IAU Symposium 276 The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution Torino, Oct 11, 2010

What can core accretion model explain? What can not?

population synthesis model M-a distributions: neglecting

planet-planet interactions – Ida & Lin(2004-08), Mordasini et al.(2009)

Planet-planet scattering & collisions

* e-distribution of jupiters * distant jupiters

* close-in super-Earths – Ida & Lin (2010, ApJ ; 2011)

Theoretical Predictions of Theoretical Predictions of M,M, aa && ee -- Distributions of Jupiters/Super-Distributions of Jupiters/Super-

EarthsEarths

Shigeru IdaShigeru Ida (Tokyo Institute of Technology)(Tokyo Institute of Technology)collaborators: Doug Lin (UCSC), E. Kokubo (NAOJ)collaborators: Doug Lin (UCSC), E. Kokubo (NAOJ)M. Nagasawa, T. Sasaki, M. Ogihara (Tokyo Tech)M. Nagasawa, T. Sasaki, M. Ogihara (Tokyo Tech)

gas giants

Core accretion model - sequential processes of different physics

planetesimals

©Newton Press

cores

protoplanetary disk:H/He gas (99wt%) + dust grains (1wt%)

core accretion

gas envelope contraction

runaway gas accretion

>100M

> 5-10M

coagulation of planetesimals

terrestrialplanets

gas accretion onto cores

type I migration

type II migrationorbital instability

Detailed studies on individual processes: important. But, NOT directly compared with obs. of exoplanets Population synthesis model: combine these processes to predict distributions of

exoplanets explain existing data, predict future observations, & constrain a theoretical model for each process -- link theory and observation

derive semi-analytical formulas for individual processesintegrate equations of

planetary growth/migration

Population synthesis modelIda & Lin (2004a,b,2005,2008a,b,2010), Mordasini et al. (2009a,b)

dM

dt

M

planetesimal

+Membyo M

gas

da

dt a

migration

ascatt/coll

The modeling of each process: must be based on detailed simulations

(N-body, fluid dynamical, ...)

Otherwise, the results are meaningless

But, the modeling must be simple enough, while it must properly reflect essential physical ingredients...

Population synthesis model

dM

dt

M

planetesimal

+Membyo M

gas

da

dt a

migration

ascatt/coll

Example of the integrationsIda & Lin (in prep)

evolution

type-I migration

planetesimalaccretion

gas accretiononto a core

type-II migration

rockyplanets

gas giant

icyplanets

diskgas

diskedge

type-I migration

final state

0.6 sec on Mac air

dM

dt

M

planetesimal

+Membyo M

gas

da

dt a

migration

ascatt/coll

Simple “one-planet-in-a-disk” “one-planet-in-a-disk” modelIda & Lin (2004a,b,2005,2008a,b), Mordasini et al. (2009a,b)

neglect Dynamical Interactions (scattering, collisions) between planets

w/o. dynamical interactions: e can NOT be evaluated & many problems evaluated

must collide

must scatter

diskgas

diskedge

““Multiple-planets-in-a-disk” Multiple-planets-in-a-disk” modelIda & Lin (2010, 2011)

Dynamical Interaction modeling: quantitatively reproduce N-body simulations

DI between rocky/icy planets Resonant Trapping -- Sasaki, Stewart & Ida (2010, ApJ) RT & Giant Impacts -- Ida & Lin (2010, ApJ)

DI between all planets [+ close encounters & ejection of giants (secular perturbations: not yet)]

-- Ida & Lin (in prep)

preliminary results: shown today

- high e of jupiters & distant jupiters - multiple close-in super-Earths

dMdt

M planetesimal

+Membyo M gas

da

dt

a

migration

ascatt/coll

dedt

escatt/coll

Effects of Dynamical Interaction

““Multiple-planets-in-a-disk” Multiple-planets-in-a-disk” ““One-planets-in-a-disk” One-planets-in-a-disk”

giant impacts

resonant trapping

ejection

diskgas

evolution final state

rockyplanets

gas giant

icyplanets

diskgas

eccentricity distributioneccentricity distribution

Dynamical Interaction eccentricity distribution

Ida & Lin (in prep)

Population synthesis modelIda & Lin (in prep)

3000 systems3000 systemsMM**=0.8-1.25=0.8-1.25M

type-I: type-I: 0.1x0.1xTanakaTanaka

45 min on Mac air

Eccentricity Distributions

Eccentricity excitation of jupiters by scattering

- good agreement with observation - good agreement with observation Theory Theory

ObservationObservation

Theory(Ida & Lin) Theory

Observation

Observation

massive disks: multiple massive giants close scattering

larger e for larger M

Theoryvr >1m/s

& a<5AU

Eccentricity vs. mass

disk mass dependence

>1000M

100-1000M

10-100M

Dis

k m

ass [

MM

SN

]

e vs. M : weak parameter dependences

Tanaka/1:I type aaC

C1 0.03

C1 0.1

C1 0.3

rH h or

g3 M

(g e t /dep)

M r2g

rH h or

faster migration

more limitedgas accretion

Eccentricity vs. semimajor axis [jupiters]

Theory Theory(Ida & Lin)

ObservationObservation

multiple giants < 10AU small e for a >10AU emax~ Vesc /VKep~2(a/1AU)1/2

smaller e for smaller a

At a < 0.05AU, e is tidally damped. -- tide is not included in the theoretical model

e -- peaked at ~1AU

e vs. a : weak parameter dependences

Tanaka/1:I type aaC

C1 0.03

C1 0.1

C1 0.3

M r2g

g3 M

Distant Jupiters (>100AU)by scattering

Theory disk instability can make core accretion? * in situ: impossible * outward mig. (Masset) ? * scattering: possible - systems - small e core scattering + gas accretion Ed Thommes’ N-body

(*) ejected jupiters free floating planets - 6% of systems

Distant jupiters with small e

Mass – Semimajor axis Distribution

ObservationTheory(Ida & Lin)

Broad distribution of a is explained by core accretion + type II mig.Remaining problems: 1)over-density at > 1AU migration trap? (dead zone, Paardekooper’s torque...)2) (hot jupiters) ~ 15% [theory] vs 1% [obs] disruption of HJs ? (no inner cavity, tide, evaporation, ...) -- (other jupiters) ~25% [OK?]3) planet desert at 10-100M ? -- observationally unclear faster type I migration? how to stop planetesimal/gas accretion?

Mass vs. semimajor axis [jupiters]

M vs. a : parameter dependences

C1 0.03

C1 0.1

C1 0.3

M r2g

g3 M

close-in Super-Earthsclose-in Super-EarthsJupitersJupiters

22%22%22%22%

25%25%26%26%

33%33%16%16%

8%8%46%46%

16%16%39%39%

11%11%35%35%

more limitedgas accretion

Formation of close-in super-Earths

ObservationTheory(Ida & Lin)

1) a peak at ~0.1AU simulations: disk inner edge at 0.03-0.04AU (hot jupiters ~ 0.03-0.04AU)2) multiple, non-resonant3) (close-in super-earths) ~ 26%

These theoretical predictions are almost independent of type-I migration speed

Mass vs. semimajor axis [super-earths]

e

a [AU]

t

[yr]

Formation of non-resonant, multiple, close-in super-Earths Ida & Lin (2010, ApJ)

type-I migration(Tanaka x 0.1)

giant impacts

105

0.1 10

106107108

1

y6103exp

t

resonant trapping

disk gas

M [

M]

disk edge

too small to startgas accretion

non-res. multiple super-Earths(~0.1AU, missed gas accretion)

high abundance

M vs. a : parameter dependences

C1 0.03

C1 0.1

C1 0.3

M r2g

g3 M

close-in Super-Earthsclose-in Super-EarthsJupitersJupiters

22%22%22%22%

25%25%26%26%

33%33%16%16%

8%8%46%46%

16%16%39%39%

11%11%35%35%

c

Disks forming super-Earths and Jupiters

>100M

rocky, 1-20M

icy, 1-20M

massive disks: form massive multiple jupiters destroy SEs medium-mass disks: retain Super-Earths - SE + J systems: only 9%

Dis

k m

ass [

MM

SN

]

Summary

What observational data can core accretion model explain? What can not?

using population synthesis model

Distributions of Jupiters e-M, e-a -- well explained - refinement of scattering model is still needed. [talks by E. Ford, S. Chatterjee] M-a -- some problems remain - calculations with Paardekooper’s type-I mig are

needed [talk by W. Kley] distant Jupiters with small e -- possible

Distributions of super-Earths look consistent but more obs. data are needed

Modeling of dynamical interactionsamong gas giants

Nagasawa & Ida 2010

a

- high eccentricities of jupiters- distant (>30AU) jupiters [direct imaging]-

explained by scattering?

e

3/18

If more than 3 giant planets form on circular orbitsOrbit crossing starts on tcross

One is ejected. The others remain in stable eccentric orbits.

Δa [rH]Marzari & Weidenschilling (2002)tcross

t cros

s [y

r]

Origin of eccentric planets: jumping jupiterWeidenschilling & Marzari (1996), Lin & Ida(1997),...

Solar system: 2 giants

stable

RV

Zhou et al. (2007)

tcross

3/18Origin of eccentric planets: jumping jupiterWeidenschilling & Marzari (1996), Lin & Ida(1997),...

a0 = 5, 7.25, 9.5AU

M = MJ

a

Nagasawa et al. (2008)

N-body simulations:100 runs with different initial angular locations

The system is chaotic, but shows a well determined distribution

modeling (Monte Carlo) e

N-body: Nagasawa et al. (2008)~ an hour/run on a PC

Modeling + Monte Carlo~ 0.02sec/1000runs on a PC

tidalcicularization

M=MJ, a0=5.0, 7.25, 9.0AU ( 非等質量の場合も比較済） Comparison between N-body and ModelingComparison between N-body and Modeling -- Scattering of 3 giant planets -- Scattering of 3 giant planets

e e

a[AU]

no tide

N-body: Nagasawa et al. (2008)~ an hour/run on a PC

Modeling + Monte Carlo~ 0.02sec/1000runs on a PC

tidalcicularization

M=MJ, a0=5.0, 7.25, 9.0AU ( 非等質量の場合も比較済）

3/18Semi-analytical modelingIda & Lin (in prep.)

select an ejected planet (mass-weighted random chaos) select an inwardly scattered

planet (random) excited e of scattered planets:

evK ~ (2GMdom/Rdom)1/2

( mean value – deterministic dispersion – random(Rayleigh) )

a of outer planet q = a(1- e) with appropriate q ( initial a’s; calibrated by N-body) (deterministic + random)

a of inner planet by conservation of E (that of L: useless) (deterministic)

1

ain

1

aout

1

a01

1

a02

1

a03

(initial E)

Modeling of dynamical interactions

among rocky planetary embryos

ecc

ent

rici

ty e

semimajor axis a [AU]0.5 1.0 1.5 2.0

oligarchic growthKokubo & Ida (2002)

Post-oligarchic giant impactsKokubo et al. (2006)

M ~ 0.1-0.2Misolation mass (deteministic)

M ~1M

MMSN case

no ejection collisions after many scatterings

a [

AU

]

a [

AU

]t [yr]

Monte Carlo: Ida & Lin (2010, ApJ) deterministic celestial dynamics + (reasonable) chaotic features< 0.1sec/run on a PC

Modeling of giant impactsModeling of giant impacts- stochastic process -- stochastic process -

t [yr] 3x107107 2x107 108

1

2 2

1

02x107 6x107

N-body : Kokubo et al. (2006)~ a few days/run on a PC

0.5

1.5

0.5

1.5

00

eccentricity

M [

M]

MMSN

10xMMSN

0.1xMMSN

final largest bodies 20 runs each

Monte Carlo

N-bodyKokubo et al. (2006)

semimajor axis [AU]

Modeling of giant impacts of rocky planetsModeling of giant impacts of rocky planets- stochastic process -- stochastic process -

Ida & Lin (2010, ApJ)

Ida & Lin (2010, ApJ)

Modeling Modeling reveal intrinsic physics reveal intrinsic physics

meta-stabletcross~ tsystem

stabletcross>>tsystem

e ~ evK~ 0.3 e < 0.1

Implication:formation of multiple, non-resonant,

close-in super-Earths

Ida & Lin (2010, ApJ)

Recent radial velocity surveys Large fraction (10-40%; why so common?) of solar-

type stars have super-Earths (why didn’t accrete gas?) at ~0.1AU (why > ahot jup?) without signs of gas giants in the same systems

Most of the super-Earth systems are non-resonant, multiple systems (why?)

e

a [AU]

t [y

r]

Formation of non-resonant, multiple, close-in super-Earths Ida & Lin (2010, ApJ)

type-I migration(conventional)

giant impacts

105

0.1 10

106107108

1

y6103exp

t

resonant trapping

disk gas

M [

M]

disk edge

too small to startgas accretion

non-res. multiple super-Earths(~0.1AU, missed gas accretion)

high abundance

Ubiquity of short-P rocky planets

M [

M]

a [AU]10.1

M [

M]

10

slowtype I mig

moderatetype I mig

Solar system vs. Super-Earth systems

corotation radius

channel flow

strong magnetic coupling

Inner CavityInner Cavityweak magnetic coupling No CavityNo Cavity

spin period [day]

num

ber

of

stars

10 1550

Herbst & Mundt (2005)

Observation of spin periodsof young stars

Spitzer: positiveSpitzer: positiveCorot: negativeCorot: negative

Diversity of short-P rocky planets

M [

M]

a [AU]10.110.1

a [AU]M

[M

]

M [

M]

M [

M]

no cavity cavity

Solar systemSaturnian satellite system?

Short-P super-EarthsJovian satellite system?

10 10

Sasaki, Steawrt & Ida (2010, ApJ)

slowtype I mig

moderatetype I mig

Different a between hot super-Earths and jupiters

Super-Eaths systemsOgihara, Duncan & Ida (2101, ApJ)Ogihara, Duncan & Ida (2101, ApJ)

type I migration of resonantly trapped embryos type I migration of resonantly trapped embryos

type II migration of gas giantstype II migration of gas giants

aaHSEHSE > > aaHJHJ