Icarus 226 (2013) 1431–1437

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Icarus

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On the chemical composition of ’s dry lakebed evaporites ⇑ D. Cordier a, , J.W. Barnes b, A.G. Ferreira c a Université de Franche-Comté, Institut UTINAM, CNRS/INSU, UMR 6213, 25030 Besançon Cedex, France b Department of Physics, University of Idaho, Engineering-Physics Building, Moscow, ID 83844, USA c Departamento de Engenharia Quimica, Universidade de Coimbra, Coimbra 3030-290, Portugal article info abstract

Article history: Titan, the main satellite of , has an active cycle of methane in its troposphere. Among other evi- Received 10 March 2013 dence for a mechanism of evaporation at work on the ground, dry lakebeds have been discovered. Recent Revised 15 July 2013 Cassini infrared observations of these empty lakes have revealed a surface composition poor in water ice Accepted 22 July 2013 compared to that of the surrounding terrains—suggesting the existence of organic evaporites deposits. Available online 2 August 2013 The chemical composition of these possible evaporites is unknown. In this paper, we study evaporite composition using a model that treats both organic solids dissolution and solvent evaporation. Our Keyword: results suggest the possibility of large abundances of butane and acetylene in the lake evaporites. How- Satellites, surfaces ever, due to uncertainties of the employed theory, these determinations have to be confirmed by labora- Saturn, satellites Titan tory experiments. Titan, hydrology Ó 2013 Elsevier Inc. All rights reserved. Titan, surface Prebiotic environments

1. Introduction et al. (2010) reported evidences for active shoreline processes. Although evidence for short-term changes in the extent of Ontario For a long time the existence of liquid hydrocarbons at the sur- Lacus has been put forward (Turtle et al., 2011b), a subsequent face of Titan has been suspected (Sagan and Dermott, 1982; Lunine reanalysis came to the conclusion that there is no indication of lake et al., 1983; Lunine, 1993a,b). The dark features observed by Stofan extent changes in the Cassini dataset (Cornet et al., 2012). Hayes et al. (2007) in the north polar region were the first confirmed et al. (2011) noticed that some observed dry lakebeds in Titan’s lakes or seas of hydrocarbons. Subsequently, other evidence for arctic appear to be brighter than their exteriors in both nadir and the RADAR-dark areas’ lacustrine nature was found in the RADAR off-nadir observations, which suggests compositional differences. and IR ranges, to the extent that the existence of lakes/seas is However Hayes et al. (2011) were not able to exclude the possibil- now rather well established. In fact, the number of detected man- ity of an infiltration of liquids into a subsurface hydrologic system. ifestations (e.g. Turtle et al., 2011a,b) of an active tropospheric Barnes et al. (2011a) used a sample of several lakes and lakebeds methane hydrologic cycle is increasing. The lakes are expected to located in a region south of the . They obtained a strong take part in this cycle, providing methane and/or ethane to the correlation between RADAR-empty lakes and 5-lm-bright unit atmosphere through evaporation processes. interpreted as low-water ice content areas. In past years, the signature of lake evaporation has been ac- As mentioned by Barnes et al. (2011a) these observed dry lake tively researched. Already, Stofan et al. (2007) noticed features floors cannot be made only of sediments, indeed a pure sedimen- showing margins similar to those of established lakes but having tary origin of these deposits would produce lakebed showing a a RADAR surface backscatter similar to the surrounding terrain, 5-lm-brightness similar to that of their surrounding zones. One suggesting the occurrence of an evaporation process in the recent possible explanation proposed by Barnes et al. (2011a) consists past. Barnes et al. (2009) performed a detailed study of shoreline of evaporation of the solvent (here a mixture of methane and eth- features of , the largest southern latitude lake. These ane) yielding to the saturation of the dissolved solutes. The top authors interpreted the 5-lm bright annulus around Ontario Lacus layer of the resulting evaporites is being observed now in dry lake- as a dry, low-water ice content zone, possibly corresponding to a beds if this idea is correct. This paper is devoted to an exploration deposit of fine-grained organic condensates. These patterns, cre- of the evaporite scenario on the theoretical side. We have devel- ated by the shoreline recession, could have been caused by an oped a model allowing for the computation of the chemical compo- evaporation episode. In their study of the same system, Wall sition of such evaporites. This paper is organized as follows. In Section 2, we outline our ⇑ Corresponding author. model for calculating chemical composition of putative evaporite E-mail address: [email protected] (D. Cordier). deposits in dry lakebeds. Section 3 is devoted to evaporite

0019-1035/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2013.07.026 1432 D. Cordier et al. / Icarus 226 (2013) 1431–1437 Table 1 DHi;m Ti;m Solids assumed to be dissolved in the lake and some of their properties. The ln CiXi;sat ¼ 1 ð1Þ RTi;m T Hildebrand’s solubity parameter d has to be compared to the value for methane and ethane at the same temperature (i.e. 90 K), which are respectively 1.52 104 (J m3)1/ This relation can be found, for instance, in Section 8s–16 of the 2 4 3 1/2 4 3 1/2 and 2.19 10 (J m ) . For comparison purposes, for H2O d 5 10 (J m ) . textbook by Poling et al. (2007) (hereafter POL07). The physical sig- Species Precipitation rate d 104 Melting Enthalpy of nificance of Eq. (1) is the existence of a thermodynamic equilib- molecules (m2 s1) (J m3)1/2 temperature melting rium between the considered precipitated solid i and the liquid (K) (kJ mol1) solution. The enthalpy of melting is denoted DHi,m, whereas T HCN 1.3 108a 2.99 260.0 8.406 and Ti,m are respectively the current temperature of the lake and 7a C4H10 5.4 10 1.91 136.0 4.661 7a the melting temperature of molecule i; R is the constant of ideal C2H2 5.1 10 2.28 192.4 4.105 6a gases and Ci is the activity coefficient. Although Eq. (1) has previ- CH3CN 4.4 10 2.92 229.3 6.887 6a CO2 1.3 10 1.98 216.6 9.020 ously been used in several published works (Dubouloz et al., 1989, 6b C6H6 1.0 10 2.48 279.1 9.300 hereafter D89, and also C09, C10 and C12), we recall that it is

a Lavvas et al. (2008a,b). approximate and its validity will be discussed in Section 4. b Vuitton et al. (2008). As the thermodynamic computations in the frame of the reg- ular solution theory are uncertain (see C12) due to the lack of composition computations, and we discuss our results and con- knowledge of thermodynamic data, we have distinguished two clude in Section 4. cases: the approximation of the ideal solution for which all the Ci’s are equal to unity, and the non-ideal regular solution. 2. Model description In the case of an ideal solution, the molecules of the same spe- cies and those of different species interact with same intensity. We consider a portion of a Titan lake of uniform depth h that For a non-ideal solution model, the Ci’s are computed in the has a free surface of area S in contact with the atmosphere. For frame of regular solution theory (see D89, C09, POL07) in which the sake of simplicity, methane, ethane and nitrogen are consid- the intermolecular interactions of involved species are such that ered to be the only volatile compounds; they form a ternary mix- the resulting entropy of mixing is equal to that of an ideal solu- tion with the same composition: zero excess entropy, with the ture which will be our solvent. The presence of H2, Ar and CO is neglected as they have low abundances in the atmosphere and as volume of mixing at zero. However in contrast with ideal solu- tions, regular solutions have mixing enthalpy with nonzero val- a consequence in the solution; C3H8 and C4H8 are also not taken ues. The regular-solution theory provides a good and useful into account because C2H6 seems to be much more abundant and their behaviors should not be very different than that of ethane. semiquantitative representation of real behavior for solution In addition to the solvent chemistry itself, we considered species containing nonpolar components as is the case of the mixtures in the solid state under Titan’s surface thermodynamic conditions under study in this work and the results based on this theory that may dissolve in the solvent. In the following, for short, we will are in general considerably improved over those calculated by simply call these compounds ‘‘dissolved solids’’ or ‘‘solutes’’: they Raoult’s law. In the context of the mixtures studied here it is include all the species, except those belonging to the solvent (i.e., expected that even though results may not possess extreme methane, ethane and nitrogen). These supposed dissolved species accuracy they are also hardly ever very bad, providing a valu- are ultimately the products of the complex photochemistry taking able guide for future work. We emphasize that the Ci’s are place in the upper Titan atmosphere. In this work, we used the functions of Xi’s, a fact which leads to numerical complications. same list of solid compounds as in previous papers (Cordier The temperature T of the liquid remains unchanged during the et al., 2009, 2010, 2012 hereafter respectively C09, C10 and C12. whole evaporation process. Note, by the way, that for the tem- Note that Cordier et al. (2013) is an erratum of Cordier et al. peratures relevant (see Table 1 for melting temperatures values) (2009).) These species appear to be among the main products in our context, the right-hand side of Eq. (1) is negative, leading found by photochemical 1D-models of Lavvas et al. (2008a,b) and to mole fractions lower than the unity, at least in the case of an Vuitton et al. (2008); the list is displayed in Table 1. This list differs ideal solution. 1 The equilibrium solid-solution written as Eq. (1) must be com- from the list of species detected by CIRS (i.e.,CH4,C2H2,C2H4,C2H6, plemented by the Principle of Matter Conservation. If we denote C3H8,CH3C2H, C4H2,C6H6, HCN, HC3N, C2N2, CO, CO2 and H2O, see Vinatier et al., 2010) as CIRS observations relate to Titan’s strato- the total number of moles of all species at time t in the liquid by sphere and do not imply that these species reach the thermodynamic N(t); at time t +dt, one can write for a lake with surface area S conditions of their precipitation to the ground. In addition, some Nðt þ dtÞ¼NðtÞF S dt F S dt F S CH4 C2H6 N2 species (for instance C4H3,C4H4,C4H5; see Table 5 of Lavvas et al., X ideal 2008a) are included in models while they are not yet observed by dt XiðtÞ NðtÞXi;sat Nðt þ dtÞ ð2Þ Cassini instruments. Thanks to their melting temperatures ranging i;sat;tþdt between 136.0 K (C4H10) and 279.1 K (C6H6), all these molecules where FCH4 ; FC2 H6 and FN2 are the assumed respective evaporation are in solid state under the Titan’s surface conditions (T 90 K in 2 1 rates (in mole m s )ofCH4,C2H6 and N2. The terms containing the region of lakes; Jennings et al., 2009). Although it has still to the Fi’s represent the evaporation while the sum, which refers to be confirmed by laboratory experiments, the materials listed in Ta- species reaching the saturation at t +dt, corresponds to matter that ble 1 are theoretically predicted to be soluble in a mixture of meth- precipitates and deposits on the lake floor. ane and ethane. Indeed, the Hildebrand’s solubility parameters d’s The number of mole of species i available in the volume S H of for these solids (see Poling et al., 2007; Ahuja, 2009) are close to lake, at time t, is denoted by ni(t). Thus we arrive at the simple rela- the ethane value (see Table 1). We implement a numerical calcula- tion ni(t)=XiN(t). Our algorithm consists of several steps. For the tion for the dynamic composition evolution of liquid mixtures using first one, we compute N(0)(t +dt). This is an estimation of the total discrete timesteps. At each time t, the saturation mole fraction Xi,sat number of moles (in volume S H of lake) remaining after the time of each dissolved solid species i is computed via step dt during which only evaporation of methane, ethane and nitrogen is taken into account:

ð0Þ 1 N t dt N t F F F S dt: 3 Composite Infrared Spectrometer, an instrument onboard the Cassini spacecraft. ð þ Þ¼ ð Þð CH4 þ C2H6 þ N2 Þ ð Þ D. Cordier et al. / Icarus 226 (2013) 1431–1437 1433

From this, we can infer the corresponding mole fraction oration of CH4 and the evaporation of C2H6. Methane is known to be much more volatile than ethane. An order of magnitude of the ratio n ðt þ dtÞ Xð0Þ i 4 a ¼ F =F can be evaluated thanks to the Hertz-Knudsen i ¼ ð0Þ ð Þ evap C2H6 CH4 N ðt þ dtÞ (see Ward and Fang, 1999, and references therein): one finds that 4 aevap 10 for a temperature T ’ 90 K. In our model we fixed with ni(t +dt)=ni(t) for all species except those belonging to the solvent. If, as a first attempt, we work in the frame of the ideal solu- aevap to this value. The evaporation rate of nitrogen is scaled to the ð0Þ C2H6 one, in order to insure a N2 content in the liquid preventing tion theory, then we have to compare the Xi ’s to the mole fractions ideal it from freezing (see Mitri et al., 2007). Therefore, all the CH4 content at saturation (for an ideal solution) Xi;sat . The molecules for which evaporates on a short time-scale during which the time t is the criterion is fulfilled are presumed to precipitate. Their abun- sCH4 CH4 defined so that the evaporation rate F is constant. We emphasize dances are fixed to the saturation value CH4 that this operation is equivalent to an implicit non-linear re-scaling ideal Xiðt þ dtÞ¼Xi;sat ðonly species that saturateÞ; ð5Þ of time. A similar definition is adopted for tC2H6 , the ‘‘variable time’’

valid during ethane evaporation, as FCH4 FC2 H6 , the quantity of eth- and the total number of moles at t +dt in the volume S H is ane escaping the lake during methane evaporation, is negligible. This recomputed to be P way, all the details of the possible events (e.g., low or high humidity, ½1 X NðtÞðF þ F þ F ÞS dt strong winds) that could affect the evaporation rates can be ignored. sat i;sat PCH4 C2H6 N2 : Nðt þ dtÞ¼ ideal 1 satXi;sat ð6Þ 3. Evaporites upper layer composition calculation Finally, the abundances at t +dt of species that do not saturate can be easily derived First we build plausible chemical compositions relevant for a lake before its evaporation. Previous calculations made at thermo- niðtÞ dynamic equilibrium (D89, C09) correspond to an averaged com- Xiðt þ dtÞ¼ ð7Þ Nðt þ dtÞ position in time and space. Atmospheric precipitation rates are For a given species i that saturates, the rate of evaporite forma- likely to undergo substantial secular variations—this is supported tion is then given by by some Cassini observations (see for instance Turtle et al., 2011a). In addition, the flux of hydrocarbons falling from the atmo- ideal XiðtÞNðtÞX Nðt þ dtÞ sphere likely varies significantly from one location to another: in Fevapðt þ dtÞ¼ i;sat : ð8Þ i S dt the equatorial regions the presence of the fields indicates an arid climate while lakes, evidences for a wet weather, are lo- The chemical composition of the formed evaporite at time t +dt is cated in the polar regions. These tendencies are confirmed by Glo- given by bal Circulation Models (see for instance Fig. 4 of C12 based on Fevap t dt Crespin et al., 2008). Thus we have considered methane-poor and evap P i ð þ Þ X ðt þ dtÞ¼ evap : ð9Þ i -rich solvents, always containing a few percent of N2. Concerning j;satFj ðt þ dtÞ the solids possibly in solution, we used precipitation rates derived When the solution is considered as a ‘‘real’’ solution, i.e. the from 1D photochemical models by Lavvas et al. (2008a,b) and Vuit- activity coefficients are not taken to be equal to the unity and de- ton et al. (2008)—the precipitation rates are recalled in Table 1.We pend on the mole fractions, then stress that these rates have to be taken with caution because of the lack of micro-physics in the models. A compound that meets an Ciðt þ dtÞ¼CiðX1ðt þ dtÞ; X2ðt þ dtÞ; ...Þ: ð10Þ altitude where the temperature equals its condensation tempera- The scheme allowing the computation of evaporite composition ture rains out. In addition, 3D physical processes (mainly trans- when the solution is non-ideal is rather similar to that of the case port) are ignored, although they can affect significantly the of an ideal solution. However, there are some differences: the total amounts of solid hydrocarbons reaching the surface at a given number of moles N(t +dt) can no longer be computed with Eq. (6). place at a particular time. Two possibilities have been studied. Instead, if Nsat is the number of species saturating at t +dt, then we solve the system of (Nsat + 1) equations composed of Eq. (2) and the In Type 1 solids mixture, where the abundances of these solids Nsat equations similar to Eq. (1). The unknowns are N(t +dt) and have been scaled to atmospheric precipitation rates, the most nonideal the Nsat mole fractions at saturation Xk;sat . The resolution of that abundant species (i.e., HCN) has its mole fraction set to its value non-linear system is performed using a multi-dimensional New- at saturation (ideal solution case). This way, the precipitation ton–Raphson’s method (see Press et al., 1992). (i.e., saturation) of solids in solution in the liquid begins at the Several authors (Mitri et al., 2007; Tokano, 2005, 2009) have initial time. An assumed initial value below the saturation studied the dynamics of Titan’s lakes. They have used the bulk one, only delaying the starting time of precipitation, keeps the aerodynamical model, introduced for Earth’s climate model by final composition of the upper layer of evaporites unchanged. Fairall et al. (1996). In this model the evaporation rate is given by Type 2 solids mixture, in order to appreciate the effect of evap- oration/solids evaporites deposition, we constructed also initial E ¼ q Kðq qÞur ð11Þ air mixtures with uniform abundances, and starting values fixed to 2 1 where E is expressed in kg m s , qair as the density of the air, K is a the smallest mole fraction at saturation (i.e. that relative to ⁄ transport coefficient (a purely aerodynamic quantity), q and q are C6H6). At the evaporation initial time, one species begins to pre- saturation specific humidity and specific humidity respectively, cipitate (i.e. C6H6); the others saturate latter. and ur is the horizontal component of the averaged wind speed rel- ative to the surface at a given height zr. As we can see, the rate E de- In Table 2, results relevant for an ideal solution have been gath- pends on q and ur, quantities that are supposed to undergo ered. Two initial mixtures have been considered—both ethane rich substantial variations during a Titan’s year. Thus the rate E is ex- (89% of C2H6 when evaporation begins) with 1% of nitrogen to pected to experience significant variations during Titan’s seasonal ensure the liquid physical state. This abundance of N2 is typical cycle. To obviate this problem we have chosen to use two definitions of what has been inferred by computations at equilibrium in previ- ini of time and two time-scales, respectively corresponding to the evap- ous works. While Xliq quantifies the initial chemical composition of 1434 D. Cordier et al. / Icarus 226 (2013) 1431–1437

Table 2 Table 3 fin Type 1 mixtures in the case of a non-ideal solution. A methane poor and a methane Computed chemical composition Xevap of upper layer Titan’s lakes drybeds rich case are considered. evaporites, in the ideal solution hypothesis. Two types of dissolved solids composition have been considered (see text for explanation). Xi,sat is the mole fraction at Non-ideal solution saturation, Xi,liq represents the initial composition of the liquid and Xi,sol represents Species ini ini fin D (%) the initial abundances of dissolved solids. The D’s show enrichment/empoverishment Xliq Xsol Xevap of the resulting upper layer of the evaporite deposit. The assumed temperature is Mixture type 1, methane poor T = 90 K. The notation x y(n)=x y 10n has been used. One can notice that ideal CH4 10.018% – – – solubility of CO2 is comparable to the values reported by Preston and Prausnitz (1970) C2H6 88.804% – – – and Preston et al. (1971) for somewhat higher temperatures around 130–140 K. N2 1.002% – – – Ideal solution HCN 6.46(4) 3.65(1) 1.52(4) 100

ini ini fin C4H10 5.93(4) 3.35(1) 5.72(1) +71 Species Xi,sat (ideal) D (%) Xliq Xsol Xevap C2H2 3.62(4) 2.05(1) 4.20(1) +105 Mixture type 1 CH3CN 5.42(5) 3.06(2) 7.14(4) 98

CH4 – 10.018% – – – CO2 3.43(5) 1.94(2) 6.53(3) 66

C2H6 – 88.804% – – – C6H6 8.06(5) 4.55(2) 6.82(4) 99

N2 – 1.002% – – – Mixture type 1, methane rich HCN 6.46(4) 6.46(4) 3.65(1) 3.82(3) 99 CH4 90.160% – – – C4H10 1.22(1) 5.93(4) 3.35(1) 6.48(1) +94 C2H6 8.662% – – – C2H2 5.40(2) 3.62(4) 2.05(1) 3.20(1) +56 N2 1.002% – – – CH3CN 3.73(3) 5.42(5) 3.06(2) 2.21(2) 28

CO2 8.72(4) 3.43(5) 1.94(2) 5.16(3) 73 HCN 6.46(4) 3.65(1) 6.92(5) 100

C6H6 2.20(4) 8.06(5) 4.55(2) 1.31(3) 97 C4H10 5.93(4) 3.35(1) 6.69(1) +100 C2H2 3.62(4) 2.05(1) 3.24(1) +58 Mixture type 2 CH3CN 5.42(5) 3.06(2) 2.94(4) 99

CH4 – 10.013% – – – CO2 3.43(5) 1.94(2) 6.03(3) 69

C2H6 – 88.853% – – – C6H6 8.06(5) 4.55(2) 3.65(4) 99

N2 – 1.001% – – – HCN 6.46(4) 2.20(4) 1.67(1) 6.86(3) 96

C4H10 1.22(1) 2.20(4) 1.67(1) 4.71(1) +183 Table 4 C2H2 5.40(2) 2.20(4) 1.67(1) 4.71(1) +183 Type 2 mixtures in the case of a non-ideal solution. A methane poor and a methane CH3CN 3.73(3) 2.20(4) 1.67(1) 3.96(2) 76 rich case are considered. CO2 8.72(4) 2.20(4) 1.67(1) 9.26(3) 94 C H 2.20(4) 2.20(4) 1.67(1) 2.34(3) 99 6 6 Non-ideal solution

Species ini ini fin D (%) Xliq Xsol Xevap Mixture type 2 methane poor ini CH 10.013% – – – the solution, PXsol represents the abundances of solutes regarded as 4 a single set: Xini ¼ 1. The Xfin ’s are the mole fractions of com- C2H6 88.853% – – – sol evap N 1.001% – – – pounds finally deposited in the evaporites upper layer. The param- 2 eter of enrichment D measures the relative enrichment/ HCN 2.20(4) 1.67(1) 2.18(4) 100 C H 2.20(4) 1.67(1) 4.95(1) +197 empoverishment of a given species in the surface evaporites, as 4 10 C2H2 2.20(4) 1.67(1) 4.95(1) +197 compared to the initial composition of solids in solution. CH3CN 2.20(4) 1.67(1) 1.04(3) 99 As can be noticed in Table 2, the only species undergoing an CO2 2.20(4) 1.67(1) 8.54(3) 95 enrichment in the surface evaporites layer, compared to abun- C6H6 2.20(4) 1.67(1) 9.55(4) 99 dances initially taken into account for the dissolved solids, are bu- Mixture type 2 methane rich tane (C H ) and acetylene (C H ). This behavior can be explained 4 10 2 2 CH4 90.119% – – – by their high solubilities (i.e. high Xi,sat’s). The higher Xi,sat is, the C2H6 8.747% – – – greater the quantity of dissolved material is. Consequently the sat- N2 1.001% – – – uration occurs later during the evaporation process. If we compare HCN 2.20(4) 1.67(1) 6.97(5) 100 evap C H 2.20(4) 1.67(1) 6.68(1) +301 Xfin obtained for type 1 and type 2 mixtures of solids, we see that 4 10 evaporite composition (perhaps unsurprisingly) depends on the C2H2 2.20(4) 1.67(1) 3.25(1) +95 CH CN 2.20(4) 1.67(1) 2.97(4) 100 initial abundances of solutes. Our simulation clearly shows, within 3 CO2 2.20(4) 1.67(1) 6.03(3) 96 the framework of our current assumptions, that dissolution in C6H6 2.20(4) 1.67(1) 3.67(4) 100 methane/ethane solution, followed by evaporation of the solvent, yields surface evaporite compositions with high abundances of the most soluble species. We stress that an identical value of the enrichment D is the con- sequence of a saturation of solutes that occurs at the very end of The difference between the results of methane rich and poor are the evaporation. Of course, a solvent of a different composition explained by the non-ideality of the solution: in such a situation (e.g., a methane rich one) leads strictly to the same result because the molecules undergo interactions. In this way, solvents with dif- here we are making the calculations by adopting the ideal solution ferent compositions are not equivalent. hypothesis. The content of nitrogen is expected to vary slightly for different The results of non-ideal simulations for the regular solution Ci’s bodies of liquid. Hence we test for sensitivity of evaporite compo- have been gathered in Tables 3 and 4. Tables 3 and 4 are respec- sition regarding the abundances of nitrogen in the solvent. Table 5 tively devoted to dissolved solids mixture type 1 and type 2. For shows the enrichment parameter D for all solutes in three cases: each of these types, cases of methane rich and poor solvent are Xini ¼ 0:5%, 1% and 3%. All of these computations have been made N2 considered. As can be noticed in Tables 3 and 4, the general trend for a methane rich solvent for a temperature of 90 K. Clearly, sol- remains the same: butane and acetylene, if present in the initial vents with a high nitrogen abundance appear to favor C4H10 as a mixture, are the dominant species in the upper evaporite layer. main constituent of surface evaporites. D. Cordier et al. / Icarus 226 (2013) 1431–1437 1435

Table 5 The behavior of those solid species that are not taken into con- Influence of the initial nitrogen abundance on final evaporite layer composition. sideration in this work could be estimated if their enthalpy of melt- T = 90 K, non-ideal. Methane rich solvent Xini ’ 90 % CH4 ing were known. For instance, laboratory experiments suggest that Xini 0.5% 1% 3% HC N could be an evaporite candidate in lake drybeds (Clark et al., N2 3 DD D2010). In their Appendix II, Sagan and Thompson (1984) published HCN 99.9 100.0 100.0 a list of species with their estimated or estimated enthalpies of C4H10 +270.5 +300.9 +377.5 melting. HC3N belongs to this list, these authors have found C H +125.0 +95.1 +19.1 1 1 2 2 DHm(HC3N) = 40 cal g , corresponding to 8.5 kJ mol . This value CH3CN 99.7 99.8 100.0 is a factor of 2 larger than enthalpies of melting for C4H10 and CO2 96.2 96.4 96.7 C2H2. Coupled to an estimation of the temperature of melting of C6H6 99.7 99.8 100.0 this molecule 235 K (235 K, obtained using a ‘‘group contribu- tion’’ method, see Poling et al., 2007), one can derive that Xideal ’ 103. Consequently, HC N should have a behavior rea- sat;HC3N 3 Table 6 sembling that of CH3CN. Thus, even if HC3N has a precipitation rate Influence of the temperature on final evaporite layer composition. The initial nitrogen larger than the acetylene rate, after a dissolution/evaporation pro- mole fraction is fixed to Xini ¼ 1%, the solution is a non-ideal one, and type 1 for the N2 cess C2H2 should remain a dominant species in the final deposits initial dissolved solids mixture has been considered. layer. Species T =85K T =90K T =95K Although the composition of tholins has not been directly mea- fin D fin D fin D sured, Quirico et al. (2008) identified in their experiments that Xevap Xevap Xevap molecules derived from hydrazine R1R2N–NH2 as a possible Methane poor solvent constituent of Titan’s atmosphere tholins. Taking the most simple HCN 1.17(4) 100 1.52(4) 100 1.84(4) 100 molecules of that family: CH CH N–NH , one can estimate the C4H10 5.19(1) +54.9 5.72(1) +70.7 6.20(1) +85.0 3 3 2 C2H2 4.76(1) +132.4 4.20(1) +105.3 3.70(1) +80.8 value of the enthalpy DHm thanks to a ‘‘group contribution’’ meth- CH CN 6.52( 4) 97.9 7.14( 4) 97.7 7.39 ( 4) 97.6 1 3 od (see Poling et al., 2007). We found DHm ’ 9.15 kJ mol CO2 4.59(3) 76.3 6.53(3) 66.3 8.77 (3) 54.7 and Tm ’ 228 K (for methylhydrazine Aston et al., 1951, C6H6 5.54(4) 98.8 6.82(4) 98.5 7.88(4) 98.3 1 ideal found D Hm 10.42 kJ mol and Tm ’ 220.8 K), yielding Xsat Methane rich solvent 4 (CH3CH3N–NH2) ’ 6 10 —a value much smaller than the HCN 5.18(5) 100 6.92(5) 100 8.76(5) 100 butane or acetylene ones. C4H10 6.31(1) +88.3 6.69(1) +99.8 7.01(1) +109.4

C2H2 3.65(1) +78.1 3.24(1) +58.4 2.90(1) +41.6 However, hydrazine derivatives probably belong to tholins but CH3CN 2.62(4) 99.2 2.94(4) 99.0 3.17 (4) 99.0 are probably not representative of the whole. We recall that exper- CO2 4.29(3) 77.9 6.03(3) 68.9 8.07 (3) 58.3 iments and theoretical works made in the past have shown the C6H6 2.96(4) 99.4 3.65(4) 99.2 4.28(4) 99.1 poor solubility of tholins in non-polar solvents (McKay, 1996; Rau-

lin, 1987). In a general manner, we can notice that DHm increases The temperature also influences the solubility of solids. For a when the number of -CH3 get larger, suggesting that molecules range of temperatures (i.e., 85 K, 90 K, and 95 K), the computed with long carbon chains would be easily buried under layers rich final compositions have been reported in Table 6. High values of in C4H10 and C2H2. temperature favors high-butane evaporite content, while acetylene The precipitation of solids previously dissolved in ternary is disfavored at high temperature. However the major tendency, solvent CH4–C2H6–N2 implies heterogeneous nucleation, the prominence of butane and acetylene, is robust. Finally, we which occurs much more often than homogeneous nucleation stress that during all our calculations, for each time, we have in the real world. Nucleation that forms at preferential sites such checked that the density of species precipitating remained lower as phase boundaries or impurities like dust requires less energy than the liquid solution value. Then, according to the simulations than homogeneous nucleation (see for instance Vehkamäki, performed in this work, the organic precipitated solids would 2006). Depending on the initial turbidity of the lake, which never float at the surface of the Titan’s lakes (at least not without might possibly caused by sediments produced during drainage unusual circumstances such as those suggested by Hofgartner and/or organic aggregates fallen from the atmosphere, the depo- and Lunine, 2013). sition of evaporites could begin either on the lake floor alone or simultaneously on this floor and on the particules contributing 4. Discussion and conclusion to the initial turbidity. Moreover, the formation of evaporite has to occur on a time-scale significantly shorter than that of As it has been shown in the previous section, the composition evaporation, otherwise the concept used for our non-linear obtained for the superficial layer of evaporite is the result of the evaporation time-scale would no longer be relevant. In influence of two main factors: (1) the initial composition of dis- other words, solution cannot remain ‘‘supersaturated’’ for a long solved solids, and (2) the mole fraction at saturation values of time. the solids, provided by Eq. (1). For a given initial composition, spe- If the formation of evaporite on the lake bed is the dominant ef- cies with the highest Xi,sat (i.e., the lowest energy of cohesion) re- fect, then a model based on solubility is fully valid. Otherwise, if main dissolved for a longer time in the solvent during the the evaporites form preferentially on possible turbidity particu- evaporation and finally become the major constituents of the last lates, then the scenario of lake drybed deposition formation could layer of deposits. The value of the melting temperature Tm and en- be very different as it could involve transport processes like con- thalpy of melting determine the concentration at saturation. We vection and sedimentation. Unfortunately, given that the turbidity furthermore emphasize that, due to the special non-linear scale of Titan’s lakes is unknown, one can only guess that it should be of time used in this work, the depth of different layers of evaporite very variable from one lake to another, being a function of the ex- cannot be computed. In a same way, the composition of possible act history of the lake (drainage, occurence of a recent methane evaporite annuli around a lake (see for instance Hayes et al., rainfall, etc.). Insight into turbidity and its time-variability could 2010) could not be estimated. For a given initial composition of be acquired by direct measurements from a floating capsule, as solids in solution, we can only compute the composition of the were proposed by the (TiME) (Lorenz et al., external surface of the evaporite deposit. 2012). 1436 D. Cordier et al. / Icarus 226 (2013) 1431–1437

Finally, the validity of the theory presented in this article has to Acknowledgments be considered. As indicated in Section 2, the Eq. (1) is an approxi- mation, and the rigourous formula is (see or instance Hojjati and We acknowledge financial support from the Observatoire des Rohani, 2006) Sciences de l’Univers THETA Franche-Comt-Bourgogne, France. Z Z We thank Sandrine Vinatier and Panayotis Lavvas for scientific dis- T T DHi;m Ti;m 1 1 Dcp cussion; and the anonymous Reviewers who improved the clarity ln CiXi;sat ¼ 1 Dcp dT þ dT RTi;m T RT Tm R Tm T of the paper with their remarks and comments. J.W.B. is funded ð12Þ by the NASA CDAPS Program Grant #NNX12AC28G. with References

Dcp ¼ cp ðsubcooled liquid soluteÞcpðsolid soluteÞð13Þ Ahuja, P., 2009. Chemical Engineering Thermodynamics. Prentice-Hall of India, New Dehli. (see p. 8.181 of POL07). Eq. (1) is a good approximation of Eq. (12) Aston, J.G., Finke, H.L., Janz, G.J., Russell, K.E., 1951. The heat capacity, heats of fusion when the contributions of the second and the third terms of the and vaporization, vapor pressures, entropy and thermodynamic functions of right-hand side are negligible, as is often the case as emphasized methylhydrazine. J. Am. Chem. Soc. 73, 1939–1943. Barnes, J.W., Brown, R.H., Soderblom, J.M., Soderblom, L.A., Jaumann, R., Jackson, B., in the literature (see Poling et al., 2007; Hojjati and Rohani, 2006). Le Mouélic, S., Sotin, C., Buratti, B.J., Pitman, K.M., Baines, K.H., Clark, R.N., This assumption has been made in previous work (D89, C09, C10 Nicholson, P.D., Turtle, E.P., Perry, J., 2009. Shoreline features of Titan’s Ontario Lacus from Cassini/VIMS observations. Icarus 201 (May), 217–225. and C12). Unfortunately, reliable estimations of Dcp are not feasible Barnes, J.W., Bow, J., Schwartz, J., Brown, R.H., Soderblom, J.M., Hayes, A.G., Vixie, G., with available data. The Dulong and Petit law is probably not ade- Le Mouélic, S., Rodriguez, S., Sotin, C., Jaumann, R., Stephan, K., Soderblom, L.A., quate for cp (solid solute) at such a low temperature (90 K), in Clark, R.N., Buratti, B.J., Baines, K.H., Nicholson, P.D., 2011a. Organic which case the use of more sophisticated formulation like Debye’s sedimentary deposits in Titan’s dry lakebeds: Probable evaporite. Icarus 216 (November), 136–140. model (Kittel et al., 2004) would be required. However a Debye for- Barnes, J.W., Soderblom, J.M., Brown, R.H., Soderblom, L.A., Stephan, K., Jaumann, R., mulation is not currently applicable due to the lack of data. Besides Mouélic, S.L., Rodriguez, S., Sotin, C., Buratti, B.J., Baines, K.H., Clark, R.N., this, Rùzicka and Domalski’s method for determining cp (subcooled Nicholson, P.D., 2011b. Wave constraints for Titan’s and Kraken liquid solute) (see p. 6.19 of POL07) is not relevant as interpolation Mare from VIMS specular reflection lightcurves. Icarus 211 (January), 722–731. Clark, R.N., Curchin, J.M., Barnes, J.W., Jaumann, R., Soderblom, L., Cruikshank, D.P., expressions have a domain of validity limited to temperatures rang- Brown, R.H., Rodriguez, S., Lunine, J., Stephan, K., Hoefen, T.M., Le Mouélic, S., ing from the melting point to the boiling point. For our purposes, Sotin, C., Baines, K.H, Buratti, B.J., Nicholson, P.D., 2010. Detection and mapping the relevant temperature is well below the typical boiling point of hydrocarbon deposits on Titan. J. Geophys. Res. (Planets) 115 (October), 10005. http://dx.doi.org/10.1029/2009JE003369. temperatures of considered species (see Table 1). Cordier, D., Mousis, O., Lunine, J.I., Lavvas, P., Vuitton, V., 2009. An estimate of the However, even if the second and the third terms of the right- chemical composition of Titan’s lakes. Astrophys. J. 707 (December), L128– hand side of Eq. (12) have significant values compared to that of L131. Cordier, D. et al., 2010. About the possible role of hydrocarbon lakes in the origin of the first term, the process of solid dissolution and formation of Titan’s noble gas atmospheric depletion. Astrophys. J. 721 (October), L117– an evaporite deposit is certainly not neutral concerning the chem- L120. ical composition of the solids visible at the surface. If quantitative Cordier, D. et al., 2012. Titan’s lakes chemical composition: Sources of uncertainties and variability. Planet. Space Sci. 61 (February), 99–107. determinations could be changed by the contribution of those two Cordier, D., Mousis, O., Lunine, J.I., Lavvas, P., Vuitton, V., 2013. Erratum: ‘‘An additional terms compared to present results, then the scenario of estimate of the chemical composition of Titan’s lakes’’ (2009, ApJL, 707, L128). dissolution of solids coming directly from the atmospheric precip- Astrophys. J. 768 (May), L23–L25. Cornet, T. et al., 2012. Edge detection applied to Cassini images reveals no itation or surrounding terrains (washing and deposition in lake- measurable displacement of Ontario Lacus’ margin between 2005 and 2010. J. beds) after an evaporation episode would be robust. Such a Geophys. Res. (Planets) 117 (July), 7005. scenario provides an explanation for the strong correlation of Crespin, A., Lebonnois, S., Vinatier, S., Bézard, B., Coustenis, A., Teanby, N.A., 5-lm brightness observations with morphologic dry beds RADAR Achterberg, R.K., Rannou, P., Hourdin, F., 2008. Diagnostics of Titan’s stratospheric dynamics using Cassini/CIRS data and the 2-dimensional IPSL detections. Several authors (McKay and Smith, 2005; Schulze-Mak- circulation model. Icarus 197 (October), 556–571. uch and Grinspoon, 2005; Lunine, 2010) have proposed the Dubouloz, N., Raulin, F., Lellouch, E., Gautier, D., 1989. Titan’s hypothesized ocean hypothesis of an exotic form of life based on a metabolism involv- properties – The influence of surface temperature and atmospheric composition uncertainties. Icarus 82 (November), 81–96. ing a chemical reaction between surface acetylene and atmo- Fairall, C.W., Bradley, E.F., Rogers, D.P., Edson, J.B., Young, G.S., 1996. Bulk spheric hydrogen. We underline that in such a context, our parameterization of air–sea fluxes for tropical ocean-global atmosphere results have to be handled with extreme caution. coupled-ocean atmosphere response experiment. J. Geophys. Res. 101 (C2), 3747–3764. As previously suggested by C12 for the composition of lakes, Hayes, A.G., Wolf, A.S., Aharonson, O., Zebker, H., Lorenz, R., Kirk, R.L., Paillou, P., more reliable predictions of Titan’s lakes’ drybeds could be made Paillou, P., Lunine, J., Wye, L., Callahan, P., Wall, S., Elachi, C., 2010. Bathymetry using in vitro simulations. But that would require a huge experi- and absorptivity of Titan’s Ontario Lacus. J. Geophys. Res. (Planets) 115 (September), 9009. http://dx.doi.org/10.1029/2009JE003557. mental effort that couples the evaporation of a ternary mixture Hayes, A.G., Aharonson, O., Lunine, J.I., Kirk, R.L., Zebker, H.A., Wye, L.C., Lorenz, R.D., and dissolution of solids hydrocarbons and nitriles in a cryogenic Turtle, E.P., Paillou, P., Mitri, G., Wall, S.D., Stofan, E.R., Mitchell, K.L., Elachi, C., range of temperature. Already, Luspay-Kuti et al. (2012) have 2011. Transient surface liquid in Titan’s polar regions from Cassini. Icarus 211 (January), 655–671. determined the evaporation rate of CH4 and Malaska and Hodyss Hofgartner, J.D., Lunine, J.I., 2013. Does ice float in Titan’s lakes and seas? Icarus 223 (2013) haved obtained promising preliminary results concerning (March), 628–631. the solubility of benzene. Hojjati, H., Rohani, S., 2006. Measurement and prediction of solubility of In the recent past, an infrared VIMS observation (Stephan et al., paracetamol in water – Isopropanol solution. Part 2. Prediction. Org. Process Res. Develop. 10, 1110–1118. 2010; Barnes et al., 2011b; Soderblom et al., 2012) has been ex- Jennings, D.E. et al., 2009. Titan’s surface brightness temperatures. Astrophys. J. 691 plained by the occurrence of a probable specular reflection on a (February), L103–L105. filled Titan’s lake. A search for similar specular or near-specular Kittel, C., Zettl, A., McEuen, P., 2004. Introduction to Solid State Physics. John Wiley & Sons. reflections over dry beds could be of interest to constrain the nat- Lavvas, P.P., Coustenis, A., Vardavas, I.M., 2008a. Coupling photochemistry with ure of the evaporitic surface. A glint associated to an empty lake haze formation in Titan’s atmosphere. Part I: Model description. Planet. Space could be the signature of a smooth and thick evaporite layer, while Sci. 56 (January), 27–66. Lavvas, P.P., Coustenis, A., Vardavas, I.M., 2008b. Coupling photochemistry with no glint or a diffuse glint could help to constrain the evaporites’ haze formation in Titan’s atmosphere. Part II: Results and validation with particle size distribution. Cassini/ data. Planet. Space Sci. 56 (January), 67–99. D. Cordier et al. / Icarus 226 (2013) 1431–1437 1437

Lorenz, R.D., Stofan, E., Lunine, J.I., Zarnecki, J.C., Harri, A.M., Karkoschka, E., Sagan, C., Thompson, W.R., 1984. Production and condensation of organic gases in Newman, C.E., Bierhaus, E.B., Clark, B.C., Yelland, M., Leese, M.R., Boldt, J., the . Icarus 59 (August), 133–161. Darlington, E., Neish, C.D., Sotzen, K., Arvelo, J., Rasbach, C., Kretsch, W., Schulze-Makuch, D., Grinspoon, D.H., 2005. Biologically enhanced energy and Strohbehn, K., Grey, M., Mann, J., Zimmerman, H., Reed, C., 2012. MP3 – A carbon cylcing on Titan? Astrobiology 5, 560–567. meteorology and physical properties package for Titan air–sea studies. LPI Soderblom, J.M., Barnes, J.W., Soderblom, L.A., Brown, R.H., Griffith, C.A., Nicholson, Contrib. 1683 (October), 1072–1073. P.D., Stephan, K., Jaumann, R., Sotin, C., Baines, K.H., Buratti, B.J., Clark, R.N., Lunine, J.I., 1993a. Does Titan have an ocean? A review of current understanding of 2012. Modeling specular reflections from hydrocarbon lakes on Titan. Icarus Titan’s surface. Rev. Geophys. 31 (May), 133–149. 220 (August), 744–751. Lunine, J.I., 1993b. Erratum: ‘‘Does Titan have an ocean? A review of current Stephan, K., Jaumann, R., Brown, R.H., Soderblom, J.M., Soderblom, L.A., Barnes, J.W., understanding of Titan’s surface’’ [Rev. Geophys. 31, 133–149 (1993)]. Rev. Sotin, C., Griffith, C.A., Kirk, R.L., Baines, K.H., Buratti, B.J., Clark, R.N., Lytle, D.M., Geophys. 31, 355–356. Nelson, R.M., Nicholson, P.D., 2010. Specular reflection on Titan: Liquids in Lunine, J.I., 2010. Titan and habitable planets around M-dwarfs. Faraday Discuss. . Geophys. Res. Lett. 37 (April), 7104. http://dx.doi.org/10.1029/ 147, 405–418. 2009GL042312. Lunine, J.I., Stevenson, D.J., Yung, Y.L., 1983. Ethane ocean on Titan. Science 222 Stofan, E.R. et al., 2007. The . Nature 445 (January), 61–64. (December), 1229–1230. Tokano, T., 2005. Thermal structure of putative hydrocarbon lakes on Titan. Adv.

Luspay-Kuti, A. et al., 2012. Experimental simulations of CH4 evaporation on Titan. Space Res. 36, 286–294. Geophys. Res. Lett. 39 (October), L23203. Tokano, T., 2009. Limnological structure of Titan’s hydrocarbon lakes and its Malaska, M., Hodyss, R., 2013. Laboratory investigation of benzene dissolving in a astrobiological implication. Astrobiology 9 (March), 147–164. Titan Lake. LPI Contrib. 1719 (March), 2744–2745. Turtle, E.P., Perry, J.E., Hayes, A.G., Lorenz, R.D., Barnes, J.W., McEwen, A.S., West, McKay, C.P., 1996. Elemental composition, solubility, and optical properties of R.A., Del Genio, A.D., Barbara, J.M., Lunine, J.I., Schaller, E.L., Ray, T.L., Lopes, Titan’s organic haze. Planet. Space Sci. 44 (August), 741–747. R.M.C., Stofan, E.R., 2011a. Rapid and extensive surface changes near Titan’s McKay, C.P., Smith, H.D., 2005. Possibilities for methanogenic life in liquid methane equator: Evidence of April showers. Science 331 (March), 1414–1417. on the surface of Titan. Icarus 178 (November), 274–276. Turtle, E.P., Perry, J.E., Hayes, A.G., McEwen, A.S., 2011b. Shoreline retreat at Titan’s Mitri, G., Showman, A.P., Lunine, J.I., Lorenz, R.D., 2007. Hydrocarbon lakes on Titan. Ontario Lacus and Planitia from Cassini Imaging Science Subsystem Icarus 186 (February), 385–394. observations. Icarus 212 (April), 957–959. Poling, B.E., Prausnitz, J.M., O’Connell, J., 2007. The Properties of Gases and Liquids, Vehkamäki, H., 2006. Classical Nucleation Theory in Multicomponent Systems. fifth ed. McGraw-Hill Professional, Englewood Cliffs. Springer, Berlin, Heidelberg. Press, W., Teukolsky, S., Vetterling, W., Flannery, B., 1992. Numerical Recipes in Vinatier, S., Bézard, B., Nixon, C.A., Mamoutkine, A., Carlson, R.C., Jennings, D.E., Fortran 77. Cambridge University Press. Guandique, E.A., Teanby, N.A., Bjoraker, G.L., Michael Flasar, F., Kunde, V.G., Preston, G.T., Prausnitz, J.M., 1970. Thermodynamics of solid solubility in cryogenic 2010. Analysis of Cassini/CIRS limb spectra of Titan acquired during the nominal

solvents. Ind. Eng. Chem. Process Des. Develop. 9, 264–271. mission. I. Hydrocarbons, nitriles and CO2 vertical mixing ratio profiles. Icarus Preston, G.T., Funk, E.W., Prausnitz, J.M., 1971. Solubilities of hydrocarbons and 205 (February), 559–570. carbon dioxide in liquid methane and in liquid argon. J. Phys. Chem. 75, 2345– Vuitton, V., Yelle, R.V., Cui, J., 2008. Formation and distribution of benzene on Titan. 2352. J. Geophys. Res. (Planets) 113 (May), E05007. http://dx.doi.org/10.1029/ Quirico, E., Montagnac, G., Lees, V., McMillan, P.F., Szopa, C., Cernogora, G., Rouzaud, 2007JE002997. J.-N., Simon, P., Bernard, J.-M., Coll, P., Fray, N., Minard, R.D., Raulin, F., Reynard, Wall, S. et al., 2010. Active shoreline of Ontario Lacus, Titan: A morphological study B., Schmitt, B., 2008. New experimental constraints on the composition and of the lake and its surroundings. Geophys. Res. Lett. 37, L05202. structure of Tholins. Icarus 198 (November), 218–231. Ward, C.A., Fang, G., 1999. Expression for predicting liquid evaporation flux: Raulin, F., 1987. Organic chemistry in the oceans of Titan. Adv. Space Res. 7, 71–81. Statistical rate theory approach. Phys. Rev. E 59, 429–440. Sagan, C., Dermott, S.F., 1982. The tide in the seas of Titan. Natur 300 (December), 731–733.