Late Delivery of Nitrogen to Earth

Draft version December 19, 2018 Typeset using LATEX twocolumn style in AASTeX62

Late delivery of nitrogen to Earth

Cheng Chen,1 Jeremy L. Smallwood,1 Rebecca G. Martin,1 and Mario Livio1

1Department of Physics and Astronomy, University of Nevada, Las Vegas, 4505 S. Maryland Pkwy.Las, Box 454002, Vegas, NV 89154, USA

(Received October 19, 2018; Revised December 14, 2018; Accepted December 16, 2018)

ABSTRACT Atmospheric nitrogen may be a necessary ingredient for the habitability of a planet since its presence helps to prevent water loss from a planet. The present day nitrogen isotopic ratio, 15N/14N, in the Earth’s atmosphere is a combination of the primitive Earth’s ratio and the ratio that might have been delivered in comets and asteroids. Asteroids have a nitrogen isotopic ratio that is close to the Earth’s. This indicates either a similar formation environment to the Earth or that the main source of nitrogen was delivery by asteroids. However, according to geological records, the Earth’s atmosphere could have been enriched in 15N during the Archean era. Comets have higher a 15N/14N ratio than the current atmosphere of the Earth and we find that about 5% ∼ 10% of nitrogen in the atmosphere of the Earth may have been delivered by comets to explain the current Earth’s atmosphere or the enriched 15N Earth’s atmosphere. We model the evolution of the radii of the snow lines of molecular nitrogen and ammonia in a protoplanetary disk and find that both have radii that put them farther from the Sun than the main asteroid belt. With an analytic secular resonance model and N–body simulations we find that the ν8 apsidal precession secular resonance with Neptune, which is located in the Kuiper belt, is a likely origin for the nitrogen-delivering comets that impact the Earth.

Keywords: accretion, accretion disks – comets: general – Kuiper belt: general

1. INTRODUCTION derstood. The reservoir of nitrogen in the crust and the Nitrogen may be an essential part of an atmosphere mantle of the Earth currently is thought to be between for a planet to be habitable (e.g. Stueken¨ et al. 2016). 0.4 and 7 times the present day atmospheric amount Nitrogen is a component of chemical compounds that (e.g. Marty 1995; Halliday 2013; Johnson & Goldblatt are necessary for growth and reproduction of all ani- 2015). Isotopic measurements suggest that most of the mal and plant life on Earth. It is found in amino acids current atmospheric nitrogen is from the inner solar sys- that make up proteins as well as in nitrogenous bases in tem (Furi¨ & Marty 2015). The relative abundance of the 15 14 nucleic acids that store, transcribe and translate the ge- two isotopes of nitrogen N/ N in the Earth is similar netic code. Furthermore, nitrogen influences the surface to Venus, Mars and primitive meteorites such as chon- temperature and water content of the atmosphere, both drites (e.g. Hutsemékers et al. 2009; Marty 2012; Harries of which affect planet habitability. The nitrogen content et al. 2015; Bergin et al. 2015). In the case of the Earth we know that most of the arXiv:1812.06956v2 [astro-ph.EP] 18 Dec 2018 in the atmosphere plays a significant role in the rate of water–loss from a planet (e.g. Wordsworth & Pierrehum- nitrogen was accreted locally. However, this may not bert 2013, 2014). If the nitrogen level is too low, water be universally the case. Therefore, a study of potential loss may be very efficient for all surface temperatures. habitability (assuming that nitrogen is a necessary in- Nitrogen is the most abundant molecule in the atmo- gredient) needs to explore other potential delivery mech- sphere of the Earth, comprising about 78% of our at- anisms. mosphere by volume, but still, its origin is not well un- The isotopic ratio of nitrogen in the present day atmosphere is measured to be 15N/14N = 3.676 × 10−3 (Junk & Svec 1958). However, the Earth’s mantle is relatively Corresponding author: Cheng Chen depleted in 15N compared to the Earth’s atmosphere. [email protected] 2 Chen et al.

+ We compare the ratios with only a small amount of N2 was detected due to the en- ! richment of CO over N2 in amorphous ice (Notesco & (15N/14N) δ15N = mantle − 1 × 1,000. (1) Bar-Nun 1996). The abundance of nitrogen in the sur- 15 14 ( N/ N)atmosphere face layer of a comet measured by a satellite does not necessarily represent the ratio in its nucleus (Prialnik & In the Earth’s mantle, δ15N is estimated to be in the Bar-Nun 1992). In the case of Halley’s comet, most of range -5 % to -30 %(Cartigny & Marty 2013). Thus, the nitrogen is in the form of compounds (Krankowsky the isotopic ratio of nitrogen in the Earth’s mantle is in 1991; Geiss 1987, 1988; Meier et al. 1994). The amount the range between 15N/14N = . × −3 to . × −3 3 566 10 3 658 10 of nitrogen that can be trapped in ice at temperatures of (Cartigny et al. 1998; Cartigny & Marty 2013; Javoy around 30K is five orders of magnitude higher than in ice et al. 1986; Jia & Kerrich 2004; Marty & Zimmermann at a temperature of 100K (Bar-Nun & Kleinfeld 1988). 1999; Murty & Mohapatra 1997). Moreover, according However, in comets, noble gases have about an equal to the record of Archean sedimentary rocks and crustal abundance as molecular nitrogen. If these were delivered hydrothermal systems, the Earth may have had a 15N- to the Earth, the Earth would have had an overabun- enriched atmosphere with δ15N % and 15N/14N = = 30 dance of noble gases (Owen & Bar-Nun 1995; Marty . × −3 in Archean eon (Jia & Kerrich 2004), 4 to 2.5 3 786 10 et al. 2017). Nevertheless, a recent analysis from the billion years ago. This high estimate has later been ques- Rosetta Orbiter Spectrometer for Ion and Neutral Anal- tioned because it was based on the analysis of metamor- ysis (ROSINA) revealed that the relative abundance of phosed crustal rocks (Papineau et al. 2005; Ader et al. Ar/N inside the icy nucleus of the 67P/Churyumov- 2006; Stueken et al. 2015). Different geological records 2 ¨ Gerasimenko is 9.1 ± 0.3 × 10−3 (Balsiger et al. 2015). of less metamorphosed Archean sedimentary rocks sug- Therefore, comets may not contain the same amount gest a lower value δ15N in the range 0% to 15%(Sano of noble gases as they do nitrogen. Moreover, the xenon & Pillinger 1990; Pinti et al. 2001) and more recent es- isotopic composition shows a deficit in heavy xenon iso- timates based on the analysis of fluid inclusions hav- topes from ROSINA. By considering the origin of a pri- ing trapped Archean seawater concluded that the N iso- mordial atmospheric xenon component is a mixture of tope composition of the Archean atmosphere was close chondritic and cometary xenon, the present Earth’s at- to 0%(Marty et al. 2013; Avice et al. 2018). In our mosphere contains 22±5% cometary xenon (Marty et al. calculations (see Sec.3), we consider both a 15N-rich 2017). atmosphere and the present day atmosphere. The nitrogen isotopic ratio could change in the outer Several possible mechanisms may explain a high value regions of the solar system where comets formed at ex- of 15N/14N during the Archean era, such as hydrody- tremely low temperature. Large enhancements of the namic escape of light isotopes or heterogeneous accre- isotopic ratio 15N/14N can occur in cold, dense gas where tion of the Earth that forms from material with 15N- CO is frozen out. Particularly, if the temperature is depleted and then accretes a late veneer composed of around 7 − 10K, then the upper layers of the grains can chondritic material and a minor contribution of 15N- be enhanced in 15N by up to an order of magnitude enriched comets. However, these mechanisms are dif- (Rodgers & Charnley 2008). This mechanism introduces ficult to quantify (Cartigny & Marty 2013; Javoy 1998; an uncertain factor in the measured 15N/14N isotopic Marty 2012). It is most likely that to reach the current ratio in comets. Some comets have an anomalous nitro- nitrogen isotopic ratio of the Earth’s atmosphere or the gen isotopic ratio that is about twice the terrestrial ratio 15N-enriched atmosphere in the Archean era, there must (Manfroid et al. 2009). have been some comets delivered to the Earth after the In this work we explore the possibility of late delivery Earth formed and differentiated (Jia & Kerrich 2004; for the 15N-enriched nitrogen in the atmosphere of the Rice et al. 2018). Earth. In Section2 we examine the evolution of a pro- Enstatite chondrites formed in the inner solar system toplanetary disk in which planetesimals later form. We and could be the primary ingredient to form terrestrial calculate the location of the ammonia and nitrogen snow planets (Wasson & Kallemeyn 1988). These chondrites lines – the radius outside of which each would have con- can carry nitrogen in osbornite, sinoite and nierite (Ru- densed out of the gas and would have been incorporated bin & Choi 2009). On the other hand, nitrogen was into the solid bodies. While there is evidence that most probably delivered to the Earth by comets in the form of the nitrogen was delivered locally it is still interesting of ammonia ices or simple organic compounds such as to explore whether some of it could be delivered at late HCN. In laboratory studies, molecular nitrogen can be times, via comets or asteroids. In Section3 we consider trapped and released by amorphous ice (Bar-Nun & Kle- what isotopic nitrogen ratios tell us about how much of infeld 1988). Although in the case of Halley’s comet, LATE DELIVERY OF NITROGEN TO EARTH 3 the nitrogen could have been delivered by comets and 30 find that it could have been a significant fraction. In Section4 we examine possible delivery mechanisms to 25 Earth for the relevant solid bodies. In particular, we show how comets are perturbed by mean motion and 20 secular resonances with the planets in the solar system

and we use N-body simulations to show that resonances au 15 can play a role in the delivery of comets to the Earth. R/

Finally, we draw our conclusions in Section5. 10

2. PROTOPLANETARY DISK EVOLUTION 5 The temperature of a protoplanetary disk generally decreases with distance from the central star. A snow 0 10-6 10-7 10-8 10-9 10-10 ˙ 1 line marks the radial distance from the star outside M/(M ⊙ yr ) of which the temperature drops below the condensa- tion temperature of a particular compound. The con- Figure 1. Nitrogen (blue) and ammonia (green) snow lines as a function of accretion rate in a steady state disk with M = densation temperature for hydrated ammonia is about ? M , T? = 4000K, R? = 3R , TN2,snow = 58K and TNH3,snow = Tsnow,NH3 = 131K, and for hydrated nitrogen is about 131K. The dashed lines show the snow lines with the fully Tsnow,N2 = 58K (Lodders 2003). In this Section we con- MRI turbulent disk with αm=0.01. The solid lines represent sider the evolution of these snow lines in a protoplane- the snow lines in a disk in a self-gravitating dead zone. tary disk. The snow lines determine where ammonia and nitrogen were incorporated in a solid form into planetes- (Pringle 1981). The surface temperature is determined imals that formed there. through the balance of heating from viscous effects and Material in the disk interacts through viscosity that irradiation from the central star is thought to be driven by the magnetorotational insta- ˙ bility (MRI) that drives turbulence in the disk (Balbus 4 9 M 2 4 σTe = Ω + σT (4) & Hawley 1991). We first consider the snow line radii 8 3π irr in a steady-state fully turbulent disk model. However, (e.g. Cannizzo 1993; Pringle et al. 1986), where σ is the protoplanetary disks are thought to contain a region of Stefan-Boltzmann constant and the irradiation temper- low turbulence at the disk midplane, known as a ”dead ature is zone”, where the disk is not sufficiently ionized for the ! 1 ! 3 2 4 R 4 magnetorotational instability to operate (e.g., Gammie T = ? T (5) irr 3π R ? 1996; Gammie & Menou 1998). Thus, we also consider how the presence of a dead zone affects the evolution of (Chiang & Goldreich 1997), where T? is the temperature the snow lines. We follow Martin & Livio(2014) and and R? is the radius of the star. The mid-plane temper- derive analytic solutions for the snow line radii in each ature is related to the surface temperature through case. 4 4 Tc = τTe , (6) 2.1. A Fully Turbulent MRI Disk Material in an accretion disk orbits the central star where the optical depth, τ, is given by of mass, M , with Keplerian velocity at radius R with ? p 3 Σ angular velocity Ω = GM /R3 (Pringle 1981). The vis- τ = κ (7) ? 8 2 cosity in a fully MRI turbulent disk is and the opacity is κ = aT b. In our model, we take a = c2 c ν = α s , (2) 0.0001 and b = 2.1 since dust dominates the absorption m Ω properties of matter in the disk (Armitage et al. 2001). where α is the viscosity parameter (Shakura & Sunyaev m p The snow line radius in the disk is found by solving 1973) and the sound speed is cs = RTc/µ, where R is the Tc = Tsnow. In our model, we assume M? = 1M , R? = gas constant, µ is the gas mean molecular weight and Tc 3R and T? = 4000K. There remains some uncertainty is the mid-plane temperature. With a constant accretion in the value of the viscosity parameter (e.g. King et al. rate, M˙ , through all radii, the surface density of a steady 2007). Observations of FU Ori show αm ≈ 0.01 (Zhu state disk is et al. 2007) while from observations of X-ray binaries M˙ Σ = (3) and cataclysmic variables, it is estimated that α ≈ 0.1 ∼ 3πν m 4 Chen et al.

0.4 (King et al. 2007). Since we consider young stellar 104 objects, we assume that αm = 0.01 in a fully turbulent MRI disk. We adapt the approximate analytical steady state so- 103 lution of the CO snow line in Martin & Livio(2014) and

find analytic fits to the nitrogen snow line radius 2 2 ! 1 ! 2 10 − 9 ˙ 9 αm 9 M? M ≈ / RN2,snow 3.6 − − 0.01 M 10 8 M yr 1 (8) 2 8 !−0.64 ! ! 101 TN ,snow R 3 T 9 × 2 ? ? au 58K 3R 4000K and the ammonia snow line radius 100 10-6 10-7 10-8 10-9 10-10 1 2 M/˙ − 2 ! ! ⊙ α 9 M 9 M˙ 9 R ≈ 2.1 m ? NH3,snow −8 −1 0.01 M 10 M yr Figure 2. Surface density at the snow line radius, R = Rsnow, (9) in the steady state disk for the nitrogen snow line radius !−0.64 ! 2 ! 8 TNH ,snow R 3 T 9 (blue lines) and the ammonia snow line radius (green lines). × 3 ? ? au. 131K 3R 4000 K The solid lines are disks with self-gravitating dead zone and dashed lines, which lie on top of each other, are fully MRI ˙ These are valid for relatively low accretion rates, M . turbulent disks with αm = 0.01. −8 −1 10 M yr , where irradiation dominates the viscous heating term. a protoplanetary disk are hot enough to be thermally The numerical values of the snow line radii in equa- ionized where Tc ≥ Tcrit. The critical temperature, Tcrit, tions (8) and (9), for the standard parameters chosen, is thought to be around 800K for activating the MRI are uncomfortably small. The ammonia snow line lies (Umebayashi & Nakano 1988). However, farther from inside of the main asteroid belt while the nitrogen snow the host star, external sources such as cosmic rays and line lies within it. Fig.1 shows the full numerical solu- X-rays from the central star ionize only the surface lay- tion for the snow line radii for nitrogen and ammonia in ers up to a critical surface density, Σcrit. The value of a fully turbulent disk as a function of the steady-state the critical surface density is not well determined (Mar- accretion rate (dashed lines) found by solving Tc = Tsnow tin et al. 2012a,b). For T Tauri stars, cosmic rays ion- along with equations (4) to (6). This exposes the prob- 2 ize a critical surface density of Σcrit ≈ 100gcm (Gam- lem with fully turbulent disks, in that the snow line mie 1996). However, this value could be much lower if moves in too close to the host star during the low ac- we consider the chemical reaction of charged particles cretion rate phase when the disk is near the end of its (Sano et al. 2000). Bai & Goodman(2009) and Turner lifetime (Garaud & Lin 2007; Oka et al. 2011; Martin & Sano(2008) found that the MRI could operate in & Lubow 2011; Martin & Livio 2014). This contradicts the surface layer of a disk ionized by stellar X-rays with observations of the composition of asteroids in the aster- −2 Σcrit ≈ 1 − 30gcm . Where the surface density is larger oid belt (e.g. DeMeo & Carry 2014). To explore possible than this, Σ ≥ Σcrit, a dead zone forms at the disk mid- solutions to this problem, we consider a more realistic plane where the MRI cannot operate (e.g. Gammie 1996; disk – one with a dead zone – in following Section. Gammie & Menou 1998). The dashed lines in Fig.2 show the surface density at In the dead zone layer, material builds up due to the snow line radius as a function of the accretion rate. the lower viscosity and the small mass transport rate. For low accretion rates, the surface density at the snow The disk becomes self-gravitating when the Toomre line radius becomes very small, Σ . 10gcm−2. Assum- (1964) parameter, Q = cs Ω/πGΣ is less than the criti- ing a gas to solid ratio of 100 (e.g. Bohlin et al. 1978; cal, Qcrit = 2. Then, a second type of turbulence, gravi- Hayashi 1981), the surface density of solid material is tational turbulence, is driven, with a viscosity given by . 0.1gcm−2. In the fully turbulent disk model there is little solid material available for planetesimal formation 2 cg in the outer parts of the disk. ν = α (10) g g Ω 2.2. A Disk With A Dead Zone and the alpha parameter is The MRI requires a sufficiently high level of ioniza- 4 tion in the disk for it to operate. The inner regions of αg = αm exp(−Q ) (11) LATE DELIVERY OF NITROGEN TO EARTH 5

(e.g. Zhu et al. 2010). The disk can reach a steady state defines the Lambert function, W. with a self–gravitating dead zone (e.g. Martin & Lubow The steady state energy equation of a disk with a self– 2013, 2014; Rafikov 2015). Martin & Livio(2012) found gravitating dead zone is that the evolution of the snow line is significantly al- 9 tered in a time–dependent disk with a dead zone com- 4 2 4 σTe = νgΣΩ + σTirr. (18) pared with a fully turbulent disk model. The build up of 8 material can lead to the disk being gravo-magneto un- The mid–plane temperature of the disk is related to stable (see the disk structure sketches in Martin & Livio the disk surface temperature with equations (5)–(7). In 2013). The temperature in the dead zone increases suf- Fig.1, the two solid lines show the snow line radii that ficiently for the MRI to be triggered there, leading to an are the solutions to Tc = Tsnow with equation (18). The accretion outburst. However, the outer parts of the disk snow line radius in the disk model with a dead zone that we are interested in here remain in a steady state. is farther from the central star than in the fully tur- Thus, we consider only steady state self-gravitating disk bulent disk model since the temperature of the disk is solutions in this work. higher. With a dead zone, for low accretion rates the We follow Martin & Livio(2012) to obtain an ana- snow line radius is insensitive to the accretion rate. The lytic solution for the snow line radii assuming that both self–gravitating dead zone prevents the snow lines from the ammonia and nitrogen snow lines are in the self– moving too close to the central star in the late stages of gravitating part of the dead zone. The disk has MRI disk evolution. −8 −1 active layers over a self-gravitating dead zone but we as- For lower accretion rates (M˙ ≤ 10 M yr ), irradi- sume that Σ Σcrit ≈ 0. The self-gravitating disk has a ation dominates over the viscous heating term and we surface density approximate equation (18) with Te = Tirr and find the cgΩ Σ = . (12) analytic snow line radius for nitrogen to be πGQ " #− 1 0 1 0 2 0 8 0 18 The accretion rate of the steady disk is 9 3 9 −0.31 W(x) RN2,snow = 12.6 M? R? T? TN ,snow au (19) 2 W(x0)  3  4 3cgαm  exp(−Q ) M˙ = 3πνg Σ =   . (13) and for ammonia  G  Q " #− 1 0 1 0 2 0 8 0 W(x) 18 The term in brackets is constant for a fixed snow line 9 3 9 −0.31 RNH3,snow = 9.8 M? R? T? TNH ,snow au. (20) temperature. This expression depends sensitively on Q 3 W(x0) but Q is approximately constant in the range of accre- These values are given approximately by tion rates we use. We scale the variables to T 0 = N2,snow , 0 , 0 , ! 1 ! 2 ! 8 TN2,snow/58K TNH ,snow = TNH3,snow/131K αm = αm/0.01 M 9 R 3 T 9 0 0 3 0 ? ? ? M? = M?/M , R? = R?/3R and R = R/au. Then, we RN2,snow = 12.6 M 3 R 4000K can solve equation (13) to calculate the scaled Toomre !−0.31 TN ,snow parameter × 2 au (21) 58K " # 1 Q W(x) 4 Q0 = = 0.69 , (14) and Qcrit W(x0) ! 1 ! 2 ! 8 M 9 R 3 T 9 where we define ? ? ? RNH3,snow = 9.8 M 3 R 4000K 0 0 4 6 !−0.31 αm TN ,snow T x = x 2 (15) NH3,snow N2 0,N2 04 × au. (22) M? 131K 10 The numerical values of equations (21) and (22) for our with x0,N2 = 3.86 × 10 and standard parameters are consistent with the solid lines 0 0 α 4T 6 in Fig.1 at low accretion rates. m NH3,snow xNH = x0,NH (16) 3 3 M04 The solid lines in Fig.2 show the surface density of ? the disk with a self–gravitating dead zone at the snow 12 line radius, for nitrogen (blue line) and for ammonia with x0,NH3 = 5.13 × 10 . The equation (green line). The disk with the dead zone has a roughly x = W(x)exp[W(x)] (17) constant surface density with accretion rate, particularly 6 Chen et al. for low accretion rates. The surface density is much respectively. The terrestrial isotopic ratio weighted by higher than even the maximum possible value for the the relative abundances of nitrogen from comets and critical surface density that may be MRI active, Σcrit ≈ from the primitive Earth is −2 200gcm . Thus, our assumption of Σ Σcrit is justified. 14 14 n ( N) np( N) Furthermore, the surface density at the snow line radii (15N/14N) = c (15N/14N) + (15N/14N) . t 14 c 14 p is significantly higher in a disk with a dead zone thus nt( N) nt( N) (25) allowing for more solid bodies to form. Combining this with equation (23) gives the fraction of For the low accretion rates expected at the end of the abundance of 14N in comets to the total abundance the disk lifetime, the snow line radii for nitrogen and 14 15 14 15 14 ammonia in the solar system are both farther from the n ( N) ( N/ N)p − ( N/ N)t c = . (26) 14 15 14 15 14 Sun than the main asteroid belt. The ammonia snow nt( N) ( N/ N)p − ( N/ N)c line lies at about 9au while the nitrogen snow line is at 12au. Thus, comets in the Kuiper belt are expected to This is the fraction of the nitrogen that was delivered to form with significantly more nitrogen than asteroids in the Earth by comets compared to the total amount of the main asteroid belt. In the next Section we consider nitrogen in the atmosphere (Hutsemékers et al. 2009). observational constraints from the isotopic ratio of ni- The isotopic ratio of nitrogen in comets is uncertain. trogen, and estimate the fraction of the present Earth’s McKeegan et al.(2006) analyzed COMET 81P/Wild2 atmosphere that could have been delivered by comets. grains returned by Stardust and found a bulk isotopic ratio that is close to the terrestrial and chondritic value 3. 15 14 −3 THE DELIVERY OF COMETARY NITROGEN ( N/ N)c = 3.55 × 10 but most comets have a higher TO EARTH value. For comets measured remotely using optical-UV For the Earth’s atmosphere, the present ratio of spectroscopy of CN and radio observations of HCN, the 15N/14N is the combined result of the isotopic ratio isotopic ratio of nitrogen was found to be in the range 15 14 −3 of the primitive Earth’s atmosphere, of asteroids and of ( N/ N)c = 4.87 − 7.19 × 10 (Arpigny et al. 2003; of comets. We follow the model of Hutsemékers et al. Bockelée-Morvan et al. 2008a,b; Hutsemékers et al. 2005; (2009) to find the percentage of nitrogen that may have Jehin et al. 2004; Jehin et al. 2006, 2008; Manfroid et al. 15 14 been brought to Earth by comets. 2009). In our models, we consider ( N/ N)c values in The isotopic ratio in the present atmosphere is mea- the range of 5.00 − 7.00 × 10−3. 15 14 −3 sured to be ( N/ N)t = 3.676 × 10 (Junk & Svec The current isotopic ratio of nitrogen in the Earth’s 15 14 −3 1958). In contrast, the isotopic ratio of the primitive atmosphere is ( N/ N)t = 3.676 × 10 . The blue line 15 14 Earth, ( N/ N)p, is uncertain. Based on the value of in Fig.3 shows that about 3 - 8 % of the Earth’s atmo- the ratio in enstatite chondrite-type material and mea- spheric nitrogen was delivered by comets if no other pro- surement of the Earth’s interior, we shall therefore con- cesses have changed the isotopic ratio since the comets sider the isotopic ratio of the primitive Earth’s atmo- were delivered. However, this current day isotopic ra- 15 14 −3 sphere ( N/ N)p, to be 3.55 × 10 which reflects the tio may be lower that of the Archaean atmosphere ingredients of the Earth in the protosolar nebula (Car- which reflects the effect of the late heavy bombardment tigny et al. 1998; Cartigny & Marty 2013; Javoy et al. (LHB). Nitrogen content of the Archaean atmosphere 1986; Jia & Kerrich 2004; Marty & Zimmermann 1999; was brought to subduction zones (Mallik et al. 2018) Murty & Mohapatra 1997). and it results in the current isotopic ratio of nitrogen in The nitrogen isotopic ratio of the primitive Earth is the Earth’s atmosphere. very similar to that observed in asteroids, thus we con- If we consider the higher isotopic ratio of nitrogen 15 14 sider the nitrogen isotopic ratio of the present Earth as in Archean Earth’s atmosphere of ( N/ N)t = 3.786 × a mixture of that from comets and that from the prim- 10−3 (Jia & Kerrich 2004), the yellow line in Fig.3 shows itive Earth’s atmosphere. The abundances of each iso- that about 6 - 15% of the Earth’s atmospheric nitrogen tope are equal to the sum of that in comets and that in was delivered by comets. the primitive Earth so that In summary, if the isotopic ratio of nitrogen has not changed since the Archean era, the cometary contribu- n 14 n 14 n 14 (23) p( N) + c( N) = t( N) tion of nitrogen is only about 5%. On the other hand, and if in the Archean era, the Earth has an enriched 15N atmosphere, the cometary contribution of nitrogen may n (15N) + n (15N) = n (15N), (24) p c t be about 10 %. where n is the abundance and the subscripts p, c and t represent the primitive Earth, comets and present Earth, 4. DEBRIS DISK EVOLUTION LATE DELIVERY OF NITROGEN TO EARTH 7

Table 1. The apsidal eigenfrequencies for each of the solar system planets.

Planet Apsidal Eigenfrequency (gi) (arcsec/yr) Mercury (Me) 5.46347 Venus (V) 7.35054

Earth (E) 17.2968

Mars (M) 17.9887 Jupiter (J) 3.72802 Saturn (S) 22.5375

Uranus (U) 2.70839 Neptune (N) 0.633873 5 55 55 55 5 5 5 5 A secular resonance arises when the free precession Figure 3. The fraction of the present Earth’s nitrogen rate of a test particle is equal to the eigenfrequency that was delivered by comets, nc(N)/nt(N), as a function 15 14 of the cometary isotopic nitrogen ratio, ( N/ N)c. The of one of the planets (e.g. Froeschle & Scholl 1986; blue line is the model with the primitive Earth ratio of Yoshikawa 1987; Minton & Malhotra 2011; Smallwood 15 14 −3 ( N/ N)p = 3.676 × 10 and the yellow line is the model et al. 2018a,b). The planetary eigenfrequencies are ob- 15 14 −3 with ( N/ N)p = 3.786 × 10 . tained by calculating the eigenvalues from the Laplace- Lagrange equations in the context of the generalized We now consider possible delivery mechanisms for ni- secular perturbation theory (see for example Murray & trogen containing comets in the Kuiper belt to collide Dermott 1999). The eigenfrequencies for each of the with Earth. We first consider an analytic secular res- solar system planets are shown in Table1. The free onance model and then we use N–body simulations to precession rate of a test particle with orbital frequency, model the delivery of comets to the Earth. n, and semi–major axis, a, in the potential of the solar system is N 4.1. Resonances in the Kuiper belt n X m j (1) ω˙ = α jα¯ jb3/2(α j), (27) 4 m∗ In the context of the Kuiper belt, interior mean- j=1 motion resonances with Neptune generally produce scat- (Murray & Dermott 1999) where m j are the masses of tering events from eccentricity excitations compared ( j) with exterior mean-motion resonances that provide res- the solar system planets, m∗ is the mass of the Sun, bs onant capture of debris (Beauge & Ferraz-Mello 1994). is the Laplace coefficient and the coefficients α j and α¯ j Thus, we narrow our investigation of a nitrogen trans- are defined as  port mechanism to secular resonances rather than in-  a j/a, if a j < a, cluding mean-motion resonances, since there are no in- α =  (28) j  terior mean-motion resonances within the Kuiper belt. a/a j, if a j > a, There are two types of secular resonances, apsidal and and nodal. An apsidal resonance excites eccentricity, while   a nodal resonance excites inclination (Froeschle et al. 1, if a j < a, 1991). Apsidal resonances are the most important sec- α¯ j =  (29) a/a , if a > a. ular resonances for transporting material to the Earth, j j since the comets remain in the orbital plane of the sys- The top panel of Fig.4 shows the eigenfrequencies of the tem’s solid large bodies with an increased eccentricity planets as horizontal dashed lines. The test particle free and are more likely to collide with the Earth. Here, we precession rate is represented by the solid lines. Where apply a first-order secular resonance model to the solar the solid lines cross a horizontal line there is an apsidal system to find all of the the apsidal resonance locations. secular resonance. We are particularly interested in secular resonances that We now consider the strength of the apsidal reso- are outside of the ammonia snow line (at around 9au at nances. In the bottom panel of Fig.4 we show the forced the end of the gas disk lifetime, see Section2) since ob- eccentricity of a test particle in the solar system (for de- jects outside of this location may contain large amounts tails on these calculations see Murray & Dermott(1999) of nitrogen. and Minton & Malhotra(2011)). Planetary debris that 8 Chen et al.

60.0

50.0 ) yr / 40.0 arcsec ( 30.0

20.0 Precession rate 10.0

0.0 0 10 20 30 40 a (au) 0.25

0.20

0.15 forced e 0.10

0.05

V E 0.00 0 10 20 30 40 a (au) Figure 4. Top panel: The apsidal precession rate of a test particle as a function of semi–major axis (solid lines) and the eigenfrequencies for the planets (horizontal-dotted lines) (see Table1 for specific values). The intersection of the test particle’s precession rate with a planetary eigenfrequency represents the location of a apsidal secular resonance. Bottom panel: The maximum forced eccentricity of a test particle as a function of semi–major axis. The wider the gray region, the more asteroids/comets will undergo resonant perturbations. falls within the high eccentricity parts of the gray-shaded Nesvornýet al. 2017). In particular, the ν8 secular reso- regions undergoes eccentricity growth that leads to ejec- nance swept through the inner parts of the Kuiper belt tion or collision with a larger object. In the context of (Nagasawa & Ida 2000) and caused a large fraction of nitrogen transport to Earth, the source of nitrogen may the comets to acquire free precession frequencies simi- originate from the Kuiper belt which extends roughly lar to that of Neptune. Comets that originated or got from 30au to 50au (Duncan et al. 1995). The ν8 secu- ”bumped” into this sweeping resonance would have un- lar resonance is the most prominent secular resonance dergone increased eccentricity excitations leading to col- within the Kuiper belt (Froeschle & Scholl 1986). It is lisions with Earth, allowing for the transport of nitrogen. produced when the free precession rate of the comets is close to the eigenfrequency of Neptune. According to 4.2. N–body simulations of Earth impacts our linear secular resonance model, the ν8 resonance is located at 40.9au (the resonance location is based on To study the delivery of comets to the Earth, we use first-order approximations) which is consistent with the the N-body simulation package, REBOUND, to model actual location of the resonance (Nagasawa & Ida 2000). the Kuiper belt including the Earth, the four giant plan- Populations of Kuiper belt objects that are in reso- ets and Sun in the solar system (Rein & Liu 2012). We nance suggest that Uranus and Neptune underwent out- use a hybrid integrator called mercurius. This integrator ward migration (Fernandez & Ip 1984; Malhotra 1993, uses WHFast which is an implementation of a Wisdom- 1995; Hahn & Malhotra 1999; Tsiganis et al. 2005; Hahn Holman symplectic integrator to simulation the long- & Malhotra 2005; Chiang & Jordan 2002; Chiang et al. term orbit integrations of the planetary system. For 2003; Murray-Clay & Chiang 2005; Morbidelli et al. close encounters of test particles and planets, it switches 2007; Nesvorný 2015; Nesvorný& Vokrouhlický 2016). smoothly to IAS15 which is a 15th-order integrator to During this dynamical phase, resonant bodies in the simulate gravitational dynamics (Rein & Spiegel 2015; Kuiper belt were destabilized and there was a sudden Rein & Tamayo 2015). Thus, we can calculate the evo- massive delivery of planetesimals to the inner solar sys- lution of the Kuiper belt for a duration of one hundred tem (e.g. Levison & Morbidelli 2003; Gomes et al. 2005; million years (Myr) quickly and precisely. In our simulation, we take a snapshot every 0.1 Myr. LATE DELIVERY OF NITROGEN TO EARTH 9

Comets interact with the Earth, the gas giant planets and the Sun due to gravitational forces while there is no interaction between comets. The interaction time scale of some of the largest asteroids are of the order of magnitude of the age of the Solar System (Dohnanyi 1969). The obit of each comet is deﬁned initially by six orbital elements, a,i,e,ω,Ω,ν. In our model, we assume the semi–major axis, a, is distributed uniformly in the range amin = 38 to amax = 45 au including the region of the ν8 secular resonance (see Fig.4). The uniform distribution is given by

acomet = (amax − amin) × χr + amin (30)

(Lecar & Franklin 1997; Smallwood et al. 2018a) and χ Figure 5. Initial distribution of semi–major axis and eccen- r tricity of 50,000 test particles. Blue dots are particles that is a randomly generated number between 0 and 1. The collide with the Earth. inclination, i, is randomly allocated in the range from 0◦ to 10◦ and the eccentricity, e, is randomly allocated 39.5 and 42au also contribute a few of the collisions with in the range from 0 to 0.1. The argument of periapsis, the Earth. ω, the longitude of the ascending node, Ω and the true On the other hand, a test particle that has semi–major anomaly, ν are all uniformly distributed in the range axis a > 43au is quite stable and the region is regarded from 0◦ to 360◦. as the classic Kuiper belt objects and the final distribu- The present-day orbital elements for each of the plan- tion of eccentricity and semi–major axis of the comets ets are set as the initial parameters for the planets be- in fig.6 is roughly consistent with that observed scat- cause the Solar system is stable over long time-scales tered Kuiper belt objects. However, there are still many (Duncan & Lissauer 1998; Ito & Malhotra 2006). RE- particles in the inner region where a < 40au. Current BOUND queries those data automatically from NASA observations show that this region is quite clear (see fig. HORIZONS database. A test particle that has a semi– 7 in Jewitt et al. 2009). Since we do not consider the major axis beyond 200au is considered to be ejected. outward migration of Uranus and Neptune in our simu- In our simulation we inflate the size of the Earth to lation, we do not reproduce this clearing. The region of its Hill radius. The Hill radius is given by the ν8 resonance is not completely cleared out of comets !1/3 yet. About 50% of the test particles that were initially Mplanet RH = ap , (31) distributed in the region of the ν8 resonance are still in 3M this region. Resonances in the Kuiper belt excite the eccentricities where Mplanet is the mass of the planet and ap is the semi–major axis of the planet (Delsanti & Jewitt 2006). of the test particles and this increases the chance of a The Hill radius for the Earth is 2×106 km. In principle, close encounter with a planet. These close encounters three Hill radii is the range of the planet’s gravitational result in outward or inward migration of test particles. force and comets cannot remain on stable orbits within Once a test particle comes in to the inner solar system, this region (Gladman 1993; Chatterjee et al. 2008; Mor- the Earth has an opportunity to capture it. Fig.7 shows rison & Malhotra 2015). The increased size of the Earth that particles begin colliding with the Earth after about artificially increases the rate of collisions with the Earth 25 Myr and there are more than 4 impact particles every allowing us to simulate fewer particles than would have 5 Myr years after 30 Myr. In the next section we use been present in the early Kuiper belt. the results of our N–body simulation to estimate the Fig.5 shows the initial eccentricity and semi–major amount of nitrogen that was delivered to the Earth from axis distribution of 50,000 test particles. There are a to- the Kuiper belt. tal of 104 test particles that collide with the Earth within 100 Myr and the initial conditions for these are shown 4.3. Nitrogen delivery to the Earth by the blue dots. 70 of these test particles originate from We now consider a simple calculation to scale our sim- the region of the ν8 resonance around 40−42au. The 3:2 ulation result to calculate how much mass may have and 5:3 mean motion resonances of Neptune that are at been delivered to the Earth by comets. Most of the 10 Chen et al.

simulation there are still 50% of the original particles in the region of the ν8 resonance, we multiply the number of collisions by a factor of 2 to ﬁnd the mass to be ≈ 1 × 1024 g. For comparison, the total mass that was delivered to the Earth during LHB is estimated to be around 2 × 1023 − 2 × 1024g by modeling the thermal effects of the LHB (Abramov et al. 2013). However, according to the constraint of atmospheric 36Ar, Marty et al.(2016) estimated the cometary contribution to be about 2.0 × 1022 g. This value is 2 orders of the magnitude lower than our estimate. However, we have not taken into account the fact that a comet starts to sub- lime volatile when it enters the inner solar system. For example, the dynamical lifetime of comet Halley is about 3000 perihelion passages or 0.2Myr (Olsson-Steel 1988). Figure 6. Final distribution of semi–major axis and eccentricity of the test particles that remain in the simulation. It has lost about 0.4% of the total mass of the nucleus over the last 2,200 yr (Schmude 2010). From observations, we have already found some small comets that have radius < 0.4km that have lost of most their mass

10 (see table 9.4 in Fernández 2006). If we consider a comet that has a nucleus radius of 1km, the bulk density is −3 and the perihelion distance is , the dy- 8 0.5gcm 1au namical lifetime is less than 1000 orbits (see fig. 9.2 in Fernández 2006). Due to the mass loss of comets, 6 comets only possess 1 % to 10 % of their original mass when they collide with the Earth. Thus, the mass deliv-

number of collisions of number 4 ered by comets in our model is in the approximate range of 1022 to 1023 g. 2 To calculate how much nitrogen could have been delivered in these comets, we use data of 16 comets from

0 Le Roy et al.(2015); Paganini et al.(2012) to esti- 0 20 40 60 80 100 time/Myr mate the mean values of highest relative abundances of NH3 and HCN to be 0.7% and 0.28% with respect to Figure 7. Histogram of the number of collisions of comets water. Besides, in a recent study, ROSINA measured with the Earth as a funciton of time. There are 104 impact the N /CO ratio by mass to be 0.570 % on the comet particles within 100 Myr. 2 67P/Churyumov-Gerasimenko and CO in this comet is about 10% with respect to water (Le Roy et al. 2015). impacts come from the ν resonance region and we fo- 8 Thus, we use 0.057 % for the relative abundance of N cus on these. The fraction of comets that begin in the 2 with respect to water. H O takes up 50% of the compo- region we are interested in 40-42 au, assuming a uniform 2 sition of the comet by mass and thus the total mass of distribution of the number of test particle in semi–major nitrogen from comets is estimated to be in the range of axis. However, we inflated the size of the Earth to in- 3.9 ×1019 to 3.9 ×1020g. crease the possibility of a collision. Smallwood et al. The total mass of the Earth’s atmosphere is 5.136 × (2018a) calculated that the number of collisions is re- 1021g (Weast et al. 1989). Nitrogen makes up 78 % of the duced by a factor of 800/5 if we shrink the size of the composition of the current Earth’s atmosphere so that Earth from its Hill’s radius to the radius of the Earth. the mass of nitrogen in the atmosphere is 3.8 × 1021 g Thus, the collision fraction should be × −5 collisions 3 10 (Verniani 1966). If 10% of nitrogen was delivered by per particle per Myr. 100 comets (see Section3) the mass of cometary nitrogen The initial mass of the Kuiper belt was at least 10 is 4 × 1020g and our simulation is consistent with this times the mass of Earth, × 27g (Delsanti & M⊕ = 6 10 value. Jewitt 2006). The amount of mass that originated in Note also that here we only consider the contribution the ν8 resonance and collided with the Earth is approx- from the ν8 region. There would have been additional imately 5 × 1023g in 100Myr. Because at the end of our LATE DELIVERY OF NITROGEN TO EARTH 11 collisions as a result of mean-motion resonances of Nep- contain a large amount of nitrogen. Besides, the Kuiper tune (see fig.5) and the migration of Uranus and Nep- belt provides an extremely cold environment where CO tune which we did not include in our simulation. In the is frozen out and large enhancements of the isotopic ra- Archaean era, the partial pressure of nitrogen was at tio 15N/14N occur there. Since the Earth’s atmosphere least 1.4 ∼ 1.6 times higher than today’s atmosphere. might be enriched in 15N in the Archean era, the nitro- Mallik et al.(2018) estimated this value by subtracting gen in the Kuiper belt is a possible source. the net degassing flux of N from arcs and back-arc basins Apsidal secular resonances played an essential role in (Hilton et al. 2002), mid-ocean ridges and intraplate- bringing comets to the Earth. The most prominent sec- settings (Sano et al. 2001) from the influx of N at sub- ular resonance in the Kuiper belt, the ν8 resonance, duction zones today. Due to N recycling efficiency, some might have excited the eccentricity of the comets. In nitrogen in the Earth’s atmosphere was brought to the the early stages of the solar system evolution, Uranus subduction zones and the deep mantle (Mallik et al. and Neptune both underwent outward migration during 2018). However, there are some contradictory results which the ν8 resonance swept through comet-like ob- that the partial pressure of the nitrogen in Archaean at- jects from the inner Kuiper belt to its present location mosphere is similar or less than the present atmosphere’s at around 41au. With numerical N–body simulations we based on different analyses of Archean samples (Avice have shown that comets around this region are scattered et al. 2018; Som et al. 2016). Consequently, it leaves and may collide with the Earth when they enter the in- some uncertainties and our simulations cannot solve this ner solar system. The period of the LHB corresponds problem. with the early Archean era. During this time, the resonance most probably delivered comets and thus nitrogen 4.4. Water delivery to the Earth to the Earth. With the supplement of the late delivery Because comets also contain a large amount of water, of nitrogen to the Earth, the isotopic ratio 15N/14N of they deliver both nitrogen and water and the D/H ra- the Earth’s atmosphere increased slightly. Our research tio in the Earth may also be changed. Since the D/H quantifies the amount of nitrogen that is delivered by ratios of comets are much higher than terrestrial water comets. and enstatite chondrites do not contain large amount Exoplanetary systems that contain both a warm and of water, it could be used to constrain the contribution a cold debris belt (like the solar system) may be com- of water from comet to the Earth and it should be less mon (e.g Moro-Mart´ınet al. 2010; Morales et al. 2011). than about 10% (Bockelée-Morvan et al. 2004; Dauphas The outer debris disk is a potential source of nitrogen et al. 2000). Since water takes up 50% of a comet’s to terrestrial planets in the inner regions. For example, composition, we estimate the amount of water that de- the planetary and debris disk system HR 8799 closely livered from comets and this value is 5×1021 ∼ 5×1022g. resembles that of the outer Solar system by having two The total mass of the water on the Earth is 1.35×1024g. massive debris disks that bracket four giant planets, with Therefore, the water contribution from comets is just the outermost disk consisting of cold dust (T ∼ 45 K) about 0.4% ∼ 4%. This value is more in agreement with (Marois et al. 2008). Investigating the delivery of nitro- Marty et al.(2016) that states the cometary contribu- gen in such systems can contribute to the understanding tion of water is ≤ 1 %,whatever the reservoir considered. of the atmospheric properties of exoplanets and planetary habitability. 5. CONCLUSIONS Although it is not the main source of nitrogen in the Earth’s atmosphere, a significant fraction of the present ACKNOWLEDGMENTS Earth’s nitrogen may have come from comets (about All the simulations were run at the UNLV National 10%). The present isotopic ratio of 15N/14N in the Supercomputing Institute on the Cherry Creek clus- Earth’s atmosphere is a combination of the primitive ter. CC acknowledges support from a UNLV gradu- Earth value and the value contained in asteroids/comets ate assistantship. JLS acknowledges support from a that hit the Earth. With steady state protoplanetary graduate fellowship from the Nevada Space Grant Con- disk models that include a self–gravitating dead zone, sortium (NVSGC). RGM acknowledges support from we find that the ammonia and nitrogen snow line radii NASA grant NNX17AB96G. Simulations in this paper were around 9au and 12au, respectively, at the end of the made use of the REBOUND code which can be down- disk’s lifetime. Thus, comets in the Kuiper belt probably loaded freely at http://github.com/hannorein/rebound. 12 Chen et al.

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