The solubility of 40Ar and 84Kr in liquid hydrocarbons: Implications for Titan's geological evolution



[1] The solubility of argon and krypton in methane and ethane has been experimentally determined at Titan-relevant temperatures. At typical Titan surface temperature (94 K), argon and krypton solubilities are very large (47% in methane and 15% in ethane for Ar, 29% in methane and 43% in ethane for Kr), making liquid alkanes on Titan an important potential reservoir of 40Ar and other noble gases. Large subsurface reservoirs of liquid ethane and methane could be sufficient to trap much of the argon outgassing from Titan's interior, which can help explain the discrepancy between the potential amount of 40Ar produced inside Titan's interior and the amount observed in the atmosphere by Cassini-Huygens. Consequently, on Titan, liquid hydrocarbons may function as a buffer in the outgassing of volatiles from the interior, and they may strongly influence the evolution of the atmosphere's composition through the release of soluble gases upon evaporation and/or intake upon condensation.

1 Introduction

[2] Before the Cassini/Huygens mission arrived at Saturn in 2004, it was believed that an ocean of hydrocarbons covered Titan's surface. This would explain the specular reflection identified during Earth-based radar observations [Campbell et al., 2003] and provide the methane reservoir that can explain the amount of methane in its atmosphere. However, the first Cassini images, both at radar and optical wavelengths, dramatically altered this picture, revealing a predominantly solid surface with a wealth of geological features including impact craters, mountains, valley networks, and dune fields. In addition, radar images of the north pole of Titan show a number of sharp-edged, dark features, most likely lakes of liquid hydrocarbons [Stofan et al., 2007]. Ethane has been spectrally identified in Ontario Lacus [Brown et al., 2008]. Methane cannot be identified by remote sensing in the lakes because of its presence in the atmosphere. Its presence is predicted by 3-D global circulation models (GCMs) that simulate the methane cycle in Titan's atmosphere [Schneider et al., 2012]. At Titan's surface pressures and temperatures, a mixture of liquid methane and photochemically produced ethane is the most likely composition of the lakes [Cordier et al., 2009]. This mixture serves as a solvent for gases and the complex mixture of photochemical products formed in the upper atmosphere of Titan, which eventually fall to the surface.

[3] Three noble gas isotopes (40Ar, 36Ar, and 22Ne) have been identified in Titan's atmosphere by the GCMS (Gas Chromatograph Mass Spectrometer) onboard the Huygens probe [Niemann et al., 2010]. 40Ar is produced by the decay of 40K, which is the main long-lived radioactive element responsible for the volumetric heating of planets and moons. The presence of 40Ar in the atmosphere is an indicator of exchange processes between the interior and the surface since K is contained in the silicate fraction of the icy moons [Atreya et al., 2006]. It further suggests interaction between the silicates and water-ice or liquid water early in Titan's history [Castillo-Rogez and Lunine, 2010] and is an important tracer used to determine vertical mixing in the atmosphere [Lavvas et al., 2008a, 2008b]. The amount of 40Ar on Titan is proportionally about half the terrestrial atmospheric amount, following Atreya et al. [2006]. The amount of 36Ar in Titan's atmosphere is unexpectedly low compared to nitrogen, which led Atreya et al. [1978] to suggest that atmospheric N2 comes from the photolysis of NH3. 22Ne has been tentatively observed [Niemann et al., 2010] at a mole fraction of 2.8 (±2.1) × 10−7. Although 20Ne should be more abundant, it is not observed because the Huygens GCMS mass spectrometer cannot distinguish between peaks due to 20Ne+ and the more abundant 40Ar2+. The other noble gases, krypton and xenon, were not detected by the Huygens probe to a mixing ratio limit of 10−8 [Niemann et al., 2010]. Several explanations have been offered for the lack of krypton and xenon in Titan's atmosphere, including trapping in clathrates [Mousis et al., 2011; Thomas et al., 2008] and trapping in aerosol particles [Jacovi and Bar-Nun, 2008]. Here we explore an alternative scenario for the low amounts of noble gases in the atmosphere: trapping in hydrocarbon lakes and/or subsurface liquid alkane reservoirs.

[4] Indeed, the presence of liquid hydrocarbons on the surface of Titan naturally motivates questions about the solubility of surface materials and atmospheric species in the liquid. The solubilities of the rare gases Ar Kr and Xe are of particular interest on Titan as the lakes are potentially large sinks for these species. We have conducted experimental measurements on the solubility of Ar and Kr in liquid methane and ethane under simulated Titan conditions. We present our experimental results and describe their relevance to Titan's geology and evolution but do not attempt a theoretical treatment of the effect of temperature on solubility, which is beyond the scope of this paper. Unlike argon, the amount of krypton on Titan is small, and its solubility in liquid hydrocarbons probably does not have important implications for Titan's evolution. Krypton solubility measurements were performed in order to elucidate the parameters controlling rare gas solubilities in ethane and methane and assess the lakes' potential for dissolving krypton. We present experimental data indicating a very high solubility for argon and krypton in liquid ethane and methane. While the surface lakes likely do not contain sufficient argon to explain the anomalously low atmospheric value, subsurface reservoirs without substantial connection to the surface could prevent significant argon from outgassing from the interior to the atmosphere.

2 Experimental Setup and Results

[5] A diagram of the experimental setup is given in Figure 1a. Solubilities are measured as follows. Methane (Matheson 99.97%) or ethane (Aldrich ≥99%) is condensed in a Pyrex test tube held at 94 K in a custom-built temperature-controlled dewar cooled with liquid nitrogen. After approximately 2 mL of liquid is condensed, argon (Airgas 99.999%) or krypton (Airgas 99.995%) is bubbled through the liquid from a 1/16 in. stainless steel tube. The liquid is sampled through a fused silica capillary (1 m in length with a 20 µm inner diameter (I.D.) into a small vacuum system fitted with an Stanford Research Systems (SRS) 200 Residual Gas Analyzer (RGA) mass spectrometer and a Bayard-Alpert ionization gauge. Ethane (30 m/z), methane (16 m/z), argon (40 m/z), and krypton (84 m/z) signals are monitored as a function of time in the mass spectrometer. Figure 1b shows typical experimental data for argon in ethane. The argon signal rises rapidly before reaching equilibrium. This is taken as an indication of saturation, and the ratio between the argon and ethane (or methane) pressures is then the ratio of argon in methane or ethane in the liquid, respectively. In the data shown in Figure 1b, the temperature is raised twice, and a new equilibrium is obtained at each temperature.

Figure 1.

(a) Schematic of experimental apparatus. (b) Argon and ethane pressures in the mass spectrometer for a typical experimental run. Temperature changes lead to new equilibrium Ar saturations.

[6] The sensitivity of the mass spectrometer to each gas is calibrated by sampling pure gaseous methane, ethane, argon, or krypton into the mass spectrometer. The current measured by the mass spectrometer for a particular mass is divided by the pressure measured by the ion gauge, after dividing by the appropriate gas correction factor (ethane 2.60, methane 1.40, argon 1.29, and krypton 1.94). Errors are estimated at 20%, primarily from the stated accuracy of the ion gauge.

[7] Solubilities of argon in liquid methane and ethane as a function of temperature are shown in Figure 2. The starred point is not an experimental measurement but represents the boiling point of argon, 87.3 K. A mole fraction of 1 is assigned here since the solubility curve must intersect this point, where liquid argon will begin to condense. At 94 K, the solubility of argon in liquid methane is 0.47 mol fraction and is 0.15 mol fraction in liquid ethane. The solubility of Ar in both methane and ethane decreases rapidly as the temperature increases. The solubility of krypton in liquid methane is 0.29 mol fraction and is 0.43 mol fraction in liquid ethane at 94 K. The value for argon in methane is consistent with, although slightly lower than, previous work that calculated solubility based on a nonideal solution theory [Hibbard and Evans, 1968]. Note that the methane and ethane solutions are most likely saturated in nitrogen, since the hydrocarbon is condensed under a 1 bar nitrogen atmosphere created as a result of boil-off from the liquid nitrogen cooling the dewar. This may explain the deviation from Hibbard and Evans [1968]. Nitrogen saturation is consistent with conditions on Titan as well, since Titan's atmosphere is predominantly nitrogen with a surface pressure of 1.5 bar.

Figure 2.

Solubility of argon in liquid methane and ethane as a function of temperature. The starred point is not an experimental measurement but represents the boiling point of argon. Dashed lines are exponential fits meant only to guide the eye. The solid line is the solubility of argon in liquid methane from Hibbard and Evans [1968].

[8] Argon is nearly three times as soluble in liquid methane as in liquid ethane at typical Titan surface temperature (94 K). Krypton, in contrast, is more soluble in ethane than in methane. The large difference in solubility between argon in methane and ethane can be explained by the value of the Hildebrand solubility parameter [Gerrard, 1976]. The Hildebrand parameter is the square root of the energy of vaporization per cubic centimeter, the amount of energy necessary to transfer a unit volume of molecules away from their neighbors to infinite separation. Two species are likely to be soluble if their Hildebrand parameters are close in value. According to Dubouloz et al. [1989], the values of the solubility parameter for C2H6, CH4, and Ar at 101 K are 9.07, 6.23, and 5.80, respectively. Ar should therefore be much more soluble in methane than in ethane, as we observe. The Hildebrand parameter for Kr is 9.3 (94 K, using thermodynamic properties for solid Kr) [Ferreira and Lobo, 2008]. This is in accord with the increased solubility of krypton in ethane relative to methane.

3 Discussion

3.1 Hydrocarbon Lakes and Alkanifers as a Trap for Noble Gases on Titan

[9] The tropospheric mixing ratio of 40Ar is 3.39 ± 0.1 × 10−5 mol fraction from 18 km to the surface according to the measurements made by the GCMS instrument on the Huygens probe [Niemann et al., 2010]. The value measured by the Ion and Neutral Mass Spectrometer instrument above 1100 km altitude is 7.1 ± 0.1 × 10−6 mol fraction [Waite et al., 2005]. Using the model described in Lavvas et al. [2008a, 2008b], the total mass of 40Ar in Titan's atmosphere is 5.4 × 1014 kg (540 GT), about 4.95 × 10−5 Titan's atmospheric mass and 4 × 10−9 Titan's mass.

[10] The total mass of 40Ar depends on the amount of 40K initially present in the silicate portion from the formation of Titan. The half-life of 40K is 1.277 Gyr, which implies that 82.6% of 40K has decayed at present. Eleven percent of the decay of 40K produces 40Ar. Assuming that Titan's primordial 40K content in its silicate fraction is identical to that of the Earth, the total mass of 40Ar that has been produced is on the order of 2–2.7 × 1015 kg. This is a factor of 4 larger than the amount of 40Ar present in the atmosphere, presenting a discrepancy between the expected amount of argon on Titan and the amount observed by Cassini-Huygens.

[11] We constructed a simple model that predicts lake composition based on the assumption that the lakes are in equilibrium with the atmosphere [similar to Cordier et al., 2010], for comparison with argon values at saturation. The ideal solution theory is expressed through Raoult's law in this case:

display math(1)

where Pi is the partial pressure of a component i in the atmosphere, Yi its atmospheric mole fraction, Patm the atmospheric pressure, Xi its mole fraction in the solution, and Psat its saturation vapor pressure at the relevant conditions. Using the atmospheric abundances of Ar and Kr (Kr being under Huygens' GCMS detection limit, 1 × 10−8) and their saturation vapor pressures of 1.7 and 4.5 × 10−2 bar at 92 K, respectively, suggest that Ar and Kr could be concentrated in the lakes at mole fractions of 4 × 10−5 and <3 × 10−7, respectively. These values are much lower than their solubility.

[12] The volume of liquids Vlakes can be approximated by multiplying the surface of lakes Slakes by their average depth dlakes. Titan's lakes cover an area of 400,000 km2 at the present time [Hayes et al., 2008; Sotin et al., 2012; Stofan et al., 2007]. Then the number of moles of hydrocarbons Nhydro can be calculated as:

display math(2)

where mhydro is the mass of hydrocarbon contained in the lakes, Mhydro is their molar mass, and ρhydro is the liquid hydrocarbon density at Titan's conditions.

[13] Knowing the molar fraction of Ar dissolved in the lakes XAr, we can then calculate the corresponding mass of 40Ar mAr as follows:

display math(3)

where NAr is the number of moles of Ar dissolved in the liquids and MAr its molar mass.

[14] The typical density of liquid hydrocarbon at Titan's conditions is ρhydro ~ 650 kg m−3 [Lorenz et al., 2008a], MAr = 40 g mol−1, Slakes = 4.2 × 1011 m2. We assume a 65% C2H6-35% CH4 composition for the hydrocarbon mixture, whose evaporation rate [Wagner et al., 2013] matches well those expected from Cassini data [Hayes et al., 2011; Mitri et al., 2007] with a molar mass of Mhydro = 25.1 g mol−1. All parameters fixed, we calculated the mass of 40Ar dissolved in the lakes as a function of their depth for four different molar fractions of Ar in the lake fluid: (i) 4 ppm, based on the model of Cordier et al. [2009]; (ii) 30 ppm, which is the equilibrium value using Raoult's law for ideal solutions, considering the 40Ar atmospheric partial pressure and its saturation vapor pressure of 1.7 bar at 92 K; (iii) 15%, the Ar saturation value for liquid C2H6 found in this study; and ( iv) 47%, the Ar saturation value measured in liquid methane. The results of the calculations are shown in Figure 3.

Figure 3.

Mass of 40Ar dissolved in liquids as a function of depth of the lakes, which for values greater than 50–100 m is taken as a proxy for the depth to which liquids percolate the icy crust beneath. The current amounts of 40Ar present in the atmosphere are indicated by the thin solid black line. The grey shaded area and the thick dashed line represent the total range of 40Ar amounts possible for Titan and the expected amount, respectively. See text for details.

[15] At depths greater than ~100 m, it is likely that the depth value represents percolation within the crust beneath. Crustal porosity will reduce the volume of liquids since they can only percolate between grains. This is not taken into account in our calculations, because the porosity is not known on Titan, and modeling by Hayes et al. [2008], as well as laboratory experiments [Sotin et al., 2009], suggests that wetting will also occur laterally around the lakes, increasing Slakes and thus compensating for the reduction in liquid volume.

[16] The calculations shown in Figure 3 imply the following: (1) In the case of equilibrium with the atmosphere, the 4–30 ppm Ar expected in the lakes shows that the equivalent of all Titan's atmospheric argon can be dissolved in lakes 25–250 m deep. (2) Trapping all of Titan's accreted and radiogenic argon in liquid hydrocarbons could be achieved if alkane reservoirs (lakes + subsurface percolation) connected to the atmosphere extend a few hundred meters to 1–2 km below the surface. (3) Given the very large solubility of Ar and Kr in liquid hydrocarbons measured in this study, small hydrocarbon liquid pockets trapped within the crust and isolated from the atmosphere could also be a very important reservoir of noble gases outgassed from the interior, explaining the low abundance measured for Ar and the absence of detection of Kr and Xe. (4) These calculations suggest that the temporal evolution of the hydrocarbon lakes (evaporation, condensation, and percolation) and/or crustal reservoirs over seasons and geologic history on Titan may influence the atmospheric abundance of noble gases and other soluble volatiles. These volatiles may also be involved in reactions occurring over geologic time scales between liquid hydrocarbons and subsurface materials, as suggested by Choukroun and Sotin [2012] to explain Titan's shape and contribute to its hydrocarbon cycle.

[17] We have shown that the lakes do not require being extremely extended to contain large amounts of Ar. The same considerations would apply to Kr and Xe. The saturation vapor pressures of Ar, Kr, and Xe at 92 K are 1.7, 4.5 × 10−2, and 1 × 10−5 bar, respectively. Using the ideal solution model presented in section 'Degassing on Titan', and under the assumption that Titan's degassing in these three primordial species is identical to that of Earth, we can predict equilibrium concentrations in the lakes in 36Ar, Kr, and Xe on the order of 0.18, 0.25, and 88 ppm, respectively. Actual measurements in the atmosphere and the lakes by a future in situ mission would provide further constraints on the abundances of Kr and Xe and trapping/outgassing processes for noble gases.

3.2 Degassing on Titan

[18] It is instructive to compare outgassing on the terrestrial planets (Venus, Earth, and Mars) with outgassing on Titan, considering that the processes involved in the degassing history of Titan may be quite different than those invoked for the Earth. On the terrestrial planets, outgassing is achieved by the melting at depth of mantle rocks during their adiabatic decompression associated to convection. Then, melts migrate to form volcanic chambers, and magma eventually erupts and releases the gases trapped in the deep interior.

[19] For Titan, the situation is quite different. If silicate volcanism happens, then it is very likely that Titan is fully differentiated as is its Jovian cousin, Ganymede. This contradicts Titan's value of the moment of inertia, which is much larger than that of Ganymede [Iess et al., 2010]. Other models involve leaching of the silicates by late heating of an undifferentiated hydrated core [Castillo-Rogez and Lunine, 2010]. The fate of potassium in such a process is not clear.

[20] Table S1 in the supporting information gives the ratio of atmospheric 40Ar compared to the potential total 40Ar for the three terrestrial planets and Titan. Several possibilities can explain why only 27% of the potential 40Ar is in Titan's atmosphere:

  1. [21] The silicate fraction of Titan has not fully outgassed its argon—since argon is produced gradually, if outgassing stopped 3 Gyr ago, then the remaining argon is still trapped in the core;

  2. [22] Titan may have a deep liquid water ocean [Beghin et al., 2012; Iess et al., 2012; Lorenz et al., 2008b], and a large part of the argon is dissolved there. If we take 80% of the potential 40Ar that gives 2 × 1015 kg in a 100 km ocean whose mass is about 8 × 1021 kg, this results in a mole fraction of 3 × 10−7, which is very small compared to the solubility of argon in water at 0°C and room pressure (10−4). On the other hand, the presence of argon in the atmosphere seems to imply that the ocean was not able to dissolve all the argon during its transit from the deep interior to the atmosphere.

  3. [23] Argon has been trapped in subsurface pockets of liquid methane or ethane as the present laboratory experiments suggest.

[24] Scaled to Earth, the values of 36Ar, Kr, and Xe are 5.8 × 10−5, 3.4 × 10−9, and 1.5 × 10−10 in mole fraction, respectively (7.5 × 10−5, 1.03 × 10−8, and 7.2 × 10−10 in kg/kg atmosphere). They would be in the atmosphere if they degassed during the accretion period and had not escaped. One can use the terrestrial atmospheric ratios of 36Ar to Kr and Xe to estimate the extent of outgassing of other noble gases on Titan. This approach is equivalent to making the assumption that the same fractionation occurred due to escape in planetesimals that formed Titan and Earth compared to the solar nebula abundances. The 36Ar mole fraction in Titan's atmosphere is 2.06 × 10−7 [Niemann et al., 2010], which is a factor of 250 lower than the value found if scaled to Earth's abundance. This very low value can be explained by the escape of the primordial argon during the accretion process. The “scaled to Earth” atmospheric abundances for Kr and Xe would be 3.4 × 10−9 and 1.5 × 10−10, respectively. Both mole fractions are below the detection threshold of Huygens' GCMS of 1 × 10−8, raising the question of whether any differential trapping mechanism such as clathration or adsorption on aerosols is actually needed to explain the absence of detection of these two species. These processes, if they occur, would decrease the atmospheric concentrations of Kr and Xe in the atmosphere even more.

4 Conclusions

[25] We have measured the solubilities of argon and krypton in liquid methane and ethane.

[26] These values are both in accord with theoretical values derived from solution theory. The total volume of Titan's lakes is more than sufficient to trap enough argon to deplete the atmosphere. However, measurements of the mixing ratio of argon in Titan's atmosphere imply that the lakes contain orders of magnitude less argon than the solubility if the lakes are in equilibrium with the atmosphere. The presently observed lakes may trap all of Titan's argon if they and the area of the crust where liquids percolate extend down to a few hundred meters to 1–2 km. Deep liquid alkane reservoirs, isolated from the atmosphere, could function as a very efficient trap for argon and other noble gases on Titan since the solubilities are orders of magnitude larger than the amounts dissolved in equilibrium with the atmosphere. This can help explain the discrepancy between the expected amount of argon on Titan and the amount observed by Cassini-Huygens.

[27] In the broad sense, we show that, even in relatively small amounts, liquid hydrocarbons may be important buffers in the processes of volatile outgassing from the interior and may influence the atmospheric composition in soluble gases through condensation and evaporation cycles. Future measurements by Cassini, ground-based observations, and in situ missions, would provide further insights into the contribution of hydrocarbon reservoirs to the geochemical cycle of volatiles on Titan and help constrain models of Titan's global evolution.


[28] Support from the NASA Astrobiology Institute is gratefully acknowledged. This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Government sponsorship acknowledged.

[29] The Editor and authors thank Vincent Chevrier and an anonymous reviewer for their assistance in evaluating this paper.