Terrestrial Planets Formation under Migration: the Systems near 4:2:1 Mean Motion Resonance

8.1 MB·

by  Zhao Sun

Mon.Not.R.Astron.Soc.000,1–??(2015) Printed12January2017 (MNLATEXstylefilev2.2)
Terrestrial Planets Formation under Migration: the Systems near
4:2:1 Mean Motion Resonance
Zhao Sun1,2, Jianghui Ji1⋆, Su Wang1, Sheng Jin1
7
1 1CASKeyLaboratoryofPlanetarySciences,PurpleMountainObservatory,ChineseAcademyofSciences,Nanjing210008,China
0 2UniversityofChineseAcademyofSciences,Beijing100049,China
2

n
a Accepted.Received;inoriginalform
J

1
1 ABSTRACT
Inthiswork,weextensivelyinvestigatetheformationofnear4:2:1meanmotionresonances

] (MMRs)configurationbyperformingtwosetsofN-bodysimulations.Wemodeltheeccen-
P
tricitydamping,gasdrag,typeI and typeIIplanetarymigrationofplanetesimals,planetary
E embryosand giant planetsin the first sets. For the simulations of giantplanets with type II
. migration,the massiveterrestrialplanets,with amass uptoseveralEarthmasses, arelikely
h
p producedinthesystems.Wefurthershowthatbyshepherdingand/orscatteringmechanisms
- throughJovianplanet’stypeIImigration,theterrestrialplanetsandgiantplanetsinthesys-
o tems can be evolved into a near 4:2:1 MMRs. Moreover, the models are applicable to the
r
t formationofKepler-238and302systems.Inthesecondset, westudythe4:2:1MMRsfor-
s mation in the terrestrial planetary systems, where the planets undergotype I migration and
a
eccentricitydamping.ByconsideringtypeImigration,∼17.1%ofthesimulationsindicate
[
thatterrestrialplanetsareevolvedinto4:2:1MMRs.However,thisprobabilityshoulddepend

1 ontheinitialconditionsofplanets.Hence,weconcludethatbothtypeIandtypeIImigration
v
canplayacrucialroleinclose-interrestrialplanetformation.
4
9 Keywords: planetarysystems–methods:numerical–planetsandsatellites:formation.
9
2
0
.
1
1 INTRODUCTION 2014; Zhangetal. 2014),such as the4:2:1 MMRs. For example,
0
Kepler-238(Roweetal.2014)andKepler-302(Roweetal.2014)
7 The number of exoplanets has substantially increased in re-
systems harbor close-in giant planets in near mean motion reso-
1 cent years. At the time of writing, over 3500 exoplanets (see
: nance (MMR) configuration with other planets. Therefore, these
v www.exoplanet.eu) are discovered, mostly through radial veloc-
exciting observations motivate us to explore and understand the
i ityand transiting surveys. In particular, asof Nov. 10, 2015, Ke-
X formationandevolutionoftheplanetarysystems,especiallytoin-
plermissionreleasedapproximately1030confirmedplanets,along
vestigatetheshort-periodterrestrialplanetformationandthecon-
r withover4696transitingplanetarycandidates(Fressinetal.2013).
a figurationformationofthe4:2:1MMRs.
Thismayimplythattheplanetsappeartobeverycommon,orbiting
otherstarsbeyondourownsolarsystem. Severalmodelshavebeenproposed toexplaintheformation
Theobservations show thatclose-in(short-period) terrestrial of close-in terrestrial planets (Raymondetal. 2008), and the for-
planetsaretypicallycommonintheexoplanetarysystems.Roughly mationscenariosincludeinsituaccretion,orbitalmigrationarising
speaking, one third to half of solar-type (FGK) stars can host fromplanetaryembryos(typeImigration(Goldreich&Tremaine
at least one planet with a mass less than 10 M⊕ and an or- 1980))andgasgiantplanets(typeIImigration(Lin&Papaloizou
bital period ranging from 50 to 100 days (Howardetal. 2010; 1986)), dynamical instabilities in systems of multiple gas gi-
Mayoretal.2011).Thefrequencyofshort-periodterrestrialplan- ant planets, tidal circularization of eccentric terrestrial planets,
ets is at least as high around M stars as around FGK stars, or and photo-evaporation of close-in giant planets. For the systems
evenhigher(Howardetal.2012;Bonfilsetal.2013;Fressinetal. that are composed of short-period terrestrial planets, their pro-
2013). These terrestrial planets are usually found in multi-planet toplanetary disks are suggestive of very massive (Raymondetal.
systems on compact but non-resonant orbits (Udryetal. 2007; 2008; Hansen&Murray 2012, 2013; Chiang&Laughlin 2013;
Lovisetal. 2011; Lissaueretal. 2011). However, from the statis- Raymond&Cossou 2014), thus the planets can accrete in situ
tical results of Kepler release data, a great many of planet pairs from a large number of planetesimals and planetary embryos in
inthe systems areobserved tobe in near-resonant configurations thedisk. Theformationandfinalconfiguration of close-interres-
(Zhangetal. 2010; Leeetal. 2013; Mart´ıetal. 2013; Wang&Ji trial planets are closely related to the strength of type-I migra-
tion,andthesuppressionoftypeImigrationisrequiredincaseof
in-situsuper-Earthsformation(Ogihara&Ida2009;Ogiharaetal.
⋆ E-mail:[email protected] 2015).Theobservedsystemsofhotsuper-Earthsmostlycancon-
(cid:13)c 2015RAS
2 Z. Sun et al.
tain 20 - 40 M⊕ in mass within a fraction of an AU of the host nally, we summarize the outcomes and give a brief discussion in
star(Batalhaetal.2013).Star-planettidalinteractionsmayplaya Section4.
roleincircularizingplanetsinhighly-eccentricorbitsandtherefore
reducetheirsemi-majoraxisintheevolution(Ford&Rasio2006;
Fabrycky&Tremaine2007;Beauge´&Nesvorny´ 2012;Dong&Ji
2013).However,Raymondetal.(2008)suggestedthattidaleffect
canproducehotsuper-Earths,butonlyforthoserelativelymassive 2 MODELS
planets (& 5M⊕) with very small perihelion distances (. 0.025
Following the empirical minimum-mass solar nebula (MMSN,
AU),andeventhentheinwardmovementinorbitaldistanceisonly
Hayashi 1981) model, the surface density of solid disk at stellar
0.1-0.15AUatmost,thereforetidesarenotstrongenoughtomove
manyoftheKeplerplanetstothenowadaysobservedseparations, distanceaisdescribedas
andadditionaldissipativeprocessesareatplay(Leeetal.2013).
Alternatively, terrestrial planet may form inside a migrat- Σd =10fdγice a −3/2 gcm−2, (1)
ing giant planet (Raymondetal. 2006). Gas-giants can shepherd 1AU
planetesimals and embryos interior to their orbits as they mi- (cid:16) (cid:17)
grate inward, which can further collide and merge into Earth- wherefdandγicearethesolidandthevolatileenhancementfactor,
likeplanets (Zhouetal. 2005). Mandelletal. (2007) showed ma- respectively. γice is 4.2 exterior to the snow line or 1 interior to
snowline.Theprofileofgasdensityisgivenas
terials that have been shepherded interior to the migrating gi-
ant planet by moving MMRs can accrete into close-in terres-
trial planets. In addition, Izidoroetal. (2014) indicated that fast- a −3/2
migratingsuper-Earthsonlyweaklyperturbtheplanetesimalsdisk Σg =2.4×103fgfdep 1AU gcm−2, (2)
and planetary embryos, whereas slowly migrating super-Earths (cid:16) (cid:17)
shepherd rocky material interior totheir orbits inresonances and wherefgandfdeparethegasenhancementfactorandgasdepletion
push toward the star. Moreover, the orbital migration and planet- factor, respectively. fdep=exp(−t/τdep), where t isthe timeand
planet scattering play a vital role in producing short-period ter- thetimescaleτdep isaboutfewmillionyears(Haischetal.2001).
restrial planets (Brunini&Cionco 2005; Terquem&Papaloizou Herein we adopt τdep = 106 yr. The inner edge of the gas disk
locatesat0.1AU.
2007; Raymondetal. 2008; Cossouetal. 2014). According to
As they are considered small bodies in our simulations, the
core-accretion model, the planetary embryos in the terrestrial
planet formation region, and the solid cores of giant planets, are planetesimalswillbeaffectedbytheaerodynamicaldragofthegas
around them (Adachietal. 1976; Tanaka&Ida 1999). The force
bothformedwithin∼ 1 Myrfromkilometer-sizedplanetesimals
(Safronov1969;Wetherill1980).Subsequently, themassivesolid thataplanetesimalwithamassmwillsufferfromaerodynamical
corescanfurtheraccretegasfromtheprotoplanetarydisktoform dragiswrittenas
gas-giants(Kokubo&Ida2002;Ida&Lin2004)atMyrtimescale,
beforethediskdisperses (Haischetal. 2001).Inthelatestageof 1
planetformation,afterthegasdiskclears,thegiantplanetsceases Faero =− CDπS2ρg|U|U, (3)
2
migrating, the numerous planetesimals and planetary embryos in
thediskbecometurbulentduetodynamical stirringbygas-giants whereU=Vk−Vgistherelativevelocitybetweentheplanetesi-
overhundredsofMyrsorevenlonger.Consequently,frequentor- mal’sKeplerianmotionVkandthegasmotionVg.CDisthedrag
bital crossings and giant impacts are likely to occur, which may coefficient. If an object has a large Reynold number, CD can be
eventually yield short-period Earth-like planets (Chambers 2001; takenas0.5. S andρg aretheplanetesimal’sradiusandgasden-
Raymondetal.2004;Zhang&Ji2009;Jietal.2011). sity,respectively.
Foraplanetaryembryoembeddinginthegaseousdisk,their
Raymondetal. (2006) investigated terrestrial planets for-
mutualinteractionswillleadtoaneccentricitydampingoftheem-
mation under type II migration and in the model they in-
bryowithatimescaleτ writtenas(Cresswell&Nelson2006)
cluded a giant planet and gas drag. Based on Raymond et al’s damp
model,Mandelletal.(2007)furtherconsideredanadditionalnon-
tmheig3ra:2tinagndgi2a:n1tMplManRets.cInonofiugrueraatriloienrfsotrumdya,tiowne(hWavaengin&veJsiti2g0a1te4d) τdamp1= ee˙ = 0Q.7e8 Mm∗ ΣMa∗2 hr 4Ω−1
inthesystemobservedbyKeplermission,andsimplyconsidered (cid:16) (cid:17) (cid:18) (cid:19)(cid:18) g (cid:19)(cid:18) (cid:19)
1 r 3
the planets with their nominal masses that are over a few Earth × 1+ e , (4)
4 h
masses without any growth (Wangetal. 2012; Wang&Ji 2014). (cid:20) (cid:16) (cid:17) (cid:21)
Inthepresentwork,weaimtoexploreterrestrialplanetformation
whereh, r, Ω,andearediskscaleheight,distancefromcentral
especiallyinthesystemwith4:2:1configurationunder migration
star,Keplerianangularvelocity,andtheeccentricityoftheembryo,
by performing N-body simulations. In short, we have carried out
respectively.Q = 0.1isanormalizedfactor inassociationwith
e
twokindsofsimulations,whereinthefirstmodel weincludethe
hydrodynamicalsimulationresults.Moreover,theangularmomen-
presenceofgiantplanetandasacomparison,inthesecondmodel
tumexchangebetweentheembryosandthegasdiskwillresultin
we consider the configuration formation in the system with only
orbitalmigrationofplanets.Whentheplanetsarelessmassive,they
terrestrialplanets.
will undergo type I migration, whereas they grow large enough,
The paper is structured as follows. In Section 2, we de- theywillexperiencetypeIImigration(Ida&Lin2004).
scribe the adopted models of planetary formation, including the ThetimescaleoftypeImigrationcanbeassessedusinglinear
diskmodelandtheplanetarymigrationscenarios.InSection3we model and the net loss on embryo (Goldreich&Tremaine 1979;
presentnumericalsetupandmajorresultsofourinvestigation.Fi- Ward1997;Tanakaetal.2002)isexpressedas
(cid:13)c 2015RAS,MNRAS000,1–??
TerrestrialPlanetsFormationunderMigration 3
where r and V represent the position and velocity vectors of
i i
planetm andallvectorsaregiveninstellar-centriccoordinates.
τmigI= |aa˙| = (2.7+11.1β) Mm∗ ΣMa∗2 i
(cid:18) (cid:19)(cid:18) g (cid:19)
h 2 1+( er )5
× 1.3h Ω−1, (5)
(cid:18)a(cid:19) "1−(1e.1rh)4#
wheree, r, h,andΩarethesamemeaningasgiveninEquation
4. Using the gas density profile in Equation (2), we can achieve 3 NUMERICALSIMULATIONSANDRESULTS
β=−dlnΣ /dlna=1.5.
g
3.1 Initialconditions
Recent workshowed that type Imigration couldbe directed
eitherinwardoroutwarddependingondifferentplanetaryandgas
Inoursimulations,allbodiesareassumedtobeinitiallyincopla-
diskproperties(Cossouetal.2013),butingeneral,outwardtypeI
narandnear-circulartrajectoryorbitingthecentralstar,wherethe
migrationcansimplyatworkwhenthemassoftheplanetscanbe
argumentofpericenter,meananomaly,andlongitudeofascending
severalM⊕(Cossouetal.2014;Legaetal.2014),whicharemuch nodearerandomlydistributedbetween0◦to360◦,respectively.In
largerthantheembryosandplanetesimalsinourmodel,sowedo
total, fiveruns were carried out for theinvestigation of planetary
notconsideroutwardtypeImigrationinthiswork.
formation.
The planet will experience type II migration when a planet
InsimulationS1-S5,theplanetarysystemiscomposedofthe
grows to a massive one (M > Mcrit) in the viscous disk hoststar,oneortwogiantplanets,and2000equal-massplanetes-
(Lin&Papaloizou1993).ThetimescaleoftypeIImigrationisde-
imals. As shown in Table 1 and Equation (8), each planetesimal
scribedas(Ida&Lin2008)
performsaerodynamicaldrag,eccentricitydamping,TypeImigra-
tionandthegravitationalperturbationsfromJupiterorSaturnand
τmigII1≃5×105fg−1 otherplanetesimalsinthesystem.Thegiantplanetsaremodeledto
sufferfromeccentricitydamping,TypeIImigration,andtheinter-
× C2α −1 m a 1/2 M∗ −1/2, actionfromtheplanetsandsmallbodies.Inseveralruns,thegiant
(cid:18)10−4(cid:19) (cid:18)MJ(cid:19)(cid:16)1AU(cid:17) (cid:18)M⊙(cid:19) planetsareassumed tobefixedabout theoriginal region without
τmigII2= |aa˙| =0.7×105(cid:16)10α−3(cid:17)−1(cid:16)1AaU(cid:17)(cid:18)MM⊙∗(cid:19)−1/2, (6) metaigryraIntfiootrnhm.eaIsnteiotshniemufunoldlaletoirwotnihnse,g,wcwiercemuwmaiislnltlabynrcieeexflpoylfosrutehmetmheexaritsieztreerneecsaetcrihoaflcapgslieaa.nn-t
whereαandC2areefficiencyfactorofangularmomentumtrans- planets.Thus,ineachsimulationwestartwithaswarmofplanetes-
port and reduce factor. Herein C2α = 10−4. τmigII1 is fit tothe imals,togetherwithoneortwogiantplanetsinthesystem,orbiting
case that the planet mass is comparable to theentire mass of the thecentralstar.TheinitialpositionsforJupiterandSaturnaresetto
gasdisk.Whiletheplanetmassislowerthanthemassofthegas be5.0AUand9.54AU,respectively.Originally,theinnerregionof
disk,τmigII2istherightfit.Weadoptanempiricalformulaforthe thesystemconsistsof2000planetesimalsthateachownsamassof
eccentricity damping from the gasdisk, (τdamp2)−1 = (e˙/e) = 5×10−3M⊕,therebyleadingtoanentiremassoftheplanetesimal
−K|a˙/a|(Lee&Peale2002).Herein,wechooseK=10.Thecriti- diskof10M⊕.Hereinforallcases,theplanetesimalsareinitially
calmassofplanetthatcanproduceagapisgivenas distributedintheregion[0.5,3.78]AU.
S1:Inthisscenario,theplanetarysystemcomprisesthehost
Mcrit ≃30(cid:16)10α−3(cid:17)(cid:16)1AaU(cid:17)1/2(cid:18)MM⊙∗(cid:19)M⊕. (7) ssdtuyamnr,aetmsheitchpaalltaetnvheoetelgusitiaimonnatl.ps,laannedtosunfefeJruspfitreorm-mtayspsepIlIanmeitg.rTahtieonmoovdeerltahse-
In thiswork, besides mutual gravitational interactionamong
S2: Theinitialsparameters for Jupiter and planetesimals are
the objects in the system, we also consider the orbital migration,
thesameasthosegiveninS1.Asacomparison,inthissimulation
eccentricitydampingandaerodynamicaldragofplanetaryembryo
themodeldoesnotaccountfortypeIImigrationforJupiter.
(planetesimal).Theaccelerationoftheplanetorplanetaryembryo
S3, S4 and S5: in this three runs, the initial system consists
(planetesimal)withmassm isexpressedas
i ofthehoststar,theplanetesimals,twogiantplanets–Jupiterand
Saturn.InsimulationS3,bothJupiterandSaturndonotmigratein-
ddtVi =−G(Mr∗+2 mi) rri + N Gmj |(rrj−−rri|)3 − rrj3 wanadrdSbaututrrnemaraeinalsltoawbleedotrobimtsi.gIrnatseiminuwlaatriodninS4thaenddySn5a,mbioctahlJeuvpoiltue-r
i (cid:18) i(cid:19) Xj6=i (cid:20) j i j(cid:21) tion.
+ Fdamp1+Faero+FmigI(forplanetesimals/embryos) (8) WeintegrateEquation(8)usingahybridsymmetricalgorithm
Fdamp2+FmigII (forgiantplanets) inMERCURYpackage(Chambers1999).However,wehavemod-
(cid:26)
ifiedcodestoincorporategasdragandorbitalmigrationscenarios
where
foroursimulation.Intheseruns,mutualinteractionsofallbodies
are fully taken into account. Two bodies are considered to be in
F =−2(Vi·ri)ri , collisionstagewhenevertheirdistanceislessthanthesumoftwo
damp1,2 ri2τdamp1,2 physicalradii(Chambers1999).Iftwoobjectscollideeachother,
theycanmergeandformasinglelargerbodywithoutanyfragmen-
FmigI=−2τVmiigI, (9) taattiiomne.Isnteopuorfsi2mdualaytsioann,deaacBhurulinrsicshi-nStetogerratteodlefroarn2ce-1o0f01M0−y1r2w.Aiths
usual, when the simulation ends up, the variations of energy and
V
FmigII=−2τmiigII, angularmomentaare10−3and10−11,respectively.
(cid:13)c 2015RAS,MNRAS000,1–??
4 Z. Sun et al.
Table1.Theinitialconditionsoftheruns.ThemeaningofForceisgivenbyEquation8.
Name Massofplanetesimal No. Jupiter Saturn Force
M⊕ Planetesimals YesorNot YesorNot ongiantplanets
S1 5×10−3 2000 Y N FmigII
S2 5×10−3 2000 Y N Nomigration
S3 5×10−3 2000 Y Y Nomigration
S4 5×10−3 2000 Y Y FmigII
S5 5×10−3 2000 Y Y FmigII
Table2.Thestatisticsofthefinaldestinationoftheplanetesimalsineachruns.
Name Time Percentageofmass PercentageofMass Saturn Force
Myr (inside0.1AU) (beyond5AU) YesorNot ongiantplanets
S1 5 79.5% 8% N FmigII
S2 3.9 14.1% 0 N Nomigration
S3 3.7 17.9% 0 Y Nomigration
S4 5 50.5% 14.8% Y FmigII
S5 5 36.9% 5.9% Y FmigII
3.2 Terrestrialplanetsformationwithgiantplanets somecaseswater-richearth-massplanetcanformoutsidethemi-
gratinggiant,locatedinsidethehabitablezone.SimulationS1also
ThesimulationsofS1-S5exhibitclassicalterrestrialplanetaryac-
showssimilarshepherdmechanism,asshowninFigure1.Interest-
cretion scenarios in their late stage formation (Chambers 2001;
ingly,thetwoinnerterrestrialplanets,aswellasthemigratinggiant
Raymondetal.2004,2006;Fogg&Nelson2005,2009).
planet,arediscoveredtofinallyforma4:2:1MMRorbitalconfig-
uration.However,wedonotobservematerialaroundthehabitable
zone. In simulation S1, the massive giant planet sweeps away or
3.2.1 Terrestrialplanetsformationwithonegiantplanet
accrete most of the materialsalong its pathway when it migrates
Figure 1 shows the orbital evolution of the planetesimals and inward.Furthermore,wepointoutthatsuchmaterialdepletionof
the Jupiter-mass planet in the first 5 Myr for simulation S1. At migratinggiantplanetcanbeobservedinoursimulationS5(Fig-
an early time, the Jupiter-mass planet migrates inward in the ure7),inwhichthesystemcontainstwomigratinggiants.
disk, thereby giving rise to the planetesimals nearby the giant
planet to either be scattered outward into high-eccentric orbits
(Mandell&Sigurdsson 2003) or shepherded inward by the gi-
antplanet’smovingmeanmotionresonances(Tanaka&Ida1999; InitialsinsimulationS2arethesameasthoseinS1,however
Fogg&Nelson2005).Thebuildupofinnermaterialinducesrapid inthismodel wesimplydonotletJupiterundergotypeIImigra-
growth of two close-in planets within a few Myr. At 5 Myr, five tion.Figure3showstheorbitalevolutionoftheplanetesimalsand
terrestrialplanetsforminside0.1AU.Thetotalmassofthesefive theJupiter-massplanetforsimulationS2.Insimilarcase,theplan-
planetsis7.95M⊕,correspondingto∼80%oftheinitialbuilding etesimalsarequicklyexcitedduetotheirmutualgravitation,along
materialssetinthesimulation.Thereare16planetesimalsthatwere withthatoftheJupiter-massplanetlocatingat5.0AU.Theobjects,
scatteredtoorbitsbeyond5AU,thetotalmassofthemis∼0.08 involvedinthe3:1MMRat2.50AU,2:1MMRat3.28AU,andthe
M⊕, the final destination of the planetesimals is shown in Table 5:3MMRat3.70AU,arestirredwithin0.1Myr.Thistrendcanbe
2.ThesimulationS1continuesevolvingfor100Myr.Bytheend clearlyseenbytheriseoftheeccentricitiesoftheplanetesimalsat
of100Myr,mostoftheplanetesimalintheinitialdiskhavebeen theselocationsasshowninFigure3.Allstuffintheplanetesimal
nearly cleared up by ejection or collision scenarios, arising from diskexterior tothe3:2resonance at 3.97AU isquickly removed
frequent orbital crossings over the chaotic evolution. Weobserve fromthesystemviacollisionandejectionresultingfromthegiant
that therealsoexistacouple of moderate-eccentric planetesimals planet.Inthetimeevolution,theplanetesimals’eccentricitiescan
whicharenotinvolvedinaccretionprocessbeyond∼5AUforthe increase and the system becomes chaotic when the eccentricities
remainingdisk. arelargerenough. Thebodiesintheinner diskbegintogrowvia
Moreover, wefindthattwoterrestrialplanetswithamassof accretionarycollisionswithin1Myr.Thelargerbodiestendtohave
5.48M⊕and1.62M⊕areeventualsurvivorsinthesystem,locat- smallereccentricitiesandinclinations,duetothedissipativeeffects
ingat0.069AUand0.104AU,respectively.Thesetwoterrestrial ofdynamicalfriction.At3.9Myr,therearefourlessmassiveter-
planetsandtheJupiterforma4:2:1MMRorbitalconfigurationat restrialplanets(ascomparedtoS1)withamassof0.15−0.51M⊕
∼10Myr,asshowninFigure2.Thediscoveryoftheexoplanets formedintheregion[0.07,0.095]AU.Theentiremassoffourter-
showsthattheplanetarysystemsintheuniversearequitediverse. restrialplanetsis1.41M⊕,correspondingto∼14.1%ofthetotal
Oursimulationspresentveryinterestingresults,whichmayprovide initialmaterialsasshowninTable2.
somecluestofutureobservationsforsuchsystems.
OursimulationS1issimilarwiththeworkinRaymondetal.
(2006) that investigated habitable terrestrial planet formation un-
deramigratinggiantplanet.Intheirmodel,theyadoptedahigher In comparison, we can see that an inward-migrating giant
mass of 17 M⊕ and a more extended planetesimal disk that ar- planetcansignificantlyincreasetheaccretionrateintheinnerpart
rangesfrom0.25to10AU.Theyfound thathot Earthscanform ofplanetesimaldiskbytheshepherdeffect.Meanwhile,itcanscat-
interiortoamigratinggiant duetotheshepherding effect,andin terthebodiesintheinnerdisktotheouterdisk.
(cid:13)c 2015RAS,MNRAS000,1–??
TerrestrialPlanetsFormationunderMigration 5
Table3.Physicalparametersofthe3runsthatform4:2:1MMRat100Myrandcomparisonwithexoplanetsystems.
Name Mass Radius Period a e Name Massa Radius Period a e
M⊕ R⊕ day AU M⊕ R⊕ day AU
S1Planet1 5.48 2.47 6.62 0.069 0.001 Kepler-238c 6.0 2.39 6.16 0.069 -
S1Planet2 1.62 1.65 12.25 0.104 0.038 Kepler-238d 10 3.07 13.23 0.115 -
S1Jupiter 333.55 9.72 24.91 0.167 0.000 Kepler-238e 77 8.26 23.65 0.169 -
S4Saturn 95.69 6.41 5.64 0.062 0.001 Kepler-302b 18 4.06 30.18 0.193 -
S4Planet1 5.05 2.41 11.72 0.101 0.012 - - - - - -
S4Jupiter 333.46 9.72 24.91 0.167 0.001 Kepler-302c 180 12.45 127.28 0.503 -
S5Planet1 3.69 2.16 10.02 0.0911 0.142
S5Jupiter 333.02 9.71 20.15 0.1449 0.025
S5Saturn 95.12 6.40 40.79 0.2315 0.014
a
KeplerplanetarymassesestimatedwithEq.(1)in(Lissaueretal.2011b).
3.2.2 Terrestrialplanetsformationwithtwogiantplanets theorbitalcrossingbetweentwogiantplanetshappenswithinsev-
eral thousand years and brings about fairly chaotic behaviors for
In the following, we will present the simulation outcomes of the
them. Hence, a sudden jump in the Jupiter’s eccentricity occurs
terrestrialplanetaryformationco-existencewithtwogiantplanets
upto ∼0.72 at 0.037 Myr, whereas Saturnmay obtain amoder-
intheplanetarysystems.
ateeccentricity right after theclose encounter but itseccentricity
In simulation S3, two giant planets, which bear a Jupiter or isquicklydampedbythegasdisk.Fromthesimulations,wefind
Saturnmass,respectively,donotperformtypeIImigrationinthe thatJupiter experiencedcloseencounters withSaturnatthemax-
simulation.Therefore,similartosimulationS2,theplanetesimals imum star-centric distance at ∼ 2.41 AU, which leads to strong
inthediskcanbeswiftlyexcitedduetogravitationalperturbations interaction between them. From ∼ 0.037 Myr to 0.04 Myr, note
fromtwogiantplanets.Inparticular,thebodies,whichareinvolved that the semi-major axis of Jupiter drops down from 3.58 AU to
in the MMR with the Jupiter-mass planet, then acquire moderate 1.63AU,whereasthatofSaturndramaticallydecreasesfrom5.75
eccentricitieswithin0.1Myr.AscomparedtoJupiter,theSaturn- AUto0.45AU.Furthermore,suchchaoticmotionsforJupiterand
massplanetplaysalessdominantroleinthemassaccretionofplan- Saturntriggercatastrophicfatefortheplanetesimalsinthesystem,
etesimalsinformingterrestrialplanets.Inthemeanwhile,owingto where most of their orbits are severely excited and scattered. As
theco-existenceoftwogiantplanets,theterrestrialformationpro- Figure6 shown, the eccentricity of the planetesimal (Planet 1) is
cesscanbespeededupalthoughJupiterandSaturndonotdeviate firstkickedtobe0.88thenfallsto0.13,whileitssemi-majoraxis
much from their initial orbits in this run. Figure 4 shows tempo- cansuddenlyincreaseamountupto5.18AU,thensoondropdown
ralorbitalevolutionofalltheplanetesimalsandthegiantplanetsin to0.26AUoverthetimespan.
simulationS3.At∼2Myr,threeterrestrialplanetsareyieldedwith As the two giant planets continue migrating inward, the 2:1
amassintherange0.10−0.57M⊕,andtheyorbitinthebroadre- MMRbetweenthemisbrokenup.Subsequently,Saturniskicked
gionfrom0.07AUto1AU.Atthetimeof3.7Myr,theentiremass
intotheregion∼0.1AUduetodynamicalinstabilities.By10Myr,
offourterrestrialplanetsformedinside0.1AUis1.79M⊕,occu- thegiantplanetshavemovedveryclosetotheircentralstar.Inthe
pying 17.9% of the initialmass of theplanetesimal disk. Similar late stage, the eccentricity of Jupiter is gradually damped by dy-
withthesimulationS2,thereisnoplanetesimalbeyond5AU.
namicaldissipation.However,aninnerterrestrialplanet(Planet1)
InordertoinvestigatetheroleoftypeIImigration,wehave isexcitedontoahighlyeccentricorbitexteriortotheregimeoftwo
performed two additional runs for the systems composed of two giantplanets,andsooncrossesJupiter’sorbit,thenfinallycaptured
giantplanets,SimulationS4andS5.Inthistworuns,bothJupiter insidetheorbitsofJupiterandSaturn.ThemassgrowthforPlanet
andSaturnundergotypeIImigration.Ourresultsprovideevidence 1startsfromoneplanetesimalat∼0.06MyrtoasuperEarthwith
thatterrestrialformationmaytakeplaceintheinnerregionofthe a mass of 5.05 M⊕ at ∼ 0.40 Myr. Finally, Planet 1 remains at
planetary systems (Fogg&Nelson (2005); Mandelletal. (2007); 0.101AU,whereasSaturnandJupiterceasemigratingat0.062AU
Fogg&Nelson(2009)).However,newrunsfurthershowsomein- and 0.167 AU, respectively. This planetary system shows a very
terestingoutcomes-the4:2:1MMRconfigurationsareformedfor interestingconfigurationthatasuperEarthlocatesbetweentwogi-
thesesystems. antplanets’orbits,andthreeplanetsaretrappedintoanear 4:2:1
Figure5showstemporalorbitalevolutionofalltheplanetes- MMR (see Figure 8). Accordingly, the residual materials of disk
imals and giant planets. According toEquation 6, τmigII1 is pro- areeitherremovedoutofthesystemorscatteredintodistantorbits.
portionaltotheplanetarymass,thuswelearnthatSaturnmigrates Theireccentricitiesrisealongwiththeirsemi-majoraxes.
fasterthanJupiterdoes,indicatingthattherewouldbeapossibil- ThescenarioofS4showsaresemblancetoNICEModel(e.g.,
ityfortwogiantplanetstorendezvousinthesystem.At0.02Myr, Tsiganisetal. 2005; Morbidellietal. 2007), which proposes that
Jupiter’seccentricityisgraduallypumpedupto0.30duetogravi- theLateHeavyBombardment (LHB)–aspikeintheimpactrate
tationalinteractionfromSaturnwhenitmovesinwardclosertothe onmultiplesolarsystembodies that lastedfromroughly 400 un-
Jovianplanet. til 700 Myr after the start of planet formation (Teraetal. 1974;
At0.036 Myr,Jupiter andSaturnreachtheorbitat 5.75AU Cohenetal.2000;Chapmanetal.2007)–wastriggeredbyanin-
and3.58AU,respectively,indicatingthattheypassthrougha1:2 stabilityinthegiantplanets’orbits.IntheNiceModel,theorbits
mean motion resonance. This resonance crossings may have ex- ofthegiant planetswouldhavebeeninamorecompact configu-
cited the orbital eccentricities of the planets which cross the res- ration,withJupiterandSaturninteriortothe2:1resonance.Inour
onance (e.g., Tsiganisetal. 2005; Morbidellietal. 2007). Thus, modelofsimulationS4,theJupiter-massandSaturn-massplanets
(cid:13)c 2015RAS,MNRAS000,1–??
6 Z. Sun et al.
canswitcheachplace,similartothecaseofUranusandNeptune giants,andinthiscasethematerialoftheregionbetween0.2and
in the NICE Model. Raymondetal. (2008b) showed that planet- 4.5AUofthediskwasfullyclearedbytwogiantplanets.
planet scattering could create MMRs, most of these resonances
areindefinitelystable.Thepreviousinvestigationsreportedthatin
a convergent migration scenario for two giant planets in the so-
4 THEEMERGENCEOF4:2:1MMRSONLYWITH
larsystem, the2:1MMR couldbeformedand thendisintegrated
TERRESTRIALPLANETS
intheevolution(Morbidelli&Crida2007b;Zhang&Zhou2010).
Zhang&Zhou(2010b)statedthatwhenJupiterliesoutsideSaturn, Theinvestigationsimplythattheplanetaryconfigurationsinasso-
convergentmigrationcouldoccur,Saturnisthenforcedtomigrate ciationwithanear4:2:1MMRswouldbecommonintheuniverse.
inward by Jupiter where the two planets are trapped into MMR, Herein,weconsidertwoplanetswithaperiodratiointherangeof
andSaturnmaymoveonitstracksofapproachingthecentralstar. [1.83, 2.18] as a pair near 2:1 MMR (Lissaueretal. 2011b). For
Furthermore, to apply our model to explain the planetary forma- example, Jupiter’s Galilean moons are known to be locked into
tionofthesystems,weextensivelyexaminethepublisheddataby a so-called three-body Laplacian resonance (i.e., 4:2:1 MMR) in
Keplermissionandfindarelevant planetarysystem(Kepler-302) our solar system. On the other hand, other evidences are found
similartothissimulation.Kepler-302isasystemconsistingoftwo intheexoplanetarysystems,inwhichthreeplanetsoftheGJ876
planets orbiting a star with a mass of 0.97 M⊙, as shown in Ta- system(Marcyetal.2001;Riveraetal.2010;Batyginetal.2015;
ble 3. The outer planet of Kepler-302c is more massive than the Nelsonetal.2016)andKepler-79(KOI-152)(Steffenetal.2010;
inner companion Kepler-302b, and the two planets have approx- Wangetal. 2012) arereported tobe close to4:2:1MMR. Inthis
imate sizes as compared with those of the giant planets in simu- work,wehaveprovidedsubstantialevidencesonthisfromthesim-
lation S4, whereas their orbital distances fromthe host star area ulations. For example, in simulation S1, S4 and S5 of Section 3,
bit farther than those of the planets in the present run. Interest- weshow that the systems initiallycomposed of one or two giant
ingly, the two giant planets of Kepler-302 are nearly close to a planetscanfinallyproduce4:2:1MMRs,inwhichtheformedter-
4:1MMR(Roweetal.2014),suggestingthatthesystemmayhave restrialplanetsareinvolvedin.Naturally,aquestionarises-what
gonethroughsimilarmigrationprocessasinoursimulation.There- ifthesystemsonlycontainterrestrialplanets?
fore,ourmodelhereinpresentsalikelyformationscenariofortwo As mentioned previously, the released Kepler outcomes re-
planetsthatareclosetoa4:1commensurability,andalsoprovides portthatagreatnumberofplanetarysystemsharboringterrestrial
evidencethatterrestrialplanetformationundertheinfluenceoftwo planetsinvolvedinanear2:1resonance.Furthermore,aportionof
giantplanetsinthecompactsystem. the terrestrial planets discovered by Kepler are in near 4:2:1 res-
InsimulationS5,althoughSaturnmigratesfasterthanJupiter, onance.Herein,wefurtherinvestigatetheconfigurationformation
thereisnorendezvous betweenSaturnandJupiter.Instead, when ofthosesystemsonlywithterrestrialplanetstounderstandwhether
Saturnentersthe2:1MMRorbitofJupiterat0.02Myr,thesetwo the4:2:1MMRscanbeproducedinsuchsystems.Withthesepur-
giantplanetswerelockedinthe2:1MMRconfigurationandthey pose,weperformadditionalrunstoexplorethesystemsthatsimply
migrateinwardtogether.Figure7showstemporalorbitalevolution consistofterrestrialplanetsthroughsimulations.
of the simulation S5 for the first 5 Myr. Jupiter’s eccentricity is Inouradditional simulations,therearethreeterrestrialplan-
graduallypumpedupto0.30duetogravitationalinteractionfrom etsinitiallywithmasseslessthan30M⊕ aroundcentralstar,and
Finally,aterrestrialplanet of 3.69 M⊕ forminside0.1AU. This they are assumed to migrate from the outer region of the system
newterrestrialplanetandthetwogiantplanetsforma4:2:1MMR undertheeffectofthegasdisk.Thegasdensityprofileispropor-
orbitalconfigurationat∼5Myr.AlthoughJupiterkeepsmigrating tionaltor−1,andanemptyholelocatedintheinnerregionofthe
until 10MyrinS1,Jupiterceasesitsmigrationat1.5Myrand3.5 system.Duringtheformationprocess,theterrestrialplanetssuffer
MyrinS4andS5,respectively.Thisisprobablyduetothetorque fromtypeI migrationand gasdamping. Thetimescalesof typeI
fromPlanet1,andthetorquedependsontheedge. migrationandgasdampingareshowninEquation(4)and(5),re-
UnlikeinsimulationS3,insimulationS4andS5wecansee spectively.Intotal,wecarryoutsevengroupsofsimulations,and
planetesimalsbeyond5AUduetoscatteringofinward-migrating eachgroupcontainsfiverunsbyconsideringdifferentspeedoftype
giantplanets.At5Myr,thereareabout1.48M⊕materialsbeyond Imigration.WeaddanenhancefactorηtothetimescaleoftypeI
5AUinsimulationS4,correspondingto14.8%oftheinitialtotal migration.Thefiverunscorrespondtoηtimesoftypicaltimescales
mass.WhileinsimulationS5,thereare∼0.59M⊕beyond5AU. of type I migration as shown in Equation 5. The values of η are
Figure8showsthefinalconfigurationintheinnerdiskforthe 100, 33.3, 10,3.3, and1,respectively. Figure9showsoneof the
threerunsthathaveturned ontypeIImigration. Interestingly, all runswithtypicaloutcomes.ConsideringvariousspeedoftypeImi-
theserunsyield4:2:1MMR.InsimulationS1,twoterrestrialplan- gration,threeplanetsarelocatedat140,500,and1450dwhenη
etsformedinteriortotheJupitermassplanet.Themigratinggiant islargerthan33.3,otherwisetheyarelocatedat100,250,and600
increasedtheaccretionrateintheinnerdiskandclearedallmate- d,respectively.Themassesoftheplanetsinfivegroupsare5,10,
rialinitspathway.Asaresult,thereisnothingleftbetween0.2to and15M⊕,respectively,whileinothertwogroupstheyaresetto
4.5AU.InsimulationS4,therewasanorbitalcrossingbetweenthe be5,5,and5M⊕,respectively.InFigure9,theformationofthe
migratingJupitermassandSaturnmassplanets,andsuchachaotic innermost,themiddleandtheoutermostplanetsaremarkedbythe
event changed the orbital configuration of the two giant planets. black,redandbluelines,respectively.Panel(a),(b)and(c)show
Hence, we note that a close-in terrestrial planet formed between the evolution of the orbital periods, eccentricities, and the period
twogiant planets. Thereare some residual materialsbetween 0.2 ratios,respectively.Panel(d)and(e)displaythe2:1meanmotion
to5AUinthisrun,andthiscouldbeaconsequenceofthequickly resonanceangles.Inthecasewithterrestrialplanetsinthesystem,
orbitalchangeofthetwogiantsat0.1Myr,asshowninFigure6. theyallundergotypeImigration.Duetotheshorttimescalesforthe
While in simulation S5, there is no chaotic orbital change of the firsttwoplanets,theyaretrappedinto2:1MMRfirst.FromPanel
JupitermassandSaturnmassplanets.SimilartosimulationS1,we (c)inFigure9,wefindthatthefirstandsecondplanetsareinvolved
seethatonlyoneterrestrialplanetformedinteriortotwomigrating into2:1MMRat∼0.5Myr,andthenthreeterrestrialplanetsare
(cid:13)c 2015RAS,MNRAS000,1–??
TerrestrialPlanetsFormationunderMigration 7
trapped into 4:2:1 MMRs at ∼ 1.3 Myr. From Panel (b), we can 5 CONCLUSIONSANDDISCUSSIONS
learnthatwhentheplanetpairsenterintoMMRs,theireccentrici-
In this work, we have investigated terrestrial planetary formation
tiesareexcited,butduetothedampingofgasdisk,theycannotbe
,especiallytheconfigurationformationofanear4:2:1MMRsby
stirreduptohighvalues.The4:2:1MMRisusuallyproducedwhen
carryingouttwosetsofsimulationswithandwithoutgiantplanets.
thefirstplanetistrappedintheedgeoftheholesinthegasdisk.The
From the results we find that 4:2:1 MMRs configuration can be
formationprocessissimilartothatmentionedinPierens&Nelson
formedinthesystemsbothwithandwithoutgiantplanets.Herein
(2008),theMMRformedwhentheplanetiscapturedinthegapof
wesummarizethemajorresultsasfollows.
theotherplanet.Inaddition,weinvestigatetheresonanceanglesof
eachpairwhichareshowninPanel(d)and(e)ofFigure9andfind (i) In the first sets, we place one or two giant planets into the
thatθ21 =2λ1−λ2−̟1libratesat∼0◦,θ32 =2λ2−λ3−̟2 initialsystemsaswellastheplanetesimals,tounderstandterrestrial
libratesat∼ 0◦,andθ33 = 2λ2 −λ3−̟3 libratesat∼ 180◦, formationinsuchcasesinS1-S5.
wherethesubscript1and2representtheorbitalelementsofPlanet InsimulationsS2andS3,thegiantplanetsdonotundergomi-
1 and 2, respectively. At the end of the simulation, three planets gratinginthedisk,andtheterrestrialformationprocedurecanbe
locate at about 11.52, 23.26, 47.17 days, respectively. This con- expeditedbecauseoftheexistenceofJupiter-massandSaturn-mass
figurationissimilartothesystemKepler-92whichcontainsthree planets.Infinal,severallow-massclose-interrestrialplanetscanbe
planetsintheorbitalperiodsof13.75, 26.72, and49.36 days, re- formedasaresultofradialmixingandtypeImigration.Inthetwo
spectively. Infinal, by examining all runs fromseven groups, we runs,thereisno4:2:1MMRsintheevolution.
find that 6 out of 35 runs (17.1%) show three planets are finally InsimulationS1,S4,andS5,weplaceoneortwogiantplanets
involvedin4:2:1MMRs,whereas10runsreportthatonlythetwo in the system , which undergo type II migration during the evo-
innerplanetsenterinto2:1MMR,andtworunsfortwoinnerplan- lution. Thus the planetesimals are shepherded inward, cleared or
etsin3:2MMR.Abouthalfofthesimulations(48.6%)arenotin ejectedalongwithmigrationofgiantplanets.Theclose-interres-
MMR.Basedonoursimulations,theproportionthatplanetspairs trial planets are yielded with a mass up to several Earth-masses.
trappednear4:2:1MMRsappearstobehigh.Thereareseveralrea- ForsimulationS1,wefindthattwoshort-periodterrestrialplanets
sonsthatcouldleadtosuchresults.Firstly,wesettheinitialorbital andonegiantplanetarefinallyinvolvedin4:2:1MMR,whereasin
separation of planets at ∼ 20 Hill radius, which is a little larger therunsofS4,andS5,weshowthatoneterrestrialplanetandtwo
thantheempiricalvalueof12Hillradius(Ida&Lin2004).Insuch giantplanetsenterintothe4:2:1MMR.TheresultantresultsofS1
cases,mostoftheplanetsarefirsttrappedbythe2:1MMRsdur- andS4aresimilartoKepler-238and302systemsinorbitalspac-
ingtheirevolution.However,asacomparison,iftheyareinitially ing.WeexaminethemassconcentrationstatisticS andtheorbital
c
inacompactconfiguration,theprobabilityoftheformingplanets spacingstatisticS (Chambers2001;Hansen&Murray2012)for
s
in2:1MMRswillsignificantlydecrease.Asshownintheworkof thesesystems.ComparingthesystemS1andKepler238, wecan
Wang&Ji(2014),theyfoundthatiftheplanetspairswereinitially notethattheorbitalspacingstatisticsareclosetoeachother.Their
incompactconfigurationattheseparationsof∼15Hillradius,the valuesfortwosystemsare1.8and2.76,respectively,indicatingthat
probabilityof2:1MMRsdecreasedto10%in50runsandtherewas S1andKepler238aresimilarintheorbitaldistribution.However,
no simulation that three planets were evolved into 4:2:1 MMRs. the mass concentration statistics of them differ from each other,
Secondly,inoursimulationsweslowdownthespeedoftypeImi- and their values are 125.7 and 30.3, respectively. One reason for
gration for low-mass planets, and this could further explain why thisdifferenceinmassconcentrationstatisticisthatthemassesof
twoplanetsarefairlyeasiertobetrappedinto2:1MMRs.Finally, planetsinour simulationsarequiteuncertain. Hereinweadopted
thefinalorbitalperiodsoftheplanetsinallsimulationsarelessthan anestimatedmassesfromEq.(1)inLissaueretal.(2011b).Ifwe
50dayswhichmaybeaffectedbythetidalforcethatarisesfrom can obtain the true masses of planets in S1, the difference of S
c
thecentralstar.Thetidaleffectmayleadtothedeviationfrom2:1 couldbenarroweddown.Moreover,wefurthercompareS andS
s c
MMRs(Leeetal.2013).Insummary,theabove-mentionedfactors ofthesystemS4withthoseofKepler302,whereS foreachsys-
s
mayplayamajorroleincausingtheplanetspairsevolvedinnear temis5.43and4.0,respectively,andS fortwosystemsis10.4and
c
4:2:1MMRsatarelativelymoderatepossibility.Thesimulationsin 23.3,respectively.ThismayimplythatthesystemS4andKepler
Raymondetal.(2006)utilizedthetypicalspeedoftypeImigration 302 have similar orbital distribution. Therefore, wecan conclude
whichwasveryfast,andtheembryoswereinitiallylocatedclose that S1 and Kepler 238, S4 and Kepler 302 have similar orbital
toeachotherincompactconfiguration.Thesemaybetheleading configurations.
differencesproducingdiverseresultsbetweenoursimulationsand Thepresentobservationsshowthatthereisalackofcompanion
thoseofRaymondetal.(2006). planetsintheobservedhotJupitersystems.However,fromoursim-
BycomparingS1,S4andS5simulationcontaininggiantplan- ulationresults,wecanlearnthatterrestrialplanetscansurvivein-
etsandtherunsthatsimplyconsistofterrestrialplanetsinthissec- sidetheinnerregionofhotJupitersystemsbasedonourformation
tion, we find that the timescales of the planet pairs trapped into scenario.AsshowninthesystemS1,thefinalformedconfiguration
MMRs are various for different cases. For the systems that only issimilartothatinRaymondetal.(2006).Moreover,ifthegasdisk
contain terrestrial planets, the two inner planets are found to be issmallenough,thehotJupitercouldhaveterrestrialcompanions
trapped into 2:1 MMRs within 1 Myrs, and the two outer pairs formedinthesystem(Ogiharaetal.2013).Nevertheless,currently
are in resonance at approximately 2-3 Myrs. Therefore, we may suchterrestrialcompanionsinthehotJupitersystemshavenotdis-
concludethatthreeterrestrialplanetsarein4:2:1MMRswithin3 coveredyet,thisisbecausetheymaybeunderthedetectionlimit.
Myrsonaverage.Incomparison,forthesystemsconsistingofone Intheforthcoming,wehopethatthehotJupitersystemswithlow-
ortwogiantplanets,the4:2:1MMRsemergesatover2Myrswhen mass companions could be discovered with the assistance of the
theterrestrialplanetscompleteitsmassaccretion.Additionally,the improvementofobservationalprecisionandtechniques.
eccentricities of planets which is in MMR with giant planets are (ii) Furthermore, in the second sets, we also explore the 4:2:1
alwaysexcitedtobehighvalues,whiletheeccentricitiesofplanets MMRsformationinthecaseofthreeterrestrialplanets.Undertype
insystemswithoutgiantplanetswillbesuppressedtolowvalues. I migration, ∼ 17.1% of all runs, indicate that terrestrial planets
(cid:13)c 2015RAS,MNRAS000,1–??
8 Z. Sun et al.
are evolved into 4:2:1 MMRs. However, as aforementioned, the Fabrycky,D.&Tremaine,S.,2007,ApJ,669,1298
probability that planets are trapped into MMRs depends on their Fogg,M.J.,&Nelson,R.P.2005,A&A,441,791
initial separation and the speed of type I migration. Comparing Fogg,M.J.,&Nelson,R.P.2009,A&A,498,575
the processes with and without giant planets, the timescales that Ford,E.B.,&Rasio,F.A.,2006,ApJL,638,L45
three planet are in 4:2:1 MMRs in systems without giant planets Fressin,F.,etal.,2013,ApJ,766,81
are shorter than systems with giant planets. Additionally, eccen- Genda,H.,Kokubo,E.,&Ida,S.,2012,ApJ,744,137
tricities are exited to higher values in systems with giant planets Goldreich,P.,&Tremaine,S.,1979,ApJ,233,857
thanwithoutgiantplanets. Goldreich,P.,&Tremaine,S.,1980,ApJ,241,425
Haisch, K.E.,Jr.,Lada,E.A.,&Lada,C.J.,2001, ApJL,553,
However, in the treatment of accretion scenario in MER-
L153
CURY package (Chambers 1999), the collisions between two
Hansen,B.M.S.,&Murray,N.,2012,ApJ,751,158
bodies are assumed to be perfect gravitational aggregations.
Hansen,B.M.S.,&Murray,N.,2013,ApJ,775,53
Leinhardt&Stewart (2012) pointed out that real collisions could
Hayashi,C.,1981,Prog.THeor.Phys.Suppl.,70,35
suffer from partially accreting collision, hit-and-run impacts, or
Howard,A.W.,etal.,2010,Science,330,653
graze-and-merge events,ratherthanacompletemerger.Recently,
Howard,A.W.,etal.,2012,ApJS,201,15
Chambers (2013) showed that fragmentation does have anotable
Ida,S.,&Lin,D.N.C.,2004,ApJ,604,388
effect on accretion under consideration of fragmentation and hit-
Ida,S.,&Lin,D.N.C.,2008,ApJ,673,487
and-runcollisions(Leinhardt&Stewart2012;Gendaetal.2012).
Ida,S.,&Makino,J.,1992,Icarus,96,107
The final stages of accretion are lengthened by the sweep up of
Izidoro,A.,Morbidelli,A.,&Ramond,S.N.,2014,ApJ,794,11
collisionfragments.Theplanetsthatformedwithfragmentationin
Ji,J.H.,Jin,S.,&Tinney,C.G.,2011,ApJL,727,L5
thesimulationshavesmallermassesandlowereccentricitieswhen
Jin,S.,&Ji,J.H.,2011,MNRAS,418,1335
comparedtothosesimulationswithoutfragmentation.Inthissense,
Kokubo,E.,&Ida,S.,1998,Icarus,131,171
thescenariosthatincludeimperfectmergercollisionwillnotalter
Kokubo,E.,&Ida,S.,2002,ApJ,581,666
the conclusions of this study. In forthcoming work, we will take
LeeM.H.,PealeS.J.,2002,ApJ,567,596
into account hit-and-run and fragmentation process in our model
Lee,M.H.,Fabrycky,D.,&Lin,D.N.C.,2013,ApJL,774,L52
forfurtherinvestigation.
Lega,E.,et.al.,2014,MNRAS,440,683
Leinhardt,Z.M.,&Stewart,S.T.,2012,ApJ,745,79
Lin,D.N.C.,&Papaloizou,J.C.B.,1986,ApJ,309,846
ACKNOWLEDGMENTS Lin,D.N.C.,&Papaloizou,J.C.B.,1993,in:E.H.Levy&J.I.
Lunine(eds.),ProtostarsandPlanetsIII,(Tucson:Unv.Arizona)
Wethanktheanonymousrefereeforinsightfulcommentsandgood
Lissauer,J.J.,etal.,2011,Nature,470,53
suggestions that helped to improve the contents. This work is fi-
Lissauer,J.J.,etal.,2011,ApJS,197,8
nancially supported by National Natural Science Foundation of
China(GrantsNo.11273068,11473073,11503092,11573073), the Lovis,C.,etal.,2011,A&A,528,A112
StrategicPriorityResearchProgram-TheEmergenceofCosmolog- Mandell,A.M.,&Sigurdsson,S.,2003,ApJ,591,L111
ical Structures of the Chinese Academy of Sciences (Grant No. Mandell,A.M.,Ramond,S.N.,&Sigurdsson,S.,2007,ApJ,660,
XDB09000000), the innovative and interdisciplinary program by 823
CAS(GrantNo.KJZD-EW-Z001),theStrategicPriorityResearch Marcy,G.W.,etal.,2001,ApJ,556,296
Program on Space Science, CAS (Grant No. XDA04060901), Marcy,G.W.,etal.,2014,ApJS,210,20
the Natural Science Foundation of Jiangsu Province (Grant No. Mart´ı,J.G.,Giuppone,C.A.,&Beauge´,C.,2013,MNRAS,433,
BK20141509), and the Foundation of Minor Planets of Purple 928
MountainObservatory. Mayor,M.,etal.,2011,arXiv:1109.2497
Morbidelli,A.,etal.,2007,AJ,134,1790
Morbidelli,A.,&Crida,A.,2007,Icarus,191,158
Nelson,B.E.,etal.,2016,MNRAS,455,2484
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Figure1.OrbitalevolutionoftheplanetesimalsandJupitermassplanetinsimulationS1.Thesolidpointsshowtheplanetesimals.Theradiioftheplanetesimals
areproportionaltotheirmass.Thecolorofeachpointshowstheorbitaleccentricity.Theopencircleshowsthegiantplanet.AstheJupitermassplanetmigrating
inward,theplanetesimalsattheMMRorbitswereexcitedtohigheccentricorbits.Duetotheinward-migratinggiantplanet,planetesimalswereshepherded
inwardandhencetheaccretionrateintheinnerpartoftheplanetesimaldiskincreases.Therearealsosomeplanetesimalswerescatteredtotheouterpartof
thedisk.Severalterrestrialplanetsformat5Myr.
(cid:13)c 2015RAS,MNRAS000,1–??