Dynamical Evolution of Compact Multi-Planet Systems:
Effects of External Giant Planets
Dong Lai Cornell University
TripleEvolu,onandDynamics,LorentzCenter,Leiden,9/11/2018
Kepler:4700planetsin3600systems (mostlysuper-earthsorsub-neptunes,<200days)
NumberofTransi:ngplanets
Num
bero
fsystems
ObservedTransitMul:plicityDistribu:onF(Ntran)2900
500
160
61
20
3
1
AnEmergingTrend:
SystemswithsmallernumberofplanetsaredynamicallyhoJer:highereccentrici:esandmutualinclina:ons(Xie+16;Zhu+18)RelatedTrends:---ExcessofKeplerSingles–Keplerdichotomy(?)Modelswithsinglemutualinclina,ondispersionfallshorttoexplaintheobservednumberofKeplersingles(Lissauer+11;Johansen+12;Ballard&Johnson16)--KeplerSingleshavehigherstellarobliqui:es(Morton&Winn14)
AnEmergingTrend:
SystemswithsmallernumberofplanetsaredynamicallyhoJer:highereccentricityandmutualinclina:ons(Xie+16;Zhu+18)RelatedTrends:---ExcessofKeplerSingles–Keplerdichotomy(?)Modelswithsinglemutualinclina,ondispersionfallshorttoexplaintheobservednumberofKeplersingles(Lissauer+11;Johansen+12;Ballard&Johnson16)--KeplerSingleshavehigherstellarobliqui:es(Morton&Winn14)
Super-EarthsandColdJupiterConnec:on
30-50%ofinnersuper-Earths(P<200d)haveCJcompanions(P>400d);TheseCJsareoZeneccentric,havingundergonescaJerings(observa,onsfrommanygroups…seeLai&Pu2017;Zhu&Wu2018forrefs)
How Cold Jupiters (and scatterings) affect Inner planet system (& stellar obliquity)?
WithBonan(Michael)PuKassandraAnderson
References:Lai&Pu2017“HidingPlanetsbehindaBigFriends…”Pu&Lai2018“Eccentrici,esandInclina,onsofmul,planetsystems....”Pu&Lai2018“ScaeeringsofColdJupitersanditsInfluenceonInnerSystems”(inprep)Lai,Anderson&Pu2018“Howdocompanionsaffectspin-orbitmisalignments?”Anderson&Lai2018“Teeteringstars:Resonantexcita,onofstellarobliqui,es…”
Ninnerplanets+oneperturber(CJ)
Perturber:CJoninclinedandeccentricorbit!excitesmutualinclina,onsandeccentrici,esintheinnersystem
m1 m2
✓p
mp
m3 m4
NumericalSimula:onsAnaly:caltheory/scalings… Lai&Pu2017
Hansen2017Becker&Adams2017Readetal.2017Jontof-Hueeretal2017Pu&Lai2018Denhametal.2018
LpL1
⌦1p ⇠ mp
M?
✓a1ap
◆3
n1 / mp
a3pa3/21
PrecessionofL1aroundLp:
✓p
m1 m2
mp
PrecessionofL2aroundLp:
⌦2p / mp
a3pa3/22
m1 m2
mp
⌦1p
⌦2p
!12
!21
L1andL2precessaroundeachotheratrate !12,!21
m1 m2
mp
⌦1p
⌦2p
!12
!21
Mutualinclina,oninducedbyperturberdependsonCouplingParameter
L1andL2precessaroundeachotheratrate !12,!21
✏12 =⌦2p � ⌦1p
!12 + !21⇠ mp
m1,2
✓a1,2ap
◆3
MaximumMutualInclina:onInducedbyexternalperturber
✓p = 10�
(✓12
)max
' ✏12
sin 2✓p
DL&Pu2017✏12 =
⌦2p � ⌦1p
!12 + !21⇠ mp
m1,2
✓a1,2ap
◆3
mp
m1 m2
⌦1p
⌦2p
!12
NodalPrecessionResonance
ResonanceFeature:exists when m2 & m1
✏12 ⇠ 1
In the m2 � m1 limit:Resonance occurs at ⌦2p = ⌦1p + !12 or ✏12 = 1
ResonanceFeature:✏12 ⇠ 1
Can produce much larger mutual inclination than ✓p
EccentricityExcita:onbyExternalPerturber
Pu&DL2018Apsidalprecessionresonance
4planetsystemwithanexternalperturber
averaged coupling parameter / mp/a3p
dispersionofmutualinclination
DL&Pu2017
Ninnerplanets+2ColdJupiters
Ninnerplanets+2ColdJupiters
Whathappentoinnerplanetsduringouter“violence”?
• PreviousworkshaveconsideredexamplesusingN-bodysimula,ons(e.g.Carrera,Davies+16,Gra,a&Fabrycky17;Huang,Petrovich+16;Mus,ll,Davies+17)• Issuesof:me-scales:InnerplanetshaveP~10days,outerplanetshaveP>5yrs;giantplanetejec,on,mescaleuptotej~109yrs,orNej~108outerorbits! DifficulttogainunderstandingwithonlyasmaeeringofN-bodysimula,ons
HybridN-Body-SecularMethod Pu&DL2018(inprep)
GiantplanetscaJeringisastochas:cprocess…
GiantplanetscaJerings:Simula,ons+Sta,s,calTheory(randomwalkinenergy)
GiantplanetscaJerings:Simula,ons+Sta,s,calTheory(randomwalkinenergy)• Planetscanwanderinward!maydirectly“destroy”theinnersystem
Pu&Lai2018(inprep)
GiantplanetscaJerings:Simula,ons+Sta,s,calTheory(randomwalkinenergy)• Canhaveawiderangeofejec,on,mes...
Pu&Lai2018(inprep)
“1+2”Problem(oneplanet+twounstablegiants)
ExpectedResultsfor“N+2”PlanetSystems
Pu&Lai2018,2019(inprep)
Stellarspinaxis
Innerplanetm1(AhotorwarmJupiter)
Perturbermp
Howexternalcompanionaffectsstellarobliquity?
Spin-orbitdynamicsdependstronglyon
𝜔★1
𝜔1p
S
L
Lp
Lai,Anderson&Pu(2018)SeeBoue&Fabrycky(2014)forgeneralcases
ResonantExcita:onofstellarobliquityasstarspinsdown
KassandraAnderson&Lai2018
Summary
References:Lai&Pu2017“HidingPlanetsbehindaBigFriends…”Pu&Lai2018“Eccentrici,esandInclina,onsofmul,planetsystems....”Pu&Lai2018“ScaeeringsofColdJupitersanditsInfluenceonInnerSystems”(inprep)Lai,Anderson&Pu2018“Howdocompanionsaffectspin-orbitmisalignments?”Anderson&Lai2018“Teeteringstars:Resonantexcita,onofstellarobliqui,es…”
• Orbitalarchitectureofsuper-EarthscanbestronglyaffectedbyColdJupiters.CJscanexciteeccentrici,esandmutualinclina,ons,andmaydestroySEs.
• “Simple”analy,cal/scalingrela,onsfor“N+1”systems• “N+2”systemsaresubtle:Resultdependsonejec,on,mescale…(sta,s,caltheoryfor2-planetscaeerings)• Stellarobliqui,esarealsoaffected...
Thanks
Top Related