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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? - PowerPoint PPT Presentation
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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?
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