 formation of non-resonant, multiple close-in super-earths (which exist around 40-60% (?) of...

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  • Slide 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-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
  • Slide 2
  • 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
  • Slide 3
  • N-body simulation (3D) Ogihara & Ida (2009, ApJ 699, 824) type-I mig & e-damp: Tanaka et al. 2002 Tanaka & Ward 2004 resonantly trapped stable even after gas depletion Terquem & Papaloizou 2007 gg
  • Slide 4
  • N-body simulation (3D) Ogihara & Ida (2009, ApJ 699, 824) slower mig adiabatic get stacked at the edge Why? detailed analysis
  • Slide 5
  • 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
  • Slide 6
  • e a [AU] t [yr] Semi-analytical calculation of Accretion & migration of solid planets type-I migration (0.1x Tanaka et al.) giant impacts 10 5 0.110 10 6 10 7 10 8 1 resonant trapping disk gas M [M ] disk edge
  • Slide 7
  • a [AU] t [yr] Monte Carlo Model : - Ida & Lin (2009) Modeling of giant impacts t [yr] 3x10 7 10 7 2x10 7 10 8 1 22 1 0 2x10 7 6x10 7 N-body : - Kokubo, Kominami, Ida (2006) 0.5 1.5 0.5 1.5 0 0
  • Slide 8
  • e a [AU] t [yr] Semi-analytical calculation of Accretion & migration of Solid planets type-I migration (0.1x Tanaka et al.) giant impacts 10 5 0.110 10 6 10 7 10 8 1 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
  • Slide 9
  • gg Min. Mass Solar Nebula x10x0.1 log normal 1100.1 Population Synthesis ~30% Solar-type stars various mass disks (1000 systems) rigid wall edge
  • Slide 10
  • Disk inner cavity ? corotation radius channel flow strong magnetic coupling Cavity weak magnetic coupling No Cavity spin period [day] number of stars 101550 Herbst & Mundt 2005 Is this picture still valid?
  • Slide 11
  • N-body simulation (3D) Ogihara & Ida (2009, ApJ 699, 824) slower mig adiabatic get stacked at the edge Why? detailed analysis
  • Slide 12
  • 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
  • Slide 13
  • 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 !
  • Slide 14
  • Condition for stacking t e /t a = 0.003 r edge /r edge = 0.01 t e /t a = 0.003 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
  • Slide 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
  • Slide 16
  • a [AU] t [yr] Monte Carlo Model : - Ida & Lin (2009) Modeling of giant impacts t [yr] 3x10 7 10 7 2x10 7 10 8 1 22 1 0 2x10 7 6x10 7 N-body : - Kokubo, Kominami, Ida (2006) 0.5 1.5 0.5 1.5 0 0
  • Slide 17
  • 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]
  • Slide 18
  • 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
  • Slide 19
  • 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 10 5 0.110 10 6 10 7 10 8 1 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
  • Slide 20
  • a [AU] 0.1101 Formation of dust-debris disks 110 10 -2 1 10 -4 / 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
  • Slide 21
  • e a [AU] t [yr] No-cavity case type-I migration giant impacts 10 5 0.110 10 6 10 7 10 8 1 disk gas M [M ] no disk edge 2xMMSN case type-I mig: Tanaka et al.s speed x0.1
  • Slide 22
  • a [AU] t [yr] Effect of entropy gradient Paardekooper et al. 2009 10 5 0.1 10 10 6 10 7 10 8 1 disk gas M [M ] disk edge e type-I mig: Tanakas torque is connected to Paardekoopers at ~10e -t/ dep AU Paardekooper Tanaka
  • Slide 23
  • averaged over 20 runs (mean values, dispersion) a [AU] M [M ] e blue: 3xMMSN right blue: MMSN red: 1/3xMMSN cavity Tanakas torque 0.11100.1110
  • Slide 24
  • 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
  • Slide 25
  • Diversity of short-P terrestrial planets M [M ] a [AU] 10.1 1 a [AU] M [M ] no cavitycavity Solar system Saturn satellite system? Short-P super-Earths Jupiter satellite system? Sasaki, Stewart, Ida (submitted) 10
  • Slide 26
  • gg Min. Mass Solar Nebula x10x0.1 log normal 1100.1 Population Synthesis ~30% Solar-type stars various mass disks (1000 systems) rigid wall edge
  • Slide 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?