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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?

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formation of non-resonant, multiple close-in super-Earths

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  1. 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-interrestrial planets: disk inner boundary, disk-planet interactions and giant impactsShigeru Ida (Tokyo Tech) collaborators: Masahiro Ogihara (Tokyo Tech), Doug Lin (UCSC) INI, Cambridge, Oct 23, 2009

  2. Motivation: RV observation of super-Earths • ~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 • 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?

  3. N-body simulation (3D) Ogihara & Ida (2009, ApJ 699, 824) type-I mig & e-damp: Tanaka et al. 2002 Tanaka & Ward 2004 Sg resonantly trapped stable even after gas depletion  Terquem & Papaloizou 2007

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

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

  6. Semi-analytical calculation of Accretion& migration of solid planets e M [M] giant impacts 108 107 106 resonant trapping disk gas t [yr] type-I migration (0.1x Tanaka et al.) 105 0.1 1 10 disk edge a [AU]

  7. Modeling of giant impacts 2 2 1.5 1.5 a [AU] a [AU] 1 1 0.5 0.5 0 0 0 107 2x107 3x107 2x107 6x107 108 t[yr] t [yr] • Monte Carlo Model : • Ida & Lin (2009) • N-body : • Kokubo, Kominami, Ida (2006)

  8. Semi-analytical calculation of Accretion& migration of Solid planets • 2xMMSN case • rigid wall edge e M [M] non-res. multiple super-Earths (~0.1AU, missed gas accretion) too small to start gas accretion giant impacts 108 107 106 resonant trapping disk gas t [yr] type-I migration (0.1x Tanaka et al.) 105 0.1 1 10 disk edge a [AU]

  9. Population Synthesis ~30% Min. Mass Solar Nebula • Solar-type stars • various mass disks • (1000 systems) • rigid wall edge x0.1 x10 log normal 0.1 1 10 Sg

  10. Disk inner cavity ? strong magnetic coupling Cavity weak magnetic coupling No Cavity channel flow corotation radius Is this picture still valid? number of stars Herbst & Mundt 2005 0 5 10 15 spin period [day]

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

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

  13. Planet trap due to e-damping Tidal e-damping (+resonant e-excitation) outward migration ! Vgas(~VK) type-I migraion torque: changes sign near cavity  modulated by Sg-grad (Masset et al. 2006) e-damping torque: not affected by Sg-grad? Tanaka & Ward formula is OK in this case?

  14. Condition for stacking te/ta= 0.003 Dredge/redge = 0.01 Both te/ta &Dredge/redge must be small for stacking. te/ta ~ (H/r)2 Dredge/redge~ (H/r) ? (H/r) r1/4  likely to be satisfied at the disk inner edge te/ta= 0.003 Dredge/redge = 0.05 te/ta= 0.03 Dredge/redge = 0.01

  15. 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

  16. Modeling of giant impacts 2 2 1.5 1.5 a [AU] a [AU] 1 1 0.5 0.5 0 0 0 107 2x107 3x107 2x107 6x107 108 t[yr] t [yr] • Monte Carlo Model : • Ida & Lin (2009) • N-body : • Kokubo, Kominami, Ida (2006)

  17. Monte Carlo model of giant impacts [close scattering & accretion of rocky embryos] final largest bodies 20 runs each 10xMMSN M [M] N-body Kokubo et al. (2006) MMSN Monte Carlo 0.1xMMSN eccentricity semimajor axis [AU]

  18. Monte Carlo model of giant impacts [scattering & accretion of rocky embryos] final largest bodies 20 runs each • N-body : • Kokubo, Kominami, Ida (2006) • CPU time ~ a few days / run 10xMMSN M [M] N-body Kokubo et al. (2006) • Monte Carlo : • Ida & Lin (2009) • - CPU time < 0.1 sec / run MMSN Monte Carlo 0.1xMMSN eccentricity semimajor axis [AU]

  19. Accretion& migration of planetesimals [Gas accretion onto cores is neglected in this particular set of simulation] • 2xMMSN case • No gas giant • rigid wall edge • type-I mig: • Tanaka et al.’s • speed x0.1 e M [M] giant impacts 108 107 106 resonant trapping disk gas t [yr] type-I migration 105 0.1 1 10 disk edge a [AU] CPU time: a few sec. on a PC

  20. Formation of dust-debris disks • 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? 1 DF is strong S/SMMSN 106yrs 10-2 108yrs 10-4 1 10 continuous collisions of planetesimals stirred by embryos stochastic collisions of embryos 0.1 1 10 a [AU]

  21. No-cavity case • 2xMMSN case • type-I mig: • Tanaka et al.’s • speed x0.1 e M [M] giant impacts 108 107 106 t [yr] disk gas type-I migration 105 0.1 1 10 a [AU] no disk edge

  22. Effect of entropy gradient Paardekooper et al. 2009 e • type-I mig: • Tanaka’s torque • is connected to • Paardekooper’s • at ~10e-t/tdepAU M [M] 108 Tanaka 107 t [yr] 106 disk gas Paardekooper 105 0.1 1 10 disk edge a [AU]

  23. averaged over 20 runs (mean values, dispersion) e M [M] blue: 3xMMSN right blue: MMSN red: 1/3xMMSN cavity Tanaka’s torque 0.1 1 10 0.1 1 10 a [AU] a [AU]

  24. Non-resonant, multiple, short-P Earths/super-Earths • 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 M [M] 1 M [M] 10 a [AU]

  25. Diversity of short-P terrestrial planets no cavity cavity M [M] M [M] M [M] M [M] 0.1 1 10 0.1 1 10 a [AU] a [AU] Solar system Saturn satellite system? Short-P super-Earths Jupiter satellite system? Sasaki, Stewart, Ida (submitted)

  26. Population Synthesis ~30% Min. Mass Solar Nebula • Solar-type stars • various mass disks • (1000 systems) • rigid wall edge x0.1 x10 log normal 0.1 1 10 Sg

  27. 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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