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The Dynamical Evolution of the Asteroid Belt AlessandroMorbidelli Dep.Lagrange,CNRS,ObservatoiredelaCoted’Azur,Universite´deNiceSophia-Antipolis;Nice,France KevinJ.Walsh SouthwestResearchInstitute;Boulder,Co. DavidP.O’Brien PlanetaryScienceInstitute;Tucson,Az. 5 1 DavidA.Minton 0 PurdueUniversity,DepartmentofEarth,Atmospheric,andPlanetarySciences;WestLafayette,IN 2 n WilliamF.Bottke a J SouthwestResearchInstitute;Boulder,Co. 5 2 The asteroid belt is the leftover of the original planetesimal population in the inner solar system. However, currentlytheasteroidshaveorbitswithallpossiblevaluesofeccentricities ] andinclinationscompatiblewithlong-termdynamicalstability,whereastheinitialplanetesimal P orbitsshouldhavebeenquasi-circularandalmostco-planar. Thetotalmassnowcontainedin E the asteroid population is a small fraction of that existing primordially. Also, asteroids with . h different chemical/mineralogical properties are not ranked in an orderly manner with mean p heliocentricdistance(orbitalsemimajoraxis)asonecouldexpectfromtheexistenceofaradial - gradient of the temperature in the proto-planetary disk, but they are partially mixed. These o propertiesshowthattheasteroidbelthasbeenseverelysculptedbyoneoraseriesofprocesses r t duringitslifetime. Thispaperreviewstheprocessesthathavebeenproposedsofar,discussing s a the properties that they explain and the problems that they are confronted with. Emphasis [ is paid to the interplay between the dynamical and the collisional evolution of the asteroid population,whichallowstheuseofthesizedistributionorofthecraterdensitiesobservedinthe 1 asteroidbelttoconstrainthedynamicalmodels.Wedividetheasteroidbeltevolutionintothree v phases. The first phase started during the lifetime of the gaseous proto-planetary disk, when 4 the giant planets formed and presumably experienced large-scale migrations, and continued 0 2 after the removal of the gas, during the build-up of the terrestrial planets. The second phase 6 occurredaftertheremovalofthegaseousproto-planetarydiskanditbecameparticularlylively 0 fortheasteroidbeltwhenthegiantplanetssuddenlychangedtheirorbits,asaresultofamutual . dynamicalinstabilityandtheinteractionwiththetrans-Neptunianplanetesimaldisk. Thethird 1 phasecoverstheaftermathofthegiantplanetinstability,untiltoday. 0 5 1 : v 1. INTRODUCTION importantobservationalconstraintsontheasteroidbeltare i X and what they suggest. Then, in section 3, we will review The asteroid belt helps us in reconstructing the origin the main models proposed, from the oldest to the most re- r andtheevolutionoftheSolarSystem,probablybetterthan a cent ones, and from the earliest to the latest evolutionary the planets themselves. This is because the asteroid belt phases they address. In Section 4, we will discuss several providesseveralkeyconstraintsthatcanbeusedeffectively implicationsforasteroidsciencefromourcurrentpreferred to guide the development, the calibration and the valida- viewofthedynamicalevolutionoftheasteroidbelt. tionofevolutionarymodels. Comparedtoothersmallbody Thedynamicalevolutionoftheasteroidbelthasalready populations, suchastheKuiperbeltortheOortcloud, the beentheobjectofareviewchapterbyPetitetal. (2002)in constraintsprovidedbytheasteroidbeltareprobablymore theAsteroidIIIbook. Thisreviewhasthereforeanimpor- stringent,duetothefactthatthenumberandtheproperties tant overlap with that chapter. Nevertheless, both our ob- of the asteroids are better known, thanks to ground based servationalknowledgeoftheasteroidbeltandourtheoreti- observations,spacemissionsandmeteoriteanalysis. calunderstandingofSolarSystemevolutionhaveimproved The structure of this review chapter is therefore as fol- significantly since the early 2000, providing an emerging lows. We start by reviewing in section 2 what the most viewofaverydynamicearlySolarSystem,inwhichvari- 1 Fig. 1.— Thepointsshowmeanpropereccentricity(circles)andmeanproperinclination(squares)fortheD > 100kmasteroids, divided into three bins of semi major axis. The error bars show the 1-σ standard deviation. There is little systematic difference in excitationacrossthemainbelt. Theslightlyincreaseofinclinationfromtheinnertotheouterbeltisduetotheeffectoftheg = g 6 secularresonance(seesect.3),whichmoststronglyaffectshighinclinationasteroidsintheinnerbelt. ousepisodesofplanetmigrationplayedafundamentalrole proper eccentricity is 0.145. More importantly, the values insculptingthesmallbodyreservoirsanddisplacingplan- ofeccentricitiesandinclinationsofthelargestasteroidsare etesimals far from their original birth places. Thus this considerablydispersed,withtheformerrangingbetween0 chapter will present in greater details models proposed af- and0.30,whilethelatterrangesbetween0and33degrees ter2002,focusingontheirimplicationsforasteroidscience. (see Fig. 1). It has been shown that asteroids of modest Moreover,whenreviewingmodelsalreadypresentedinPe- inclinations(i < 20◦)filltheentireorbitalspaceavailable tit et al., we will refer to numerical simulations of these for long-term dynamical stability, though some stable re- modelsmadeafterthePetitetal. chapter. gionsaremoredenselypopulatedthanothers(Mintonand Malhotra, 2009, 2011). The reader should be aware that, 2. Observational constraints on the primordial evolu- whateverthepreferredformationmechanism(seeJohansen tionoftheasteroidbelt et al. chapter), planetesimals are expected to have formed oncircularandco-planarorbits. Thus,oneormoredynam- The observational constraints most useful for recon- icalexcitationmechanism(s)withintheprimordialasteroid structingtheformationandevolutionoftheasteroidbeltare beltwereneededtostirupeccentricitiesandinclinationsto thoserelatedtolargeasteroids(largerthan∼50–100kmin randomly dispersed values. Asteroid eccentricities and in- diameter). In fact, it has been argued that these asteroids clinationsdonotshowastrongdependenceonsemimajor are the most likely to be “pristine” in the sense that they axis(Fig. 1) were not generated in large numbers in collisional break- Asecondfundamentalcharacteristicoftheasteroidbelt up events of larger parent bodies (Bottke et al. 2005a; see is the partial mixing of taxonomic classes. Asteroids can chapterbyBottkeetal.),norhavetheybeenaffectedbygas be grouped into many taxonomic classes on the basis of dragandothernon-gravitationalforces(e.g.,theYarkovsky theirvisualandinfra-redspectroscopicsignatures(Tholen, effect;seechapterbyVokrouhlickyetal.). Moreover,there 1984; Bus and Binzel, 2002; DeMeo et al., 2009). As is an emerging view that the first planetesimals were big, shown first by Gradie and Tedesco (1982) for the largest with a preferred diameter in the range mentioned above asteroids, the inner belt is dominated by S-complex aster- (Morbidelli et al., 2009; see chapter by Johansen et al.). oids,manyofwhichareprobablyrelatedtothemeteorites Thus, throughout this chapter we will limit our discussion knownasordinarychondrites(Binzeletal. 1996; seealso to the properties of large asteroids and refer to smaller as- the chapter by Vernazza et al.). The central belt (2.5-3.2 teroidsonlywhenexplicitlymentioned. AU)isdominatedbyC-complexasteroids,probablyrelated A key major characteristic of the asteroid belt popula- to carbonaceous chondrites (Burbine et al., 2002; see also tion is the orbital excitation, i.e. the fact that the eccen- the chapters by DeMeo et al. and Rivkin et al.). The Cy- tricitiesandinclinationsofmanyasteroidalorbitsarequite belesasteroids(3.2-3.7AU),theHildaasteroids(inthe3/2 large (e.g, Petit et al. 2002). The median proper inclina- meanmotionresonancewithJupiter)andtheJupiterTrojan tionofD >100kmasteroidsis11degreesandthemedian asteroids(inthe1/1resonancewithJupiter)aredominated 2 Fig. 2.—Therelativedistributionoflargeasteroids(D > 50km)ofdifferenttaxonomictypesasoriginallyobservedbyGradieand Tedesco(1982). FurtherworksbyMothe´-Dinizetal. (2003),Carvanoetal. (2010)andDeMeoandCarry(2014)demonstratethatthe levelofmixingincreasesforsmallerasteroidsizes. by P-and D-type asteroids (see chapter by Emery et al.). diate physical properties between those of adjacent types; The C2 ungrouped meteorite “Tagish Lake” has been pro- insteaditisduetothecoexistenceofasteroidsofdifferent posed to be a fragment of a D-type asteroid (Hiroi et al., typeswithvariousrelativeproportionsateachvalueofsemi 2001). major axis. Some mixing could come from the fact that Thisstratificationofthemainbeltmakesintuitivesense the thermal and chemical compositional properties of the intermsofageneralviewthatproto-planetarydisksshould disk probably changed over time. However, given that no havetemperaturesdecreasingwithincreasingdistancefrom systematicdifferencesinaccretionagesisobservedamong the central star. In fact, ordinary chondrites are less abun- the main group of chondrites (Villeneuve et al., 2009), it dant in organics and water than carbonaceous chondrites is more likely that some mechanism, possibly the same and therefore are more likely to have formed in a warmer that excited the orbital eccentricities and inclinations, also partofthedisk. Thesmallwatercontentinordinarychon- changed somewhat in a random fashion the original semi drites, well below the solar proportion, suggests that these majoraxesofthebodies,causingtheobservedpartialmix- bodies accreted closer to the Sun than the snowline. The ing. fact that some water is nevertheless present is not in con- Theasteroidbeltcontainsoverallverylittlemass. From tradiction with this statement. A small amount of water the direct determination of the masses of the largest as- couldhavebeenaccretedbycollisionswithprimitivebod- teroids and an estimate of the total mass of the ring of ies scattered or drifting into the inner part of the disk. At bodieswhichcannotbeindividually”weighted”, basedon the opposite extreme, the CI meteorites show no chemical the collective gravitational perturbations exerted on Mars, fractionationrelativetothesolarcomposition,exceptH,C, Krasinskyetal. (2002),KuchynkaandFolkner(2013)and N,Oandallnoblegases, suggestingthattheyformedina Somenzi et al. (2010) concluded that the total mass con- regionofthediskwherethetemperaturewaslowenoughto tained in the asteroid belt is ∼ 4.5 × 10−4 Earth masses allowthecondensationofmostelements. (M ). Thisvalueisverylowcomparedtothatestimatedto ⊕ AsshowninFig. 2,however,asteroidsofdifferenttaxo- haveoriginallyexistedintheprimordialasteroidbeltregion nomictypesarepartiallymixedinorbitalsemimajoraxis, byinterpolatingthemassdensitiesrequiredtoformtheter- which smears the trend relating physical properties to he- restrial planets and the core of Jupiter at both ends of the liocentric distance. The mixing of taxonomic type should belt(Weidenschilling,1977),whichisoftheorderof1M ⊕ not be interpreted as the existence of asteroids of interme- (withinafactorofafew).Thus,themassintheasteroidbelt 3 haspotentiallybeendepletedbythreeordersofmagnitude tudesofnodeofanasteroid(denotedbys)andofaplanet comparedtotheseexpectations. areequaltoeachotherexcitetheasteroid’sinclination. In We can glean insights into how the primordial belt lost thecaseofasteroidsinthemainbelt,theplanets’precession itsmassbyinvestigatingwhatweknowaboutitscollisional frequenciesthatmostinfluencetheirdynamicsarethoseas- evolution. Thecollisionalhistoryofasteroidsisthesubject sociated with the orbits of Jupiter and Saturn. These are ofthechapterbyBottkeetal.,butwereportthehighlights called g and g forthelongitudeof perihelionprecession 5 6 here that are needed for this discussion. In brief, using (the former dominating in the precession of the perihelion a number of constraints, Bottke et al. (2005a) concluded ofJupiter,thelatterinthatofSaturn),ands forthelongi- 6 thattheintegratedcollisionalactivityoftheasteroidbeltis tude of the node precession (both the nodes of Jupiter and equivalenttotheonethatwouldbeproducedatthecurrent Saturnprecessatthesamerate,ifdefinedrelativetothein- collisionalrateover8-10Gy. variableplane,definedastheplaneorthogonaltotheirtotal This result has several implications. First, it strongly angularmomentumvector). suggests that the three orders of magnitude mass deple- The dissipation of gas from the proto-planetary disk tion could not come purely from collisional erosion; such changes the gravitational potentials that the asteroids and intense comminution would violate numerous constraints. planetsfeel,andhencechangestheprecessionratesoftheir Second,itarguesthatthemassdepletionoftheasteroidbelt orbits. Given that the planets and asteroids are at differ- occurred very early. This is because, once the eccentrici- entlocations,theywillbeaffectedsomewhatdifferentlyby tiesandinclinationsareexcitedtovaluescomparabletothe thischangeofgravitationalpotentialandconsequentlytheir current ones, for a given body every million year spent in precessionrateswillnotchangeproportionally. Itisthere- anasteroidbelt1,000timesmorepopulatedbringsanum- forepossiblethatsecularresonancessweepthroughtheas- ber of collisions equivalent to that suffered in 1 Gy within teroidbeltasthegasdissipates. Thismeansthateveryas- the current population. For this reason, the third implica- teroid,whateveritslocationinthebelt,firsthasorbitalpre- tionisthatthedynamicalexcitationandthemassdepletion cession rates slower than the g ,g frequencies of Jupiter 5 6 event almost certainly coincided. This argues that the real and Saturn when there is a lot of gas in the disk, then en- dynamicalexcitationeventwasstrongerthansuggestedby tersresonance(g = g org = g )whensomeappropriate 5 6 thecurrentdistributionofasteroideccentricities. Oneway fractionofthegashasbeenremoved, andeventuallyisno toreconcileamassiveasteroidbeltwiththisscenarioisto longerinresonance(itsorbitalprecessionfrequencybeing assumethatover99%oftheasteroidshadtheirorbitssoex- fasterthanthoseofthegiantplanets: i.e. g > g )afterall 6 citedthattheylefttheasteroidbeltforever(hencethemass thegashasdisappeared. Thesameoccursfortheasteroid’s depletion). This would make the eccentricities (and to a nodal frequency s relative to the planetary frequency s . 6 lesserextenttheinclinations)weseetodaytobethosede- This sweeping of perihelion and nodal secular resonances fined by the the lucky survivors, namely the bodies whose has the potential to excite the orbital eccentricities and in- orbitswereexcitedtheleast. clinationsofallasteroids. Using these constraints, we discuss in the next session This mechanism of asteroid excitation due to disk dis- thevariousmodelsthathavebeenproposedfortheprimor- sipation has been revisited with numerical simulations in dialsculptingoftheasteroidbelt. LemaitreandDubru(1991),LecarandFranklin(1997),Na- gasawa et al. (2000,2001,2002), Petit et al. (2002), and 3. Modelsofprimordialevolutionoftheasteroidbelt finally by O’Brien et al. (2007). Nagasawa et al. (2000) found that of all the scenarios for gas depletion they stud- 3.1. Earlymodels ied (uniform depletion, inside-out, and outside-in), inside- The first attempts to explain the primordial dynamical out depletion of the nebula was most effective at exciting excitationoftheasteroidbeltweremadebyHeppenheimer eccentricities and inclinations of asteroids throughout the (1980) and Ward (1981) who proposed that secular reso- mainbelt. However,they(unrealistically)assumedthatthe nances swept through the asteroid belt region during the nebula coincided with the ecliptic plane. Proto-planetary dissipation of gas in the proto-planetary disk. Secular res- diskscanbewarped,buttheyaretypicallyalignedwiththe onances occur when the precession rate of the orbit of an orbitofthelocallydominantplanet(Mouilletetal.,1997). asteroid is equal to one of the fundamental frequencies of Thus, there is no reason that the gaseous disk in the aster- precessionoftheorbitsoftheplanets. Therearetwoangles oid belt region was aligned with the current orbital planet thatcharacterizetheorientationofanorbitinspace,thelon- oftheEarth(whichwasnotformedyet). Almostcertainly gitudeofperihelion((cid:36))andthelongitudeoftheascending it was aligned with the orbits of the giant planets. Taking node (Ω), each of which can precess at different rates de- the invariable plane (the plane orthogonal to the total an- pendingonthegravitationaleffectsoftheotherplanetsand gular momentum of the Solar System) as a proxy of the nebular gas (if present). The resonances that occur when original orbital plane of Jupiter and Saturn, Nagasawa et the precession rates of the longitudes of perihelion of an al. (2001, 2002) found that the excitation of inclinations asteroid (denoted by g) and of a planet are equal to each would be greatly diminished. Furthermore, since nebular other excite the asteroid’s eccentricity. Similarly, the res- gasintheinside-outdepletionscenariowouldberemoved onances occurring when the precession rates of the longi- from the asteroid belt region before the resonances swept 4 throughit,therewouldbenogasdrageffecttohelpdeplete Excitation would be much stronger in the outer belt than materialfromthemainbeltregion. intheinnerbelt(becausetheembryoscomefromJupiter’s TheworkofO’Brienetal. (2007)accountedforthefact region)anditwouldbemuchstrongerineccentricitythan that the giant planets should have had orbits significantly ininclination. Bycontrast,themainasteroidbeltshowsno less inclined and eccentric than their current values when such trend (see Fig. 1). So, again, this model has since theywerestillembeddedinthediskofgas,becauseofthe been abandoned. If massive embryos have been scattered strongdampingthatgasexertsonplanets(Cresswelletal. fromJupiter’szone,theymusthavecrossedtheasteroidbelt 2008; Kley and Nelson, 2012). They concluded that sec- verybrieflysothattheirlimitedeffectscouldbecompletely ularresonancesweepingiseffectiveatexcitingeccentrici- overprintedbyotherprocesses,suchasthosediscussedbe- tiesandinclinationstotheircurrentvaluesonlyifgasisre- low. movedfromtheinside-outandveryslowly,onatimescale of∼20My. Thisgas-removalmodeisverydifferentfrom 3.2. Wetherill’smodel ourcurrentunderstandingofthephoto-evaporationprocess The first comprehensive model of asteroid belt sculpt- (Alexanderetal.,2014),andinconsistentwithobservations ing,whichlinkedtheevolutionoftheasteroidbeltwiththe suggestingthatdisksaroundsolar-typestarshavelifetimes process of terrestrial planet formation, was that proposed ofonly1-10My, withanaverageof∼3My(eg. Stromet byWetherill(1992)andlatersimulatedinanumberofsub- al. 1993; Zuckerman et al. 1995; Kenyon and Hartmann sequent papers (e.g., Chambers and Wetherill, 1998; Pe- 1995;Haischetal. 2001). tit et al., 2001, 2002; O’Brien et al., 2006, 2007). In this Earlier studies found that the final eccentricities of the model, at the time gas was removed from the system, the asteroidsarequiterandomizedbecausetwoperihelionsec- proto-planetary disk interior to Jupiter consisted of a bi- ularresonancessweeptheentireasteroidbeltinsequence– modalpopulationofplanetesimalsandplanetaryembryos, first the resonance g = g5, then the resonance g = g6. the latter with masses comparable to those of the Moon Thefirstresonanceexcitestheeccentricitiesoftheasteroids or Mars. Numerical simulations show that, under the ef- fromzerotoapproximatelythesamevalue,butthesecond fectofthemutualperturbationsamongtheembryosandthe resonance, sweeping an already excited belt, can increase resonantperturbationsfromJupiter,embryosaregenerally or decrease the eccentricity depending on the position of clearedfromtheasteroidbeltregion,whereasembryoscol- theperihelionofeachasteroidatthetimeoftheencounter lide with each other and build terrestrial planets inside of withtheresonance(Wardetal.,1976; MintonandMalho- 2 AU. While they are still crossing the asteroid belt, the tra, 2011). O’Brien et al. (2007) found that when Jupiter embryosalsoexciteandejectmostoftheoriginalresident and Saturn were on orbits initially closer together, as pre- planetesimals. Only a minority of the planetesimals (and dicted by the Nice Model (e.g., Tsiganis et al. 2005), the often no embryos) remain in the belt at the end of the ter- resonancewithfrequencyg6 wouldonlysweeppartofthe restrialplanetsformationprocess,whichexplainsthemass outer belt, leading to less randomization of eccentricities depletionofthecurrentasteroidpopulation. Theeccentric- in the inner belt. In all studies in which the mid-plane of ities and inclinations of the surviving asteroids are excited theproto-planetarydiskofgascoincideswiththeinvariable and randomized, and the remaining asteroids have gener- planeofthesolarsystemfindthatthefinalinclinationstend allybeenscatteredsomewhatrelativetotheiroriginalsemi tohavecomparablevalues.Thisisbecausethereisonlyone majoraxes. Aseriesofsimulationsnapshotsdemonstrating dominant frequency (s6) in the precession of the nodes of thisprocessisshowninFigure3. JupiterandSaturnandhencethereisonlyonenodalsecu- Whereas earlier simulations assumed that Jupiter and larresonanceandnorandomizationofthefinalinclinations Saturnwereoriginallyontheircurrentorbits,O’Brienetal. oftheasteroids. Clearly, thisisincontrastwiththeobser- (2006, 2007) performed simulations with Jupiter and Sat- vations. Foralltheseproblems,themodelofsecularreso- urn on the low-inclination, nearly circular orbits predicted nancesweepingduringgasremovalisnolongerconsidered in the Nice Model. The resulting asteroids from a set of tobeabletoexplain,alone,theexcitationanddepletionof simulations with these initial conditions are shown in Fig- theprimordialasteroidbelt. ure4. Overall,therangeofvaluescomparewellwiththose Analternativemodelforthedynamicalexcitationofthe observedfortherealasteroids,althoughthefinalinclination asteroid belt was proposed by Ip (1987). In this model, distribution is skewed towards large inclinations. The rea- putative planetary embryos are scattered out of the Jupiter sonforthisisthatitiseasiertoexcitealow-inclinationas- region and cross the asteroid belt for some timescale be- teroidtolargeeccentricityandremoveitfromthebeltthan fore being ultimately dynamically ejected from the So- it is for a high-inclination asteroid, because the encounter lar System. If the embryos are massive enough, their re- velocities with the embryos are slower and more effective peated crossing of the asteroid belt can excite and ran- indeflectingthelow-inclinationasteroid’sorbit. Also,with domize the eccentricities and inclinations of the asteroids, thegiantplanetsonnearlycircularorbits,ittakeslongerto throughcloseencountersandseculareffects. Thatscenario clearembryosfromtheasteroidbelt,allowingmoretimeto has been revisited by Petit et al. (1999), who found that, exciteasteroidstolargeinclinations. whatever the mass of the putative embryos, the resulting As noted earlier, the surviving asteroids have their or- excitationintheasteroidbeltoughttobeveryunbalanced. 5 Fig. 3.— SnapshotsoftheevolutionofthesolarsystemandoftheasteroidbeltinasimulationofWetherill’smodelperformedin O’Brien et al. (2006) and assuming Jupiter and Saturn on initial quasi-circular orbits. Each panel depicts the eccentricity vs. semi majoraxisdistributionoftheparticlesinthesystematdifferenttimes,labeledontop.Planetesimalsarerepresentedwithgraydotsand planetaryembryosbyblackcircles, whosesizeisproportionaltothecubicrootoftheirmass. Thesolidlinesshowtheapproximate boundariesofthecurrentmainbelt. bital semi major axes displaced from their original values, tionsleftopenbyWetherill’smodel: whyisMarssosmall asaresultoftheembryos’gravitationalscattering. O’Brien relativetotheEarth? WhyisJupitersofarfromtheSunde- et al. (2007) found that the typical change in semi major spiteplanetshavingatendencytomigrateinwardsinproto- axisisoftheorderof0.5AU(comparabletoearliersimula- planetary disks? Nevertheless, this scenario has profound tions),withatailextendingto1–2AU,andthesemimajor implicationsfortheasteroidbelt,aswediscussbelow. axiscanbeeitherdecreasedorincreased. Thisprocesscan The Grand Tack scenario is built on results from hy- explainthepartialmixingoftaxonomictypes. Asshownin drodynamics simulations finding that Jupiter migrates to- Fig.2thedistributionoftheS-typeandC-typeasteroidshas wards the Sun if it is alone in the gas-disk, while it mi- a Gaussian-like shape, with a characteristic width of ∼0.5 grates outward if paired with Saturn (Masset and Snell- AU.Thus,ifonepostulatesthatallS-typeoriginatedfrom grove,2001;MorbidelliandCrida,2007;PierensandNel- thevicinityof2AUandallC-typeoriginatedinthevicinity son, 2008; Pierens and Raymond, 2011; D’angelo and of3AU,Wetherill’smodelexplainsthecurrentdistribution. Marzari, 2012). Thus, the scenario postulates that Jupiter formedfirst. Aslongastheplanetwasbasicallyalone,Sat- 3.3. TheGrandTackmodel urn being too small to influence its dynamics, Jupiter mi- A more recent, alternative model to Wetherill’s is the gratedinwardsfromitsinitialposition(poorlyconstrained so-called Grand Tack scenario, proposed in Walsh et al. butestimatedat∼3.5AU)downto1.5AU.Then,whenSat- (2011). InitiallytheGrandTackscenariohadnotbeende- urnreachedamassclosetoitscurrentoneandanorbitclose velopedtoexplaintheasteroidbelt,buttoanswertwoques- tothatofJupiter, Jupiterreversedmigrationdirection(aka 6 Fig. 4.— ThefinaleccentricitiesandinclinationsofasteroidsinWetherill’s(1992)model(blackdots),accordingtothesimulations presentedinO’Brienetal.(2007).Forcomparison,theobserveddistributionoflargeasteroidsisdepictedwithgraydots. it ”tacked”, hence the name of the model) and the pair of primitivebodies(whosedistributionissketchedasadotted planets started to move outwards. This outward migration areainFig. 5),whichareinitiallyoncircularorbitsbeyond continued until the final removal of gas in the disk, which theorbitofSaturn. Thesebodies,beingformedbeyondthe the model assumes happened when Jupiter reached a dis- snowline,shouldberichinwatericeandothervolatileele- tanceof∼5.5AU.Themigrationofthecoresofgiantplan- ments,andthereforeitisagainreasonabletoassociatethem etsisstillnotfullyunderstood(seeKleyandNelson,2012 withC-typeasteroids. for a review). Thus, the Grand Tack model comes in two Afterreaching∼1.5AU(thisvalueisconstrainedbythe flavors. In one, Saturn, while growing, migrates inwards requirementtoformasmallMarsandabigEarth;Walshet withJupiter.Inanother,Saturnisstrandedatano-migration al., 2011; Jacobson et al., 2014; Jacobson and Morbidelli, orbital radius until its mass exceeds 50 M (Bitsch et al., 2014), Jupiter reverses its migration direction and begins ⊕ 2014);thenitstartsmigratinginwardsanditcatchesJupiter itsoutwardmigrationphase,duringwhichthegiantplanets inresonancebecauseitmigratesfaster. Bothversionsexist encounterthescatteredS-typedisk,andthenalsotheprim- with and without Uranus and Neptune. All these variants itive C-type disk. Some of the bodies in both populations are described in Walsh et al. (2011); the results are very arescatteredinwards,reachtheasteroidbeltregionandare similar in all these cases, which shows the robustness of implantedthereasJupitermovesoutofit. themodel,atleastwithingtherangeoftestedpossibilities. The final orbits of the planetesimals, at the end of the TheschemepresentedinFig. 5. hasbeendevelopedinthe outward migration phase, are shown in Fig. 6. A larger frameworkofthefirst“flavor”. dot size is used to highlight the planetesimals trapped in Assuming that Jupiter formed at the snowline (a usual theasteroidbeltregionanddistinguishthemfromthosein assumptiontojustifythelargemassofitscoreanditsfast the inner solar system or at too large eccentricity to be in formation), the planetesimals that formed inside its initial theasteroidbelt. Noticethattheasteroidbeltisnotempty, orbit should have been mostly dry. It is therefore reason- although it has been strongly depleted (by a factor of sev- abletoassociatetheseplanetesimals(whosedistributionis eral hundred relative to its initial population). This result sketched as a dashed area in Fig. 5) with the S-type as- isnottrivial. OnecouldhaveexpectedthatJupitermigrat- teroids and other even dryer bodies (enstatite-type, Earth ing through the asteroid belt twice (first inwards then out- precursorsetc.). Duringitsinwardmigration,Jupiterpene- wards)wouldhavecompletelyremovedtheasteroidpopu- tratesintothediskoftheseplanetesimals.Indoingso,most lation,invalidatingtheGrandTackscenario. Theeccentric- planetesimals(andplanetaryembryos)arecapturedinmean itiesandtheinclinationsoftheparticlesintheasteroidbelt motionresonanceswithJupiterandarepushedinwards,in- are excited and randomized. The S-type particles (black) creasingthemassdensityoftheinnerpartofthedisk.How- arefoundpredominantlyintheinnerpartofthebeltandthe ever,some10%oftheplanetesimalsarekickedoutwardsby C-typeparticles(gray)intheouterpart,butthereisawide an encounter with Jupiter, reaching orbits located beyond overlappingregionwherebotharepresent. Thisisqualita- Saturn,whichcollectivelyhaveanorbital(a,e)distribution tivelyconsistentwithwhatisobserved. thatistypicalofascattereddisk(i.e.withmeaneccentricity As discussed above, the Grand Tack scenario solves increasingwithsemimajoraxis). Insemimajoraxisrange, open problems in Wetherill’s model. The small mass of thisscattereddiskoverlapswiththeinnerpartofthediskof Mars is explained as a result of the disk of the remaining 7 Fig. 5.—AschemeshowingtheGrandTackevolutionofJupiterandSaturnanditseffectsontheasteroidbelt.Thethreepanelsshow threeevolutionarystates,intemporalsequence. Firsttheplanetmigrateinwardsthen,whenSaturnreachesitscurrentmass,theymove outwards. Thedashedanddottedareasschematizethe(a,e)distributionsofS-typeandC-typeasteroidsrespectively. Thedashedand dottedarrowsinthelowerpanelillustratetheinjectionofscatteredS-typeandC-typeasteroidsintotheasteroidbeltduringthefinal phaseofoutwardmigrationoftheplanets. solid material being truncated at ∼1 AU (Hansen, 2009; tionaryphaseofthesolarsystem. Thisisalsopartiallytrue Walsh et al., 2011). Fischer and Ciesla (2014) reported alsofortheinclinationdistribution. So, forwhatconcerns that they could obtain a small-mass Mars in a few percent theeccentricityandinclinationdistributionsonemightde- of simulations conducted in the framework of Wetherill’s clareatieinthecompetitionbetweenthetwomodels. model. However, the rest of the planetary system in these The Grand Tack model makes it conceptually easier to simulationsdoesnotresembletherealterrestrialplanetsys- understand the significant differences between S-type and tem(JacobsonandWalsh,2015).Forinstanceanothermas- C-type asteroids and their respective presumed daughter sive planet is formed in Mars-region or beyond. The out- populations: theordinaryandcarbonaceouschondrites. In wardmigrationofJupiterexplainswhythegiantplanetsin fact, in the Grand Tack model these two populations are oursolarsystemaresofarfromtheSun,whereasmostgi- sourced from clearly distinct reservoirs on either sides of antplanetsfoundsofararoundotherstarsarelocatedat1-2 the snowline. Instead, in Wetherill’s model these bodies AU.Forallthesereasons,onecanconsidertheGrandTack wouldhaveformedjustatthetwoendsoftheasteroidbelt, model more as an improvement of Wetherill’s model than so less than 1 AU apart. Despite such a vast difference in analternative,becauseitisbuiltinthesamespiritoflinking predictedformationlocationsforthesetwopopulationsthe theasteroidbeltsculptingtotheevolutionoftherestofthe debateisopen. Someauthors(e.g. Alexanderetal.,2012) solar system (terrestrial planet formation, giant planet mi- think that bodies formed in the giant planet region would gration–thelatterbeingstillunknownatWetherill’stime). be much more similar to comets than to asteroids, others ItisneverthelessinterestingtocomparetheGrandTack (Gounelleetal., 2008)argue thatthereisacontinuum be- model and Wetherill’s model on the basis of the final as- tween C-type asteroids and comets and a clear cleavage teroidbeltsthattheyproduce. ComparingFig. 6withFig. of physical properties between ordinary and carbonaceous 4,itisapparentthattheGrandTackmodelprovidesabet- chondrites. We review the available cosmochemical con- ter inclination distribution, more uniform that Wetherill’s, straintsandtheiruncertaincompatibilitywiththemodelin but it produces a worse eccentricity distribution, which is sect.3.4. nowmoreskewedtowardstheuppereccentricityboundary A clear distinction between the Grand Tack model and oftheasteroidbelt. Wetherill’s model is that the former provides a faster and AswewillseeinSect.3.5,however,theeccentricitydis- more drastic depletion of the asteroid belt. This point is tributioncanberemodeledsomewhatduringalaterevolu- illustrated in Fig. 7, showing the fraction of the initial as- 8 Fig. 6.— Final semi major axis, eccentricity and inclination distribution of bodies surviving the inward and outward migration of JupiterandSaturn. TheblackparticleswereoriginallyplacedinsideoftheinitialorbitofJupiterandthegrayparticlesoutsideofthe initialorbitofSaturn.Theparticlesfinallytrappedintheasteroidbeltaredepictedwithlargersymbolsthantheothers.Thedashedcurve inthelowerpanelshowstheapproximateboundariesoftheasteroidbeltinwardofthe2/1resonancewithJupiter.Thisfinaldistribution wasachievedinthesimulationsofWalshetal. (2011)accountingonlyforJupiterandSaturn(i.e.,notincludingUranusandNeptune) movingtogetherinthe2/3resonance,assketchedinFig.5. teroidpopulationthatisinthemainbeltregionatanytime. modeldepletestheasteroidbeltonatimescaleof100My. TheGrandTackscenariodepletestheasteroidbeltdown Also, about 2-3 % of the initial population remains in the to0.3%,anddoessobasicallyin0.1My.Assumingthatthe belt at the end. Thus, to be consistent with constraints on finalasteroidbeltconsistedofonecurrentasteroidbeltmass thecurrentpopulationanditsintegratedcollisionalactivity, in S-type asteroids and three current asteroid belt masses theinitialmassinplanetesimalsintheasteroidbeltregion in C-type asteroids (the reason for 4x more total mass in should have been no larger than 200 times the current as- the asteroid beltwill be clarified inSect. 3.6), this implies teroidbeltmass,orlessthanoneMarsmass(Bottkeetal., thattheasteroidbeltatt=0shouldhavecontained0.6Earth 2005b). massesinplanetesimals(therestinembryos). Also,acal- 3.4. Arecosmochemicalconstraintsconsistentwiththe culation of the collision probability of the asteroids as a GrandTackmodel? functionoftime(bothamongeachotherandwiththeplan- etesimals outside of the asteroid belt) shows that the inte- The Grand Tack model predicts that C-type asteroids grated collisional activity suffered by the surviving aster- have been implanted into the asteroid belt from the giant oids during the first 200 My would not exceed the equiva- planetsregion. Isthissupportedorrefutedbycosmochem- lentof4Gyinthecurrentpopulation. Thus,assumingthat icalevidence? the exceeding factor of 4 in the asteroid population is lost Although there is a spread in values, the D/H ratios of within the next 500 My (see Sects. 3.5 and 3.6), the inte- carbonaceous chondrites (with the exception of CR chon- gratedcollisionalactivityofasteroidsthroughouttheentire drites)areagoodmatchtoEarth’swater(Alexanderetal., solar system age would probably remain within the 10 Gy 2012). Oort cloud comets are usually considered to have constraint described in Section 2. In contrast, Wetherill’s formedinthegiantplanetregion(e.g. Donesetal.,2004). 9 Fig. 7.—ThedepletionoftheasteroidbeltinWetherill’smodel(black)andGrandTackmodel(gray).IntheGrandTackmodelnotice thebumpbetween0.1and0.6Myduetotheimplantationofprimitiveobjectsintothemainbelt. Overall,thedepletionoftheasteroid beltisfasterandstrongerintheGrandTackmodel. TheD/HratiowasmeasuredforthewaterfromsevenOort 2008;Abbasetal. 2010;Nixonetal. 2012). cloud comets see Bockelee-Morvan et al., 2012 and refer- Alexanderetal. alsonoticedacorrelationbetweenD/H encesinthatpaper). Allbutone(comet153P/Ikeya-Zhang; andC/Hinmeteoritesandinterpreteditasevidenceforan Biver et al., 2006) have water D/H ratios of about twice isotopic exchange between pristine ice and organic matter higher than chondritic. This prompted Yang et al. (2013) withintheparentbodiesofcarbonaceouschondrites. From to develop a model where the D/H ratio of ice in the gi- thisconsideration,theyarguedthattheoriginalwaterreser- ant planet region is high. However, Brasser et al. (2007) voir of carbonaceous asteroids had a D/H ratio lower than showedthatcomet-sizebodiescouldnotbescatteredfrom Titan,Enceladusoranycomet,againmakingasteroidsdis- thegiantplanetregionintotheOortcloudinthepresenceof tinctfrombodiesformedinthegiantplanetregionandbe- gasdrag(i.e.,whenthegiantplanetsformed),andBrasser yond. However, a reservoir of pristine ice has never been and Morbidelli (2013) demonstrated that the Oort cloud observed;thefactthatEarth’swaterandothervolatilesare populationisconsistentwithanoriginfromtheprimordial in chondritic proportion (Marty, 2012; however see Halli- trans-Neptunian disk at a later time. The recent measure- day, 2013) means that carbonaceous chondrites –wherever ment(Altweggetal.,2014)ofahighD/Hratiofortheice theyformed–reachedtheircurrentD/Hratiosveryquickly, ofcomet67P/Tchourioumov-Guerassimenko,whichcomes beforedeliveringvolatilestoEarth. Possibly,alsotheD/H from the Kuiper belt, supports this conclusion by showing ratio measured for comets and satellites might have been that there is no systematic difference between Oort cloud theresultofasimilarrapidexchangebetweenapristineice comets and Kuiper belt comets. So, care should be taken andtheorganicmatter. in using Oort cloud comets as indicators of the D/H ratio Another isotopic constraint comes from the Nitrogen in the giant planet region. Conflicting indications on the isotope ratio. Comets seem to have a rather uniform localD/HratiocomefromtheanalysisofSaturn’smoons. 15N/14N (Rousselot et al., 2014). Even the comets with Enceladus’D/HratioisroughlytwiceEarth’s(Waiteetal. achondriticD/Hratio(e.g. Hartley2;Hartoghetal. 2011) 2009), but Titan’s D/H ratio is Earth-like (Coustenis et al. have a non-chondritic 15N/14N ratio (Meech et al., 2011). 10