I. INTRODUCTIONFIG. 1.II. THE RESULTING ASTEROID BELT IN OUR REFERENCE SIMULATIONFIG. 2.FIG. 3.FIG. 4.FIG. 5.FIG. 6.III. RESULTS FROM OTHER SIMULATIONSFIG. 7.TABLE ITABLE IIFIG. 8.IV. DISCUSSIONACKNOWLEDGMENTSREFERENCESIcarus 153, 338–347 (2001)doi:10.1006/icar.2001.6702, available online at http://www.idealibrary.com onThe Primordial Excitation and Clearing of the Asteroid BeltJean-Marc Petit and Alessandro MorbidelliCentre National de la Recherche Scientifique, Observatoire de Nice, B.P. 4229, 06304 Nice Cedex 4, FranceE-mail: [email protected] ChambersArmagh Observatory, College Hill, Armagh BT61 9DG, United Kingdom; and NASA Ames Research Center, Moffett Field, California 94035Received April 18, 2000; revised March 23, 2001In this paper, we use N-body integrations to study the effect thatplanetary embryos spread between ∼0.5 and 4 AU would have onprimordial asteroids. The most promising model for the formationof the terrestrial planets assumes the presence of such embryos atthetimeofformation ofJupiter.At theend oftheir runawaygrowthphase,theembryos areonquasi-circularorbits,withmassescompa-rable to thatofthe Moon or Mars.Dueto gravitational interactionsamong them, and with the growing Jupiter, their orbits begin tocross each other, and they collide, forming bigger bodies. A generaloutcome of this model is that a few planets form in a stable con-figuration in the terrestrial planet region, while the asteroid belt iscleared of embryos. Due to combined gravitational perturbationsfrom Jupiter and the embryos, the primordial asteroids are dynam-ically excited. Most of theasteroids are ejected from the system in averyshorttime,thedynamical lifetimebeingontheorder of1My.Afewasteroids(lessthan1%)survive,mostlyintheregion2.8–3.3AU,and their eccentricity and inclination distribution qualitatively re-sembles the observed one. The surviving asteroids have undergonechanges in semimajor axis of several tenths of an AU, which couldexplain the observed radial mixing of asteroid taxonomic types.When the distribution of massive embryos is truncated at 3 AU, weobtaintoo manyasteroidsin theouterpartofthe belt,especiallytoomany Hildas. This suggests that the formation of Jupiter did notprohibittheformationoflarge embryosinthe outerbeltandJupiterdid not accrete them while it was still growing.c° 2001 Academic PressKey Words: asteroids, origin; Solar System, planetary embryos.I. INTRODUCTIONRecent observations, together with the development of newcomputational techniques and computers in the past few years,have launched a renewed interest in the study of the origin andearly evolution of our Solar System. In the present paper, we in-vestigate a scenario that tends to reproduce the observed charac-teristics of the asteroid belt. The asteroids represent a negligiblefraction of the mass of the planets, but we believe that their largenumber means that they carry statistically significant clues forunderstanding the early evolution of our Solar System.We now review the most important characteristics of the aste-roid belt. In order to determine these, we have considered onlyasteroids with diameters larger than 50 km, for the followingreasons. During the 4.5 Gyr of existence of the Solar System,the asteroids have evolved greatly through high-velocity col-lisions. Collision velocities are typically a few kilometers persecond, very often resulting in the complete shattering and dis-ruption of the colliding bodies. Therefore, most of the asteroidswesee todayarenot primordial,butfragments oflargerasteroidsdestroyed in a collision. Only the largest asteroids retain charac-teristics that relate to the formation of the asteroid belt and werenot drastically changed by the later evolution. Forthis reason weconsider only asteroids with diameters D > 50 km. These aster-oids have collisionallifetimes on theorder of theage of the SolarSystem or longer. Most of these are primordial asteroids; i.e.,they were already present in the belt at the end of the excitationand mass depletion of the belt, when the terrestrial planets werecompletely formed. Note, however, that some of these objectscould be fragments from gigantic collisions between embryosduring the very early phases. The few large bodies that were de-stroyedgenerally yielded atmost onelarge fragment(largerthan50 km), with mostly unchanged dynamical characteristics, and aswarm of smaller fragments (Tanga et al. 1999) In addition, it isvery likely that we have discovered all the asteroids larger than50 km; the completeness size is currently assumed to be about35km.Soourstatisticsare not contaminatedbyobservationalbi-ases. From Fig. 1a, we can naturally distinguish three zones: theinner belt, with a < 2.5 AU (3 :1 mean motion resonance withJupiter), the central belt,at2.5<a<3.28 AU (2: 1 resonance),andthe outerbelt, beyond 3.28AU.In theouter belt,all asteroidsbeyond 3.8 AU are in mean motion resonances with Jupiter.The most striking features of the asteroid belt that one wouldlike to explain with a unitary model are as follows:3380019-1035/01 $35.00Copyrightc° 2001 by Academic PressAll rights of reproduction in any form reserved.EXCITATION OF ASTEROID BELT 339FIG. 1. (a) Osculating inclination (top) and eccentricity (bottom) versus semimajor axis for the asteroid belt for bodies larger than 50 km in diameter (solidline: aphelion distance at 4.5 AU; dashed line: perihelion distance at 1.7 AU). (b) Mass distribution of asteroids versus semimajor axis for all asteroids larger than50 km (top) and excluding Vesta (bottom). The dotted lines give the boundaries of the inner belt (left), central belt (middle), and outer belt (right). This diagramhas been drawn from Bowell’s asteroid database (ftp.lowell.edu/pub/elgb/astorb.dat.gz). We used the sizes provided in this database. When no size was given, weused the absolute magnitude H, the albedo Pv, and the relation D = 10(6.244−0.4H−LogPv)/2. The albedo was estimated according to the taxonomic type: 0.2 fortypes K, M, and S; 0.4 for types A and E; 0.05 for types C, D, F, and G; 0.12 otherwise. The density is also chosen depending on the taxonomic type: 1.5 for typesC, D, E, G, and K; 2.5 for types A, E, and S; 3.5 for types M, R, and V.(i) Its strong dynamical excitation. The median eccentricityand inclination of the bodies larger than 50 km are 0.15 and 6◦,respectively, in the inner belt; 0.14 and 10.7◦in the central belt;and 0.1 and 12.1◦in the outer belt. In the outer belt, the me-dian
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