formation of non-resonant, multiple close-in super-Earths (which exist around 40-60% (?) of solar type stars) N-body simulation (Ogihara & Ida 2009, ApJ)

• disk inner edge -- cavity or not ; stacked or penetrate planet trap due to e-damping?

population synthesis model (Ida & Lin, in prep.) • type-I migration -- Tanaka et al. (2002) or

Paardekooper et al. (2009)• resonant trapping & giant impacts

Formation of close-inFormation of close-in terrestrial terrestrial planets: planets: disk inner boundary, disk-planet interactions disk inner boundary, disk-planet interactions and giant impacts and giant impacts

Shigeru Ida Shigeru Ida (Tokyo Tech)

collaborators: Masahiro Ogihara (Tokyo Tech), Doug Lin (UCSC)

INI, Cambridge, Oct 23, 2009

Motivation: RV observation of super-Earths

Why so common? Why no short-P planet in

Solar system? Why not becoming jupiters? Why a~0.1AU (> HJs’ a) ? Why non-resonant?

( Terquem & Papaloizou 2007) Why multiple?

~40-60%(?) of FGK dwarfs have short-P (~0.1AU) super-Earths without signs of gas giants

~80%(?) of the super-Earth systems are non-resonant, multiple systems

N-body simulation (3D)Ogihara & Ida (2009, ApJ 699, 824)

type-I mig & e-damp:Tanaka et al. 2002

Tanaka & Ward 2004

resonantly trappedstable even after gas depletion Terquem & Papaloizou 2007

g

N-body simulation (3D)Ogihara & Ida (2009, ApJ 699, 824)

slower mig adiabatic

get stacked at the edgeWhy?

detailed analysis

N-body simulation (3D)Ogihara & Ida (2009, ApJ 699, 824)

slower mig adiabatic

get stacked at the edge instability after gas depletionnon-resonant multiple planets

at relatively large a population synthesis calculation

e

a [AU]

t [y

r]Semi-analytical calculation of

Accretion & migration of solid planets

type-I migration(0.1x Tanaka et al.)

giant impacts

105

0.1 10

106107108

1

y6103exp

t

resonant trapping

disk gas

M [

M]

disk edge

a [

AU

]

a [

AU

]t [yr]

Monte Carlo Model :- Ida & Lin (2009)

Modeling of giant impacts

t [yr] 3x107107 2x107 108

1

2 2

1

02x107 6x107

N-body :- Kokubo, Kominami, Ida (2006)

0.5

1.5

0.5

1.5

00

e

a [AU]

t [y

r]Semi-analytical calculation of

Accretion & migration of Solid planets

type-I migration(0.1x Tanaka et al.)

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)

• 2xMMSN case• rigid wall edge

g

Min. Mass Solar Nebula

x10x0.1

log normal

1 100.1

Population Synthesis

~30%

Solar-type stars• various mass disks (1000 systems)• rigid wall edge

Disk inner cavity ?

corotation radius

channel flow

strong magnetic coupling Cavity

weak magnetic coupling No Cavity

spin period [day]

nu

mb

er

of

sta

rs

10 1550

Herbst & Mundt2005

Is this picturestill valid?

N-body simulation (3D)Ogihara & Ida (2009, ApJ 699, 824)

slower mig adiabatic

get stacked at the edgeWhy?

detailed analysis

Why stacking at the edge ?

e-damping

type-I mig

planet-planet int.torq

ue o

n

bod

y 1

torq

ue o

n

bod

y 2

torq

ue o

n

bod

y 1

disk edge

€

L∝ a(1− e2)

1M1M

toy model

€

rF = −

1

te

(ρ g (r))(r v −

r v K (r))

−1

ta

(ρ g (r))

r v K (r)

*) Martin got the same result

Planet trap due to e-damping

Vgas(~VK)

type-I migraion torque: changes sign near cavity modulated by g-grad (Masset et al. 2006)

e-damping torque: not affected by g-grad? Tanaka & Ward formula is OK in this case?

Tidal e-damping(+ resonant e-excitation)

outward migration !

Condition for stacking te/ta = 0.003 redge/redge = 0.01

te/ta = 0.003 redge/redge = 0.05

te/ta = 0.03 redge/redge = 0.01

Both te/ta & redge/redge

must be small for stacking.

te/ta ~ (H/r)2 redge/redge~ (H/r) ?(H/r) r1/4

likely to be satisfied at the disk inner edge

€

∝

Planet formation model (core accretion)

Ida & Lin (2004a,b,2005,2008a,b)start from planetesimalscombine following processes

planetesimal accretiontype-I & II migrationsgas accretion onto coresdynamical interactions between planets

(resonant trapping, giant impacts) – Ida&Lin(in prep)

semi-analytical formulae based on N-body & fluid dynamical simulations

a [

AU

]

a [

AU

]t [yr]

Monte Carlo Model :- Ida & Lin (2009)

Modeling of giant impacts

t [yr] 3x107107 2x107 108

1

2 2

1

02x107 6x107

N-body :- Kokubo, Kominami, Ida (2006)

0.5

1.5

0.5

1.5

00

eccentricity

M [

M]

MMSN

10xMMSN

0.1xMMSN

final largest bodies 20 runs each

Monte Carlo model of giant impacts[close scattering & accretion of rocky embryos]

Monte Carlo

N-bodyKokubo et al. (2006)

semimajor axis [AU]

eccentricity

M [

M]

MMSN

10xMMSN

0.1xMMSN

final largest bodies 20 runs each

Monte Carlo model of giant impacts[scattering & accretion of rocky embryos]

Monte Carlo

N-bodyKokubo et al. (2006)

semimajor axis [AU]

Monte Carlo :- Ida & Lin (2009)- CPU time < 0.1 sec / run

N-body :- Kokubo, Kominami, Ida (2006)- CPU time ~ a few days / run

e

a [AU]

t [y

r]Accretion & migration of

planetesimals[Gas accretion onto cores is neglected in this particular set of simulation]

type-I migration

giant impacts

105

0.1 10

106107108

1

y6103exp

t

resonant trapping

CPU time: a few sec. on a PC

disk gas

M [

M]

disk edge

•2xMMSN case•No gas giant•rigid wall edge•type-I mig: Tanaka et al.’s speed x0.1

a [AU]0.1 101

Formation of dust-debris disks

1 10

10-2

1

10-4

/ M

MS

N

DF is strong

stochastic collisionsof embryos

inner regions: giant impacts – common outer regions: planetesimals remain unless gas giants form debris disks:

commonly produced weak [Fe/H]-dependence anti-correlated with jupiters?

108yrs106yrs

continuous collisionsof planetesimals

stirred by embryos

e

a [AU]

t [y

r]No-cavity case

type-I migration

giant impacts

105

0.1 10

106107108

1

y6103exp

t

disk gas

M [

M]

no disk edge

•2xMMSN case•type-I mig: Tanaka et al.’s speed x0.1

a [AU]

t [y

r]Effect of entropy gradient

Paardekooper et al. 2009

105

0.1 10

106107108

1

€

∝exp −t

3×106 y

⎛

⎝ ⎜

⎞

⎠ ⎟

disk gas

M [

M]

disk edge

e

• type-I mig: Tanaka’s torque is connected to Paardekooper’s

at ~10e-t/depAU

PaardekooperPaardekooper

TanakaTanaka

averaged over20 runs

(mean values,dispersion)

a [AU] a [AU]

M [

M]

e

blue: 3xMMSNright blue: MMSNred: 1/3xMMSN

cavityTanaka’s torque

0.1 1 10 0.1 1 10

linear/1 aaC

Non-resonant, multiple, short-P Earths/super-Earths

10

1

a [AU]

M [

M]

M [

M] Theoretical predictions

a ~ 0.1AU ( > disk inner edge =

0.04AU) rely on stacking (rigid wall)

non-resonant, multiple (have undergone close scattering & giant impacts)

common indep. of type-I migration rate

avoid gas accretion (have grown after disk gas

depletion via giant impacts)

observation

linear/1 aaC

Diversity of short-P terrestrial planets

M [

M]

a [AU]10.110.1

a [AU]M

[M

]

M [

M]

M [

M]no cavity cavity

Solar systemSaturn satellite system?

Short-P super-EarthsJupiter satellite system?

Sasaki, Stewart, Ida (submitted)

10 10

g

Min. Mass Solar Nebula

x10x0.1

log normal

1 100.1

Population Synthesis

~30%

Solar-type stars• various mass disks (1000 systems)• rigid wall edge

Summary

N-body simulations + Synthetic planet formation model including giant

impacts & resonant trapping Non-resonant, multiple, short-P Earths/super-Earths Diversity of close-in planets (Solar system: no close-in planets) diversity of disk inner boundary? 1) cavity or non-cavity

2) migration trap due to e-damping?