Orbital Evolution and Migration of Giant Planets M

arXiv:astro-ph/9801292v128Jan1998SubmittedtotheAstrophysicalJournalOrbitalEvolutionandMigrationofGiantPlanets:ModelingExtrasolarPlanetsD.E.TrillingLunarandPlanetaryLaboratory,UniversityofArizona,Tucson,AZ85721W.BenzStewardObservatory,UniversityofArizona,Tucson,AZ85721andPhysikalischesInstitut,UniversitaetBern,Sidlerstrasse5,CH-3012Bern,SwitzerlandT.GuillotUniversityofReading,DepartmentofMeteorology,POBox243,ReadingRG66BB,UKandObservatoiredelaCˆoted’Azur,BP4229,06304NiceCedex04,FranceJ.I.LunineandW.B.HubbardLunarandPlanetaryLaboratory,UniversityofArizona,Tucson,AZ85721A.BurrowsDepartmentofAstronomyandStewardObservatory,UniversityofArizona,Tucson,AZ85721ABSTRACTGiantplanetsincircumstellardiskscanmigrateinwardfromtheirinitial(formation)positions.Radialmigrationiscausedbyinwardtorquesbetweentheplanetandthedisk;byoutwardtorquesbetweentheplanetandthespinningstar;andbyoutwardtorquesduetoRochelobeoverflowandconsequentmasslossfromtheplanet.Wepresentself-consistentnumericalconsiderationsoftheproblemofmigratinggiantplanets.Summingtorquesonplanetsforvariousphysicalparameters,wefindthatJupiter-massplanetscanstablyarriveandsurviveatsmallheliocentricdistances,thusreproducingobservedpropertiesofsomeoftherecentlydiscoveredextra-solarplanets.Inwardmigrationtimescalescanbeapproximatelyequaltoorlessthandisklifetimesandstarspindowntimescales.Therefore,therangeoffatesofmassiveplanetsisbroad,andgenerallycomprisesthreeclasses:(I)planetswhichmigrateinwardtoorapidlyandlosealltheirmass;(II)planetswhichmigrateinward,losesomebutnotalloftheirmass,andsurviveinverysmallorbits;and(III)planetswhichdonotloseanymass.SomeplanetsinClassIIIdonotmigrateveryfarfromtheirformationlocations.OurresultsshowthatthereisawiderangeofpossiblefatesforJupiter-massplanetsforbothfinalheliocentricdistanceandfinalmass.Subjectheadings:extra-solarplanets,orbitalmigration,massloss–2–1.IntroductionTherecentdiscoveries(Mayor&Queloz1995;Marcy&Butler1996;Butler&Marcy1996;Butleretal.1997;Cochranetal.1997;Noyesetal.1997)ofextra-solarplanetshaverevitalizeddiscussionsonthetheoryofplanetarysystemformationandevolution.Inparticular,severaloftheseplanetsarefoundtobeontheorderofaJupiter-mass(1MJ=2×1030g)orgreater,andinverycloseproximitytotheircentralstars(Table1).Previoustothediscoveriesofplanetarycompanionsinverysmallorbits,itwaspredictedthatJupiter-typeplanetswouldform(and,byimplication,exist)onlyatoroutsideoftheiceline(3-5AU)(Boss1995).Inaddition,althoughclosegiantplanetformationmaybetheoreticallypossible(Wuchterl1993,1996),thisrequirestheinitialformationofasolidcoreofatleast5to10Earthmasseswhichmaybedifficulttoachieveveryclosetotheparentstar.ItisthereforemostlikelythatJupiterscannotformatsmallheliocentricdistances(seealsoBoss1995;Guillotetal.1996),whichthusleavesthequestion:Howdidtheobservedmassiveclosecompanionstoseveralstarsgettotheircurrentlocations?Jupiter-massplanetscanmigrateinwardfromtheirformationlocations(see,forexample,Goldreich&Tremaine1980;Ward&Hourigan1989;Lin&Papaloizou1986;Lin&Papaloizou1993;Lin,Bodenheimer,&Richardson1996).Weconsiderunderwhatphysicalconditionsplanetsmaymigrateinward,andhow,where,why,andwhenaplanetwillstopitsinwardmigration.Ratherthanconsidercatastrophicinteractionsamongmorethanoneplanet(Weidenschilling&Marzari1996;Rasio&Ford1996),wemodelisolatedmassiveplanetswhichsmoothlymigrateasaresultofthenettorquesonthebody.Wefindthreebroadclassesformassiveplanets:(I)planetswhichmigrateinwardveryquicklyanddisappearduetomasslossfromRochelobeoverflow;(II)planetswhichmigrateinward,losesomebutnotalloftheirmass,andstablysurviveatsmallheliocentricdistances;and(III)planetswhichdonotloseanymassduringmigration.SomeplanetsinClassIIImoveradiallyonlyasmalldistancefromtheirformationlocations.Inthecontextofthispicture,massiveclosecompanionscanresultfromavarietyofinitialconditions,andformapopulationwhichoverlapswithandincludesthedetectedclosecompanionpopulation.Ourdistributionoffinalmassesandheliocentricdistancespredictsthatmassiveplanetscanbepresentatanyheliocentricdistancebetweentheirformationlocationsandextremelysmallorbits,andwepredictthatasdetectionsensitivitiesincrease,massiveplanetswillbefoundtohaveanalmostcontinuousdistributionofheliocentricdistances,fromafractionofanAUallthewayouttotheicelineorbeyond.Ourgeneralmodelistosumupthetorquesonaplanetandfinditsradialmotioninthecircumstellardisk.Wecompute,inaonedimensionalmodel,torquesonaplanetduetodiskinteractions(inwardfortheparameterswhichweadopt);torquesonaplanetduetointeractionswiththerapidly-spinningstar(outward);andtorquesontheplanetduetomasslossontothestar(outwardfortheconservativemasstransfercase).Sections3,4,and5,respectively,describethecalculationofthesetorquesandtheresultingradialmotions.Thesetorquesmustbecalculatednumericallyinordertocombinetheresultsinaself-consistentmodel.InSection6,wepresenttheresultsofaddingthesetorquestogetherandcalculatingtheorbitalevolutionofmassiveplanets.–3–Ourworkisthefirsttoquantitativelyandself-consistentlyconsiderthesethreetorquesandtheproblemofextrasolarplanets.Lastly,inSection7wediscuss