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

Since its discovery in the first half of the 20th century, scientists have puzzled over the origins of Titan’s atmosphere. Current models suggest that atmospheric N2 on Titan may have originated from NH3-bearing ice with N-isotopic ratios similar to those observed in NH2 in cometary comae (14N/15N ∼ 136). In contrast, N2 ice appears to be too 15N poor to explain Titan’s atmosphere (14N/15N ∼ 168). Additionally, data from the Rosetta mission to comet 67P/Churyumov–Gerasimenko suggest that the Ar/N2 ratio of outer solar system planetesimals may be too high for a comet-like N2 source on Titan. The Rosetta mission also revealed an astonishing abundance of N-bearing complex organic material. While thermal fractionation of cometary sources during Titan accretion may explain the loss of N2- and Ar-rich ices, more refractory materials such as complex organics would be retained. Later heating in the interior may lead to volatilization of accreted organics, consistent with Cassini–Huygens measurements of 40Ar that suggest outgassing from the interior may have played a role in atmosphere formation. Here, we develop a three endmember mixing model for N isotopes and the 36Ar/14N ratio of Titan’s atmosphere, and consider the implications for the source of atmospheric methane. Our model suggests that Titan’s interior is likely warm, and that N from accreted organics may contribute on the order of 50% of Titan’s present-day nitrogen atmosphere.


Introduction
The origin of Titan's atmosphere has been an enduring mystery in planetary science. Despite its modest size-Titan is closer in terms of both mass and diameter to the Moon than to the Earth-Titan boasts a thick, N 2 -rich atmosphere that is ∼1.5 bars at the surface (Niemann et al. 2010). Based on N isotope data (Mandt et al. 2014) and the abundances of noble gases in Titan's atmosphere , the present paradigm argues that nitrogen was delivered in the form of NH 3 similar to cometary ices, and that photochemical or impact processes converted NH 3 to form present-day N 2 (Atreya et al. 1978;McKay et al. 1988;Sekine et al. 2011).
As part of this paradigm, comets are often hypothesized to be analogs of the building blocks of outer solar system bodies, including those in the Saturnian system (A'Hearn 2011; Mousis et al. 2014). Based on dynamical models, long period comets may be more appropriate analogs than short period comets like 67P/Churyumov-Gerasimenko (hereafter, 67P). However, data from long period comet Halley on the abundance and composition of refractory organics show similarities to those from 67P (Greenberg 1986;Kissel et al. 1986aKissel et al. , 1986bMcDonnell et al. 1986;Kissel & Krueger 1987), which is a short period comet. Alternatively, CI chondrites have been invoked as potential analogs for the rocky interior of Titan (Tobie et al. 2012;Glein 2015). Previous efforts along these lines have focused primarily on the accretion of cometlike ices, and have assumed a "chondritic" core. However, in situ evidence suggests that comets are C-rich, with abundant organic material, including complex organics (Kissel & Krueger 1987;Capaccioni et al. 2015;Altwegg et al. 2017; Bardyn et al. 2017;Fulle 2017). This carbonaceous material may be an important component of solid body interiors in the outer solar system, including a significant organic N reservoir (McKinnon et al. 1997(McKinnon et al. , 2008. In light of the Rosetta findings, we have undertaken a theoretical study of the possible contribution to Titan's atmosphere of volatiles that may be produced during heating of refractory cometary organics and subsequently outgassed from the interior. This study builds on previous work by Tobie et al. (2012), who calculated that the reservoir of organic N in Titan's interior based on a CI chondrite composition of accreted rock would be massive enough to constitute a significant fraction of Titan's observed atmospheric N 2 . Their work also suggested that the abundances of primordial 36 Ar and 22 Ne in CI chondrites are sufficient to account for the reported abundances of these noble gases in Titan's atmosphere (see Glein 2017 for a different perspective). In the present paper, we update these numbers to account for recent cometary data, we consider the temperature dependence of volatile N species generation from refractory organic matter, we examine the implications of organic pyrolysis on the abundance and isotopic characteristics of atmospheric methane, and we introduce new constraints on the outgassed N from dual considerations of the 15 N/ 14 N and 36 Ar/N ratios in Titan's atmosphere.

Nitrogen Reservoirs
To estimate the rock-to-ice mass ratio at Titan, we consider the densities of its components, including water (both solid and liquid), rock, and organics. We use a density of 1.2 g cm −3 as the average of all water+ice phases. For the refractory material, it is possible to reproduce the reported core density of ∼2.55 g cm −3 (Iess et al. 2010) with an assumed 45 wt.% organic material and 55 wt.% rock. To do so, we use 2.2 g cm −3 , the density of graphite, for all organic phases, and 2.9 g cm −3 , the grain density of CM chondrites (Consolmagno et al. 2008), for the rock. Titan's total radius is 2575 km (Lindal et al. 1983;Jacobson et al. 2006;Iess et al. 2010), and its core radius is inferred to be between 2050 and 2100 km (Iess et al. 2010). This yields a core volume fraction of ∼0.5, equivalent to a core mass of approximately (9.2-9.9)×10 22 kg. The corresponding ice shell mass is (3.9-4.3)×10 22 kg. Combining these values, we find a rock-to-ice mass ratio between 2.2 and 2.5. These values are consistent with the bulk density of Titan, 1.88 g cm −3 (Jacobson et al. 2006).
This rock-to-ice mass ratio falls within the range of dust-toice mass ratios suggested for 67P. Different assumptions and methods of estimating the rock-to-ice (or dust-to-ice) ratio have been utilized at 67P, resulting in a range of values. Based on the estimated density of refractory grains, the observed bulk density of 67P, and assumptions about the range of possible bulk porosities, Pätzold et al. (2016) calculated a dust-to-ice mass ratio greater than ∼0.1 but less than 11, where dust is defined as the combination of refractory organics and mineral phases. The Grain Impact Analyser and Dust Accumulator instrument team inferred a dust-to-ice mass ratio of 4±2 based on the abundance of dusty grains in the coma and the water production rates observed by the Microwave Instrument for the Rosetta Orbiter (Gulkis et al. 2015;Rotundi et al. 2015). Here, we use an estimated rock-to-ice mass ratio of 2.3 for Titan, which is consistent with cometary data and Titan density and volume constraints.
Organic material is an abundant component of refractory cometary material. The organic constituent may represent approximately 50% of the dust by mass (Greenberg & Li 1999), which is consistent with data collected at comet Halley (Kissel & Krueger 1987). Data from the Cometary Secondary Ion Mass Analyser (COSIMA) instrument at 67P support an average of 45 wt.% organic matter in the dust . Here, we assume that 45% by mass of the dust is carbonaceous in nature.
Insoluble organic matter (IOM) from carbonaceous chondrites can be considered the best available analog for the composition of refractory cometary organics. X-ray absorption near edge spectroscopy analyses of heavy organics in cometary grains collected from 81P/Wild 2 by the Stardust mission yield spectra that are similar to those from both IOM (Sandford et al. 2006;Cody et al. 2011) and interplanetary dust particles (IDPs), some of which are hypothesized to originate from comets (Brownlee et al. 1995;Joswiak et al. 2000;Busemann et al. 2009). These spectra indicate the presence of various functional groups, including aromatic carbon, carbonyls (C=O), and carbamates (N-C=O) (Sandford et al. 2006;Cody et al. 2011). COSIMA data demonstrate that the mass spectrum of IOM from the Murchison meteorite is similar to those from dust grains at 67P (Fray et al. 2016). Murchison IOM may therefore serve as an analog for refractory organic molecules at 67P.
Based on the assumption that IOM and cometary refractory organics are similar in terms of bulk chemistry, we calculate the total organic N inventory accreted by Titan. Titan's total mass is 1.3×10 23 kg (Jacobson et al. 2006). Using a rock-to-ice mass ratio of 2.3 from above yields a total non-ice mass of 9.4×10 22 kg. Of this mass, we assume 45 wt.% refractory organic material, for a total accreted organic mass of 4.2×10 22 kg.
The composition of IOM varies from one chondrite group to another (Alexander et al. 2007). However, the key constraint from IOM, aside from its general behavior at elevated temperatures, is the N/C ratio. Measurements from IDPs suggest that their N/C ratio is <0.1 (Keller et al. 1995). COSIMA measurements exhibit an average N/C atomic ratio of 0.035 (Fray et al. 2017), comparable to measurements by PUMA-1 at comet Halley (Jessberger et al. 1988 (Okumura & Mimura 2011), which gives the same N/C ratio as cometary organics measured by COSIMA. This stoichiometry has an intermediate N/C ratio compared to other CM and CR chondrites (Alexander et al. 2007). Our adoption of a value of 2.8 wt.% N for Titan's accreted organics leads to an N/C molar ratio of 0.035 and 1.2×10 21 kg of N accreted by Titan in refractory organics.
To calculate the reservoir of N from N-bearing ices, we consider three cases, which are summarized in Table 1. In the first two, we use relative abundance data from the Rosetta Orbiter Spectrometer for Ion and Neutral Analysis for most volatiles at 67P from Le Roy et al. (2015), and for N 2 at 67P from Rubin et al. (2018). Relative volatile abundances differ depending on the orientation of the spacecraft near the summer or winter hemisphere of 67P (Le Roy et al. 2015). Calculations from both data sets are presented here; note that thermal fractionation effects may be reduced at the summer hemisphere. Scaling to the estimated mass of ice at Titan, we calculate (8.4-9.7)×10 19 kg N derived from accreted ices using data from the winter and summer hemispheres, respectively. For N 2 , we use the lower limit from Table 1 for Notes. * Data from 67P are from the Rosetta Spectrometer for Ion and Neutral Analysis (ROSINA) mass spectrometer, which cannot distinguish between HCN and HNC. Data from Hale-Bopp are from spectroscopy, which can distinguish between these species. a The N 2 /CO ratio is from Rubin et al. (2015), who observed that the N 2 /H 2 O ratio is much more variable. b This value represents an upper limit based on values from Cochran et al. (2000). See the text for further discussion. The N 2 /CO ratio is used together with the CO/H 2 O ratio to derive the N 2 /H 2 O ratio. c The N 2 /H 2 O ratio given is the bulk estimate from Rubin et al. (2018).
References.Le Roy et al. (2015) and references therein; Rubin et al. (2015Rubin et al. ( , 2018. the winter hemisphere and the upper limit for the summer hemisphere; this approach encompasses the full compositional range. Alternatively, we consider the icy composition of comet Hale-Bopp. As a long period comet with a single perihelion event in the last ∼4600 yr (Bailey et al. 1996), comet Hale-Bopp should be more primitive than 67P. Cochran et al. (2000) reported an upper limit constraint on the + + N CO 2 molar ratio at comet Hale-Bopp of 9.9×10 −5 . Depending on the photoproduction rates of + N 2 and CO + , the neutral ratio may be greater by a factor of up to two (Cochran et al. 2000). Using data compiled in Le Roy et al. (2015) for major volatiles in comet Hale-Bopp and a N 2 /CO ratio of 2.0×10 −4 , the same calculation applied above to 67P yields a total mass of N from Hale-Bopp ices of 2.3×10 20 kg.
For comparison, the total vertically integrated mass of Titan's atmospheric N 2 and CH 4 is about 9.2×10 18 kg, approximately 9×10 18 kg of which is N 2 (Niemann et al. 2010;Tobie et al. 2012). The accreted refractory organic and icy N reservoirs are both more massive by orders of magnitude than the present-day atmospheric N (Figure 1). Tobie et al. (2012) reported that ∼20 times the present-day atmospheric mass of N could have been accreted in organic material; here, our estimate of ∼133 times the present-day atmospheric mass of N reflects a cometary (rather than chondritic) heritage.

Thermal Volatilization
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×10 20 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 timedependent outgassing depths are shown in Figures 2(a) and (b).
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, 14 N/ 15 N and 36 Ar/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 presentday 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 40 Ar mixing ratio near the top of the atmosphere of (7.1 ± 0.1)×10 −6 (Waite et al. 2005). The mixing ratio of 40 Ar increases in the lower atmosphere to (3.35 ± 0.25)×10 −5 (Niemann et al. 2010). This suggests approximately 3×10 14 kg of atmospheric 40 Ar. From Tobie et al. (2012), Titan's interior may contain approximately 5×10 15 kg of 40 Ar assuming chondritic abundances of 40 K. 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 40 Ar 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.

Nitrogen Speciation
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 N 2 , NH 3 , and + NH 4 , which are expected to be the dominant volatile compounds. If so, the fraction of N that exists as N 2 will depend on temperature (T), pressure (P), oxygen fugacity ( ) f O 2 , pH, and the moles of N per kg of H 2 O (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 . Calculations were performed using water density values from Zhang & Duan (2005) and the dielectric constant from Sverjensky et al. (2014). In general, N 2 is favored by higher temperatures, lower pressures, higher oxygen fugacity, higher pH, and a higher N molality.
To demonstrate quantitative speciation relationships, we choose the f 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 FMQ O 2 (Glein et al. 2018; see also Shock & McKinnon 1993). Since N 2 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 N 2 is favored by higher ΣN. From Section 2, Titan's total core mass is (9.2-9.9)×10 22 , which yields a core water mass of (5.5-5.8)×10 21 kg. Also from Section 2, the total atmospheric nitrogen mass is 9×10 18 kg, corresponding to 6.4×10 20 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 H 2 O. Here we use ΣN=10 −2 moles N/kg H 2 O. 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 N 2 , NH 3 , and + NH 4 under plausible geochemical conditions still allows for a sufficient N 2 reservoir to supply a significant fraction of Titan's atmosphere.

Methane Production
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 N 2 /CH 4 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.% N 2 , with only a minor CH 4 contribution (e.g., Table1 of Krooss et al. 1995). Pyrolysis of extraterrestrial IOM up to temperatures of 550°C yields 3266 ng of CH 4 per mg of IOM (Okumura & Mimura 2011). From the above estimate of a total organic mass of 4.2×10 22 kg, this is equivalent to 3.5×10 20 kg of CH 4 . Assuming that CH 4 outgases at the same efficiency as N 2 , 6% from Section 3.1, this corresponds to a mass of 8.2×10 18 kg of outgassed CH 4 . From Section 2, the current mass of atmospheric CH 4 at Titan is approximately 2×10 17 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 × 10 9 kg/yr), our estimate for the mass of outgassed CH 4 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×10 11 molecules of methane m −2 s −1 (Bell et al. 2014), which corresponds to (1.2-1.3)×10 16 kg of methane using a surface area of 8.3× 10 7 km 2 (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×10 18 kg of methane that must be accounted for, equivalent to a C mass of 6×10 18 kg. To estimate the equivalent average global depth of organic Values shown correspond to a pressure of 10 kbar at the FMQ buffer with a total N concentration of 10 −2 molal, taken one log unit above neutral pH. The a NH 3 = a NH + 4 dividing lines in Figure 3 are analogous to the point at which the NH 3 and NH 4 + curves intersect, but for the conditions shown. However, for a N 2 = a NH 3 in Figure 3, the N 2 molal fraction is double the NH 3 molal fraction; the same is true for NH 4 + . 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×10 7 km 2 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).

Methane Isotopes
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 CH 4 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 CH 4 and M 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  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 Using Equations (1)-(5) and the values tabulated in Table 2 Glein 2015), and that primitive ice in the Saturnian system may have been close to VSMOW in terms of hydrogen isotopes. 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×10 21 kg and an ice hydrogen reservoir of (1.55-4.13)×10 21 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 a -

CH H O 4 2
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 40 Ar (∼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 ). 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 ). 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 , 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 12 C/ 13 C 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 12 C/ 13 C=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.

N Isotopic and 36 Ar/N Constraints on the Origin of Titan
Atmospheric N

N Isotopes
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 14 N/ 15 N value for N 2 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(Mandt et al. , 2014, and is broadly consistent with nitrogen isotopes in cometary comae, including CN (140-172; Manfroid et al. 2009) and NH 3 (136; Shinnaka et al. 2016).
Isotopic data for our cosmochemical model are drawn from laboratory measurements and spectroscopic observations. For N 2 , we use a 14 N/ 15 N 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 ( 14 N/ 15 N=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 NH 2 in cometary comae, which is hypothesized to be a daughter product of native NH 3 , suggest much lower isotopic ratios ( 14 N/ 15 N∼136; Shinnaka et al. 2016). These values are more similar to that observed in Titan's atmosphere at the surface ( 14 N/ 15 N=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 NH 3 by photochemical formation of HCN in Titan's atmosphere, sequestering 15 N in nitriles over time. This model predicts a primordial 14 N/ 15 N 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 15 N in nitriles would halt.
Defining the N isotope ratio for refractory organics is somewhat less straightforward than for N 2 and NH 3 . 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. 2007Alexander et al. , 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 15 N-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  Alexander et al. (2007) 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 N 2 (441; Marty et al. 2011) and values inferred for cometary NH 3 (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(McKinnon et al. , 2008.

36 Ar/N Ratio
Consideration of the abundance of 36 Ar in Titan's atmosphere provides further constraints on the origin of atmospheric N 2 . The abundances of N 2 and 36 Ar in the coma of comet 67P are correlated , 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 36 Ar and N 2 may have had similar condensation behavior in the protoplanetary disk (Owen 1982), 36 Ar and NH 3 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 N 2 clathrate condense below 60 K (Hersant et al. 2001(Hersant et al. , 2004Alibert & Mousis 2007). Ar and N 2 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) 36 Ar/N ratio for the NH 3 endmember of our mixing model (10 −10 ). Similarly, we adopt the 67P 36 Ar/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 N 2 .
What about the 36 Ar/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 3 He/ 4 He and 4 He/ 20 Ne 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 36 Ar/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 N 2 (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).

Mixing Model
For our Titan atmosphere mixing model, we adopt three different endmembers. NH 3 and N 2 are chosen as endmembers because together they represent the most abundant volatile N-bearing species in the protoplanetary disk, with N 2 dominating the gas phase and NH 3 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 , which may represent remnant building blocks of the outer solar system. Mixtures of these three  Figure 6, with values summarized in Table 3.
This model demonstrates that a mixture of bulk 67P, N 2 , and NH 3 ices cannot reproduce present-day Titan's atmosphere in terms of N isotopes and 36 Ar/N, unless additional fractionating processes are invoked. The N 2 -NH 3 mixing curves in Figure 6(a) show that a mixture of cometary N 2 and NH 3 can reproduce the nitrogen isotope ratio of Titan's atmosphere, but this mixture results in an 36 Ar/ 14 N 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 NH 3 would cleanly reproduce both the N isotopes and the 36 Ar/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 36 Ar/ 14 N 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 36 Ar/ 14 N ratio of organics is not practical.

Influence of Nebular and Internal Processes
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 15 N/ 14 N-36 Ar/ 14 N 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 N 2 and NH 3 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 N 2 , NH 3 , 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 N 2 and Ar-bearing ices from an initial cometary source, as previously suggested ; Figure 6. Three endmember mixing plots for 15 N/ 14 N and 36 Ar/ 14 N ratios. The endmembers are N 2 , NH 3 , and organic N. The solid lines show the nominal mixing curves, while the dashed lines show the uncertainty envelope on measurements. Errors on N 2 measurements are within the symbol. The crosses show 10% increments in the organic N contribution. Error bars are shown for Titan's atmosphere; horizontal error bars are within the size of the marker. Data and their sources are given in Table 3. (a) Mixing lines using the mean N isotopic composition of organics. (b) Mixing for isotopically heavy organics, with a 14 N/ 15 N ratio of 160. Symbol labels are the same as in 6(a). (c) Mixing for isotopically light organics, with a 14 N/ 15 N ratio of 320. Symbol labels are the same as in 6(a). 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 NH 3 , represented by the endmember point labeled "3." Case 4 is characterized by a mixture of NH 3 with volatilized N from organics heated in the interior, which corresponds to the organics-NH 3 mixing line marked "4" in Figure 7.
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 36 Ar/ 14 N and 15 N/ 14 N 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 15 N-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)).

Conclusions
In light of new data from the Rosetta mission regarding the high abundance of refractory organic material and its similarity to other primitive extraterrestrial organics, we have investigated the sources of N at Titan and conclude that organics may have played an important role in the formation of  Balsiger et al. (2015). c Shinnaka et al. (2016). d Negligible (but nonzero to plot the logarithm) value based on the condensation behavior outlined in Hersant et al. (2001).    Table 4. Case 1 corresponds to the upper line showing mixing between N 2 and NH 3 . Case 2 corresponds to the enclosed region. Case 3 corresponds to the NH 3 endmember point. Case 4 corresponds to the lower line showing mixing between organics and NH 3 . The mixing lines shown are the generalized version of the models shown in Figure 6; readers are referred to Figure 6 for quantitative constraints and estimates of uncertainty.
Titan's atmosphere. Laboratory work on analog organics from chondrites indicates that at temperatures above ∼200°C, IOM decomposes to produce more volatile species. These relatively low temperatures and high abundance of complex organics suggest that internal heating of refractory organics may play an important role for volatile generation inside icy worlds in the outer solar system. To test this idea, we have estimated the sizes of N reservoirs at Titan, modeled depth-dependent production of volatile N in Titan's rocky core, examined the implications for atmospheric methane at Titan, and assessed the role of refractory organics in establishing the N isotope and 36 Ar/N ratios of Titan's atmosphere. We find that outgassing of volatiles within ∼300 km of the ice-core interface may be sufficient to supply the ∼50% contribution to Titan's atmosphere suggested by isotopic considerations. Isotopic and noble gas constraints suggest that NH 3 and refractory organics may have been the dominant sources for Titan's atmospheric N. This mixture may be the result of accretion of material from a warm subnebula followed by heating of organics in Titan's interior. Future measurements of the Xe and Kr mixing ratios and their isotopic compositions in Titan's atmosphere as well as improved structural and internal heating models and greater understanding of the nature and extent of cryovolcanism at Titan will provide important constraints to test this model. Similarly, future noble gas measurements at Pluto and Triton will provide tests of the applicability of this model to other outer solar system bodies that may have accreted abundant organic material. This project was supported by NASA Rosetta funding (JPL subcontract 1296001) and Southwest Research Institute internal grant 15.R8756. C.R.G. was supported by the NASA Astrobiology Institute through its JPL-led team entitled Habitability of Hydrocarbon Worlds: Titan and Beyond. We thank Y. Sekine for valuable comments that improved the manuscript.