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-in Formation of close-in terrestrial terrestrial planets: planets: disk inner boundary, disk-planet disk inner boundary, disk-planet interactions 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
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formation of non-resonant, multiple close-in super-Earths
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