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Planetary and Space Science 52 (2004) 361–370www.elsevier.com/locate/pss

Constraints on the presence of volatiles in Ganymede and Callisto froman evolutionary turbulent model of the Jovian subnebula

Olivier Mousisa ;∗, Daniel Gautierb

aObservatoire de Besanc�on, CNRS-UMR 6091, 41 bis, avenue de l’Observatoire, BP 1615, 25010 Besanc�on, Cedex, FrancebObservatoire de Paris, LESIA, CNRS-FRE 2461, 5 place Jules Janssen, F-92195 Meudon, France

Received 13 November 2002; accepted 16 June 2003

Abstract

We describe an evolutionary turbulent one-dimensional model of the Jovian subnebula, based on the previous models of the solarnebula of Dubrulle (Icarus 106 (1993) 59), and of Drouart et al. (Icarus 140 (1999) 129), as well as on the evolutionary turbulent modelof the subnebula of Saturn of Mousis et al. (Icarus 156 (2002a) 162). We show that the conversion of N2 to NH3 and that of CO toCH4 were inhibited in the Jovian subnebula, in con3ict with the conclusions of Prinn and Fegley (Astrophys. J. 249 (1981) 308). Weargue that grains from which ultimately formed Galilean satellites were initially produced in the cooling feeding zone of Jupiter priorto the formation of the subdisk surrounding the giant planet. It is assumed that hydrates of NH3 and clathrate hydrates of CO, CH4,and N2 formed in the feeding zone (Astrophys. J. Lett. 550 (2001a) L227; Astrophys. J. Lett. 559 (2001b) L183) were incorporated inplanetesimals embedded in the cold outer part of the Jovian subnebula. Under the assumption that planetesimals which formed Ganymedeand Callisto migrated from the outer region and did not outgas during this migration, the per mass abundances of NH3, N2, CO, and CH4

with respect to H2O in the interiors of these satellites are estimated. Calculated values depend upon the poorly known relative abundancesof these species in the solar nebula. However, they provide an interpretation of the presence of NH3 suspected in subsurface oceans ofGanymede and Callisto, and which is consistent with the measurement of the internal magnetic <eld of these satellites measured by theGalileo mission (Geophys. Res. Lett. 24 (1997) 2155; J. Geophys. Res. 104 (1999) 4609).? 2003 Elsevier Ltd. All rights reserved.

Keywords: Ganymede; Callisto; Galilean satellites; Jupiter; Solar nebula; Jovian subnebula

1. Introduction

One explanation for the internal magnetic <elds discov-ered in both Ganymede and Callisto (Kivelson et al., 1997,1999) invokes the presence of subsurface oceans withinthese satellites (Sohl et al., 2002; England, 2002). Thepresence of such internal oceans in the interiors is probablylinked to the existence of ammonia, since this componentdecreases the solidus temperature by several tens of de-grees (Grasset et al., 2000; Spohn and Schubert, 2003).The presence of ammonia under the form of NH3 hydratein the interiors of Ganymede and Callisto is in agreementwith the current scenario developed by Prinn and Fegley(1981) concerning the evolution of C and N compoundsin the circum-Jovian and circum-Saturnian disks. From

∗ Corresponding author.E-mail addresses: olivier.mousis@obs-besancon.fr (O. Mousis),

daniel.gautier@obspm.fr (D. Gautier).

calculations of adiabatic temperature–density radial pro<les,Prinn and Fegley (1981) concluded that both Jovian andSaturnian subnebulae media were warm and dense enoughto permit the chemical conversion of CO to CH4 and ofN2 to NH3, respectively. Accordingly, CH4 and NH3 wereassumed to have been trapped in the form of clathrate hy-drates and of hydrates, respectively, before to be incorpo-rated in icy planetesimals which formed Ganymede and Cal-listo (Lunine and Stevenson, 1982).However, recent studies, made by Mousis et al. (2002a)

concerning the conditions of formation of Titan and byCanup and Ward (2002) concerning those of Galilean satel-lites in turbulent accretion subdisks, prompted us to recon-sider the theory of Prinn and Fegley (1981) for the chemicalevolution of C and N compounds in the Jovian subnebula.Mousis et al. (2002a) and Canup and Ward (2002) devel-oped turbulent accretion subdisks models in which temper-ature and pressure radial distributions were strongly lowerthan those proposed by Prinn and Fegley (1981) for the

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362 O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361–370

Jupiter subnebula or the Saturn subnebula. Canup and Ward(2002) examined the basic parameters of a turbulent modelof the Jovian subnebula which could satisfy the conditionsof accretion of the Galilean satellites by taking into accounttheir physical characteristics (rocks/ices mass ratios in satel-lites and apparent incomplete diEerentiation of Callisto).They proposed that the formation of Galilean satellites couldresult from the formation of a low accretion steady-statecircumplanetary disk, less massive than the minimum-masssubnebula assumed in previous works (Lunine and Steven-son, 1982; Coradini et al., 1989; Makalkin et al., 1999). Ac-cordingly, Canup and Ward (2002) argued that satellite for-mation occurred within a much lower gas density environ-ment than considered by earlier models. This includes thatused by Prinn and Fegley (1981) for the study of C and Nchemistry.Mousis et al. (2002a) derived an evolutionary turbulent

model of the Saturn’s subnebula from the semi-analyticalmodel of the solar nebula elaborated by Dubrulle (1993).Assuming an initial accretion rate consistent with the as-sumption of a geometrically thin disk, they found thatno substantial chemical conversion between CO and CH4and N2 and NH3, respectively, occurred in the subneb-ula. Instead, the authors proposed a new scenario forthe formation of Titan, consistent with the observed at-mospheric composition of the satellite. They speculatedthat planetesimals which formed Titan were initially pro-duced in the feeding zone of Saturn prior to the forma-tion of the subnebula supposed to have surrounded theplanet. They assumed that these planetesimals, havingpresumably trapped NH3, CH4 and other volatiles un-der the form of hydrates and clathrate hydrates in thefeeding zone of Saturn, did not melt when entering intothe Saturn subnebula. They proposed that subsequentlyplanetesimals accumulated at the present orbit of Titanin order to form the satellite. This scenario ignores cal-culations of migration processes which occurred in thesubnebula and may be subjected to revisions. However,it is consistent with the molecular and isotopic compo-sition of the atmosphere of Titan today (Mousis et al.,2002a, b).Given the similarities of both mechanisms of formation

of the Jovian and Saturnian subdisks (Coradini et al., 1995),we adapted the evolutionary turbulent model employed byMousis et al. (2002a) to the description of the Jovian sub-nebula. We show that, in the framework of the proposedgeometrically thin disk model, studies of the physical char-acteristics of the Jovian subnebula and the evolution of itscarbon and nitrogen chemistry lead to a scenario of the for-mation of Ganymede and Callisto similar to that of Titan.Under the assumption that CO=CH4 and N2=NH3 ratios invapor phase in the solar nebula were consistent with valuesin the interstellar medium (ISM), and that the subnebula ofJupiter became cold enough to avoid the decomposition ofclathrates within planetesimals, our scenario permits us toestimate the abundances of C and N compounds with re-

spect to water within Ganymede and Callisto. This providesnew constraints on the composition of ices in interiors ofthe satellites.The outline of the paper is as follows. Section 2 is de-

voted to the description of the structure and the evolutionof the Jovian subnebula and to the implications on the for-mation of Galilean satellites. Resulting temporal variationsof radial distributions of the CO=CH4 and N2=NH3 ratiosthroughout the Jovian subnebula are also discussed. In Sec-tion 3, conditions of trapping of volatiles in planetesimalsin the feeding zone of Jupiter are examined. In Section 4,estimates of per mass ratios with respect to water of CH4,CO, NH3 and N2 species are given for the interiors of icyGalilean satellites. Section 5 is devoted to discussions. Wesummarize in Section 6.

2. Turbulent model of the Jovian subnebula

2.1. Origin and formation

As previously mentioned, the formation of the Jovian sub-nebula is assumed to be linked to that of Jupiter. Accordingto the scenario of Pollack et al. (1996), Jupiter was formedin three phases from gases and grains present in the feedingzone of the planet during the cooling of the solar nebula.In phase 1, a solid core of ices and rocks was assembled inabout 0:5 Myr. In phase 2, which lasts several millions ofyears, a primary gaseous envelope grew up from gas andplanetesimals which fell onto the core of the planet. In phase3, detailed by Coradini et al. (1995), the runaway accretionwas initiated and most of the gas and planetesimals con-tained in the feeding zone of the giant planet hydrodynami-cally collapsed in a time no longer than 3×104 yr. Coradiniet al. (1995) calculated that a surrounding turbulent accre-tion disk was generated by the hydrodynamical collapse ofthe gas onto the core of Jupiter during the last phase of itsformation. We follow this scenario and consider the Joviansubnebula as a geometrically thin gaseous turbulent disksurrounding the giant planet. The time t = 0 of our Joviansubnebula model is arbitrarily chosen as the moment whenJupiter reached its current mass.In order to describe the structure of the Jovian subdisk,

we followed the approach of Mousis et al. (2002a) in whicha turbulent evolutionary model of the Jovian subnebula iselaborated from the solar nebula 1-D model developed byDubrulle (1993) and Drouart et al. (1999). This model isbased on the prescription of Shakura and Sunyaev (1973),who parametrizes the turbulent viscosity �t under the form

�t = �C2S�; (1)

where Cs is the local sound velocity, � the Keplerian rota-tion frequency and � the dimensionless coeIcient of turbu-lent viscosity. Since the physical origin of turbulence in ac-cretion disks has not been established (see Papaloizou andLin, 1995 for a review), the prescription of Shakura and

O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361–370 363

Sunyaev (1973) is useful to describe the qualitative in3u-ence of whichever process is responsible of the angular mo-mentum transport. It is an approximation of the real in3u-ence of the various processes which can be at the originof turbulence, and should be regarded as a “subgrid” pro-cedure. The model uses the opacity law of Ruden and Pol-lack (1991). The diEerent regimes of opacity, described inDrouart et al. (1999), are functions of the temperature anddust composition. The temporal evolution of the disk tem-perature, pressure, surface density and height radial pro<lesdepends upon the evolution of the accretion rate M for whichwe have followed the prescription given by Makalkin andDorofeeva (1991):

M = M 0(1 + t=t0)−S : (2)

M decreases with time following a power law which is de-termined by the initial accretion rate M 0 and the accretiontimescale t0. We adopted s=1:5, as in Drouart et al. (1999)and Mousis et al. (2002a), thus permitting our law to beconsistent with that derived from the evolution of accretionrates in circumstellary disks (Hartmann et al., 1998). Theaccretion timescale t0 is computed from Makalkin and Do-rofeeva (1991) as

t0 =R2D3�D

; (3)

where �D is the turbulent viscosity at the initial radius ofthe subdisk, RD. Three parameters constrain M 0 and t0: theinitial mass of the disk MD0, the coeIcient of turbulentviscosity � and the radius of the subnebula RD.For the choice of the subdisk parameters, our strategy was

to search for a maximum mass subnebula which could becompatible with the hypothesis of a geometrically thin disk.Therefore, as in Mousis et al. (2002a), we constrained H=R(where H is the half height of the disk and R the jovianocen-tric distance) to be less than 0.3. We also chose the radiusof the subnebula to be equal to the Hill’s radius of Jupiter,namely RD=704Rjup (where Rjup is for Jupiter radius). Fromthis choice of RD and from the condition H=R¡ 0:3, we de-rived a maximum value of the initial accretion rate equal to8× 10−8 Jovian mass/yr. We adopted this value because itresulted in temperatures of the subnebula low enough to per-mit the condensation of ice. Choosing a substantially loweraccretion rate would have led to a quasi-stationary modelin which the high temperature in the inner zone would va-porize ice in the whole subnebula (see Fig. 1, t = 0). Thechoice of RD is discussed in Section 5.The initial accretion rate and the radius of the disk deter-

mine the couple of variables (MD0; �). Choosing the maxi-mum value of the disk’s mass compatible with M 0 resultedin MD0 = 0:001Mjup (where Mjup is for Jupiter mass) and<xed in turn the value of � which was 0.0004. The accre-tion timescale of the disk resulting from the choice of thementioned above parameters is equal to 21; 000 yr.

Fig. 1. Temperature pro<les throughout the subnebula characterized bythe parameters MD=0:001Mjup, RD=704Rjup, and �=0:0004 for variousvalues of t in yr. The vertical bars designated by the letters I, E, G andC correspond to, respectively, the actual orbits of Io, Europe, Ganymedeand Callisto.

2.2. Structure and evolution

Figs. 1–3 show, respectively, radial pro<les of temper-ature T , pressure P and surface density � throughout theJovian subnebula at various epochs. These <gures illustrate

Fig. 2. Pressure pro<les, throughout the subnebula characterized by thesame parameters as in Fig. 1, for various values of t in yr.

Fig. 3. Surface density pro<les, throughout the subnebula characterizedby the same parameters as in Fig. 1, for various values of t in yr.

364 O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361–370

Fig. 4. Mass distribution of the Jovian subnebula as a function of time.Most of the mass is in the outer part of the disk.

Fig. 5. Condensation radius of water, outer and inner masses (delimitedby the condensation radius of water) of the Jovian subnebula as a functionof time compared to the mass of the Galilean satellites.

the decrease with time and with jovianocentric distance ofT; P and �, respectively. The water ice never vaporizes atdistances higher than 170 Jovian radii from Jupiter and thecooling of the subnebula results in moving the snow linetowards the actual orbits of Callisto (26:6Rjup), Ganymede(15:1Rjup), Europa (9:5Rjup) and Io (6Rjup). The snow linereached these orbits at t = 3:3× 105, 7:8× 105, 1:55× 106

and 3× 106 yr, respectively.Fig. 4 represents the mass of gas and mixed microscopic

grains contained in a ring of one Rjup width in the Joviansubnebula, centered at a distance R of Jupiter, at diEerentepochs. Within a ring of width dR, the mass is given by thefollowing relation:

dM = 2��R dR: (4)

This <gure shows that at every time, the mass of the diskis mainly in its outer part, similarly to the structure of theSaturnian subnebula (Mousis et al., 2002a). Fig. 5 illustratesthe time dependence of the condensation radius of waterRcond in the Jovian subnebula, of the disk’s masses betweenRcond and RD, and between the inner edge and Rcond. SinceGanymede and Callisto are icy satellites with ices/rocks permass ratios close to one (Sohl et al., 2002), it seems worth-while to examine the mass distribution in the subnebula at

the epochs corresponding to the condensation of water at thelevel of the actual orbits of icy Galilean satellites. It can benoted that when water vapor condensed at the present posi-tion of Callisto, which is the outest icy Galilean satellite, themass of the turbulent subnebula within 26:6Rjup was about330 times less than the total mass of the four Galilean satel-lites. Moreover, when the condensation front of the crys-talline water reached the orbit of Ganymede, the mass of theJovian subnebula within 15:1Rjup was 1800 times less thanthe total mass of the Galilean satellites. Therefore, when wa-ter crystallized at the actual orbits of the icy Galilean satel-lites, the mass of the Jovian subnebula within 26Rjup wasmuch smaller than the total mass of the Galilean satellites.Such an analysis suggests, as initially proposed by

Coradini et al. (1989), that the Galilean satellites weremainly formed from solid material originating from theouter part of the subnebula, where the mass of the disk wasmuch higher than that of the satellites.The question of the migration of planetesimals in giant

planets subnebulae is complex and controversial. It invokesthe structure of the subnebula as well as the scenario offormation of satellites assumed by various authors. In thepresent report, we only consider the formation of micro-scopic icy grains during the temporal evolution of the sub-nebula, grains which are well mixed to gas as long as theirsize does not exceed a few millimeter or centimeter di-ameters (Dubrulle et al., 1995). The most recent scenariosof formation of satellites are compared to our model inSection 5.

2.3. Chemistry of C and N compounds in the Joviansubnebula

Current scenarios of formation of the solar nebula con-sider that ices and gases presents in the presolar cloud fellonto the disk during the collapse of the cloud. These ices mayhave vaporized either during the shock when entering intothe disk or in the early nebula. Chick and Cassen (1997) ar-gued that water ices sublimated in the nebula within 30 AU.Accordingly, CO, CH4, N2 and NH3 must have been ingaseous phase in the nebula up to 30 AU as well. This as-sumption is consistent with the work ofMousis et al. (2002a)who, taking into account turbulent diEusion and chemicalconversions between CO and CH4, and N2 and NH3, respec-tively, calculated the temporal evolutions of the CO=CH4and N2=NH3 ratios throughout the nebula.They found that, whatever the CO=CH4 and N2=NH3 ini-

tial ratios in the nebula corresponding to the ISM values,their radial pro<les rapidly evolve towards a plateau thevalue of which is close to the initial ratios. In other words,the values of CO=CH4 and N2=NH3 ratios at the position ofJupiter in the solar nebula re3ect, in a <rst approximation,the values of these ratios in the presolar cloud.Assuming the same initial ratios in the early subnebula,

the possibility of chemical conversions between CO and

O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361–370 365

Fig. 6. Calculated ratios of CO=CH4 in the subnebula at the equilib-rium. The solid line labelled CO–CH4 corresponds to the case where theabundances of the two gases are equal. When moving towards the leftside of the solid line, CO=CH4 increases, while when moving towardsthe right side of the solid line, CO=CH4 decreases. The dotted contourslabelled −3, 0, 3 correspond to log10CO=CH4 contours. Adiabats of ourevolutionary turbulent model of the Jovian subnebula are calculated atthree epochs of the subnebula. The origin of time is the moment whenJupiter acquired its current mass. The Jovianocentric distance, in Rjup,when CO=CH4 = 1, is indicated by arrows, for t = 0 and 0:1 Myr ofour turbulent model. The extremely slow in3ow stationary model of theJovian subnebula calculated by Canup and Ward (2002, Fig. 6) and themodel of Prinn and Fegley (1989) are shown for comparison.

CH4 and N2 and NH3 can be examined in thermodynami-cal conditions corresponding to our evolutionary turbulentmodel of the Jovian subnebula.Figs. 6 and 7 represent, respectively, the gas phase

chemistries of carbon and nitrogen compounds in a subneb-ula dominated by H2, resulting from calculations detailedin Mousis et al. (2002a). At the equilibrium, CO=CH4 andN2=NH3 ratios depend only upon local conditions of tem-perature and pressure (Prinn and Barshay, 1977; Lewis andPrinn, 1980; Smith, 1998). CO=CH4 and N2=NH3 ratios of1000, 1, and 0.001 are plotted in Figs. 6 and 7, and com-pared to our evolutionary model at three epochs (0, 105 and106 yr), to the model of the Jovian subnebula described byPrinn and Fegley (1989), and to the turbulent stationarymodel favored by Canup and Ward (2002, Fig. 5d). Thismodel is discussed in Section 5. Figs. 6 and 7 reveal that,at a given temperature, the pressure derived from the modelof Prinn and Fegley (1989) is denser by <ve orders ofmagnitude than the pressure calculated in the present work.The selected turbulent model of Canup and Ward (2002)exhibits a radial distribution of pressure about three ordersof magnitude lower than that from Prinn and Fegley (1989).Figs. 6 and 7 show that, when kinetics of chemical reac-

tions are not taken into account, C and N would be mainly

Fig. 7. Same as in Fig. 6, but for calculated ratios of N2=NH3 at theequilibrium. The Jovianocentric distance, in Rjup, when N2=NH3 = 1, isindicated by arrows, for the stationary turbulent model of Canup andWard (2002).

Fig. 8. Chemical times pro<les calculated for CO=CH4 and N2=NH3conversions in our model of the Jovian subnebula. The conversion of COto CH4 and of N2 to NH3 is fully inhibited, except quite close to Jupiter.

in the forms of CH4 and NH3, respectively, in the majorpart of our evolutionary model, except close to Jupiter andat early epochs. Similar conclusions can be derived fromthe model proposed by Canup and Ward (2002), shown forcomparison in Figs. 6 and 7. Note that the outer radius ofthe model of these last authors is limited to RD = 150Rjup.Chemical times, which characterize the rates of CO to

CH4 and N2 to NH3 conversions in our model of the Jo-vian subnebula, are represented in Fig. 8. They are calcu-lated from data given by Prinn and Barshay (1977), Lewisand Prinn (1980), and Smith (1998) and depend upon thetemperature and pressure radial pro<les computed from themodel. Chemical times are represented at diEerent epochs ofthe subnebula as a function of the jovianocentric distance.Taking into account the kinetics of chemical reactions, the

366 O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361–370

eIciency of the conversion is extremely weak in the wholesubnebula and implies that the CO=CH4 and N2=NH3 ra-tios remain constant during the evolution of the subdisk.Same calculations have been made, for comparison, fromthe model preferred by Canup and Ward (2002). They leadto still longer conversions times (at least 1016 yr for the COto CH4 conversion and 1037 yr for the N2 to NH3 conver-sion). In other words, from turbulent models of the subneb-ula published so far, the CO=CH4 and N2=NH3 ratios in theJovian disk were not substantially diEerent from those ac-quired in the early nebula at 5:2 AU, as long as these specieswere in vapor phase.

3. Trapping volatiles in icy Galilean satellites: from thesolar nebula to their incorporation into planetesimals

Volatiles are assumed to have been trapped in the feedingzone of Jupiter centered at 5:2 AU during the cooling ofthe solar nebula under the form of hydrates or clathratehydrates, as discussed by Gautier et al. (2001a, b). Fig. 9illustrates this process for C and N compounds. For eachclathrate hydrate or hydrate, the domain of stability is thatlocated below the curve corresponding to the consideredhydrate. The intersection of the curves of stability with theJovian adiabats at 5:2 AU, as those calculated by Hersant etal. (2001), determines the epoch when the clathrate hydrate(or the hydrate) was formed. Following this scheme, NH3was trapped as an hydrate in the feeding zone of Jupiter0:77 Myr after the formation of the Sun. CH4, CO, and N2were, respectively, trapped as clathrates hydrates at t=1:23,

Fig. 9. Temperature–pressure values in the solar nebula at 5:2 AU cal-culated as a function of time. The origin of time is the epoch when theSun reached its current mass. Stability curves of NH3–H2O hydrate andCH4-5:75H2O, CO-5:75H2O and N2-5:66H2O clathrate hydrates interceptthe solar adiabat at the times indicated by arrows. The model of solarnebula is the nominal one of Hersant et al. (2001). For CO and CH4,their abundances are calculated assuming that all C is in the form of COand CH4 and that CO=CH4 ratio equals to 5. For N2 and NH3, theirabundances are calculated assuming that all N is in the form of N2 andNH3. Stability curve of NH3–H2O hydrate corresponds to the case whereall N is in the form of NH3. Stability curve of N2-5:66H2O clathratehydrate corresponds to the case where all N is in the form of N2.

Fig. 10. Radius of formation of water ice, NH3–H2O hydrate andCH4-5:75H2O, CO-5:75H2O, and N2-5:66H2O clathrates hydrates in theJovian subnebula, as a function of time.

1.55, and 1:89 Myr. The scenario of Gautier et al. (2001a)assumes that, once formed, clathrate hydrates agglomeratedand were incorporated in icy solids produced in the feed-ing zone of Jupiter. Planetesimals which agglomerated andreached the centimeter sizes (Dubrulle et al., 1995) decou-pled from the gas and orbited around the Sun. Since thedensity of hydrogen continuously decreased with time, theratio of the mass of solids to the mass of gas continuouslyincreased with time.In order to interpret the enrichments in volatiles observed

in Jupiter by the Galileo Probe, Gautier et al. (2001a, b) haveestimated that the feeding zone of Jupiter centered at 5:2 AUhad a total width equal to 4:46 AU. They concluded that theformation of the planet was completed in about 5:85×106 yr.The Jovian subnebula was presumably formed not earlierthan this epoch, from relics of the material contained in thefeeding zone and containing clathrated grains. Since, in ourmodel, the early subnebula was warm enough near Jupiterto vaporize icy planetesimals (Fig. 1), the next step is toexamine in what part of the subnebula clathrated grains mayhave survived or formed again when the subnebula cooleddown.Fig. 10 illustrates the story of ices in the Jovian subnebula

where water ices never vaporized in the early disk fartherthan 170Rjup. The hydrate of NH3 is initially stable from246Rjup to the outer edge of the disk and does not condenseat the orbits of Ganymede (15:1Rjup) and Callisto (26:6Rjup)before 1.36 and 0:58 Myr, respectively, after the end of theformation of Jupiter. Clathrates hydrates of CH4, CO, andN2 are initially stable from 304Rjup, 351Rjup, and 382Rjup tothe edge of the disk, respectively. The same species are notstable at times earlier than 1.87, 2.32, and 2:64 Myr at the or-bit of Ganymede and 0.8, 0.99, and 1:13 Myr at the orbit ofCallisto. Accordingly, Fig. 10 shows that icy planetesimalsoriginating from the feeding zone of Jupiter preserved theirvolatiles in the major part of the Jovian subnebula. Plan-etesimals migrating inwards at epochs prior to those deter-mined for keeping volatiles stables at the orbits of Ganymedeand Callisto are subject to decrease their ices/rocks ratios.

O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361–370 367

At the opposite, planetesimals migrating inwards at epochslater than those calculated above are expected to preservethe trapping of their volatiles and to conserve the ices/rocksratios they acquired in the feeding zone of Jupiter.The distribution of water in Galilean satellites reveals that

Io and Europa are rocky, in opposition to Ganymede andCallisto (Europa, with an ices content lower than 10 wt%(Sohl et al., 2002), is rather considered as a rocky satellite).Such a contrast may be explained by assuming that Io andEuropa were formed from planetesimals which migrated in-wards at epochs when the subdisk was warm enough to va-porize ices in the region of formation of the two satellites. Tothe contrary, Ganymede and Callisto may have been formedat times when their region of formation was cold enough topreserve icy planetesimals from vaporization, or even fromloosing volatiles from the decomposition of clathrates. Sinceour purpose is to evaluate what amount of volatiles couldhave been trapped in the most favorable case, we adopt thishypothesis. This permits us to calculate the per mass abun-dances ratios of N2, NH3, CO and CH4 with respect to H2O,as shown in the following Section.

4. An estimate of the amount of trapped C and Ncompounds in Ganymede and Callisto

Assuming that the accretion of Ganymede and Callistowas homogeneous, the per mass abundances ratios men-tioned above can be calculated as follows in the interiorsof the two satellites. The volatile to water mass ratio in thefeeding zone of Jupiter is expressed by the relation derivedfrom Mousis et al. (2002a), which is

Yi =XiXH2O

�(5:2 AU; ti)�(5:2 AU; tH2O)

; (5)

where Xi is the initial mixing ratio of the volatile with re-spect to H2 in vapor phase in the nebula, � is the surfacedensity of the nebula at 5:2 AU at the time ti of hydratationor clathration of the species i, and tH2O is the time of conden-sation of water in the feeding zone of Jupiter. Table 1 showsthe CH4=H2O and CO=H2O mass ratios deduced from thetrapping of CH4 and CO under the forms of CH4-5:75H2Oand CO-5:75H2O clathrates hydrates in the feeding zone ofJupiter. Table 2 gives the NH3=H2O and N2=H2Omass ratiosresulting from the trapping of NH3 and N2 under the form

Table 1Calculations of the ratios of trapped masses of CO and CH4 to the mass ofH2O ice in the feeding zone of Jupiter with a 2.5 times (O/H) solar ratio

a CH4=H2b CO=H2b CH4=H2Oc CO=H2Oc

CO=CH4 = 5 9:6× 10−4 8:4× 10−3 2:6× 10−2 1:9× 10−1

aPer volume CO=CH4 ratios in the nebula at 5:2 AU.bPer mass CH4=H2 and CO=H2 ratios in the nebula at 5:2 AU for

solar C/H ratio.cPer mass CH4=H2O and CO=H2O ratios in the feeding zone of

Jupiter after formation of clathrate hydrates.

Table 2Calculations of the ratios of trapped masses of NH3 and N2 to the mass ofH2O ice in the feeding zone of Jupiter with a 2.5 times (O/H) solar ratio

a NH3=H2b N2=H2b NH3=H2Oc N2=H2Oc

N2=NH3 = 10 9:1× 10−5 1:5× 10−3 3:2× 10−3 3:0× 10−2

N2=NH3 = 1 6:35× 10−4 1× 10−3 2:2× 10−2 2:0× 10−2

N2=NH3 = 0; 1 1:6× 10−3 2:6× 10−4 5:7× 10−2 5:1× 10−3

aPer volume N2=NH3 ratios in the nebula at 5:2 AU.bPer mass NH3=H2 and N2=H2 ratios in the nebula at 5:2 AU for

solar N/H ratio.cPer mass NH3=H2O and N2=H2O ratios in the feeding zone of

Jupiter after formation of clathrate hydrates.

of NH3–H2O hydrate and N2-5:66H2O clathrate hydrateat 5:2 AU. C and N elements were taken in solar abun-dance (Anders and Grevesse, 1989) in the early neb-ula. Since the value of the N2=NH3 ratio in the ISM isstill an open question (see discussion in Mousis et al.,2002a), we considered the values of 0.1, 1 and 10 forthis ratio. For the CO=CH4 ratio, we adopted the valueof 5 measured in the ISM source W33A (Gerakines etal., 1999; Gibb et al., 2000). As in Gautier et al. (2001a, b),we assumed that the amount of ice available in the feedingzone of Jupiter was large enough to trap all available CO,CH4, N2 and NH3 at least.From Table 1, it can be seen that CH4=H2O and CO=H2O

mass ratios should be equal to 2.6% and 19%, respectivelyin both Ganymede and Callisto. From Table 2, dependingupon the considered ISM N2=NH3 ratio, the N2=H2O massratio should be between 0.5% and 3% in the icy Galileansatellites. For the same reasons, the NH3=H2O ratio shouldlie between 0.3% and 5.7% and is compatible with the pos-sibility of the existence of deep salty oceans in Ganymedeand Callisto. Note that only a small amount of ammoniais required to lower the melting temperature of water andlead to the preservation of deep liquid layers in icy Galileansatellites during their thermal history (Grasset et al., 2000;Mousis et al., 2002c; Leliwa-Kopystynski et al., 2002).

5. Discussion

We believe that the present description of the evolutionof the chemistry of C and N compounds in the Joviansubnebula is more plausible than the one currently quotedin the literature and which was proposed more than twodecades ago by Prinn and Fegley (1981). The adiabatic re-lationship between T and P in the subnebula used by Prinnand Fegley (1981) is derived from that assumed by Lewis(1972) for the solar nebula. This relationship is valid fora pressure-supported atmosphere and is not adequate todescribe the Jovian subnebula which was supported in itsradial dimension mostly by angular momentum rather thanpressure (Wood, 2000).

368 O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361–370

The values of the parameters we have chosen for de<ningour model re3ect our strategy, which is certainly question-able. Our choice was ruled by the two following constraints:(i) to obtain the highest possible initial mass for the disk, inorder to ease the formation of satellites and (ii) to get tem-peratures of the subnebula precluding the decomposition ofhydrates of ammonia, and eventually that of clathrates hy-drates of CO, CH4, and N2. In addition, our model is validonly for a geometrically thin disk.Condition (i) precludes us to reduce the radius of the neb-

ula or the value of the � coeIcient of turbulent viscositybecause it would result in a lower initial mass of the disk.However, we cannot guarantee that the subnebula is turbu-lent outwards to the Hill’s radius or during the whole life-time of the solar nebula. As indicated below, other model-ers of subnebula have assumed a much smaller subnebularadius than we do. Moreover, as pointed out by one referee(Mosqueira, 2003, private communication), adopting a ra-dius much larger than the location of the outermost satellitein the case of our turbulent model may be a problem for ex-plaining the reason why no regular satellites are found farfrom the planet, as well as the actual location of irregularsatellites. This remark also applies to the model of Canupand Ward (2002) who conjectured an ad hoc cut-oE butstated that in general their model leads to a more extendeddisk. Condition (ii) implies that we cannot substantially re-duce the initial accretion rate because in this case our modelwould exhibit temperatures in the inner region of the sub-nebula too high to prevent the vaporization of water ices,in con3ict with the inferred composition of Ganymede andCallisto. A modest reduction of the accretion rate would per-mit the formation of ice but not that of clathrates hydrates,and may be even not that of ammonia hydrates.Several turbulent stationary models of the Jovian sub-

nebula have been elaborated in the previous years. All re-cent models used the prescription of Shakura and Sunyaev(1973) for the parametrization of the turbulent viscosity.The high-viscosity model of Coradini et al. (1989), with atotal mass of 0:02Mjup and an accretion timescale of the or-der of 250 yr, involved the authors to consider the satelliteaccretion at a later phase, after the end of the mass in3owonto Jupiter. On the other hand, Makalkin et al. (1999)constructed two types of models of the Jovian subnebula,both having a much slower accretion rate (10−8–10−9

Jovian mass/yr). These authors considered a hot, massivedisk (0:03Mjup) ful<lling a de<ned minimum mass subneb-ula if species abundances were assumed to be solar in thismedium and a moderately warm and low mass disk (lessmassive by 2–3 orders of magnitude than their minimummass disk) which satis<ed the compositional constraintof the satellites. Makalkin et al. (1999) concluded thatit is not possible to derive from the same model a tem-perature distribution in the disk consistent with the watercontent distribution in the Galilean satellites and the min-imum mass disk derived from their masses. These authorsconcluded to the impossibility to determine which of the

two models is more appropriate for explaining the satelliteformation.The work of Canup and Ward (2002) pointed out a num-

ber of diIculties for explaining the formation of Galileansatellites and their survival in minimum mass disks likethose de<ned by Coradini et al. (1989) and Makalkin et al.(1999). Therefore, Canup and Ward (2002) argued that amuch less restrictive and self-consistent scenario consists toform Galilean satellites in a Jovian subnebula produced dur-ing the slowing of gas in3ow onto Jupiter. The scenario ofCanup and Ward (2002) is based on the recent simulationsof Lubow et al. (1999) and D’Angelo et al. (2002) whoshowed that a Jupiter-like planet opens a gap in the proto-stellar disk, but subsequently continues to accrete mass withan accretion rate decreasing down to about 4:5×10−5 planetmass/yr (Lubow et al., 1999).In Figs. 6 and 7, the model favored by Canup and Ward

(2002) is plotted together with our evolutionary modelof the Jovian subnebula. We note that the two turbulentmodels present substantial diEerences despite the fact theyare geometrically thin and have similar accretion rates(8 × 10−8Mjup=yr at t = 0 for our evolutionary model and2×10−7Mjup=yr for the stationary model of Canup andWard,2002). Among these diEerences, it can be seen that the ra-dius of our turbulent model extends up to the Hill’s radius.This leads to a more massive Jovian subnebula describedby our evolutionary model at t = 0, namely 4.7 times moreextended than the stationary model preferred by Canup andWard (2002). Another major discrepancy comes from theuse of a time dependent law for the accretion rate of ourturbulent model (see Section 2.1). As a result of this pre-scription, the surface density of our evolutionary modeldecreases by several orders of magnitude in about 107 yrfrom higher values than those of the low in3ow model ofCanup and Ward (2002) to much lower values. Moreover,the stationary model employed by Canup and Ward (2002)cannot explain the trapping or the preservation of C andN volatiles under the forms of hydrates or clathrates hy-drates in the Jovian subnebula. Indeed, the temperature andpressure ranges covered in the outer part of their stationarymodel just allow the preservation or the formation of waterice but are too high to permit C and N hydrates or clathrateshydrates to be stable.Mosqueira and Estrada (2003a, b) recently proposed a

stationary model of subnebulae of Jupiter and Saturn dras-tically diEerent from the present model and of the one ofCanup and Ward (2002). The subdisk of Jupiter is assumedto be composed of an optically thick region located within15Rjup from the planet in which turbulence is not excluded,and surrounded by a laminar and optically thin region ex-tending outwards to 150Rjup. The inner disk is supposed tohave been the leftover of the gas accreted by the formingplanet. The outer disk may result from the solar nebula gasonce Jupiter was almost completed. Mosqueira and Estrada(2003a, b) argued that Ganymede was formed from the ma-terial condensed in the inner part of the subnebula, while

O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361–370 369

Callisto derived its planetesimals from the materials presentin the outer disk.The examination of the chemical times which char-

acterize the rates of CO to CH4 and N2 to NH3 con-versions in the inner part of the model of Mosqueiraand Estrada (2003a, b) shows clearly that the eIciencyof the conversion is extremely weak, leading to thesame conclusions as in our model or the one of Canupand Ward (2002). However, Mosqueira and Estrada(2003a, b) do not rule out the presence of ammonia becauseit could have formed in the envelope of Jupiter prior to diskformation or come from the solar nebula and drift inwardsfrom the outer disk, as we propose in our model.From our analysis, the only way to justify an eventual

presence of C and N compounds in Ganymede and Callistois to assume that (i) these gases were present in a suIcientamount in the early solar nebula, (ii) they were trapped in acold region of the nebula or of the subnebula, (iii) clathratedplanetesimals were present in the region of formation ofthese two satellites. Considering the complexity of the satel-lite system of Jupiter and the scarcity of observational con-straints, it is premature to aIrm that these conditions wereful<lled.At this point, it is clear that the stationary models of Canup

and Ward (2002) and of Mosqueira and Estrada (2003a, b)are too warm to permit the formation of clathrates or hy-drates in the inner part of the Jovian subnebula, or even toavoid the outgassing of previously trapped volatiles fromplanetesimals, unless the size of these bodies was substan-tially large. In fact, our suggestion that C and N compoundscould be present in Ganymede and Callisto is only basedon the validity of the prescription of Makalkin and Doro-feeva (1991) for describing the evolution of the accretionrate of the subnebula. This assumption may be true or maynot be true. The only positive indication we have is thatthis prescription seems applicable to the solar nebula, since,as indicated in Section 2.1, it approximately reproduces thedecrease of the accretion rate with time observed in circum-stellar disks. The evolution of the subdisks of giant plan-ets may be more complex however, than that of circumstel-lar disks. Let us remind that another favorable indicationis that our evolutionary model applied to the subnebula ofSaturn permitted Mousis et al. (2002a, b) to reproduce theobserved molecular composition of the atmosphere of Titanand its D/H ratio. We have also mentioned in Section 1 thatthe presence of ammonia in the interiors of Ganymede andCallisto would favor the occurrence of subsurface oceans,which in turn, could explain the magnetic <eld discoveredin these objects (Kivelson et al., 1999). This presence ispossible only if the ammonia hydrates were trapped in plan-etesimals which formed these satellites.On the other hand, when considering the initial value

of the accretion rate we have assumed, the validity of ourmodel is questionable. The <nal accretion rate correspond-ing to the end of the formation of Jupiter deduced from theworks of Coradini et al. (1995) (2:4×10−5 Jupiter mass/yr)

and Lubow et al. (1999) (4:5 × 10−5 Jupiter mass/yr) isat least two orders of magnitudes higher than the initialaccretion rate assumed in our model. Since the calculatedheight of the disk is proportional to the accretion rate, itmight be that the assumption of a geometrically thin modelis not valid in our early subnebula. Adopting higher val-ues in our model for the initial accretion rate would requestthe use of a non-Keplerian thick disk model (Abramowiczet al., 1980). Such a complicated study is out of the scopeof the paper. Note, however, that the accretion rate rapidlydecreases with time so that the actual subnebula probablyreached in a short period of time a value consistent with theinitial value assumed in the present report. The same con-siderations apply to the model of Canup and Ward (2002)which is also geometrically thin and is calculated for a lowaccretion rate. Comparing with the input parameters of themodel of Mosqueira and Estrada (2003a, b) is diIcult be-cause their model is based on a scenario of formation whichis diEerent from ours.

6. Summary

The evolutionary model of the subnebula of Jupiter de-veloped in this report suggests that the conversion of COto CH4 and of N2 to NH3 did not occur in the subdisk ofthe planet. Therefore, assuming the presence of NH3 and ofCH4 in the subnebula implies that these gases were initiallypresent or had been previously trapped in icy grains.The presence of hydrates and clathrate hydrates of C and

N compounds within Ganymede and Callisto is possible onlyif the planetesimals from which these satellites were formednever outgassed their volatiles. The model of subnebula andthe scenario we propose satisfy this condition. However,we have no direct observational evidence so far that C–Ncompounds are present in the interiors of these satellites,although the presence of hydrate of ammonia would favorthe presence of a deep salted ocean, and accordingly wouldbe consistent with the internal magnetic <eld measured bythe Galileo spacecraft. On the other hand, the evolution ofthe accretion rate we have adopted for our model may be ormay not be right. The only positive indication we have isthat the evolutionary model of Mousis et al. (2002a) elab-orated for representing the subnebula of Saturn, and whichis similar to that of the Jovian subnebula, permitted the au-thors to reproduce the CH4 abundance and the D/H ratio inthe atmosphere of Titan.Landers deposited on the surfaces of Ganymede and Cal-

listo by future space missions could provide new constraintson the composition of these objects.

Acknowledgements

We thank Jean-Marc Petit for valuable comments on themanuscript.

370 O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361–370

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