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