the case where we omitted the constraints
on the N content and isotopic ratios of the modern continental and oceanic
crust, while the other settings are the same as in the nominal case (Figure
7). See Figure 7 caption for details. Figure 13: Cycling model results for the
case where the plate tectonics started at 4.5 Ga, while the other settings are
the same as in the nominal case (Figure 7). See Figure 7 caption for details.
Figure 14: Cycling model results for the case where N subduction started 2.5
Ga, while the other settings are the same as in the nominal case (Figure 7).
See Figure 7 caption for details.

##  Appendix D Atmospheric escape models

The isotopic fractionation factor, defined as,

$f\equiv\frac{F_{\rm{}^{15}N}/F_{\rm{}^{14}N}}{[{\rm{}^{15}N}]/[{\rm{}^{14}N}]},$
(23)

was estimated for EUV-driven hydrodynamic escape and solar wind-induced ion
pickup, where $F_{i}$ is the escape flux. Then we estimated the amounts of N
removed by the escape processes $M_{\rm lost}$ to enrich the remnant
atmosphere (1 PAN) in 15N by $\Delta{\rm{}^{15}N}=+6$‰ (Figure 9), using the
Rayleigh dissolution equation,

$M_{\rm
lost}=\biggl{(}\frac{1}{1-10^{-3}\times\Delta{\rm{}^{15}N}}\biggr{)}^{\frac{1}{1-f}}-1\
[{\rm PAN}].$ (24)

Escaping hydrogen drags 14N14N and 15N14N mass-dependently, and causes
isotopic fractionation. The fractionation factor for hydrodynamic escape was
estimated using a model of Lammer+2020. In the model, the radii of visible-
and EUV-photospheres are estimated with their Equations 5, 11, and 12. Then
escape fluxes of hydrogen and other minor species are computed with their
Equations 10, 14, and 15. For simplicity, we assumed that the model proto-
Earth had a H2 plus N2 atmosphere, whose mass is 10-3 times Earth’s mass. The
mixing ratio of N2 was assumed to be 10-3 considering a primordial dense H2
atmosphere. We assume skin and upper atmospheric temperatures to be 255 K and
400 K [Watson . (1981)], respectively. The binary diffusion coefficient
between H and N2 was taken from Zahnle+1986. EUV luminosity of the young Sun
was taken to be a parameter, and is expected to be 30–500 times the present-
day value during the first 100 Myrs, depending on its rotation rate [Tu .
(2015)].

Ion pickup by the solar wind removes N from the exobase level, where heavier
15N is depleted due to diffusive separation. The fractionation factor was
estimated by adapting an isothermal, hydrostatic structure for both 14N14N and
15N14N, given as,

$f=\exp{\biggl{[}\frac{GM_{\rm E}\Delta m}{k_{b}T_{\rm exo}r_{\rm
homo}}{\biggl{(}\frac{r_{\rm homo}}{r_{\rm exo}}-1\biggr{)}}\biggr{]}},$ (25)

where $G$ is the gravitational constant, $k_{b}$ is the Boltzmann constant,
$\Delta m$ is the mass difference between 14N14N and 15N14N, $T_{\rm exo}$ is
the exospheric temperature, and $r_{\rm homo}$ and $r_{\rm exo}$ is the radii
of homopause and exobase, respectively. We assumed $T_{\rm exo}=10^{4}\ {\rm
K}$, $r_{\rm homo}=R_{\rm E}+100\ {\rm km}$, and $r_{\rm exo}=12.7R_{\rm E}$
[Tian . (2008), Lichtenegger . (2010)].

##  Appendix E Impact erosion model

Atmospheric loss by impact-induced atmospheric erosion during late accretion
was calculated by using the model of Sakuraba+2019 (Figure 10). The model
setting is the same for the early Earth model of Sakuraba+2019 except for the
impactor composition and the initial N content, for the latter we assumed the
estimate from our partitioning model for the oxidized magma-ocean case (7.7
PAN to 150 PAN).

Here we summarize the main feature of the impact erosion model [<]see¿[for
details]Sakuraba+2019. The impact erosion model computes the loss and supply
of volatile elements by statistically-averaged impacts. Assuming the
carbonate-silicate cycle, we fixed the background CO2 partial pressure at 1
bar. A trace amount of water vapor (0.017 bar) was included assuming the
saturated vapor pressure. We assumed the surface temperature to be 288 K. The
results depend on the assumed temperature only weakly [Sakuraba . (2019),
Sakuraba . (2021)].

We assumed two cases for the N content of impactors: enstatite chondrite-like
impactors containing 400 ppm N2 [Hirschmann (2016), Bergin . (2015)] and “dry”
objects containing no N. The former is consistent with the N isotopic
signatures of Earth and enstatite chondrites [Dalou . (2019), Piani . (2020)].
The latter is an extreme case to maximize the eroded N mass case. We did not
compute the case of carbonaceous chondrite-like impactors, but they are richer
in N than enstatite chondrites [<]e.g.,¿[]Grady+Wright2003 so that the net
effect to remove N from the atmosphere is weaker [Sakuraba . (2019), Sakuraba
. (2021)]. Isotopic signatures of siderophile elements in the mantle also
point to the types of late accretion impactors containing a non-negligible
amount of N, such as enstatite or carbonaceous chondtites [Dauphas (2017),
Fischer-Gödde . (2020)].

The assumed size distribution of the impactors is
$\mathrm{d}N(D)/\mathrm{d}D\propto D^{-q}$ with $q=3$, where $N(D)$ is the
number of objects of diameter smaller than $D$. The minimum and maximum sizes
are assumed to be $D=10^{-1.5}$ km and $10^{3}$ km, respectively. A steeper
size distribution (larger $q$) leads to more efficient impact erosion. The
assumed size distribution is similar to that of the asteroid belt [Bottke .
(2005)], and is likely an upper limit for $q$ [<]see,¿[for
discussion]Sakuraba+2021.

The cumulative mass of late accretion is constrained by highly siderophile
element concentrations in Earth’s mantle [Chou (1978), Marchi . (2018)]. We
assumed 0.5% of Earth’s mass as a minimum estimate, but calculated up to 1% to
take a larger estimate into account.

###### Acknowledgements.

Data and codes to generate figures in this paper are available at
https://doi.org/10.6084/m9.figshare.17128421.v1. We thank Bernard Marty and an
anonymous reviewer for constructive comments. This work was supported by JSPS
KAKENHI Grant number 15H05832, 17H01175, 17H06457, 18K13601, 18K13602,
19H01960, 19H05072, 19K15671, 20K04126, 20KK0080, 21H04514, 20H04608, and
21K13976.

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