Formation conditions of Titan and Enceladus' building blocks in Saturn's circumplanetary disk
DDraft version February 8, 2021
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Formation conditions of Titan and Enceladus’ building blocks in Saturn’s circumplanetary disk
Sarah E. Anderson,
1, 2
Olivier Mousis, and Thomas Ronnet Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France Univ. Bourgogne Franche-Comt´e, OSU THETA, Besan¸con, France Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, 22100, Lund, Sweden (Received; Revised; Accepted February 8, 2021)
Submitted to The Planetary Science JournalABSTRACTThe building blocks of Titan and Enceladus are believed to have formed in a late-stage circumplan-etary disk around Saturn. Evaluating the evolution of the abundances of volatile species in this diskas a function of the migration, growth, and evaporation of icy grains is then of primary importance toassess the origin of the material that eventually formed these two moons. Here we use a simple pre-scription of Saturn’s circumplanetary disk in which the location of the centrifugal radius is varied, toinvestigate the time evolution of the icelines of water ice, ammonia hydrate, methane clathrate, carbonmonoxide and dinitrogen pure condensates. To match their compositional data, the building blocksof both moons would have had to form in a region of the circumplanetary disk situated between theicelines of carbon monoxide and dinitrogen at their outer limit, and the iceline of methane clathrate astheir inner limit. We find that a source of dust at the location of centrifugal radius does not guaranteethe replenishment of the disk in the volatiles assumed to be primordial in Titan and Enceladus. Onlysimulations assuming a centrifugal radius in the 66–100 Saturnian radii range allow for the formationand growth of solids with compositions consistent with those measured in Enceladus and Titan. Thespecies are then able to evolve in solid forms in the system for longer periods of time, even reachingan equilibrium, thus favoring the formation of Titan and Enceladus building blocks in this region ofthe disk.
Keywords: planets and satellites: composition — planets and satellites: formation — planets andsatellites: individual (Titan, Enceladus) INTRODUCTIONThe exploration of Saturn’s satellite system by the
Cassini-Huygens spacecraft has revealed several puz-zling features regarding the compositions of the moonsTitan and Enceladus, prompting the revision of theirformation models. While the
Huygens probe’s descentto Titan’s surface confirmed that the atmosphere isdominated by N and CH , with a very low CO:CH ratio ( ∼ − ) as previously observed by Voyager andground-based observations (Gautier & Raulin 1997), italso revealed a significant depletion of the primordialnoble gases. The only definitively observed primordialnoble gas detected by the Gas Chromatograph Mass [email protected]
Spectrometer (GCMS) aboard the Huygens probe was Ar, with a Ar/ N ratio lower than the solar valueby more than five orders of magnitude (Niemann et al.2005, 2010). The other primordial noble gases Kr andXe (and Ar) were not detected by the GCMS instru-ment down to upper limits of 10 − relative to nitrogen(Niemann et al. 2005). These absences of detectionsare puzzling as noble gases are notable in the atmo-spheres of telluric planets (Pepin 1992; Wieler 2002), aswell as in the atmosphere of Jupiter (Owen et al. 1999;Mousis et al. 2019). The depletion in CO is also astrong constraint on Titan’s composition since it is be-lieved to have been more abundant than CH in theprotosolar nebula (PSN) (Mumma, & Charnley 2011;Bockel´ee-Morvan et al. 2004; Bockel´ee-Morvan, & Biver2017). Since CO shares a similar volatility with N , itsvery low abundance in Titan’s atmosphere is consistent a r X i v : . [ a s t r o - ph . E P ] F e b Anderson, Mousis, Ronnet with the strongly supported interpretation that the ob-served N is probably not primordial and would resultfrom photolysis, shock chemistry, or thermal decompo-sition of primordial NH (Atreya et al. 1978; McKay etal. 1988; Matson et al. 2007; Sekine et al. 2011; Mandtet al. 2014; Miller et al. 2019). In addition, the flybyof Enceladus’s south pole by the Cassini spacecraft al-lowed the measurement of the composition of its plumesby the Ion and Neutral Mass Spectrometer (INMS), un-veiling a 96–99% concentration of H O, along with smallamounts of CO (0.3 to 0.8%), CH (0.1 to 0.3%), NH (0.4 to 1.3%), and H (0.4 to 1.4%) (Waite et al. 2017).Also, Ar, CO and N were not detected by the INMSinstrument in open source mode, strengthening the ar-gument that the building blocks of Enceladus may haveformed devoid of these three molecules.Together, the measurements of Titan and Enceladus’compositions suggest they could have been assembledfrom similar building blocks. This scenario has beendeveloped by Mousis et al. (2009a) and Mousis et al.(2009b) who proposed that both moons formed frombuilding blocks initially produced in the protosolar neb-ula prior to having been partially devolatilized in a tem-perature range comprised between the formation tem-peratures of CO and N pure condensates and the crys-tallization temperature of CH clathrate in Saturn’s cir-cumplanetary disk (CPD). By doing so, Titan and Ence-ladus’ building blocks would have been devoid of CO andN , while still keeping the entrapped CH to match theobserved compositions. However, these two studies didnot investigate the transport (gas diffusion and drift ofsolid particles) of key volatiles around the locations oftheir respective icelines.An iceline is defined as the radius at which the disktemperature is equal to the sublimation or condensa-tion temperature of water-ice (or any species of inter-est) in the PSN and circumplanetary disks (hereafterCPDs). Inside the iceline, ice sublimates. Outside, iceremains stable, though the motion of particles withinthe disk would allow for solids to exist in front of thisline as well as some vapors to exist beyond. Thus, theicelines induce the creation of peaks of abundances ofvolatile species in disks (Ali-Dib et al. 2014; Mousis etal. 2019; Aguichine et al. 2020). Tracking the abun-dances of volatiles in both solid and vapor states aroundtheir respective icelines should then provide tighter con-straints than previous works on the locations at whichthe building blocks of Titan and Enceladus formed, as-suming that their volatile content is essentially primor-dial.Here we aim to explore the time evolution of the ice-lines of H O ice, NH hydrate, CH clathrate, CO, and N pure condensates, i.e. the key volatiles needed toexplain Titan and Enceladus’ observed compositions,within Saturn’s CPD and derive their impact on the for-mation conditions of the two satellites’ building blocks.Our approach is based on a simple prescription of aCPD model (Canup & Ward 2002; Sasaki et al. 2010)and follows the dynamic radial evolution of icy dust andgases as they cross over the various icelines, estimatinggrowth, fragmentation, and condensation as they driftwithin the disk. The simulation also follows the evolu-tion of the different vapors as they condense on the grainsurfaces or become enriched if icy grains evaporate.An important parameter in our simulations is the lo-cation of the centrifugal radius R c , which corresponds tothe point where the angular momentum of the incominggas is in balance with the gravitational potential of Sat-urn. It is also the injection point of the solid materialentering the CPD from the PSN (Canup & Ward 2002;Sasaki et al. 2010), and its value is overall poorly con-strained in CPDs. For instance, to account for the or-bital distribution of the Galilean satellites, R c has beenestimated to be in the ∼ R Jup range in Jupiter’sCPD (Ruskol 1982). This range could be somewhatlarger if some inward type I migration of satellite em-bryos is taken into account, perhaps R c ∼ R Jup (Canup & Ward 2002). In the case of Saturn’s CPD,Sasaki et al. (2010) have opted to set R c = 30 R Sat ,by similarity with previous studies of the Jovian CPD,while Machida (2009) finds R c = 66 R Sat , by takinginto account the specificity of the disk (lower mass ofthe planet and larger Hill’s radius). On the other hand,recent simulations of gas accretion onto a CPD showthat the material infalling towards the subdisk could bedistributed out to much larger distances, of the orderof ∼ R p (Szul´agyi 2017). Here, we investigate theinfluence of the variation of R c ’s location in the forma-tion region of the satellites’ building blocks. This allowsus to show that the abundance of solid material withinthis disk strongly depends on the radial distance of itsinjection point.Section 2 is dedicated to the description of the diskand transport models. Section 3 presents the results ofseveral computations with different initial conditions forthe delivery of particles from the CPD, namely differentpositions of R c . Conclusions are presented in Sec 4. MODEL2.1.
Gas Starved Accretion Disk
We consider a circum-Saturnian accretion disk withan inflow of material from the surrounding PSN basedon the approaches of Canup & Ward (2002) andSasaki et al. (2010). It is limited by the outer radius ormation conditions of Titan and Enceladus’ building blocks Figure 1.
Disk steady-state pressure, temperature, and gassurface density for the gas starved accretion disk model ofSaturn at t = 0 (solid lines), t = 10 yr (dot-dashed lines),and t = 5 × yr (dashed lines) for R c = 30 R S at . Theevolution of these quantities is very slow in the CPD andcan even be seen as stationary over short timescales. Thepresent day locations of Enceladus and Titan are shown forreference. R d = 200 R Sat by processes such as solar torques orthrough collisions with shocked regions. The CPD isfed through its upper layers from its inner edge up tothe centrifugal radius R c by gas and gas-coupled solidsinflowing from the PSN. In the following, we start withthe assumption that R c = 30 R Sat (Canup & Ward2002), and also investigate several cases at differentradii within the CPD (see Sec. 3). In this 1D model,for each point of the radius r , we have an integratedsurface density Σ which describes the integrated densityover the vertical slice of the disk. The quantities thatinterest us are the surface density of the dust Σ d and thesurface density of the vapor Σ v . These will be comparedto the surface density of the PSN gas, Σ g . Here, “dust”refers to icy grains.The surface density of the disk gas is given by (Canup& Ward 2002):Σ g (cid:39) F p πν λ ( r ) , (1) where F p is the total infall rate, ν is disk gas turbulentviscosity. The turbulent viscosity of the CPD is de-fined via ν = αC s /Ω K (Shakura & Sunyaev 1973),where α (set to 10 − ) is the viscosity parameter.Ω K = (cid:112) GM Sat /r is the Keplerian frequency with G defined as the gravitational constant and M Sat is themass of Saturn. C s is the isothermal sound speed givenby C s = (cid:112) kT /µmp , where k the Boltzmann constant, µ the mean molecular weight, and m p the proton mass.The coefficient λ ( r ) is set equal to: λ ( r ) = 54 − (cid:114) R c R d − (cid:16) rR c (cid:17) for r < R c , and λ ( r ) = (cid:114) R c r − (cid:114) R c R d for r ≥ R c . (2)In the steady accretion state, the total infall rate isregulated by a parameter τ G = M Sat / ( dM/dt ) − ,where dM/dt is the inflow rate, so that F p, = M Sat /τ G .We adopt τ G = 5 × yr for Saturn (Sasaki et al.2010). The total infall rate follows an exponential lawdecay via F p = F p, exp( − t/τ Dep ), with the timescaleof CPD depletion τ Dep set to 3 × yr (Canup & Ward2006; Sasaki et al. 2010).The CPD is heated by luminosity from the centralplanet, viscous dissipation, and energy dissipation asso-ciated with the difference between the free-fall energy ofthe incoming gas and that of a Keplerian orbit. Assum-ing that viscous dissipation is dominant, the photosur-face temperature of the CPD ( T d ) is determined by abalance between viscous heating and blackbody radia-tion from the photosurface (Canup & Ward 2002; Sasakiet al. 2010): σ sb T d (cid:39)
98 Ω K ν Σ g = 3Ω K π F p λ ( r ) (3)The disk temperature profile at t = 0 can then be givenas follows: T d, = 3Ω K πσ sb F p, λ ( r ) (4)Using this expression, the disk temperature can be writ-ten as a function of time: T d (cid:39) T d, exp (cid:16) − t τ dep (cid:17) . (5)The inflow rate is also constrained by the requirementthat temperatures be low enough for pure condensatesto remain stable in the outer regions of Saturn’s CPD,a requirement which this model fulfills without alter-ation, showing similar values as Canup & Ward (2002) Anderson, Mousis, Ronnet for the Jupiter disk. Figure 1 presents the thermody-namic properties of the CPD model used throughoutthis paper with R c = 30 R Sat .2.2.
Grain size evolution
The dust evolution model is derived from the approachof Birnstiel et al. (2012). The particles are evenly in-jected into the disk with a uniform size a = 10 − m.These micron-sized crystalline icy grains evolve in sizeand position through collisions, fragmentation, and ra-dial drift due to gas drag. In our calculations, the size ofgrains increases before it reaches an equilibrium corre-sponding to the minimum value between fragmentationand radial drift.Fragmentation occurs when the relative velocity of thedust grains due to turbulent motion exceeds the frag-mentation velocity threshold u f . We set the latter to 10m s − (Birnstiel et al. 2012). The dust internal densityis set to ρ s = 1g cm − . The size of the grains, limitedby their fragmentation, is (Birnstiel et al. 2012): a frag = 0 .
37 2Σ g πρ s α u f c s . (6)In many cases, the grains drift inward too quickly forthem to grow any larger. The size of these grains, lim-ited by their drift, is given by: a drift = 0 .
55 2Σ d πρ s v K c s (cid:12)(cid:12)(cid:12) d ln P d ln r (cid:12)(cid:12)(cid:12) − , (7)where v K is the keplerian velocity, P = c s ρ g and ρ g = Σ g / πH g the pressure and gas density at midplane,with H g the gas scale height. The prefactor f d = 0 . Transport Model
We assume that all the species are simultaneously re-leased into the disk, and that this mixture has the com-position of the PSN, a mixture which radially diffusesand advects. The species are initially both in solid orgaseous forms, depending on where they are in the disk.Σ i represents the surface density of species i we intendto study either in vaporous or solid form. We integratethe advection-diffusion equation using a forward Eulerintegration (Birnstiel et al. 2012) :Σ i ∂t + 1 r ∂∂r (cid:34) r (cid:32) Σ i v i − D i Σ g ∂∂r (cid:32) Σ i Σ g (cid:33)(cid:33)(cid:35) + ˙ Q = 0 (8) where v i and D i are the radial velocities and the dif-fusivities of species i respectively. ˙ Q corresponds tothe source term of species i vapor released to the gasand is given by Σ ice / ∆ t beyond the iceline, with ∆ t thetimestep of the simulation. The last values to calculateare the velocity of the dust v d , the Stokes number St, theradial velocity of the gas, and the diffusivity (Birnstielet al. 2012). v d is given by: v d = − ηv K + 11 + St v g , (9)where v g is the radial inward gas velocity given by v g = − ν/ r , with ν the turbulent diffusivity of thegas described in Sec. 2.1, and η = − (1 / h g d ln P/d ln r is a measure of the pressure support of the disk, where h g ≡ H g /r is the aspect ratio of the disk. In otherwords, the parameter η describes the deviation of theazimuthal velocity of the gas from the keplerian value, v φ,g = (1 − η ) v K . The Stokes Number describes the aero-dynamic properties of the particles and is determined asfollows:St = aπρ s g . (10)Finally, the diffusivity D of the vapor species is as-sumed to be that of the gas D g = ν and the diffusivityof the dust is given by: D d = D g . (11)2.4. Source term
The dust surface density decreases in the CPD untilalmost no particles are left over very short time frames(fewer than 10 yrs). A disk that depletes at this ratewould not be able to survive over the timescales nec-essary for satellite formation. Our observations on thesustainability of particles in Saturn’s CPD agree withthose of Ronnet et al. (2017). Their model for the mo-tion of particles of different sizes evolving in the Jupitersystem model found that small particles in the order of10 − m moved very rapidly in Jupiter’s disk, often dis-persing entirely in less than 500 years. Particles over10 − m ablated in much less time, often entirely subli-mating in less than 20 years.These simulations show that no disk could be sustain-able at the rate of accretion we are seeing here. An addi-tional source of solids needs to be added so that our solidparticles could continue to exist over the timescales nec-essary for the formation of moons. To overcome this is-sue, we follow the prescription of Canup & Ward (2002) ormation conditions of Titan and Enceladus’ building blocks R c . As gas and solids are delivered to the disk,the gas then sustains a quasi-steady state, while the sur-face density of the solids build up over time. While thegas component of the disk viscously spreads outwardand onto the planet, the solids rapidly accumulate inthe region where they are initially delivered, providinga mechanism for accreting large satellites in a limitedregion extending from the surface of the planet to thecentrifugal radius R c . This would also explain why wedo not see large moons beyond this radius, despite thetidal stability of the region. The injection rate of solids˙Σ solids at the centrifugal radius R c of the CPD is then(Canup & Ward 2002):˙Σ solids = f × F p πR c [ r < R c ]0 [ r > R c ] , (12)where f is the solids-to-gas ratio in the region of regu-lar satellites, here assumed to be ∼ × − (volumemixing ratio). This value corresponds to the sum of thegas phase abundances of the species considered in ourstudy (see Table 1). RESULTSWe place our work in the context of the satellite for-mation scenario proposed by Mousis et al. (2009a,b), in
Figure 2.
Initial enrichments in water, ammonia, methane,carbon monoxide, and nitrogen in solid forms, scaled to theelemental abundances, assumed to be protosolar (Lodders2003). Current orbits of Enceladus and Titan, as well asthe location of the centrifugal radius R c , are shown for ref-erence. The blue rectangle represents the ideal location forthe formation of the building blocks of both moons in orderto match their observed compositional data. Table 1.
Parameters adopted for equations (see Sec. 2)describing the equilibrium vapor pressure curves of differentcondensates. Gas Phase abundances are provided as volumemixing ratios relative to H . Species X A B X/H H O -1750.286 7.2326 4 . × − NH -2878.23 8.00205 4 . × − CH -2161.81 11.1249 3 . × − CO -411.24 5.2426 2 . × − N -360.07 4.7459 4 . × − which the building blocks of both Titan and Enceladusare assumed to be formed between the locations of theCH clathrate iceline and those of CO and N pure con-densates in Saturn’s CPD. By doing so, the satellitesbuilding blocks are presumed to be devoid in primor-dial CO and N while they retain the trapped CH , inagreement with Titan and Enceladus’ composition mea-surements.In order to determine the positions of the icelines ofH O ice, NH hydrate, CH clathrate, CO, and N purecondensates, we compute the partial pressure of species i at each incremental radius. We then calculate theequilibrium pressure of the species based on the tem-perature at that radius and compare it to the partialpressure. Equilibrium pressure equations for H O, CO,and N pure ices derive from Mousis et al. (2008) andare in the form log P = A/ T + B, where P and T arethe partial pressure (bars) and the temperature (K) ofthe considered species, respectively. Equilibrium pres-sure equations for NH hydrate and CH clathrate de-rive from Hersant et al. (2004), and are in the form ln P = A/ T + B. If the partial pressure of the species exceedsits equilibrium pressure at that radius, the species willbe solid. Otherwise, it will sublimate. The gas phasecomposition of Saturn’s CPD is also assumed to be pro-tosolar (Mousis et al. 2009a). The abundances of thedifferent species are derived from the assumption thatall O is distributed between H O and CO, all N is inthe form of N and NH , and C only in the form of COand CH , with a CH /CO ratio of 0.014 (Mousis et al.2009a). Table 1 shows the parameters A and B derivedfrom Hersant et al. (2004) and Mousis et al. (2008) andadopted for the different equilibrium curves, as well asthe abundances of relevant species taken from Mousiset al. (2009a). In the following, we first investigate theevolution of solids within the CPD assuming the loca-tion of R c is 30 R Sat , a value consistent with those esti-mated in Jupiter’s CPD (Canup & Ward 2002), then westudy the influence of placing this parameter to highersaturnocentric distances.
Anderson, Mousis, Ronnet
Figure 3.
Evolution of water vapor (dashed lines) and ice (solid lines) in the Saturnian system over 5000 yr of evolution asa function of distance to Saturn without injection of solids (left) and with the injection of solids (right). The dust and thevapor are normalized to the initial abundance of water (H O/H ) = 4.43 × − . Two things are evident: first, how quicklythe particles move in the system. Second, how quickly the disk depletes: after a few thousand years, almost no dust or vaporremain if there is no source of solids. Each species is characterized by its own surface den-sity in the CPD, either in gas or solid phase, whose valueis derived from the disk’s surface density and its individ-ual abundance. At t = 0, the CPD model is filled withdust whose composition is determined from our initialratios. Any species located at closer distances to Saturnthan its corresponding iceline is in gaseous phase. Be-yond their respective icelines, these species are in dustform with sizes of 10 − m.3.1. Evolution of solids assuming R c = 30 R Sat
Figure 2 represents the quantity of dust in the systembefore any motion has occurred, giving us a visual rep-resentation of the location of icelines. At this epoch, thesublimation temperatures and iceline locations are 153.5K and 12.0 R Sat for H O, 96.5K and 21.1 R Sat for NH hydrate, 53.4 K and 40.7 R Sat for CH clathrate, 22.4K and 90.4 R Sat for CO, and 20.3 K and 103.7 R Sat forN pure condensates.As the disk cools with time, the icelines migrate in-ward toward Saturn. However, on the short timescalesthat we are interested in, the disk can be seen as sta-tionary and the inward migration of the icelines ignored.If Titan and Enceladus mainly assembled from pebblesformed between the iceline of CH clathrate and those ofCO and N pure condensates, as it is investigated here,the very slow cooling of our CPD model implies thatthe two moons never formed at their current positions.While it is possible for us to adjust the parameters of the Figure 4.
Evolution of H O, NH , CH , CO, and N dustnormalized to their initial abundances (see Table 1) in theSaturnian system over 10 years of evolution as a function ofdistance to Saturn with the injection of solids. Species whosecondensation radii are close to R c (here NH , and H O toa lesser extent) keep significant abundances while the others(CH , CO, and N ) deplete with time. disk so as to fit this constraint, there is no firm indica-tion that the building blocks of the two bodies actually ormation conditions of Titan and Enceladus’ building blocks O, there is no gas or dust remaining inthe disk after a mere 5 × years. This would seem toindicate that the moons would have formed very quickly,which is impossible based on even the most optimisticestimates, which require approximately 10 years (Cili-brasi et al. 2018). As a result, we are forced to add asource term as established in section 2.4, where a steadyinjection of solids is set at R c . As we inject solids intothe disk, most will continue to be sublimated as theyare pulled through the different icelines during their in-ward drift. Figure 3 shows that, at a given epoch of theCPD evolution, the solid water abundance grows andthen decreases radially because of the diffusion of va-por outward the iceline. At any given location of R c ,the water abundance also increases and then decreasesover time until it reaches a steady state. This state isreached after 3 × years. This creates a zone wherethe quantity of solid H O is stable for a long period oftime.Figure 4 depicts the evolution of H O, NH , CH , CO,and N in solid phases as a function of the distance toSaturn in the CPD over 10 years of disk evolution, withthe injection of solids. Because the icelines of NH and(to a lesser extent) of H O are closer to the locationof the injection point of solids ( R c ), these species keepsignificant solid abundances in the disk. CO, CH , andN , whose respective icelines are far beyond the positionof R c , are depleted before enough time has passed forany building blocks to form. Also, altering the solids-to-gas ratio has no effect on the lifetime of these solids asit has no influence on the location of injection. In thiscase, the building blocks of Titan and Enceladus cannotincorporate significant amounts of CH from the CPDto explain their compositional properties. Here, the onlypossible alternative is to assume a secondary origin forCH in these two bodies (see Sec. 4).3.2. Evolution of solids assuming R c > R Sat
In this section we examine the influence of the positionof R c on the solid abundances in the CPD. The distanceout to which material is accreted onto the CPD remainsuncertain and could be much larger than the current ra-dial extent of the satellite systems of the giant planets(Drazkowska & Szulagyi 2018). In order to form thebuilding blocks of the Saturnian moons, we would ide-ally need to be at a position at which the abundance ofdust significantly exceeds its initial abundance, based on the minimum conditions to develop streaming instabil-ity and planetesimals (Yang et al. 2017). By expandingthe centrifugal radius to larger distances, we are ableto inject solids nearer each species’ iceline and allow forthe formation and growth of solids at higher radii. Asa result, the species are able to evolve in the system forlonger periods of time, even reaching an equilibrium.Figure 5 shows simulations similar to those repre-sented in Fig. 4, but for R c = 66 R sat and 100 R sat ,the former value corresponding to the centrifugal radiusfound by Machida (2009). Beneath R c = 66 R sat , weare unable to form and maintain solids for long periodsof time. Above R c = 100 R sat , the abundances of COand N are too high for current observations. For themoons to form within the constraints of the estimationof the primordial composition of their building blocks, R c would have had to be within this interval, whichis also bracketed by the positions of the CH clathrateand CO icelines. Within this interval, the abundancesof primordial N and CO dust are negligible while thoseof H O, NH , and CH are significant, leading to a com-position similar to that expected for the building blocksof Titan and Enceladus.Interestingly, the variation of the location of the cen-trifugal radius R c affects both the temperature profileof the CPD and the positions of the various icelines.Species with icelines located at distances interior to R c (such as H O and NH hydrate) progress inwards with R c moving outward. In contrast, species whose icelineslie outside of R c (such as CO and N pure condensates)gradually move backwards. Table 2 summarizes the lo-cations of the various icelines in Saturn’s CPD as a func-tion of the position of R c . Table 2.
Positions of the icelines as a function of the valueof R c (in units of R sat ). Species 30 R c R c R c H O 12.0 11.2 10.5NH DISCUSSION AND CONCLUSIONBy using a classical prescription for Saturn’s CPD, wehave investigated the time evolution of the icelines ofH O ice, NH hydrate, CH clathrate, CO, and N purecondensates, as well as their impact on the formationconditions of the building blocks of Titan and Enceladus.To match their compositional data, the building blocks Anderson, Mousis, Ronnet
Figure 5.
Evolution of H O, NH , CH , CO, and N dust normalized to their initial abundances (see Table 1) in the Saturniansystem over 10 years of evolution as a function of distance to Saturn with the injection of solids at R c = 66 R sat (left) and R c =100 R sat (right). The most consistent position of the centrifugal radius would be in between these two values. If placed beyond,the carbon monoxide solids would be highly abundant, in contrast with the inference that Titan and Enceladus accreted fromCO- and N -depleted building blocks. of both moons would have had to form in a region of theCPD located between the icelines of CO and N at theirouter limit, and the iceline of CH clathrate as theirinner limit. We find however that a source of dust atthe location of R c does not guarantee the replenishmentof the disk in the volatiles assumed to be primordial inTitan and Enceladus.The centrifugal radius was initially envisioned toroughly match the radial extent of the current satellitesystems, with typically assumed values of R c ∼ R Sat , so as to account for their compactness relativeto the expected sizes of the CPDs (Ruskol 1982; Canup& Ward 2002, 2006). In this case, we show that only theabundance of solid water remains substantial irrespec-tive of time because its iceline is inside the centrifugalradius R c . Any volatile species whose iceline lies beyonddepletes too rapidly for any planetesimal formation tooccur. We also performed simulations for R c values of 66and 100 R Sat , considering the studies made by Machida(2009) and Szul´agyi (2017) regarding the structure ofSaturn’s CPD, and still assuming that the injectionpoint of matter is at the location of R c . By doing so,we are able to inject solids nearer each species’ icelineand allow for the formation and growth of solids withcompositions consistent with those measured in Ence-ladus and Titan at radii between 66 and 100 R Sat . As a result, the species are able to evolve in solid forms inthe system for longer periods of time, even reaching anequilibrium, thus favoring the formation of Titan andEnceladus’ building blocks in this region of the CPD.Our results suggest that the dynamical evolution of theCPD matters little, at least to some extent. Indeed, oneis able to predict the location of R c and moon buildingblock formation solely based on the initial pressure-temperature profile of the disk.Our results also imply that a Saturn’s CPD present-ing a large centrifugal radius is also consistent withthe formation of Iapetus, which is currently located at ∼ R Sat , because matter remains on longer timescalesin the outer CPD. Interestingly, because the clathrationtemperature of Xe is higher than that of CH , this no-ble gas should be incorporated as well in the satellitesbuilding blocks, implying that an alternative explana-tion is needed to explain its deficiency in Titan’s at-mosphere (Mousis et al. 2009a). Several post-formationscenarios have already been proposed, including the re-moval of Titan’s noble gases by their sequestration insurface clathrates (Mousis et al. 2011), or their trappingby the haze present in the atmosphere (Jacovi & Bar-Nun 2008). One can note that the Cassini INMS didnot confirm the absence of Xe shown by the Huygens ormation conditions of Titan and Enceladus’ building blocks ρ s = 1g cm − in all our calculations, corresponding to a pure icy com-position in the absence of porosity. To assess the influ-ence of the combined roles of porosity and density, weperformed dust evolution simulations for ρ s varying be-tween 0.5 and 2 g cm − . In all cases, the results are qual-itatively similar to those obtained with ρ s = 1g cm − and do not alter our conclusions.There remain many uncertainties regarding the for-mation mechanism of Saturn’s moon system. Somescenarios envision that all the moons accreted withinthe gaseous CPD of the planet (Mosqueira & Estrada2003a,b; Canup & Ward 2006). In this case, a mas-sive moon such as Titan could have migrated inwardover large distances within the CPD through tidal in-teraction with the gas disk (Canup & Ward 2002, 2006;Ronnet & Johansen 2020; Fujii & Ogihara 2020). Titancould have thus formed at much larger orbital distancesthan its present location, in line with our findings re-garding the composition of solids in the CPD. Titan’smigration could either have been stranded close to itspresent orbit due to migration traps arising from strongthermal gradients in the CPD (Fujii & Ogihara 2020)or, alternatively, it could have migrated to much closerdistances from Saturn and subsequently migrated out-wards due to tidal interaction with the planet (Laineyet al. 2020).In the case of Enceladus, its much smaller mass pre-cludes a scenario involving the migration of the moonover substantial distances. However, several scenariospropose that the small and mid-sized moons of Saturnare not primordial but rather represent a second gen-eration of satellites which would either derive from thespreading of material from Saturn’s ring (Charnoz et al.2011; Crida & Charnoz 2012; Salmon & Canup 2017),or from the disruption of a primordial system consist-ing of larger moons, akin to the Galilean system (Sekine& Genda 2012; Asphaug & Reufer 2013). In the latterscenario, it is possible that the primordial moons weremassive enough to have migrated over substantial dis-tances in the gaseous CPD during their accretion. If, onthe other hand, Enceladus accreted from material de-riving from Saturn’s ring, the relevance of our resultsdepends on the origin of the rings, which remains highlydebated (see, Ida 2019, for a recent review). Canup(2010) proposed that the rings could have originatedfrom the tidal disruption of a massive (comparable to Ti-tan) moon that would have formed in the gaseous CPDand migrated interior to the Roche radius of the planet.This scenario would remain consistent with the hypothe- sis of primordial methane accreted by the forming Titanand Enceladus, and is supported by the findings of theCassini INMS instrument which identified CH , CO ,CO, N , H O, NH , and organics in the D ring materialduring the Grand Finale (Miller et al. 2020).The accretion of primordial CH by the moons, asproposed here, implies that the subdisk was fed in low-temperature solids originating from the nebula, whichwere containing methane. Our model works only in thecase where the inward drift of grains and particles doesnot exceed the metric size. However, the bulk of the solidmaterial could have been delivered to the CPD throughthe capture and ablation of planetesimals on initiallyheliocentric orbits (Mosqueira et al. 2010; Ronnet et al.2018; Ronnet & Johansen 2020). Small planetesimals( r <
10 km) could thus contribute a significant amountof material in the outer regions of the CPD. Such plan-etesimals would be CO- and N -rich and their large sizeswould prevent the significant loss of ultravolatiles dur-ing their migration inward the CPD, due to their lowthermal conductivity (Ronnet et al. 2017).On the other hand, the presence of liquid water inthe interiors of Titan and Enceladus (Iess et al. 2012;Waite et al. 2017) could convert CO either into CO or carbonate (depending on pH) for oxidizing condi-tions, or reduce it to organic carbon and, eventually,CH (Shock & McKinnon 1993; Glein & Waite 2018).There is also evidence from the bulk composition ofcomet 67P/Churyumov-Gerasimeko that ice-poor outersolar system building blocks may exist (Choukroun etal. 2020). This process may also explain the depletionof CO in Titan’s atmosphere relative to atmospheric N and CH . It may also produce post-accretion N fromeither NH and/or organic nitrogen (Glein et al. 2009;Neveu et al. 2017). In other words, aqueous process-ing of primordial volatiles in satellite oceans could alsogenerate compositions similar to those inferred in the at-mosphere of Titan or in the plumes of Enceladus. A wayto constrain the origin of CH in the plumes of Ence-ladus would be the measurement of its D/H ratio. If theD/H ratio in CH is close to the measurement of D/H inH O made by the INMS instrument aboard the Cassinispacecraft ( ∼ × − ; Waite et al. (2009)), then thismethane should be the outcome of hydrothermal reac-tions (Mousis et al. 2009b). In contrast, a substantiallylower value would be compatible with a primordial ori-gin, i.e. methane originating from the PSN (Mousis etal. 2009b). Data on D/H in cometary methane wouldprovide a complementary test. One would also expect anet depletion in Ar in the plumes of Enceladus, sim-ilarly to Titan’s atmosphere, if the two moons formedfollowing our scenario. On the other hand, the plume0
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