Extrasolar gas giants; eccentric and close-in planets

models for orbital evolutionFormation of giant planets; core accretion model

M-a distributiondependence on stellar metallicity/mass

Origin of diversity of giant planets

Planetary Formation (architectures, theory)Shigeru Ida (Tokyo Institute of Technology)

OUTLINE

disk surface density model is very important

Orbits of discovered extrasolar planets

a(1-e)

asmall a

close-in planetshigh e

eccentric planets

mas

s x

sini

[M⊕

]

semimajor axis a [AU] a [AU]ec

cent

ricity

e

a(1+e)

detection limit

Origin of eccentric planets: jumping jupiterRasio & Ford(1996), Weidenschilling & Marzari(1996), Lin & Ida(1997),….

Δa [rHill]

Marzari & Weidenschilling(2002)

tcrosst cr

oss[y

r]

108

106

102

104

real

istic

rang

emore than 3 giant planets in circular orbitsOrbit crossing starts at ~tcrossOne is ejected. The others remain in stable eccentricorbits.

other model:tidal interaction with a gas disk. limited to e < 0.3?e.g., Sari & Goldreich (2004)

Origin of close-in planets: orbital migrationLin et al. (1996)

a giant planet at > a few AUThe planet opens up a gap

planet’s perturbation > viscous diffusion

The planet migrates inwardwith disk accretion

[If disk gas dissipates soon after the formation, no migration.]

The migration may stop near disk inner edge

⊕−≈> MM 21010p

planet’s perturbation

viscous diffusion

diffmig ττ ≈

Kley’s talk

Origin of close-in planets: slingshot

If pericenter distance a(1-e) < 0.05AU during Jumping Jupiter processe is dampedrare? (0.95 < e < 1.0)

Ford et al. (2001): 2 planets case, << 1%Marzari & Weidenschilling (2002): 3 planets case

- stable stage after ejection, ~10%Bessho, Tanaka, Ida (in prep.): 3 planets case,

tidal damping included in orbit integration- during orbit crossing, ~30% Not rare

Migration may be primary.But slingshot could also contribute.

Formation of gas giant planets(that will become close-in, eccentric, or solar-system type

giant planets)

Ida & Lin (2004a, ApJ, 604, 388-413)

formation sites of different kinds of gas giantsimplication from the results in Ida & Lin (2004a)

semimajor axis a [AU]0.1

0.11 10 100

1

eccentric

10solar-system type

close-insurface density of planetsimals

in disks

MMSNΣΣ /

formation sites of different kinds of gas giantsimplication from the results in Ida & Lin (2004a)

0.10.1

1 10 100

1

10the most massive disks

disks similar to that formed our solar system

the least massive disks

surface density of planetsimals

in disks

semimajor axis a [AU]

MMSNΣΣ /

formation sites of different kinds of gas giantsimplication from the results in Ida & Lin (2004a)

0.10.1

1 10 100

1

eccentric

10solar-system type

close-insurface density of planetsimals

in disks

semimajor axis a [AU]

MMSNΣΣ /

protoplanatery disk

gas giants

Models for formation of gas giants

terrestrialplanets

planetesimals

cores107 y

106 y

104 y

core accretion scenarioSafronov, Hayashi

Mizuno, Bodenheimer

coagulation of planetesimals

gas accretion onto cores

grav. instability scenario

Cameron, Boss

dust (micron) to planetsimals (km)

disk self-grav. instability

102-3 y

108y

107 y

106ｙ

104 y

( ) y pp

p

310710 -MMMM

⊕≈&

deterministic planet formation modelbased on core accretion scenario

Ida & Lin (2004a, ApJ, 604, 388-413)

(atmosphere collapses)gas accretion

(clear gap;global depletion）gas inflow stops

Lin&Papaloizou (1985,PPII)

(partial gap)orbital migration

Lin&Papaloizou (1985,PPII)

⊕−>≈ M M 10core 5

⊕−> MM 2p 1010

depp τ>> ⊕− tMM ;1010 32

jumping jupiter:neglected

Ikoma et al. (2000,ApJ)

, aini =(integration on 109y)⇒ Mp, afinal

dust to planetesimals: not discussed

iniΣ

protoplanatery disk

gas giants

terrestrialplanets

planetesimals

cores107 y

106 y

108y

107 y

106ｙ

104 yplanetesimal coagulation:

Kokubo & Ida (2002, ApJ)

type-II migrationincluded

planet’s perturbation

viscous diffusion

type-I migrationnot included

disk torque imbalance

yr AU p

,Imig,

MMSNg

g2/1

1

11510

≈

⊕

a-

MM

-

ΣΣ

τ

⊕−> MM )10010(

very rapid: neglected in our simulationdiscussed later

⊕−> MM )11.0(

yr AU J

p

g,

gIImig,

1-

MMSN

2/1

1

1

10610 4

≈ −

a-

MM α

ΣΣ

τ

NelsonKley

disk surface densitygasdust

Disk surface density model

ice ice

AUice

>−

≈<=

)(43)3(1

aaaa

η

( ) 2g/cmAUdepdiskgas 5.1

12400/ −− ×= aef t τΣ

( ) 2g/cmAUicediskdust 5.1110 −×= af ηΣ

Min. Mass Solar Nebula(disk that formed solar system)

orbital radius a1AU 10AU

diskf

diskf

(planetesimals)

dustΣ

gasΣ

icea

Σlog

aice= 2.7(M*/M )2 AU

gas giants（yellow region）• fdisk ~1 (MMSN): intermediate a (> aice)

-- small a: core isolation mass is too small;

-- large a: core growth istoo slow;

• fdisk > 5 (massive disks) :broad a, even inside aice

Formation sites of gas giantsIda & Lin (2004a, ApJ, 604, 388)

initial orbital radius aini [AU]

fdisk

icea

0.01M⊕

final planet massM*=1M τdep=107y

M⊕

M⊕M⊕

M⊕M⊕

isolationslow growth

100

2/34/3 )( icediskiso ηfaM ∝

110/27 )( −∝ icediskgrow ηfat

prediction of M-a distribution: Monte Carlo simulation

surface density distribution

gasdust

fdisk =0.1-10 Gaussian distribution in log scale

a - distribution : (0.1-100AU)disk lifetime:disk viscosity: α=1x10-4

type-II migration is included; artificially stopped at 0.04AU

0.001 0.1

Taurusρ Oph

N

0.1 1 10

fdisk

Beckwith & Sargent (1996)MMSNgas,dep

diskgas Σ×=Σ− τ/t

ef

MMSNdust,diskdust Σ=Σ f(planetesimals)

aa ∝∆yrsdep

76 1010 −=τ)10( AUfewaat depdiff −≈≈ aττ

final a [AU]

Pla

net m

ass

[M⊕

]

close-in planets gas giants

icy planets

terrestrial planets

1MJup= 320M⊕

● Mgas > 10Msolid● Mgas < Msolid a > aice● Mgas < Msolid a < aice

Prediction of Mp-a distribution Ida & Lin (2004a, ApJ, 604, 388)

G dwarfs

Pla

net m

ass

Mp

[M⊕

]

time106 y

Mp

100M⊕

gas disk

10M⊕

1M⊕

deficit

108 y107 y

Ida & Lin (2004a)

Planet Desert

final a [AU]

Prediction of Mp-a distribution Ida & Lin (2004a, ApJ, 604, 388)

Mp-a distribution comparison with observation

not observable

Theory Observation

fraction of close-in planetstheory >> observation

↓

many close-in planets are accreted onto stars

Diversity of gas giant planets

Diversity of gas giant planets (my suggestion)

initial a [AU]

fdisk

0.10.1

1 10 100

10

1

solar-system type

eccentric tgrow + tmig < tdeptmig > tgrow

close-in tgrow + tmig < tdeptmig< tgrow tgrow+ tmig> tdep

Stellar metallicity dependenceIda & Lin (2004b, ApJ, 616, 567)

[Fe/H]-1 -0.5 0 0.5

observation (Fischer & Valenti)apparent dependence

Metallicity dependence of disksIda & Lin (2004b, ApJ, 616, 567)

disk surface density

gasdust

• assumption • disk formation/evolution is

independent of stellar metallicity• fgas = 0.1-10 log normal

• fdust = fgas x 10[Fe/H]

• [Fe/H]star = [Fe/H]disk[Fe/H] = log10 [(Fe/H)star/(Fe/H) ]

MMSNgas,dep

gasgas ΣΣ ×= − τ/tef

MMSNdust,dustdust ΣΣ f=(planetesimals)

1AU 10AUicea

[Fe/H]10

dustΣgasΣ

[Fe/H]=+ 0.5

observation

0.1 1 10

[Fe/H] dependence

Kokubo & Ida (2002)↓

more gas giants

Pla

net m

ass

[M⊕

]

semimajor axis a [AU]

)2/3(2/3 10 [Fe/H]dustcore ∝∝ΣM

[Fe/H]= 0

[Fe/H]= -0.5

G dwarfs

detection probabilityIda & Lin (2004b, ApJ, 616, 567)

metallicity [Fe/H]

obs.Fischer&Valenti(2003)

% s

tars

with

de

tect

able

pla

nets

30

20

10

0

theoretical model- planets at 0.04AU: excluded

G dwarfs

0.5-0.5 0

Stellar mass dependenceF, G, K vs. M

Ida & Lin (2005, ApJ, in press)astro-ph/0502566

Stellar mass dependence of disksM

K

G

F

M dwarfs (mass M＊=0.1-0.5 M )most abundant in a galactic diskon-going survey

gas giants are rare(~1/10 of FGK)isolated close-in neptune(GJ436; 0.03AU, 20M⊕)

Stellar mass dependence of disks

surface density distribution of disks

gasdust

• lifetime: indep. of M* (for M to F dwarfs)

depsungas or τΣ /

*21)/( teMM −∝21)/( *

orsundust MM∝Σ

Natta et al. 2004, Muzerolleo et al. 2004

Beckwith & Sargent 1996

logΣ

M* = 1M0.2M 0.4M

Min.MassSolar Nebula

x10x0.1 log normal

2* )/( sundisk MMM ∝&

yrsdep76 1010 −=τ

Planet mass [M⊕ ]

G

M

K

F

G

F

K

M

GJ436

Ｍ dwarfs- close-in Neptunes- Jupiters are rare

0.2M

0.4M

0.6M

1.0M

1.5M

distribution of planet mass([Fe/H]=0)Ida & Lin (2005, ApJ)

FGK dwarfs- close-in Jupiters- Jupiters are abundant

close-in:afinal<0.05AU distant:afinal=0.1-1AU0.2M

0.4M

0.6M

1.0M

1.5M

1 10 102 103 104 1 10 102 103 104

M

M

Ida & Lin (2005, ApJ, in press) astro-ph/0502566

M dwarfs vs. FGK dwarfs

• FGK: cores at > a few AU migrate after full gas accretion(>100M⊕)

close-in & distant Jupiter-mass planets

M: cores (~10M⊕) at ~1AUmigrate without gas accretion

low few Jupiterssmall aice icy cores at ~1AUgap opens at ~10M⊕[low T, weak stellar gravity]

at inner edge, gas accretion stops at ~10-20M⊕

close-in Neptune-mass planets (isolated, icy)

dustΣ

aice

10.3 3 [AU]0.1

10.3 3 [AU]0.1

aice=2.7(M*/M )2 AU

stellar mass [M ]

% s

tars

with

de

tect

able

pla

nets

(jup

iters

) 20

15

10

5

00.30.1 1

2sun* )/( MM∝Σ

1sun* )/( MM∝Σ

theoretical model- planets at 0.04AU: excluded

Σsmall icelarge a

detection probabilityIda & Lin (2005, ApJ, in press) astro-ph/0502566

[Fe/H]=0

M K G F

isolated close-in neptunes around Ｍ dwarfsicy planets in warm environment300-600K (at 0.04AU for M*=0.2-0.4M )

• habitable “ocean planets”? Leger et al. (2004)• marginally observable at present

habitable “ocean planets”?

They could be more abundant than Earth-like planets around G stars

habitable zone

tidal lock0.1 10.3 [AU]

icy planet

ocean planet ice boundary

The calibrated theory also predicts distribution of extrasolar terrestrial planets. (core accretion model)

SummaryMp-a distribution of extrasolar planetsbased on core accretion model many implications:- diversity of gas giant planets- metallicity dependence- stellar mass dependense (M stars)

disk surface density (a < 10AU) model is crucialgas & planetesimals(dust), stellar mass/metallicity dependence