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