 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 terrestrial planets: disk inner boundary, disk-planet interactions and giant impacts Shigeru Ida Formation of close-in terrestrial planets: disk inner boundary, disk-planet interactions and giant impacts 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 Tanaka & Ward 2004 resonantly trapped stable even after gas depletion  Terquem & Papaloizou 2007 gg

N-body simulation (3D) Ogihara & Ida (2009, ApJ 699, 824) slower mig  adiabatic get stacked at the edge Why?  detailed analysis

N-body simulation (3D) Ogihara & Ida (2009, ApJ 699, 824) slower mig  adiabatic get stacked at the edge instability after gas depletion  non-resonant multiple planets at relatively large a  population synthesis calculation

e a [AU] t [yr] Semi-analytical calculation of Accretion & migration of solid planets type-I migration (0.1x Tanaka et al.) giant impacts resonant trapping disk gas M [M  ] disk edge

a [AU] t [yr] Monte Carlo Model : - Ida & Lin (2009) Modeling of giant impacts t [yr] 3x x x10 7 6x10 7 N-body : - Kokubo, Kominami, Ida (2006)

e a [AU] t [yr] Semi-analytical calculation of Accretion & migration of Solid planets type-I migration (0.1x Tanaka et al.) giant impacts resonant trapping disk gas M [M  ] disk edge too small to start gas accretion non-res. multiple super-Earths (~0.1AU, missed gas accretion) 2xMMSN case rigid wall edge

gg Min. Mass Solar Nebula x10x0.1 log normal 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] number of stars Herbst & Mundt 2005 Is this picture still valid?

N-body simulation (3D) Ogihara & Ida (2009, ApJ 699, 824) slower mig  adiabatic get stacked at the edge Why?  detailed analysis

Why stacking at the edge ? e-damping type-I mig planet-planet int. torque on body 1 torque on body 2 torque on body 1 disk edge 1M  toy model *) Martin got the same result

Planet trap due to e-damping Vgas(~V K ) 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 t e /t a =  r edge /r edge = 0.01 t e /t a =  r edge /r edge = 0.05 t e /t a = 0.03  r edge /r edge = 0.01 Both t e /t a &  r edge /r edge must be small for stacking. t e /t a ~ (H/r) 2  r edge /r edge ~ (H/r) ? (H/r) r 1/4  likely to be satisfied at the disk inner edge

Planet formation model (core accretion) Ida & Lin (2004a,b,2005,2008a,b) start from planetesimals combine following processes planetesimal accretion type-I & II migrations gas accretion onto cores dynamical interactions between planets (resonant trapping, giant impacts) – Ida&Lin(in prep) semi-analytical formulae based on N-body & fluid dynamical simulations

a [AU] t [yr] Monte Carlo Model : - Ida & Lin (2009) Modeling of giant impacts t [yr] 3x x x10 7 6x10 7 N-body : - Kokubo, Kominami, Ida (2006)

eccentricity M [M  ] MMSN 10xMMSN 0.1xMMSN final largest bodies20 runs each Monte Carlo model of giant impacts [close scattering & accretion of rocky embryos] Monte Carlo N-body Kokubo et al. (2006) semimajor axis [AU]

eccentricity M [M  ] MMSN 10xMMSN 0.1xMMSN final largest bodies20 runs each Monte Carlo model of giant impacts [scattering & accretion of rocky embryos] Monte Carlo N-body Kokubo 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 [yr] Accretion & migration of planetesimals [Gas accretion onto cores is neglected in this particular set of simulation] type-I migration giant impacts 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] Formation of dust-debris disks  /  MMSN DF is strong stochastic collisions of 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? 10 8 yrs 10 6 yrs continuous collisions of planetesimals stirred by embryos

e a [AU] t [yr] No-cavity case type-I migration giant impacts disk gas M [M  ] no disk edge 2xMMSN case type-I mig: Tanaka et al.’s speed x0.1

a [AU] t [yr] Effect of entropy gradient Paardekooper et al disk gas M [M  ] disk edge e type-I mig: Tanaka’s torque is connected to Paardekooper’s at ~10e -t/  dep AU Paardekooper Tanaka

averaged over 20 runs (mean values, dispersion) a [AU] M [M  ] e blue: 3xMMSN right blue: MMSN red: 1/3xMMSN cavity Tanaka’s torque

Non-resonant, multiple, short-P Earths/super-Earths 10 1 a [AU] 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

Diversity of short-P terrestrial planets M [M  ] a [AU] a [AU] M [M  ] no cavitycavity Solar system Saturn satellite system? Short-P super-Earths Jupiter satellite system? Sasaki, Stewart, Ida (submitted) 10

gg Min. Mass Solar Nebula x10x0.1 log normal 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?