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Planetary and Space Science 52 (2004) 361 – 370
www.elsevier.com/locate/pss
Constraints on the presence of volatiles in Ganymede and Callisto from
an evolutionary turbulent model of the Jovian subnebula
Olivier Mousisa;∗ , Daniel Gautierb
a Observatoire
de Besancon, CNRS-UMR 6091, 41 bis, avenue de l’Observatoire, BP 1615, 25010 Besancon, Cedex, France
de Paris, LESIA, CNRS-FRE 2461, 5 place Jules Janssen, F-92195 Meudon, France
b Observatoire
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 solar
nebula of Dubrulle (Icarus 106 (1993) 59), and of Drouart et al. (Icarus 140 (1999) 129), as well as on the evolutionary turbulent model
of 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 to
CH4 were inhibited in the Jovian subnebula, in con3ict with the conclusions of Prinn and Fegley (Astrophys. J. 249 (1981) 308). We
argue that grains from which ultimately formed Galilean satellites were initially produced in the cooling feeding zone of Jupiter prior
to 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 in
planetesimals embedded in the cold outer part of the Jovian subnebula. Under the assumption that planetesimals which formed Ganymede
and 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 H2 O in the interiors of these satellites are estimated. Calculated values depend upon the poorly known relative abundances
of these species in the solar nebula. However, they provide an interpretation of the presence of NH3 suspected in subsurface oceans of
Ganymede and Callisto, and which is consistent with the measurement of the internal magnetic <eld of these satellites measured by the
Galileo 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 discovered in both Ganymede and Callisto (Kivelson et al., 1997,
1999) invokes the presence of subsurface oceans within
these satellites (Sohl et al., 2002; England, 2002). The
presence of such internal oceans in the interiors is probably
linked to the existence of ammonia, since this component
decreases the solidus temperature by several tens of degrees (Grasset et al., 2000; Spohn and Schubert, 2003).
The presence of ammonia under the form of NH3 hydrate
in the interiors of Ganymede and Callisto is in agreement
with the current scenario developed by Prinn and Fegley
(1981) concerning the evolution of C and N compounds
in the circum-Jovian and circum-Saturnian disks. From
∗
Corresponding author.
E-mail addresses: [email protected] (O. Mousis),
[email protected] (D. Gautier).
0032-0633/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/j.pss.2003.06.004
calculations of adiabatic temperature–density radial pro<les,
Prinn and Fegley (1981) concluded that both Jovian and
Saturnian subnebulae media were warm and dense enough
to permit the chemical conversion of CO to CH4 and of
N2 to NH3 , respectively. Accordingly, CH4 and NH3 were
assumed to have been trapped in the form of clathrate hydrates and of hydrates, respectively, before to be incorporated in icy planetesimals which formed Ganymede and Callisto (Lunine and Stevenson, 1982).
However, recent studies, made by Mousis et al. (2002a)
concerning the conditions of formation of Titan and by
Canup and Ward (2002) concerning those of Galilean satellites in turbulent accretion subdisks, prompted us to reconsider the theory of Prinn and Fegley (1981) for the chemical
evolution of C and N compounds in the Jovian subnebula.
Mousis et al. (2002a) and Canup and Ward (2002) developed turbulent accretion subdisks models in which temperature and pressure radial distributions were strongly lower
than those proposed by Prinn and Fegley (1981) for the
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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 model
of the Jovian subnebula which could satisfy the conditions
of accretion of the Galilean satellites by taking into account
their physical characteristics (rocks/ices mass ratios in satellites and apparent incomplete diEerentiation of Callisto).
They proposed that the formation of Galilean satellites could
result from the formation of a low accretion steady-state
circumplanetary disk, less massive than the minimum-mass
subnebula assumed in previous works (Lunine and Stevenson, 1982; Coradini et al., 1989; Makalkin et al., 1999). Accordingly, Canup and Ward (2002) argued that satellite formation occurred within a much lower gas density environment than considered by earlier models. This includes that
used by Prinn and Fegley (1981) for the study of C and N
chemistry.
Mousis et al. (2002a) derived an evolutionary turbulent
model of the Saturn’s subnebula from the semi-analytical
model of the solar nebula elaborated by Dubrulle (1993).
Assuming an initial accretion rate consistent with the assumption of a geometrically thin disk, they found that
no substantial chemical conversion between CO and CH4
and N2 and NH3 , respectively, occurred in the subnebula. Instead, the authors proposed a new scenario for
the formation of Titan, consistent with the observed atmospheric composition of the satellite. They speculated
that planetesimals which formed Titan were initially produced in the feeding zone of Saturn prior to the formation of the subnebula supposed to have surrounded the
planet. They assumed that these planetesimals, having
presumably trapped NH3 , CH4 and other volatiles under the form of hydrates and clathrate hydrates in the
feeding zone of Saturn, did not melt when entering into
the Saturn subnebula. They proposed that subsequently
planetesimals accumulated at the present orbit of Titan
in order to form the satellite. This scenario ignores calculations of migration processes which occurred in the
subnebula and may be subjected to revisions. However,
it is consistent with the molecular and isotopic composition 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 by
Mousis et al. (2002a) to the description of the Jovian subnebula. We show that, in the framework of the proposed
geometrically thin disk model, studies of the physical characteristics of the Jovian subnebula and the evolution of its
carbon and nitrogen chemistry lead to a scenario of the formation of Ganymede and Callisto similar to that of Titan.
Under the assumption that CO=CH4 and N2 =NH3 ratios in
vapor phase in the solar nebula were consistent with values
in the interstellar medium (ISM), and that the subnebula of
Jupiter became cold enough to avoid the decomposition of
clathrates within planetesimals, our scenario permits us to
estimate the abundances of C and N compounds with re-
spect to water within Ganymede and Callisto. This provides
new constraints on the composition of ices in interiors of
the satellites.
The outline of the paper is as follows. Section 2 is devoted to the description of the structure and the evolution
of the Jovian subnebula and to the implications on the formation of Galilean satellites. Resulting temporal variations
of radial distributions of the CO=CH4 and N2 =NH3 ratios
throughout the Jovian subnebula are also discussed. In Section 3, conditions of trapping of volatiles in planetesimals
in 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 icy
Galilean satellites. Section 5 is devoted to discussions. We
summarize in Section 6.
2. Turbulent model of the Jovian subnebula
2.1. Origin and formation
As previously mentioned, the formation of the Jovian subnebula is assumed to be linked to that of Jupiter. According
to the scenario of Pollack et al. (1996), Jupiter was formed
in three phases from gases and grains present in the feeding
zone of the planet during the cooling of the solar nebula.
In phase 1, a solid core of ices and rocks was assembled in
about 0:5 Myr. In phase 2, which lasts several millions of
years, a primary gaseous envelope grew up from gas and
planetesimals which fell onto the core of the planet. In phase
3, detailed by Coradini et al. (1995), the runaway accretion
was initiated and most of the gas and planetesimals contained in the feeding zone of the giant planet hydrodynamically collapsed in a time no longer than 3 × 104 yr. Coradini
et al. (1995) calculated that a surrounding turbulent accretion disk was generated by the hydrodynamical collapse of
the gas onto the core of Jupiter during the last phase of its
formation. We follow this scenario and consider the Jovian
subnebula as a geometrically thin gaseous turbulent disk
surrounding the giant planet. The time t = 0 of our Jovian
subnebula model is arbitrarily chosen as the moment when
Jupiter reached its current mass.
In order to describe the structure of the Jovian subdisk,
we followed the approach of Mousis et al. (2002a) in which
a turbulent evolutionary model of the Jovian subnebula is
elaborated from the solar nebula 1-D model developed by
Dubrulle (1993) and Drouart et al. (1999). This model is
based on the prescription of Shakura and Sunyaev (1973),
who parametrizes the turbulent viscosity t under the form
C2
(1)
t = S ;
where Cs is the local sound velocity, the Keplerian rotation frequency and the dimensionless coeIcient of turbulent viscosity. Since the physical origin of turbulence in accretion disks has not been established (see Papaloizou and
Lin, 1995 for a review), the prescription of Shakura and
O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361 – 370
Sunyaev (1973) is useful to describe the qualitative in3uence of whichever process is responsible of the angular momentum transport. It is an approximation of the real in3uence of the various processes which can be at the origin
of turbulence, and should be regarded as a “subgrid” procedure. The model uses the opacity law of Ruden and Pollack (1991). The diEerent regimes of opacity, described in
Drouart et al. (1999), are functions of the temperature and
dust composition. The temporal evolution of the disk temperature, pressure, surface density and height radial pro<les
depends upon the evolution of the accretion rate Ṁ for which
we have followed the prescription given by Makalkin and
Dorofeeva (1991):
Ṁ = Ṁ 0 (1 + t=t0 )−S :
(2)
Ṁ decreases with time following a power law which is determined by the initial accretion rate Ṁ 0 and the accretion
timescale t0 . We adopted s = 1:5, as in Drouart et al. (1999)
and Mousis et al. (2002a), thus permitting our law to be
consistent with that derived from the evolution of accretion
rates in circumstellary disks (Hartmann et al., 1998). The
accretion timescale t0 is computed from Makalkin and Dorofeeva (1991) as
t0 =
R2D
;
3D
363
Fig. 1. Temperature pro<les throughout the subnebula characterized by
the parameters MD = 0:001Mjup , RD = 704Rjup , and = 0:0004 for various
values of t in yr. The vertical bars designated by the letters I, E, G and
C correspond to, respectively, the actual orbits of Io, Europe, Ganymede
and Callisto.
2.2. Structure and evolution
Figs. 1–3 show, respectively, radial pro<les of temperature T , pressure P and surface density throughout the
Jovian subnebula at various epochs. These <gures illustrate
(3)
where D is the turbulent viscosity at the initial radius of
the subdisk, RD . Three parameters constrain Ṁ 0 and t0 : the
initial mass of the disk MD0 , the coeIcient of turbulent
viscosity 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 be
compatible 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 jovianocentric distance) to be less than 0.3. We also chose the radius
of the subnebula to be equal to the Hill’s radius of Jupiter,
namely RD =704Rjup (where Rjup is for Jupiter radius). From
this choice of RD and from the condition H=R ¡ 0:3, we derived a maximum value of the initial accretion rate equal to
8 × 10−8 Jovian mass/yr. We adopted this value because it
resulted in temperatures of the subnebula low enough to permit the condensation of ice. Choosing a substantially lower
accretion rate would have led to a quasi-stationary model
in which the high temperature in the inner zone would vaporize ice in the whole subnebula (see Fig. 1, t = 0). The
choice of RD is discussed in Section 5.
The initial accretion rate and the radius of the disk determine the couple of variables (MD0 ; ). Choosing the maximum value of the disk’s mass compatible with Ṁ 0 resulted
in MD0 = 0:001Mjup (where Mjup is for Jupiter mass) and
<xed in turn the value of which was 0.0004. The accretion timescale of the disk resulting from the choice of the
mentioned above parameters is equal to 21; 000 yr.
Fig. 2. Pressure pro<les, throughout the subnebula characterized by the
same parameters as in Fig. 1, for various values of t in yr.
Fig. 3. Surface density pro<les, throughout the subnebula characterized
by 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 (delimited
by the condensation radius of water) of the Jovian subnebula as a function
of time compared to the mass of the Galilean satellites.
the decrease with time and with jovianocentric distance of
T; P and , respectively. The water ice never vaporizes at
distances higher than 170 Jovian radii from Jupiter and the
cooling of the subnebula results in moving the snow line
towards the actual orbits of Callisto (26:6Rjup ), Ganymede
(15:1Rjup ), Europa (9:5Rjup ) and Io (6Rjup ). The snow line
reached 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 Jovian
subnebula, centered at a distance R of Jupiter, at diEerent
epochs. Within a ring of width dR, the mass is given by the
following relation:
dM = 2R dR:
(4)
This <gure shows that at every time, the mass of the disk
is mainly in its outer part, similarly to the structure of the
Saturnian subnebula (Mousis et al., 2002a). Fig. 5 illustrates
the time dependence of the condensation radius of water
Rcond in the Jovian subnebula, of the disk’s masses between
Rcond and RD , and between the inner edge and Rcond . Since
Ganymede and Callisto are icy satellites with ices/rocks per
mass ratios close to one (Sohl et al., 2002), it seems worthwhile to examine the mass distribution in the subnebula at
the epochs corresponding to the condensation of water at the
level of the actual orbits of icy Galilean satellites. It can be
noted that when water vapor condensed at the present position of Callisto, which is the outest icy Galilean satellite, the
mass of the turbulent subnebula within 26:6Rjup was about
330 times less than the total mass of the four Galilean satellites. Moreover, when the condensation front of the crystalline water reached the orbit of Ganymede, the mass of the
Jovian subnebula within 15:1Rjup was 1800 times less than
the total mass of the Galilean satellites. Therefore, when water crystallized at the actual orbits of the icy Galilean satellites, the mass of the Jovian subnebula within 26Rjup was
much 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 were
mainly formed from solid material originating from the
outer part of the subnebula, where the mass of the disk was
much higher than that of the satellites.
The question of the migration of planetesimals in giant
planets subnebulae is complex and controversial. It invokes
the structure of the subnebula as well as the scenario of
formation of satellites assumed by various authors. In the
present report, we only consider the formation of microscopic icy grains during the temporal evolution of the subnebula, grains which are well mixed to gas as long as their
size does not exceed a few millimeter or centimeter diameters (Dubrulle et al., 1995). The most recent scenarios
of formation of satellites are compared to our model in
Section 5.
2.3. Chemistry of C and N compounds in the Jovian
subnebula
Current scenarios of formation of the solar nebula consider that ices and gases presents in the presolar cloud fell
onto the disk during the collapse of the cloud. These ices may
have vaporized either during the shock when entering into
the disk or in the early nebula. Chick and Cassen (1997) argued that water ices sublimated in the nebula within 30 AU.
Accordingly, CO, CH4 , N2 and NH3 must have been in
gaseous phase in the nebula up to 30 AU as well. This assumption is consistent with the work of Mousis et al. (2002a)
who, taking into account turbulent diEusion and chemical
conversions between CO and CH4 , and N2 and NH3 , respectively, calculated the temporal evolutions of the CO=CH4
and N2 =NH3 ratios throughout the nebula.
They found that, whatever the CO=CH4 and N2 =NH3 initial ratios in the nebula corresponding to the ISM values,
their radial pro<les rapidly evolve towards a plateau the
value of which is close to the initial ratios. In other words,
the values of CO=CH4 and N2 =NH3 ratios at the position of
Jupiter 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
Fig. 6. Calculated ratios of CO=CH4 in the subnebula at the equilibrium. The solid line labelled CO–CH4 corresponds to the case where the
abundances of the two gases are equal. When moving towards the left
side of the solid line, CO=CH4 increases, while when moving towards
the right side of the solid line, CO=CH4 decreases. The dotted contours
labelled −3, 0, 3 correspond to log10 CO=CH4 contours. Adiabats of our
evolutionary turbulent model of the Jovian subnebula are calculated at
three epochs of the subnebula. The origin of time is the moment when
Jupiter acquired its current mass. The Jovianocentric distance, in Rjup ,
when CO=CH4 = 1, is indicated by arrows, for t = 0 and 0:1 Myr of
our turbulent model. The extremely slow in3ow stationary model of the
Jovian subnebula calculated by Canup and Ward (2002, Fig. 6) and the
model of Prinn and Fegley (1989) are shown for comparison.
CH4 and N2 and NH3 can be examined in thermodynamical conditions corresponding to our evolutionary turbulent
model of the Jovian subnebula.
Figs. 6 and 7 represent, respectively, the gas phase
chemistries of carbon and nitrogen compounds in a subnebula dominated by H2 , resulting from calculations detailed
in Mousis et al. (2002a). At the equilibrium, CO=CH4 and
N2 =NH3 ratios depend only upon local conditions of temperature and pressure (Prinn and Barshay, 1977; Lewis and
Prinn, 1980; Smith, 1998). CO=CH4 and N2 =NH3 ratios of
1000, 1, and 0.001 are plotted in Figs. 6 and 7, and compared to our evolutionary model at three epochs (0, 105 and
106 yr), to the model of the Jovian subnebula described by
Prinn and Fegley (1989), and to the turbulent stationary
model favored by Canup and Ward (2002, Fig. 5d). This
model is discussed in Section 5. Figs. 6 and 7 reveal that,
at a given temperature, the pressure derived from the model
of Prinn and Fegley (1989) is denser by <ve orders of
magnitude 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 orders
of magnitude lower than that from Prinn and Fegley (1989).
Figs. 6 and 7 show that, when kinetics of chemical reactions are not taken into account, C and N would be mainly
365
Fig. 7. Same as in Fig. 6, but for calculated ratios of N2 =NH3 at the
equilibrium. The Jovianocentric distance, in Rjup , when N2 =NH3 = 1, is
indicated by arrows, for the stationary turbulent model of Canup and
Ward (2002).
Fig. 8. Chemical times pro<les calculated for CO=CH4 and N2 =NH3
conversions in our model of the Jovian subnebula. The conversion of CO
to CH4 and of N2 to NH3 is fully inhibited, except quite close to Jupiter.
in the forms of CH4 and NH3 , respectively, in the major
part of our evolutionary model, except close to Jupiter and
at early epochs. Similar conclusions can be derived from
the model proposed by Canup and Ward (2002), shown for
comparison in Figs. 6 and 7. Note that the outer radius of
the 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 Jovian subnebula, are represented in Fig. 8. They are calculated from data given by Prinn and Barshay (1977), Lewis
and Prinn (1980), and Smith (1998) and depend upon the
temperature and pressure radial pro<les computed from the
model. Chemical times are represented at diEerent epochs of
the 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 whole
subnebula and implies that the CO=CH4 and N2 =NH3 ratios remain constant during the evolution of the subdisk.
Same calculations have been made, for comparison, from
the model preferred by Canup and Ward (2002). They lead
to still longer conversions times (at least 1016 yr for the CO
to CH4 conversion and 1037 yr for the N2 to NH3 conversion). In other words, from turbulent models of the subnebula published so far, the CO=CH4 and N2 =NH3 ratios in the
Jovian disk were not substantially diEerent from those acquired in the early nebula at 5:2 AU, as long as these species
were in vapor phase.
3. Trapping volatiles in icy Galilean satellites: from the
solar nebula to their incorporation into planetesimals
Volatiles are assumed to have been trapped in the feeding
zone of Jupiter centered at 5:2 AU during the cooling of
the solar nebula under the form of hydrates or clathrate
hydrates, as discussed by Gautier et al. (2001a, b). Fig. 9
illustrates this process for C and N compounds. For each
clathrate hydrate or hydrate, the domain of stability is that
located below the curve corresponding to the considered
hydrate. The intersection of the curves of stability with the
Jovian adiabats at 5:2 AU, as those calculated by Hersant et
al. (2001), determines the epoch when the clathrate hydrate
(or the hydrate) was formed. Following this scheme, NH3
was trapped as an hydrate in the feeding zone of Jupiter
0:77 Myr after the formation of the Sun. CH4 , CO, and N2
were, respectively, trapped as clathrates hydrates at t = 1:23,
Fig. 9. Temperature–pressure values in the solar nebula at 5:2 AU calculated as a function of time. The origin of time is the epoch when the
Sun reached its current mass. Stability curves of NH3 –H2 O hydrate and
CH4 -5:75H2 O, CO-5:75H2 O and N2 -5:66H2 O clathrate hydrates intercept
the solar adiabat at the times indicated by arrows. The model of solar
nebula 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 CO
and CH4 and that CO=CH4 ratio equals to 5. For N2 and NH3 , their
abundances are calculated assuming that all N is in the form of N2 and
NH3 . Stability curve of NH3 –H2 O hydrate corresponds to the case where
all N is in the form of NH3 . Stability curve of N2 -5:66H2 O clathrate
hydrate corresponds to the case where all N is in the form of N2 .
Fig. 10. Radius of formation of water ice, NH3 –H2 O hydrate and
CH4 -5:75H2 O, CO-5:75H2 O, and N2 -5:66H2 O clathrates hydrates in the
Jovian 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 agglomerated
and were incorporated in icy solids produced in the feeding zone of Jupiter. Planetesimals which agglomerated and
reached the centimeter sizes (Dubrulle et al., 1995) decoupled from the gas and orbited around the Sun. Since the
density of hydrogen continuously decreased with time, the
ratio of the mass of solids to the mass of gas continuously
increased with time.
In order to interpret the enrichments in volatiles observed
in Jupiter by the Galileo Probe, Gautier et al. (2001a, b) have
estimated that the feeding zone of Jupiter centered at 5:2 AU
had a total width equal to 4:46 AU. They concluded that the
formation of the planet was completed in about 5:85×106 yr.
The Jovian subnebula was presumably formed not earlier
than this epoch, from relics of the material contained in the
feeding zone and containing clathrated grains. Since, in our
model, the early subnebula was warm enough near Jupiter
to vaporize icy planetesimals (Fig. 1), the next step is to
examine in what part of the subnebula clathrated grains may
have survived or formed again when the subnebula cooled
down.
Fig. 10 illustrates the story of ices in the Jovian subnebula
where water ices never vaporized in the early disk farther
than 170Rjup . The hydrate of NH3 is initially stable from
246Rjup to the outer edge of the disk and does not condense
at the orbits of Ganymede (15:1Rjup ) and Callisto (26:6Rjup )
before 1.36 and 0:58 Myr, respectively, after the end of the
formation of Jupiter. Clathrates hydrates of CH4 , CO, and
N2 are initially stable from 304Rjup , 351Rjup , and 382Rjup to
the edge of the disk, respectively. The same species are not
stable at times earlier than 1.87, 2.32, and 2:64 Myr at the orbit of Ganymede and 0.8, 0.99, and 1:13 Myr at the orbit of
Callisto. Accordingly, Fig. 10 shows that icy planetesimals
originating from the feeding zone of Jupiter preserved their
volatiles in the major part of the Jovian subnebula. Planetesimals migrating inwards at epochs prior to those determined for keeping volatiles stables at the orbits of Ganymede
and Callisto are subject to decrease their ices/rocks ratios.
O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361 – 370
At the opposite, planetesimals migrating inwards at epochs
later than those calculated above are expected to preserve
the trapping of their volatiles and to conserve the ices/rocks
ratios 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 and
Callisto (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 and
Europa were formed from planetesimals which migrated inwards at epochs when the subdisk was warm enough to vaporize ices in the region of formation of the two satellites. To
the contrary, Ganymede and Callisto may have been formed
at times when their region of formation was cold enough to
preserve icy planetesimals from vaporization, or even from
loosing volatiles from the decomposition of clathrates. Since
our purpose is to evaluate what amount of volatiles could
have been trapped in the most favorable case, we adopt this
hypothesis. This permits us to calculate the per mass abundances ratios of N2 , NH3 , CO and CH4 with respect to H2 O,
as shown in the following Section.
4. An estimate of the amount of trapped C and N
compounds in Ganymede and Callisto
Assuming that the accretion of Ganymede and Callisto
was homogeneous, the per mass abundances ratios mentioned above can be calculated as follows in the interiors
of the two satellites. The volatile to water mass ratio in the
feeding zone of Jupiter is expressed by the relation derived
from Mousis et al. (2002a), which is
Yi =
(5:2 AU; ti )
Xi
;
XH2 O (5:2 AU; tH2 O )
(5)
where Xi is the initial mixing ratio of the volatile with respect to H2 in vapor phase in the nebula, is the surface
density of the nebula at 5:2 AU at the time ti of hydratation
or clathration of the species i, and tH2 O is the time of condensation of water in the feeding zone of Jupiter. Table 1 shows
the CH4 =H2 O and CO=H2 O mass ratios deduced from the
trapping of CH4 and CO under the forms of CH4 -5:75H2 O
and CO-5:75H2 O clathrates hydrates in the feeding zone of
Jupiter. Table 2 gives the NH3 =H2 O and N2 =H2 O mass ratios
resulting from the trapping of NH3 and N2 under the form
Table 1
Calculations of the ratios of trapped masses of CO and CH4 to the mass of
H2 O ice in the feeding zone of Jupiter with a 2.5 times (O/H) solar ratio
CH4 =H2 b
a
CO=CH4 = 5 9:6 × 10−4
a Per
CO=H2 b
CH4 =H2 Oc
CO=H2 Oc
8:4 × 10−3
2:6 × 10−2
1:9 × 10−1
volume CO=CH4 ratios in the nebula at 5:2 AU.
mass CH4 =H2 and CO=H2 ratios in the nebula at 5:2 AU for
solar C/H ratio.
c Per mass CH =H O and CO=H O ratios in the feeding zone of
4
2
2
Jupiter after formation of clathrate hydrates.
b Per
367
Table 2
Calculations of the ratios of trapped masses of NH3 and N2 to the mass of
H2 O ice in the feeding zone of Jupiter with a 2.5 times (O/H) solar ratio
a
NH3 =H2 b
N2 =H2 b
NH3 =H2 Oc
N2 =H2 Oc
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
a Per
volume N2 =NH3 ratios in the nebula at 5:2 AU.
mass NH3 =H2 and N2 =H2 ratios in the nebula at 5:2 AU for
solar N/H ratio.
c Per mass NH =H O and N =H O ratios in the feeding zone of
3
2
2
2
Jupiter after formation of clathrate hydrates.
b Per
of NH3 –H2 O hydrate and N2 -5:66H2 O clathrate hydrate
at 5:2 AU. C and N elements were taken in solar abundance (Anders and Grevesse, 1989) in the early nebula. Since the value of the N2 =NH3 ratio in the ISM is
still an open question (see discussion in Mousis et al.,
2002a), we considered the values of 0.1, 1 and 10 for
this ratio. For the CO=CH4 ratio, we adopted the value
of 5 measured in the ISM source W33A (Gerakines et
al., 1999; Gibb et al., 2000). As in Gautier et al. (2001a, b),
we assumed that the amount of ice available in the feeding
zone 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 =H2 O and CO=H2 O
mass ratios should be equal to 2.6% and 19%, respectively
in both Ganymede and Callisto. From Table 2, depending
upon the considered ISM N2 =NH3 ratio, the N2 =H2 O mass
ratio should be between 0.5% and 3% in the icy Galilean
satellites. For the same reasons, the NH3 =H2 O ratio should
lie between 0.3% and 5.7% and is compatible with the possibility of the existence of deep salty oceans in Ganymede
and Callisto. Note that only a small amount of ammonia
is required to lower the melting temperature of water and
lead to the preservation of deep liquid layers in icy Galilean
satellites 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 evolution
of the chemistry of C and N compounds in the Jovian
subnebula is more plausible than the one currently quoted
in the literature and which was proposed more than two
decades ago by Prinn and Fegley (1981). The adiabatic relationship between T and P in the subnebula used by Prinn
and Fegley (1981) is derived from that assumed by Lewis
(1972) for the solar nebula. This relationship is valid for
a pressure-supported atmosphere and is not adequate to
describe the Jovian subnebula which was supported in its
radial dimension mostly by angular momentum rather than
pressure (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<ning
our model re3ect our strategy, which is certainly questionable. Our choice was ruled by the two following constraints:
(i) to obtain the highest possible initial mass for the disk, in
order to ease the formation of satellites and (ii) to get temperatures of the subnebula precluding the decomposition of
hydrates of ammonia, and eventually that of clathrates hydrates of CO, CH4 , and N2 . In addition, our model is valid
only for a geometrically thin disk.
Condition (i) precludes us to reduce the radius of the nebula or the value of the coeIcient of turbulent viscosity
because it would result in a lower initial mass of the disk.
However, we cannot guarantee that the subnebula is turbulent outwards to the Hill’s radius or during the whole lifetime of the solar nebula. As indicated below, other modelers of subnebula have assumed a much smaller subnebula
radius than we do. Moreover, as pointed out by one referee
(Mosqueira, 2003, private communication), adopting a radius much larger than the location of the outermost satellite
in the case of our turbulent model may be a problem for explaining the reason why no regular satellites are found far
from the planet, as well as the actual location of irregular
satellites. This remark also applies to the model of Canup
and Ward (2002) who conjectured an ad hoc cut-oE but
stated that in general their model leads to a more extended
disk. Condition (ii) implies that we cannot substantially reduce the initial accretion rate because in this case our model
would exhibit temperatures in the inner region of the subnebula too high to prevent the vaporization of water ices,
in con3ict with the inferred composition of Ganymede and
Callisto. A modest reduction of the accretion rate would permit 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 subnebula have been elaborated in the previous years. All recent 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 a
total mass of 0:02Mjup and an accretion timescale of the order of 250 yr, involved the authors to consider the satellite
accretion at a later phase, after the end of the mass in3ow
onto 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, massive
disk (0:03Mjup ) ful<lling a de<ned minimum mass subnebula if species abundances were assumed to be solar in this
medium and a moderately warm and low mass disk (less
massive by 2–3 orders of magnitude than their minimum
mass disk) which satis<ed the compositional constraint
of the satellites. Makalkin et al. (1999) concluded that
it is not possible to derive from the same model a temperature distribution in the disk consistent with the water
content distribution in the Galilean satellites and the minimum mass disk derived from their masses. These authors
concluded to the impossibility to determine which of the
two models is more appropriate for explaining the satellite
formation.
The work of Canup and Ward (2002) pointed out a number of diIculties for explaining the formation of Galilean
satellites and their survival in minimum mass disks like
those de<ned by Coradini et al. (1989) and Makalkin et al.
(1999). Therefore, Canup and Ward (2002) argued that a
much less restrictive and self-consistent scenario consists to
form Galilean satellites in a Jovian subnebula produced during the slowing of gas in3ow onto Jupiter. The scenario of
Canup and Ward (2002) is based on the recent simulations
of Lubow et al. (1999) and D’Angelo et al. (2002) who
showed that a Jupiter-like planet opens a gap in the protostellar disk, but subsequently continues to accrete mass with
an accretion rate decreasing down to about 4:5×10−5 planet
mass/yr (Lubow et al., 1999).
In Figs. 6 and 7, the model favored by Canup and Ward
(2002) is plotted together with our evolutionary model
of the Jovian subnebula. We note that the two turbulent
models present substantial diEerences despite the fact they
are geometrically thin and have similar accretion rates
(8 × 10−8 Mjup =yr at t = 0 for our evolutionary model and
2×10−7 Mjup =yr for the stationary model of Canup and Ward,
2002). Among these diEerences, it can be seen that the radius of our turbulent model extends up to the Hill’s radius.
This leads to a more massive Jovian subnebula described
by our evolutionary model at t = 0, namely 4.7 times more
extended than the stationary model preferred by Canup and
Ward (2002). Another major discrepancy comes from the
use of a time dependent law for the accretion rate of our
turbulent model (see Section 2.1). As a result of this prescription, the surface density of our evolutionary model
decreases by several orders of magnitude in about 107 yr
from higher values than those of the low in3ow model of
Canup 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 and
N volatiles under the forms of hydrates or clathrates hydrates in the Jovian subnebula. Indeed, the temperature and
pressure ranges covered in the outer part of their stationary
model just allow the preservation or the formation of water
ice but are too high to permit C and N hydrates or clathrates
hydrates to be stable.
Mosqueira and Estrada (2003a, b) recently proposed a
stationary model of subnebulae of Jupiter and Saturn drastically diEerent from the present model and of the one of
Canup and Ward (2002). The subdisk of Jupiter is assumed
to be composed of an optically thick region located within
15Rjup from the planet in which turbulence is not excluded,
and surrounded by a laminar and optically thin region extending outwards to 150Rjup . The inner disk is supposed to
have been the leftover of the gas accreted by the forming
planet. The outer disk may result from the solar nebula gas
once Jupiter was almost completed. Mosqueira and Estrada
(2003a, b) argued that Ganymede was formed from the material condensed in the inner part of the subnebula, while
O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361 – 370
Callisto derived its planetesimals from the materials present
in the outer disk.
The examination of the chemical times which characterize the rates of CO to CH4 and N2 to NH3 conversions in the inner part of the model of Mosqueira
and Estrada (2003a, b) shows clearly that the eIciency
of the conversion is extremely weak, leading to the
same conclusions as in our model or the one of Canup
and Ward (2002). However, Mosqueira and Estrada
(2003a, b) do not rule out the presence of ammonia because
it could have formed in the envelope of Jupiter prior to disk
formation or come from the solar nebula and drift inwards
from 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 Callisto
is to assume that (i) these gases were present in a suIcient
amount in the early solar nebula, (ii) they were trapped in a
cold region of the nebula or of the subnebula, (iii) clathrated
planetesimals were present in the region of formation of
these two satellites. Considering the complexity of the satellite system of Jupiter and the scarcity of observational constraints, it is premature to aIrm that these conditions were
ful<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 hydrates in the inner part of the Jovian subnebula, or even to
avoid the outgassing of previously trapped volatiles from
planetesimals, unless the size of these bodies was substantially large. In fact, our suggestion that C and N compounds
could be present in Ganymede and Callisto is only based
on the validity of the prescription of Makalkin and Dorofeeva (1991) for describing the evolution of the accretion
rate of the subnebula. This assumption may be true or may
not be true. The only positive indication we have is that
this prescription seems applicable to the solar nebula, since,
as indicated in Section 2.1, it approximately reproduces the
decrease of the accretion rate with time observed in circumstellar disks. The evolution of the subdisks of giant planets may be more complex however, than that of circumstellar disks. Let us remind that another favorable indication
is that our evolutionary model applied to the subnebula of
Saturn permitted Mousis et al. (2002a, b) to reproduce the
observed molecular composition of the atmosphere of Titan
and its D/H ratio. We have also mentioned in Section 1 that
the presence of ammonia in the interiors of Ganymede and
Callisto would favor the occurrence of subsurface oceans,
which in turn, could explain the magnetic <eld discovered
in these objects (Kivelson et al., 1999). This presence is
possible only if the ammonia hydrates were trapped in planetesimals which formed these satellites.
On the other hand, when considering the initial value
of the accretion rate we have assumed, the validity of our
model is questionable. The <nal accretion rate corresponding to the end of the formation of Jupiter deduced from the
works of Coradini et al. (1995) (2:4 × 10−5 Jupiter mass/yr)
369
and Lubow et al. (1999) (4:5 × 10−5 Jupiter mass/yr) is
at least two orders of magnitudes higher than the initial
accretion rate assumed in our model. Since the calculated
height of the disk is proportional to the accretion rate, it
might be that the assumption of a geometrically thin model
is not valid in our early subnebula. Adopting higher values in our model for the initial accretion rate would request
the use of a non-Keplerian thick disk model (Abramowicz
et al., 1980). Such a complicated study is out of the scope
of the paper. Note, however, that the accretion rate rapidly
decreases with time so that the actual subnebula probably
reached in a short period of time a value consistent with the
initial value assumed in the present report. The same considerations apply to the model of Canup and Ward (2002)
which is also geometrically thin and is calculated for a low
accretion rate. Comparing with the input parameters of the
model of Mosqueira and Estrada (2003a, b) is diIcult because their model is based on a scenario of formation which
is diEerent from ours.
6. Summary
The evolutionary model of the subnebula of Jupiter developed in this report suggests that the conversion of CO
to CH4 and of N2 to NH3 did not occur in the subdisk of
the planet. Therefore, assuming the presence of NH3 and of
CH4 in the subnebula implies that these gases were initially
present 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 only
if the planetesimals from which these satellites were formed
never outgassed their volatiles. The model of subnebula and
the scenario we propose satisfy this condition. However,
we have no direct observational evidence so far that C–N
compounds are present in the interiors of these satellites,
although the presence of hydrate of ammonia would favor
the presence of a deep salted ocean, and accordingly would
be consistent with the internal magnetic <eld measured by
the Galileo spacecraft. On the other hand, the evolution of
the accretion rate we have adopted for our model may be or
may not be right. The only positive indication we have is
that the evolutionary model of Mousis et al. (2002a) elaborated for representing the subnebula of Saturn, and which
is similar to that of the Jovian subnebula, permitted the authors to reproduce the CH4 abundance and the D/H ratio in
the atmosphere of Titan.
Landers deposited on the surfaces of Ganymede and Callisto by future space missions could provide new constraints
on the composition of these objects.
Acknowledgements
We thank Jean-Marc Petit for valuable comments on the
manuscript.
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O. Mousis, D. Gautier / Planetary and Space Science 52 (2004) 361 – 370
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