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

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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-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-EarthsWhy 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 2004resonantly trappedstable even after gas depletion Terquem & Papaloizou 2007

  • N-body simulation (3D)Ogihara & Ida (2009, ApJ 699, 824)slower mig adiabaticget stacked at the edgeWhy? detailed analysis

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

  • ea [AU]t [yr]Semi-analytical calculation ofAccretion & migration of solid planetstype-I migration(0.1x Tanaka et al.)giant impacts

    1050.1101061071081resonant trapping

    disk gas

    M [M]disk edge

  • a [AU]a [AU]t [yr]Monte Carlo Model : Ida & Lin (2009)Modeling of giant impactst [yr]3x1071072x107108122102x1076x107N-body : Kokubo, Kominami, Ida (2006)0.51.50.51.500

  • ea [AU]t [yr]Semi-analytical calculation ofAccretion & migration of Solid planetstype-I migration(0.1x Tanaka et al.)giant impacts

    1050.1101061071081resonant trapping

    disk gas

    M [M]disk edgetoo small to startgas accretionnon-res. multiple super-Earths(~0.1AU, missed gas accretion) 2xMMSN case rigid wall edge

  • SgMin. Mass Solar Nebulax10x0.1log normal1100.1Population Synthesis

    ~30%Solar-type stars various mass disks (1000 systems) rigid wall edge

  • Disk inner cavity ?corotation radiuschannel flowstrong magnetic coupling Cavityweak magnetic coupling No Cavityspin period [day]number of stars101550Herbst & Mundt2005Is this picturestill valid?

  • N-body simulation (3D)Ogihara & Ida (2009, ApJ 699, 824)slower mig adiabaticget stacked at the edgeWhy? detailed analysis

  • Why stacking at the edge ? e-dampingtype-I migplanet-planet int.torque on body 1torque on body 2torque on body 1disk edge1M1Mtoy model*) Martin got the same result

  • Planet trap due to e-dampingVgas(~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?

    Tidal e-damping(+ resonant e-excitation)

    outward migration !

  • Condition for stacking te/ta = 0.003 Dredge/redge = 0.01

    te/ta = 0.003 Dredge/redge = 0.05

    te/ta = 0.03 Dredge/redge = 0.01

    Both te/ta & Dredge/redgemust 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

  • Planet formation model (core accretion)Ida & Lin (2004a,b,2005,2008a,b)start from planetesimalscombine following processesplanetesimal 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 impactst [yr]3x1071072x107108122102x1076x107N-body : Kokubo, Kominami, Ida (2006)0.51.50.51.500

  • eccentricityM [M]MMSN10xMMSN0.1xMMSNfinal largest bodies20 runs eachMonte Carlo model of giant impacts[close scattering & accretion of rocky embryos]Monte CarloN-bodyKokubo et al. (2006)semimajor axis [AU]

  • eccentricityM [M]MMSN10xMMSN0.1xMMSNfinal largest bodies20 runs eachMonte Carlo model of giant impacts[scattering & accretion of rocky embryos]Monte CarloN-bodyKokubo et al. (2006)semimajor axis [AU]Monte Carlo : Ida & Lin (2009)- CPU time < 0.1 sec / runN-body : Kokubo, Kominami, Ida (2006) CPU time ~ a few days / run

  • ea [AU]t [yr]Accretion & migration of planetesimals[Gas accretion onto cores is neglected in this particular set of simulation]type-I migrationgiant impacts

    1050.1101061071081resonant trapping

    CPU time: a few sec. on a PCdisk gas

    M [M]disk edge2xMMSN caseNo gas giantrigid wall edgetype-I mig: Tanaka et al.s speed x0.1

  • a [AU]0.1101Formation of dust-debris disks11010-2110-4S/SMMSNDF is strongstochastic collisionsof embryosinner regions: giant impacts commonouter regions: planetesimals remain unless gas giants form debris disks: commonly producedweak [Fe/H]-dependenceanti-correlated with jupiters?108yrs106yrscontinuous collisionsof planetesimalsstirred by embryos

  • ea [AU]t [yr]No-cavity casetype-I migrationgiant impacts

    1050.1101061071081disk gas

    M [M]no disk edge2xMMSN casetype-I mig: Tanaka et al.s speed x0.1

  • a [AU]t [yr]Effect of entropy gradientPaardekooper et al. 20091050.1101061071081disk gas

    M [M]disk edgee type-I mig: Tanakas torque is connected to Paardekoopers at ~10e-t/tdepAU

    Paardekooper

    Tanaka

  • averaged over20 runs(mean values,dispersion)

    a [AU]a [AU]M [M]eblue: 3xMMSNright blue: MMSNred: 1/3xMMSNcavityTanakas torque0.11100.1110

  • Non-resonant, multiple, short-P Earths/super-Earths101a [AU]M [M]M [M]Theoretical predictionsa ~ 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 rateavoid gas accretion (have grown after disk gas depletion via giant impacts) observation

  • Diversity of short-P terrestrial planetsM [M]a [AU]10.110.1a [AU]M [M]M [M]M [M]no cavitycavitySolar systemSaturn satellite system?Short-P super-EarthsJupiter satellite system?Sasaki, Stewart, Ida (submitted)1010

  • SgMin. Mass Solar Nebulax10x0.1log normal1100.1Population Synthesis

    ~30%Solar-type stars various mass disks (1000 systems) rigid wall edge

  • SummaryN-body simulations + Synthetic planet formation model including giant impacts & resonant trapping Non-resonant, multiple, short-P Earths/super-EarthsDiversity 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?

    ***