NASA Technical Reports Server (NTRS) 20050166876: A Gas-Poor Planetesimal Feeding Model for the Formation of Giant Planet Satellite Systems: Consequences for the Atmosphere of Titan

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Lunar and Planetary Science XXXVI (2005) 2053.pdf
A GAS-POOR PLANETESIMAL FEEDING MODEL FOR THE FORMATION OF GIANT PLANET SATELLITE
SYSTEMS:CONSEQUENCESFORTHEATMOSPHEREOFTITAN.P.R.Estrada,NASAAmesResearchCenter,Moffett
FieldCA94035,USA,([email protected]), I.Mosqueira,NASAAmesResearchCenter/SETIInstitute,MoffettField
CA94035,USA([email protected]).
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focus of this abstract, we assume that steady hydrodynamic J
turbulenceissufficientlystrongtocausetheevolutionofthe ~ RH /2
circumplanetarygasdiskonashortertimescalethanthatfor Possible irregular satellites?
satellite accretion. This approach uses steady turbulence to
removethegasfromthecircumplanetarydiskbutnottofine-
tuneconditionsofthesubnebularenvironment. Giantplanet Satellite embryos
satelliteformationisthenunderstoodintermsofplanetesimal
dynamics that are largely uncoupled from the gas with the Figure1:Graphicrepresentationofsomeofthecharacteristics
gas surface density left unspecified. However, we do allow ofthecircumplanetaryswarmfromwhichthesatellitesofthe
forthepresenceofsomegastohelpexplaintheobservations. giantplanetswilleventuallyform.
Thissecondofthetwo-endmembermodelsthusconstitutesa
address inorder to provide a viable alternativeto the model
gas-poormodel,wheresatellitesforminamannersomewhat
of [1,2]. In particular, one must demonstrate that it is pos-
analogoustotheterrestrialplanets.
sible to deliver enough mass and angular momentum to the
circumplanetary disk to form the regular satellites. From
Someoftheplausiblefeaturesofthismodel(seeFigure1)
point (2) above, the net angular momentum of the circum-
are:(1)late-arrivingplanetesimalscollidingwithinthevicinity
planetary swarm, which will determine the size of the disk
ofthegiantplanetmaycreateadisko(cid:2)(cid:4)f(cid:3)(cid:6)pr(cid:5)(cid:8)o(cid:7)gradeandretro(cid:2)(cid:9)gr(cid:3)ade
(cid:1) f(cid:31)!r o"m$ whic h"%ıthe "sate l"li(cid:5)tesıwil l" acc r"ete,canıbe e" stimatedfrom
objectsextendingouttoasfaras [5,6],where is (cid:25)(cid:244)(cid:243) (cid:11) (cid:15)(cid:247)(cid:246) (cid:243) (cid:11) (cid:15)(cid:247)(cid:246) (cid:11) (cid:15)
where isadistribu-
theHillradiusofthegiantplanet. Weinitiallyassumeapower-
(cid:10)(cid:12)(cid:11)(cid:14)(cid:13)(cid:16)(cid:15)(cid:18)(cid:17)(cid:19)(cid:13)(cid:21)(cid:20)(cid:23)(cid:22) tionfunctionthatdescribestheaccretionofmassandangular
lawmassdistribu(cid:5)(cid:30)ti(cid:29)onofplanetesimals withan
(cid:24)(cid:26)(cid:25)(cid:28)(cid:27)(cid:8)(cid:27) momentum [9]. We will show that the size of the disk can
exponent (seefootnote2)characteristicforafrag-
belargeenoughprovidedthatmostofthemassthatgoesinto
m(cid:31)! #e"%n$ tedpopulation[6];(2)thenetspecificangularmomentum
makingthesatellitesoriginatedfromtheoutermostregionsof
ofthecircumplanetaryswarmisinitiallyverysmall;(3)
theplanet’sfeedingzone. Usingadistributio(cid:7)(cid:30)n(cid:2)(cid:9)o(cid:3) fsemi-major
closetotheplanet,hypervelocityimpactscanultimatelylead (cid:1)
axesdepletedinsideanannulusofwidth centeredon
toavarietyofoutcomes(i.e.,Jovian-likeversusSaturnian-like
theplanet,wefind
satellitesystems);(4)oncethedensityofsolidsintheswarm
becomes sufficientlylarge, the removal ofmaterialfrom the (cid:31)! (" $
outerdiskisbalancedbyplanetesimalcapturebylargerswarm (cid:31)! " $ (cid:29)(cid:8)(cid:252)(cid:253)(cid:2) (cid:3)(cid:255)(cid:254) (cid:2) ) (cid:2)
particles. Werelyonfragmentationtodecreasethesizesofin- (cid:1)ł’œøß ) (cid:1)(cid:0) (cid:25) (cid:2)(cid:4)(cid:3)(cid:6)(cid:5) (cid:1)(cid:244)ß(cid:30)’ (cid:5) ø (1)
comingplanetesimals,butnottocapturethemintotheswarm.
Excludingsatelliteembryos,atanygiventimethediskmass Point(5)aboveprovides(cid:5)(cid:30)(cid:252)anotherconstraintgiventhatan
islessthanagalileansatellite((cid:1)&(cid:27)(’*),+ g);(5)thesatellitefor- accretiontime (cid:1) (cid:20)(cid:19) (cid:0) (cid:1) (cid:27)-’ . 0 (cid:27)(’ + yearsimplies
(cid:27)-’/.(cid:6)01(cid:27)-’ + (cid:7)(cid:9)(cid:8)(cid:9)(cid:10)(cid:11)(cid:10) (cid:13)(cid:12)(cid:15)(cid:14)(cid:17)(cid:16)(cid:18)(cid:14)
mationtimescaleof years(presumablyconsistent aninnerdiskmass(excludingembryos)of
with Callisto’spartiallydifferentiated state[7])is controlled
bythefeedingofplanetesimalsontothecircumplanetarydisk
[d8is].triWbuetifiornstocfosnastterlulictteadmenosditeylwfoirthJodvisiatannscyesftreomminthwehpircimhathrye (cid:3) (cid:0) (cid:1) (cid:21) (cid:14) (cid:23)(cid:25)(cid:24) (cid:12)ß (cid:14) )(cid:29)(cid:28)(cid:31)(cid:30)(cid:4) (cid:3) !#(cid:14) "(cid:4)$ (cid:28)%(cid:30) (cid:2) (cid:0)’) &(cid:4)& (cid:3) (cid:14)(cid:20)( (2)
(cid:7)(cid:9)(cid:8)(cid:9)(cid:10)(cid:22)(cid:10) (cid:27)(cid:26)
isquiteuniform,andthenadaptanddrawconclusionsforthe
Saturniancase. where (cid:3) , , and (cid:21) are the mass, density, and orbital
(cid:14) (cid:12)(cid:15)(cid:14) (cid:14)
period of Callisto. This yields a surface density of solids
Thereareseveraloutstandingissuesthatthismodelmust (cid:19) (cid:0) (cid:1) (cid:27)-’(cid:4)01(cid:27)(’(cid:8)’ gcm(cid:20) ) . Intheouterdiskwherethebulkof
Lunar and Planetary Science XXXVI (2005) 2053.pdf
materialiscaptured,amass(cid:3) (cid:0) mustbedeliveredtotheinner volatile elements such as Ar that condense at much lower
diskandalso(cid:5) re" plenishedtotheswarmina“collisionalcycle” temperatures & ß(cid:30)’ K.Itisimportanttonote,however,thatto
(cid:7) (cid:10)(cid:1)(cid:0)(cid:3)(cid:2)(cid:4)(cid:2) (cid:1) "(cid:21) ) (cid:7) ) . This provides a constraint on the optical formtheclathrateofAr,themod(cid:29)elof[16]requiresaverylow
depth1 (cid:7) ) intheouterdisk solarnebulatemperature$ (cid:1) ß K.Sinceevenpassivedisk
" ß (cid:19) (cid:21) (cid:3)(cid:8)(cid:7) modelsofTTauristars[17,18]maybetoowarmatthelocation
(cid:7) ) (cid:25) ! ) (cid:1) ) (cid:3) (cid:0) (cid:1) (cid:9)(cid:11)(cid:10) (cid:27)-’ (cid:20) (cid:12) ( (3) ofJupiterfortheincorporationofArintoplanetesimals,itis
(cid:12)(cid:6)(cid:5)(cid:31)(cid:16) ) (cid:7) (cid:8)(cid:9)(cid:10)(cid:11)(cid:10) difficulttoexplainwhythereisanyenrichmentofArineither
wherequantitieswithsubscript“2”refertotheouterdisk, is model.
(cid:12)(cid:13)(cid:5)
thesatellitesimaldensity,(cid:16) ) isthecutoffsizeofthedistribution However, it cannot be assumed that material condenses
ofswarmpariticles,and (cid:3) (cid:7) isthefinalmassofthesystem.
from a cooling protoplanetary nebula at its solar abundance
The surface density needed in the outer disk is (cid:19) ) (cid:1)(cid:255)(cid:27)-’(cid:30)’ g and remains in place. Significant radial migration of solids
(cid:20) )
cm . Hence,forJupiter,aconstantsurfacedensity(solids)
willtakeplace. Indeedthereiscompellingobservationalev-
diskmaysatisfythesystemconstraints. (cid:1) (cid:27)-’(cid:30)’
idence that disks around T Tauri stars can be AU or
Giventheseassumptions,wecananalyticallyestimatethe
more [19,20]. Furthermore, some gas disks around young
amountofmassdepositionperunittimeintothecircumplan-
stars show flat density distributions [21,22], implying that a
etaryswarm (cid:3) (cid:14) usingamassinflowrate andprobabilityof
(cid:15) significantfractionofthemassofthediskislocatedatlarge
capture [5]
(cid:16) distances from the star. Since an ice grain may retain its
(cid:1) (cid:27)(’
amorphousstateforthelifetimeofthenebula( years)
&%
(cid:3) (cid:14) (cid:25) (cid:7) (cid:24)(cid:18)(cid:17) (cid:11) (cid:2) (cid:15) (cid:11) (cid:2) (cid:15) (cid:2) (cid:246) (cid:2) providedthetemperatureis&(’ (cid:9) K[23],itmaybepossiblefor
(cid:15) (cid:19)(cid:16) planetesimalsthattrappedargoneitherasclathrateorinamor-
(cid:2) " (cid:5) " " (4)
(cid:11) (cid:15) (cid:25) (cid:11) (cid:15) ) (cid:11) 0 (cid:15) phousiceincoldregionsofthedisktopreservethemasthey
(cid:15) (cid:12) (cid:7) ) (cid:16) ) (cid:16) (cid:28) (cid:7) ) (cid:8)(cid:22)(cid:24)(cid:23) (cid:7) ) ( migratetowarmerregions. Ifso,ourplanetesimalcollisiona(cid:29)l
$ (cid:1)ł’ ø’
where , , and$(cid:21)(cid:20) $ are the p$ lanetesimal volume density, captureformationmodelwouldappeartoimplyAr/N)
(cid:12) (cid:16)
mean velocity, and cutoff size (quantities with subscript “1” [24]andthatthemolecularnitrogeninTitan’satmospherewas
$ (cid:20) $ $
refertothesolarnebula). Duringeachcollisionalcycle, we deliveredastrapped) ) . However,beforesuchaconclusion
requireamass(cid:1) (cid:3) (cid:14) (cid:10) beprovidedtotheinnerdisk. The can be reached one must first gain an understanding of the
(cid:7) (cid:10)(cid:25)(cid:0)(cid:26)(cid:2)(cid:4)(cid:2)
totalmassdeliveredover(cid:1)&(cid:27)-’ . yearsforareasonablechoice consequencesofplanetesimalcollisionalgrindingontrapped
ofparametersis (cid:1) (cid:27)-’/),+ g[3,10]. However, acaveathereis volatiles.
(cid:24)
that the the power-law index , and the upper size cutoff of ThisworkissupportedbytheNationalResearchCouncil,
thecircumplanetaryswarm(cid:16) ) arenotwellconstrainedatthis andaNASAPGGgrant.
time2. Furthermore,thiscalculationdoesnottakeintoaccount
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(cid:1) (cid:27)-’ .
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Mostofthemassremainsinthelargestparticles.
$(cid:29)(cid:28) (cid:28) (cid:28)(cid:31)(cid:30) (cid:30)(cid:3)!#"