Contributions from Accreted Organics to Titan's Atmosphere: New Insights from Cometary and Chondritic Data

We now address whether this reservoir may have been mobilized to allow delivery to the atmosphere, or whether it has remained locked away in Titan's interior. This requires an understanding of temperatures in a presumed rocky core, where refractory organics would have been located.

The most detailed published model for the thermal evolution of Titan's core is that of Castillo-Rogez & Lunine (2010). Two of their suggested cases were consistent with Titan's moment of inertia, but only if it is assumed that 30% of ⁴⁰ K was leached into a subsurface ocean. This would limit the dehydration of rocks. The first case features a completely hydrated rocky core, while the second has a partially dehydrated inner core. The computed thermal evolution suggests that the deepest portions of the core reached temperatures of at least 575 °C, and potentially in excess of 1300 °C (Castillo-Rogez & Lunine 2010). The outer core within 300 km of the ice–rock interface may have experienced temperatures on the order of 475 °C (Castillo-Rogez & Lunine 2010).

Anhydrous pyrolysis experiments on Murchison IOM conducted from 110 °C–800 °C at a heating rate of 5 °C minute⁻¹ show that IOM organics begin to thermally decompose at <200 °C (Okumura & Mimura 2011). In a second experiment with stepped pyrolysis of IOM at temperatures between 250 °C and 800 °C, 0.8 wt.% of the total organic mass was lost via volatilized N (ibid). This percentage corresponds to volatilization of approximately 30% of organic N, suggesting that a mass of 2.6 × 10²⁰ kg of N may have been volatilized in Titan's core depending on the maximum temperature. This mass is nearly 30 times greater than the present-day mass of atmospheric nitrogen.

We matched thermal modeling data for Titan's interior from Castillo-Rogez & Lunine (2010) with the temperature release data from Okumura & Mimura (2011) to estimate the yield of volatile N as a function of depth and time. The internal thermal profile was taken from the Castillo-Rogez & Lunine (2010) case that assumed a fully hydrated core, because this case had the lowest temperatures and is therefore more conservative. Data from both references were linearly interpolated to 1 °C intervals. By assuming that refractory organic material was homogeneously distributed throughout the core and that the density of the core was approximately constant, we calculated the mass of organics subjected to each radial temperature regime. We then determined the minimum depth of outgassing required to produce the total mass of N in Titan's present-day atmosphere for different assumed outgassing efficiencies, which were treated as uniform with depth. We define the outgassing efficiency as the mass of nitrogen contributed to the atmosphere divided by the total mass of volatile nitrogen released from organics in the core. The resulting time-dependent outgassing depths are shown in Figures 2(a) and (b).

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To generate the full mass of N in present-day Titan's atmosphere, outgassing of the core to a depth of at least ∼700 km, or ∼200 km below the ice–rock interface predicted by the model of Castillo-Rogez & Lunine (2010), is required. This depth is time-dependent, increasing to ∼1000 km below the surface at 500 Myr after accretion (the earliest time modeled by Castillo-Rogez & Lunine 2010). However, ¹⁴N/¹⁵N and ³⁶Ar/N constraints suggest that only a portion of the N atmosphere may have originated from accreted organics (Section 4). This is consistent with outgassing from a shallower depth in the core. The same figures replotted with the outgassing depths required to release 50% of Titan's present-day atmospheric N mass are shown in Figures 2(c) and (d). These calculations show that outgassing of the upper core alone is sufficient for supplying the implied mass of N. The overall efficiency of outgassing required from Titan's core is less than 30% soon after accretion, and reduces to less than 5% as the core warms up (Figure 2(d)). These values neglect the effects of nitrogen speciation; consideration of speciation may require more efficient outgassing by a factor of ∼2 (see Section 3.2).

Low outgassing efficiency is consistent with data from the Cassini Ion Neutral Mass Spectrometer, which measured an ⁴⁰Ar mixing ratio near the top of the atmosphere of (7.1 ± 0.1) × 10⁻⁶ (Waite et al. 2005). The mixing ratio of ⁴⁰Ar increases in the lower atmosphere to (3.35 ± 0.25) × 10⁻⁵ (Niemann et al. 2010). This suggests approximately 3 × 10¹⁴ kg of atmospheric ⁴⁰Ar. From Tobie et al. (2012), Titan's interior may contain approximately 5 × 10¹⁵ kg of ⁴⁰Ar assuming chondritic abundances of ⁴⁰K. This assumed chondritic K abundance may be an underestimate for outer solar system objects. Flynn et al. (2006) report nominally super-chondritic abundances of K in Stardust samples from comet Wild 2. However, they acknowledge that the distribution is heterogeneous and a true mean value is difficult to measure from these samples. If real, super-chondritic K abundances in a "cometary" Titan interior may be counterbalanced by the reduction in total silicate abundance due to the high weight percent of organic material. In the absence of stronger constraints, use of the chondritic value for ⁴⁰Ar suggests an outgassing efficiency at Titan of approximately 6%, consistent with the values calculated in the present work (see also note 18 in Waite et al. 2005).

Given the stability of clathrate hydrates (e.g., Lunine & Stevenson 1985), the primary mechanism of the proposed outgassing would not have been gas diffusion from clathrates. Rather, ice-mantle dynamics should dominate outgassing, and processes such as cryovolcanism (Lopes et al. 2013) or other episodic events (Tobie et al. 2006) may have played a major role in the transport of volatiles from Titan's interior to the atmosphere. Future observational assessments of these processes and additional constraints on their timing and magnitude on Titan will provide significant constraints on the importance of volatilized organics as a source for Titan's atmosphere.

To the best of our knowledge, the speciation of N evolved in experimental decomposition of IOM has not been reported. Over geologic time and in the presence of potential mineral catalysts, volatilized N may reach a state of thermodynamic equilibrium inside Titan's core between N₂, NH₃, and ${\mathrm{NH}}_{4}^{+}$, which are expected to be the dominant volatile compounds. If so, the fraction of N that exists as N₂ will depend on temperature (T), pressure (P), oxygen fugacity $({f}_{{{\rm{O}}}_{2}})$, pH, and the moles of N per kg of H₂O (N molality; ΣN) (Mikhail & Sverjensky 2014; Mikhail et al. 2017). We summarize in Figure 3 the relative effects of these variables on nitrogen speciation in ideal dilute solution using the Deep Earth Water model (Sverjensky et al. 2014). Calculations were performed using water density values from Zhang & Duan (2005) and the dielectric constant from Sverjensky et al. (2014). In general, N₂ is favored by higher temperatures, lower pressures, higher oxygen fugacity, higher pH, and a higher N molality.

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To demonstrate quantitative speciation relationships, we choose the ${f}_{{{\rm{O}}}_{2}}$, pH, and ΣN conditions in Titan's core by analogy since geochemical conditions in Titan's core are poorly constrained at present. A pressure of 10 kbar corresponds to a depth of approximately 140 km below the rock-water interface (see Equation 2–73 from Turcotte & Schubert 2002, p. 85), assuming an average core density of 2.55 g cm⁻³ and a 525 km thick ice+water shell with an average density of 1.2 g cm⁻³. By analogy to the core of Enceladus, this relatively shallow depth (<10% of the core radius) may correspond to an oxidation state with ${f}_{{{\rm{O}}}_{2}}\gt \mathrm{FMQ}$ (Glein et al. 2018; see also Shock & McKinnon 1993). Since N₂ is favored by oxidizing conditions, use of FMQ should be a conservative case. To estimate ΣN, we adopt core water/rock mass ratios from Enceladus, which range from 0.12 to 0.13 (Waite et al. 2017). Since pressures inside Titan's core are greater than those in Enceladus, we reduce the water/rock ratio by a factor of 2. While this factor of 2 may be low, it represents a conservative estimate since N₂ is favored by higher ΣN. From Section 2, Titan's total core mass is (9.2–9.9) × 10²², which yields a core water mass of (5.5–5.8) × 10²¹ kg. Also from Section 2, the total atmospheric nitrogen mass is 9 × 10¹⁸ kg, corresponding to 6.4 × 10²⁰ moles of N. If we assume 50% of that mass is representative of N abundances in the core, then the resulting core ΣN is (5.5–5.9) × 10⁻² moles N/kg H₂O. Here we use ΣN = 10⁻² moles N/kg H₂O. Finally, Galvez et al. (2016) calculate that the range of pH conditions for silicate mineral assemblages in analogous pressure and temperature conditions tends to fall between pH_Neutral and pH_Neutral + 3, with lower pressures corresponding to less alkaline pH conditions. We use pH_Neutral + 1. The nominal case, shown in Figure 4, demonstrates that equilibrium between N₂, NH₃, and ${\mathrm{NH}}_{4}^{+}$ under plausible geochemical conditions still allows for a sufficient N₂ reservoir to supply a significant fraction of Titan's atmosphere.

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In addition to production of N-bearing compounds, pyrolysis of organics may produce a significant mass of methane. Indeed, pyrolysis of terrestrial coal yields molar N₂/CH₄ ratios between 0.13 and 0.22 depending on the maturity of the coal (Krooss et al. 1995). However, some terrestrial natural gas fields are >90 mol.% N₂, with only a minor CH₄ contribution (e.g., Table 1 of Krooss et al. 1995). Pyrolysis of extraterrestrial IOM up to temperatures of 550 °C yields 3266 ng of CH₄ per mg of IOM (Okumura & Mimura 2011). From the above estimate of a total organic mass of 4.2 × 10²² kg, this is equivalent to 3.5 × 10²⁰ kg of CH₄. Assuming that CH₄ outgases at the same efficiency as N₂, 6% from Section 3.1, this corresponds to a mass of 8.2 × 10¹⁸ kg of outgassed CH₄. From Section 2, the current mass of atmospheric CH₄ at Titan is approximately 2 × 10¹⁷ kg. However, it is estimated that the present-day atmosphere would only last 30 Myr at current photodestruction rates (Yung et al. 1984; Wilson & Atreya 2004; see Horst 2017 for a review). If we assume similar destruction rates in the past (i.e., ∼7 × 10⁹ kg/yr), our estimate for the mass of outgassed CH₄ would extend the lifetime of the atmospheric methane to 1.2 Gyr.

Carbon is largely retained during atmospheric processing. Present-day escape rates are 1.41–1.47 × 10¹¹ molecules of methane m⁻² s⁻¹ (Bell et al. 2014), which corresponds to (1.2–1.3) × 10¹⁶ kg of methane using a surface area of 8.3 ×10⁷ km² (assuming a sphere with the radius of 2575 km; Lindal et al. 1983; Jacobson et al. 2006) and a lifetime of 1.2 Gyr from above. Therefore, approximately 0.2% of the outgassed methane would be lost to escape, but most would be deposited on the surface via settling of photochemistry products, hydrocarbon rain, and related processes. Subtracting the present-day atmospheric methane mass from the total outgassed mass gives 8 × 10¹⁸ kg of methane that must be accounted for, equivalent to a C mass of 6 × 10¹⁸ kg. To estimate the equivalent average global depth of organic sediment, we assume an approximate density for complex organics of between 1.2 and 1.7 g cm⁻³ from terrestrial kerogen (e.g., Nwachukwu & Barker 1985; Okiongbo et al. 2005; Ward 2010; Stankiewicz et al. 2015). From Quirico et al. (2008) we use a tholin composition that is between 47% and 62% C by mass. With the surface area of 8.3 × 10⁷ km² calculated above, the calculated global depth of organic deposits would be between 90 and 170 m. For comparison, the deepest point in Ligeia Mare is greater than 150 m (Mastrogiuseppe et al. 2014). The processes responsible for formation of Titan's lakes and seas have not been identified, but formation via dissolution of organic sediments would require a layer with thickness of order 600–800 m (Hayes 2016 and references therein).

It is worth considering whether the isotopic composition of Titan's atmospheric methane is consistent with an IOM-like source. A notable characteristic of IOM is its high D/H ratio (e.g., Robert & Epstein 1982). Alexander et al. (2007) report D/H ratios for primitive IOM from the CR chondrites and Bells CM chondrite in the range (5.64–7.05) × 10⁻⁴. The CR chondrites and Bells were chosen because they have the least processed IOM (Alexander et al. 2007). In contrast, the D/H ratio for Titan's atmospheric methane is only 1.36 × 10⁻⁴ (Nixon et al. 2012 and references therein). However, these values are not incompatible if methane and water reached isotopic equilibrium during outgassing.

The degree of isotopic exchange required to change the D/H ratio for CH₄ from its initial, IOM-like value to the value observed in Titan's atmosphere can be calculated from the mass and molar mass of methane (${m}_{{\mathrm{CH}}_{4}}$ and ${M}_{{\mathrm{CH}}_{4}}$, respectively), the moles of hydrogen in a mole of methane (n_hyd,m = 4) and the initial fractional amounts in methane of D (f_D,m,i) and H (f_H,m,i). We calculate f_D,m,i and f_H,m,i from the D/H ratio of IOM from the most D-rich CR chondrite, LEW 85332 (7.05 × 10⁻⁴; Alexander et al. 2007), to provide a conservative estimate of the effects of isotopic equilibration of volatiles derived from IOM.

$$\begin{eqnarray}&&{D}_{m,i}=\tfrac{{m}_{{\mathrm{CH}}_{4}}}{{M}_{{\mathrm{CH}}_{4}}}\times {n}_{\mathrm{hyd},m}\times {f}_{D,m,i}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{H}_{m,i}=\tfrac{{m}_{{\mathrm{CH}}_{4}}}{{M}_{{\mathrm{CH}}_{4}}}\times {n}_{\mathrm{hyd},m}\times {f}_{H,m,i}.\end{eqnarray} \tag{ 2 }$$

Here, D_m,i and H_m,i are the number of D and H moles initially in methane. The values for D_m,f and H_m,f (the final number of D and H moles in methane) can be similarly calculated using f_D,m,f and f_H,m,f. The number of moles of hydrogen exchanged to achieve equilibrium $({{\boldsymbol{n}}}_{{\boldsymbol{x}}})$ is then calculated as

$$\begin{eqnarray}&&{{\boldsymbol{n}}}_{{\boldsymbol{x}}}={D}_{m,i}-{D}_{m,f}.\end{eqnarray} \tag{ 3 }$$

From Glein (2015) we calculate an isotopic equilibrium fractionation factor ${\alpha }_{{\mathrm{CH}}_{4}\mbox{--}{{\rm{H}}}_{2}{\rm{O}}}$ at 0 °C of 0.76. Since ${\alpha }_{{\mathrm{CH}}_{4}\mbox{--}{{\rm{H}}}_{2}{\rm{O}}}$ is defined as the ratio ${R}_{{\mathrm{CH}}_{4}}/{\text{}}{R}_{{{\rm{H}}}_{2}{\rm{O}}},$ where R is the D/H ratio, this fractionation factor suggests a D/H value for Titan's water after exchange of 1.80 × 10⁻⁴ assuming equilibrium with atmospheric methane. Using equations of the same form as Equations (1) and (2), we can calculate D_w,f and H_w,f, the final number of D and H moles in water. The initial D and H values for water, D_w,i and H_w,i, are then calculated as

$$\begin{eqnarray}&&{D}_{w,i}={D}_{w,f}-{{\boldsymbol{n}}}_{{\boldsymbol{x}}}\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{H}_{w,i}={H}_{w,f}+{{\boldsymbol{n}}}_{{\boldsymbol{x}}}.\end{eqnarray} \tag{ 5 }$$

Using Equations (1)–(5) and the values tabulated in Table 2 yields an initial D/H value for water of 1.68 × 10⁻⁴, similar to the terrestrial Vienna Standard Mean Ocean Water (VSMOW) value of 1.56 × 10⁻⁴ and the value observed for comet 103P/Hartley 2 ((1.61 ± 0.24) × 10⁻⁴; Hartogh et al. 2011). This model therefore predicts that water ice on Titan should have a D/H ratio of 1.80 × 10⁻⁴ (consistent with the values in Glein 2015), and that primitive ice in the Saturnian system may have been close to VSMOW in terms of hydrogen isotopes.

Table 2.  Values Used to Calculate Isotopic Exchange

Variable	Description	Value	Source
${m}_{{\mathrm{CH}}_{4}}$	Mass of methane	3.5 × 1020 kg	Section 3.3, this work
${M}_{{\mathrm{CH}}_{4}}$	Molar mass of methane	16 × 10−3 kg mol−1
fD,m,i	initial fraction of methane hydrogen as D	7.05 × 10−4	CR chondrite LEW 85332, Alexander et al. (2007)
fH,m,i	initial fraction of methane hydrogen as H	1-fD,m,i	CR chondrites, Alexander et al. (2007)
fD,m,f	final fraction of methane hydrogen as D	1.36 × 10−4	Nixon et al. (2012)
fH,m,f	final fraction of methane hydrogen as H	1-fD,m,f	Nixon et al. (2012)
${\alpha }_{{\mathrm{CH}}_{4}\mbox{--}{{\rm{H}}}_{2}{\rm{O}}}$	equilibrium isotopic fractionation between methane and water	0.76	Equation (10) from Glein (2015) (assuming T = 0 °C)
${m}_{{{\rm{H}}}_{2}{\rm{O}}}$	Mass of water	3.9 × 1022 kg	Section 2, this work
${M}_{{{\rm{H}}}_{2}{\rm{O}}}$	Molar mass of water	18 × 10−3 kg mol−1
fD,w,f	final fraction of water hydrogen as D	1.79 × 10−4	CR chondrites, Alexander et al. (2007)
fH,w,f	final fraction of water hydrogen as H	1-fD,w,f	CR chondrites, Alexander et al. (2007)

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Pyrolysis of IOM yields other hydrogen-bearing compounds as well; can the probable isotopic signature of these components be reconciled with the D/H ratio of Titan's methane? From the same calculations described in Section 2, we calculate an organic hydrogen reservoir of 1.63 × 10²¹ kg and an ice hydrogen reservoir of (1.55–4.13) × 10²¹ kg. At 800 °C, Okumura & Mimura (2011) report that ∼75% of IOM hydrogen had volatilized, while ∼25% remained in the residue. By assuming that the initial D/H ratio of Titan's water was VSMOW-like and the initial D/H ratio of the IOM hydrogen was similar to the CR chondrites, we can use a series of equations analogous to Equations (1)–(5) above and solve for m_org, the mass of organic hydrogen that exchanged with water. To do so, we utilize the value of ${\alpha }_{{\mathrm{CH}}_{4}\mbox{--}{{\rm{H}}}_{2}{\rm{O}}}$ from Table 2 as an estimate of isotopic equilibrium for all organic hydrogen. The result is that 5%–14% of volatilized organic hydrogen could have been exchanged. This range of values is similar to the outgassing efficiencies for N and ⁴⁰Ar (∼6%) discussed in Section 3.1 (see also Waite et al. 2005; Niemann et al. 2010; Tobie et al. 2012). We conclude that outgassing of IOM-like pyrolysis products from Titan's core is consistent with the measured D/H ratio of atmospheric methane.

The predicted VSMOW-like D/H ratio for water ice at Titan places constraints on the formation and evolution of the regular Saturnian satellites. A recent analysis of data from the Cassini Visual and Infrared Mapping Spectrometer (VIMS) is consistent with a D/H ratio similar to VSMOW for Saturn's B ring, as well as the icy surfaces of Enceladus, Rhea, Hyperion, and Iapetus (Clark et al. 2019). However, the D/H ratio for water in Enceladus' plume is (2.9+1.5/−0.7) × 10⁻⁴ (Waite et al. 2009). Using 2.9 × 10⁻⁴ as the initial D/H ratio for water in Equations (1)–(5) above yields a current D/H ratio for atmospheric methane at Titan of 2.27 × 10⁻⁴, almost 1.7 times the measured ratio (Glein et al. 2009; Mousis et al. 2009a). One possible explanation is that Titan and Enceladus had different initial bulk D/H ratios for water. This difference in initial D/H may be due to formation at different times, corresponding to either the temperature evolution of the Saturnian subnebula, or movement of the Saturnian system due to giant planet migration (Glein 2015; see also McKinnon et al. 2018b for a discussion on the origin on Enceladus' D/H ratio).

Alternatively, hydrothermal processes at Enceladus (e.g., Hsu et al. 2015; Waite et al. 2017) may increase the percentage of volatilized organic hydrogen that exchanged with water (McKinnon et al. 2018a) compared to Titan. We calculate that for the organic hydrogen reservoir and ice hydrogen reservoir given above and an initial water D/H ratio equal to VSMOW, approximately 35% to 93% of volatilized organic hydrogen must exchange with water to reach the D/H = 2.9 × 10⁻⁴ measured in Enceladus' plume (Waite et al. 2009). For a temperature of 0 °C, this suggests a methane D/H of 2.20 × 10⁻⁴ at Enceladus; at a temperature of 50 °C (Sekine et al. 2015), the methane D/H value increases to 2.33 × 10⁻⁴ and 36% to 96% exchange for equilibration.

Carbon isotopic ratios for IOM are also broadly consistent with Titan's atmospheric methane. Nixon et al. (2012) report a compilation of ¹²C/¹³C ratios for Titan methane ranging from 82–91.1 depending on the measurement method, with a mean value of 89.7 ± 1.0. Values from Bells and the CR chondrites range from ¹²C/¹³C = 90.8–92.1. Therefore, outgassing of methane derived from heating of IOM in Titan's interior is isotopically consistent with measurements of methane in Titan's atmosphere.

A key constraint in determining the source of Titan's atmospheric N is its isotopic composition. Data from different solar system objects suggest that there were at least two distinct isotopic reservoirs of N in the solar nebula (Füri & Marty 2015). Based on the similar isotopic ratios of Titan's atmosphere and cometary comae, previous studies have argued for an icy planetesimal source similar to present-day comets for Titan's atmospheric N. Measurements of Titan's atmosphere indicate that it has a bulk ¹⁴N/¹⁵N value for N₂ of 168 (Waite et al. 2005; Niemann et al. 2010). This value may not have evolved substantially from the primordial value (Mandt et al. 2009, 2014), and is broadly consistent with nitrogen isotopes in cometary comae, including CN (140–172; Manfroid et al. 2009) and NH₃ (136; Shinnaka et al. 2016).

Isotopic data for our cosmochemical model are drawn from laboratory measurements and spectroscopic observations. For N₂, we use a ¹⁴N/¹⁵N ratio of 441 ± 5 (Marty et al. 2011) determined from Genesis samples of the solar wind. This value is consistent with the high ratios measured at Jupiter (¹⁴N/¹⁵N = 435(+65, −50)) (Owen et al. 2001), supporting its use as representative of a major N reservoir throughout the planet-forming region of the solar system.

Spectroscopic measurements of NH₂ in cometary comae, which is hypothesized to be a daughter product of native NH₃, suggest much lower isotopic ratios (¹⁴N/¹⁵N ∼ 136; Shinnaka et al. 2016). These values are more similar to that observed in Titan's atmosphere at the surface (¹⁴N/¹⁵N = 168 ± 1; Niemann et al. 2010), which may have changed by much less than a factor of 2 due to atmospheric loss processes over the lifetime of the solar system (Mandt et al. 2014). Krasnopolsky (2016) suggests that the present-day N-isotopic ratio of Titan's atmosphere may be further reconciled with cometary NH₃ by photochemical formation of HCN in Titan's atmosphere, sequestering ¹⁵N in nitriles over time. This model predicts a primordial ¹⁴N/¹⁵N value for Titan's atmosphere of 129 assuming constant production rates of enriched HCN through time. However, the source of Titan's atmospheric methane is poorly constrained, and models suggest that the lifetime of methane may be much shorter than the history of the solar system, and likely less than 1 Gyr (Yung et al. 1984; Mandt et al. 2012). If the atmosphere were depleted of methane in the past, then sequestration of ¹⁵N in nitriles would halt.

Defining the N isotope ratio for refractory organics is somewhat less straightforward than for N₂ and NH₃. IOM seems to be isotopically heterogeneous, and reflects a combination of heritage and parent body alteration via thermal and aqueous processes (e.g., Sephton et al. 2003; Alexander et al. 2007, 2017). Here, we use data from three different types of material to define a range of values for organic N isotopes: (1) IDPs (Messenger 2000; Aléon et al. 2003; Keller et al. 2004; Floss et al. 2006; Busemann et al. 2009), which represent primitive solar system materials (Messenger 2000) and may originate from comets (Joswiak et al. 2000); (2) Stardust samples collected from comet Wild 2 (McKeegan et al. 2006; De Gregorio et al. 2009); and (3) IOM from CR chondrites, the Bells CM chondrite, and the CH/CB chondrite Isheyevo (Alexander et al. 2007; Briani et al. 2009). While Bells and the CR chondrites are hypothesized to have the most primitive IOM (Alexander et al. 2007), Mg and Cr isotope data suggest that both CR chondrites and the Isheyevo meteorite may incorporate material formed beyond the snowline in the outer solar system (Van Kooten et al. 2016). Refractory lithophile abundances, calcium–aluminum-rich inclusion (CAI) abundances, and the accretion age of the CR chondrite parent body are also consistent with an outer solar system origin (Desch et al. 2018).

Binned data compiled from nine different sources are shown in Figure 5. There appear to be two main modes in the data: one at 200, and another at 250. The mode at 200 is mainly driven by data from Aléon et al. (2003), who measured isotopic ratios from multiple analyses on two D-rich IDPs. They cited isotopic values of 198 and 225 as representative of the main N carrier in these grains, which is consistent with the mode at 200. The mode at 250 includes data from other IDPs, grains collected from comet Wild 2 by Stardust, and material from Isheyevo, which contains ¹⁵N-rich clasts (Ivanova et al. 2008; Bonal et al. 2010). Since data from these three different sources (IDPs, cometary grains, and outer solar system chondrites) all fall within the same range from 160 to 320, we conclude that this range likely encompasses the main refractory N reservoir(s) in the outer solar system. These values are intermediate to solar N₂ (441; Marty et al. 2011) and values inferred for cometary NH₃ (136; Shinnaka et al. 2016). Nonetheless, due to the ubiquitous nature of refractory N-bearing components in primitive solar system bodies and evidence for fractionation between volatile and refractory reservoirs in these materials, we suggest that refractory N should be treated as a separate component (McKinnon et al. 1997, 2008).

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Consideration of the abundance of ³⁶Ar in Titan's atmosphere provides further constraints on the origin of atmospheric N₂. The abundances of N₂ and ³⁶Ar in the coma of comet 67P are correlated (Balsiger et al. 2015), and both species appear to be present at 67P at least in part as clathrate hydrates that formed after condensation of crystalline ice in the protosolar nebula at temperatures between 45 and 50 K (Mousis et al. 2016). While ³⁶Ar and N₂ may have had similar condensation behavior in the protoplanetary disk (Owen 1982), ³⁶Ar and NH₃ may have been fractionated based on temperature in the early solar system (Mousis et al. 2009b). At Saturn's radial distance, ammonia monohydrate is predicted to form at 87 K, while Ar clathrate and N₂ clathrate condense below 60 K (Hersant et al. 2001, 2004; Alibert & Mousis 2007). Ar and N₂ ices condense at even lower temperatures under these conditions (Mousis et al. 2009b). Based on these fractionation patterns, we assume a negligible (but nonzero value to plot the logarithm) ³⁶Ar/N ratio for the NH₃ endmember of our mixing model (10⁻¹⁰). Similarly, we adopt the 67P ³⁶Ar/N ratio for the cometary endmember with the assumption that this ratio might be approximately uniform among comets because of the similar condensation behaviors of Ar and N₂.

What about the ³⁶Ar/N ratio of the organic endmember? In chondritic meteorites, the main Ar carrier is phase Q, where the Q stands for "quintessence" (Lewis et al. 1975; Wieler et al. 2006). This phase is hypothesized to have been distributed throughout the meteorite-forming region during accretion (Huss et al. 1996; Busemann et al. 2000), and while its exact nature is an area of ongoing research, it is associated with carbonaceous phases (Ott et al. 1981). Analyses of Ne in Stardust samples from Comet Wild 2 support a Q-like source, although the ³He/⁴He and ⁴He/²⁰Ne ratios are not explained by phase Q (Marty et al. 2008). Since phase Q was ubiquitous in the meteorite-forming region, and there is evidence for mixing between the early inner and outer solar system (Westphal et al. 2009; Berger 2011; Ogliore et al. 2012), we assume that carbonaceous material in comets may also be associated with Q-like noble gases. We therefore calculate from Lodders (2010) the ³⁶Ar/N ratio of the organic endmember (1.5 × 10⁻⁷), assuming that phase Q and IOM are the dominant carriers for Ar and N, respectively, in the CI chondrites. In the same way, we calculate a Kr/N ratio of 3.0 × 10⁻⁹ and a Xe/N ratio of 6.3 × 10⁻⁹ (Lodders 2010). These ratios could be even lower in Titan's atmosphere if Kr and Xe are outgassed less efficiently than N₂ (Glein 2015), and are consistent with the upper limit for Titan's atmosphere of 10⁻⁸ for the mole fractions of both Kr and Xe (Niemann et al. 2010).

For our Titan atmosphere mixing model, we adopt three different endmembers. NH₃ and N₂ are chosen as endmembers because together they represent the most abundant volatile N-bearing species in the protoplanetary disk, with N₂ dominating the gas phase and NH₃ dominating ice-phase N species in the inner 10 au of the disk (Piso et al. 2016), regardless of the initial N carrier (Schwarz & Bergin 2014). Refractory organics are chosen as the third endmember because of their high abundance in comets (Bardyn et al. 2017), which may represent remnant building blocks of the outer solar system. Mixtures of these three components in ¹⁵N/¹⁴N–³⁶Ar/¹⁴N space are shown in Figure 6, with values summarized in Table 3.

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This model demonstrates that a mixture of bulk 67P, N₂, and NH₃ ices cannot reproduce present-day Titan's atmosphere in terms of N isotopes and ³⁶Ar/N, unless additional fractionating processes are invoked. The N₂–NH₃ mixing curves in Figure 6(a) show that a mixture of cometary N₂ and NH₃ can reproduce the nitrogen isotope ratio of Titan's atmosphere, but this mixture results in an ³⁶Ar/¹⁴N ratio that is much higher than the measured ratio at Titan (Niemann et al. 2010). In contrast, for nominal parameter values an approximate 50/50 mixture of cometary organics with NH₃ would cleanly reproduce both the N isotopes and the ³⁶Ar/N ratio of Titan's atmosphere. Figures 6(b) and (c) show the effects of variation in the starting N isotopic composition of accreted organics across the range of isotope ratios adopted from Figure 5. The variation in the ³⁶Ar/¹⁴N ratio of the organics shown in Table 3 does not produce visible changes in Figure 6. Without additional data from outer solar system samples, a more in-depth assessment of the uncertainty on ³⁶Ar/¹⁴N ratio of organics is not practical.

Depending on the general temperature regime of the Saturnian subnebula and Titan's interior, different N-bearing reservoirs may have contributed to Titan's atmosphere. Four general cases are presented in Table 4, and the corresponding regions in ¹⁵N/¹⁴N–³⁶Ar/¹⁴N space are labeled in Figure 7. In Case 1, all N-bearing materials are retained during accretion in a cold subnebula. Organic N remains sequestered in a cold interior, and only N₂ and NH₃ contribute to the atmosphere. Case 2 differs from Case 1 in that the interior is hot, resulting in volatilization of organic N. The resulting mixture of N₂, NH₃, and organic N is described by the central enclosed region of Figure 7. Mild heating in the Saturnian subnebula would be consistent with loss of N₂ and Ar-bearing ices from an initial cometary source, as previously suggested (Niemann et al. 2005; Alibert & Mousis 2007; Mousis et al. 2009b; Glein 2015). If the interior is cool, as in Case 3, the atmosphere may be formed from only NH₃, represented by the endmember point labeled "3." Case 4 is characterized by a mixture of NH₃ with volatilized N from organics heated in the interior, which corresponds to the organics-NH₃ mixing line marked "4" in Figure 7.

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From Figures 6 and 7, Titan's present-day atmosphere matches Case 4 or Case 2 most closely, which may support a heated interior. Case 1 may explain the data depending on the magnitude of the error (see dashed lines in Figure 6 for examples of error envelopes). However, additional geologic processes may also contribute to evolution of atmospheric ³⁶Ar/¹⁴N and ¹⁵N/¹⁴N ratios. For instance, sequestration of noble gases in atmospheric organics would cause a downward shift in Figure 6 (Jacovi & Bar-Nun 2008). On the other hand, condensation of heavy nitrogen in organic photochemistry products would shift a proto-atmosphere to the right in Figure 6 (Krasnopolsky 2016). If accreted organics were ¹⁵N-rich relative to the nominal distribution shown in Figure 5, then such evolutionary processes may be necessary to explain the N isotopes of Titan's atmosphere (Figure 6(b)).