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
