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IAU Symposium 276 The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution Torino, Oct 11, 2010 What can core accretion model explain? What can not? population synthesis model M-a distributions: neglecting planet-planet interactions – Ida & Lin(2004-08), Mordasini et al.(2009) Planet-planet scattering & collisions * e-distribution of jupiters * distant jupiters * close-in super-Earths – Ida & Lin (2010, ApJ ; 2011) Theoretical Predictions of M, a & e - Distributions of Jupiters/Super-Earths Shigeru Ida (Tokyo Institute of Technology) collaborators: Doug Lin (UCSC), E. Kokubo (NAOJ) M. Nagasawa, T. Sasaki, M. Ogihara (Tokyo Tech)

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gas giants Core accretion model - sequential processes of different physics planetesimals ©Newton Press cores protoplanetary disk: H/He gas (99wt%) + dust grains (1wt%) core accretion gas envelope contraction runaway gas accretion >100M > 5 - 10M coagulation of planetesimals terrestrial planets gas accretion onto cores type I migration type II migrationorbital instability

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Detailed studies on individual processes: important. But, NOT directly compared with obs. of exoplanets Population synthesis model: combine these processes to predict distributions of exoplanets explain existing data, predict future observations, & constrain a theoretical model for each process -- link theory and observation derive semi-analytical formulas for individual processes integrate equations of planetary growth/migration Population synthesis model Ida & Lin (2004a,b,2005,2008a,b,2010), Mordasini et al. (2009a,b)

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The modeling of each process: must be based on detailed simulations (N-body, fluid dynamical,...) Otherwise, the results are meaningless But, the modeling must be simple enough, while it must properly reflect essential physical ingredients... Population synthesis model

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Example of the integrations Ida & Lin (in prep) evolution type-I migration planetesimal accretion gas accretion onto a core type-II migration rocky planets gas giant icy planets disk gas disk edge type-I migration final state 0.6 sec on Mac air

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one-planet-in-a-disk Simple one-planet-in-a-disk model Ida & Lin (2004a,b,2005,2008a,b), Mordasini et al. (2009a,b) neglect Dynamical Interactions (scattering, collisions) between planets w/o. dynamical interactions: e can NOT be evaluated & many problems evaluated must collide must scatter disk gas disk edge

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Multiple-planets-in-a-disk Multiple-planets-in-a-disk model Ida & Lin (2010, 2011) Dynamical Interaction modeling: quantitatively reproduce N-body simulations DI between rocky/icy planets Resonant Trapping -- Sasaki, Stewart & Ida (2010, ApJ) RT & Giant Impacts -- Ida & Lin (2010, ApJ) DI between all planets [+ close encounters & ejection of giants (secular perturbations: not yet)] -- Ida & Lin (in prep) preliminary results: shown today - high e of jupiters & distant jupiters - multiple close-in super-Earths

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Effects of Dynamical InteractionMultiple-planets-in-a-diskOne-planets-in-a-disk giant impacts resonant trapping ejection disk gas

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evolutionfinal state rocky planets gas giant icy planets disk gas eccentricity distribution Dynamical Interaction eccentricity distribution Ida & Lin (in prep)

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Population synthesis model Ida & Lin (in prep) 3000 systems M * =0.8-1.25 M * =0.8-1.25 M type-I: 0.1x Tanaka 45 min on Mac air

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Eccentricity Distributions

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- good agreement with observation Eccentricity excitation of jupiters by scattering - good agreement with observation Theory Observation

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Theory(Ida & Lin) Theory Observation massive disks: multiple massive giants close scattering larger e for larger M Theory v r >1m/s & a <5AU Eccentricity vs. mass

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disk mass dependence >1000M 100-1000M 10-100M Disk mass [MMSN]

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e vs. M : weak parameter dependences faster migration more limited gas accretion

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Eccentricity vs. semimajor axis [jupiters] Theory Theory(Ida & Lin) Observation multiple giants < 10AU small e for a >10AU e max ~ V esc / V Kep ~2(a/1AU) 1/2 smaller e for smaller a At a < 0.05AU, e is tidally damped. -- tide is not included in the theoretical model e -- peaked at ~1AU

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e vs. a : weak parameter dependences

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Distant Jupiters (>100AU) by scattering

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Theory disk instability can make core accretion? * in situ: impossible * outward mig. (Masset) ? * scattering: possible - systems - small e core scattering + gas accretion Ed Thommes N-body (*) ejected jupiters free floating planets - 6% of systems Distant jupiters with small e

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Mass – Semimajor axis Distribution

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Observation Theory (Ida & Lin) Broad distribution of a is explained by core accretion + type II mig. Remaining problems: 1)over-density at > 1AU migration trap? (dead zone, Paardekoopers torque...) 2) (hot jupiters) ~ 15% [theory] vs 1% [obs] disruption of HJs ? (no inner cavity, tide, evaporation,...) -- (other jupiters) ~25% [OK?] 3) planet desert at 10-100M ? -- observationally unclear faster type I migration? how to stop planetesimal/gas accretion? Mass vs. semimajor axis [jupiters]

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M vs. a : parameter dependences close-in Super-Earths Jupiters 22%22% 25%26%33%16% 8%46% 16%39% 11%35% more limited gas accretion

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Formation of close-in super-Earths

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Observation Theory (Ida & Lin) 1) a peak at ~0.1AU simulations: disk inner edge at 0.03-0.04AU (hot jupiters ~ 0.03-0.04AU) 2) multiple, non-resonant 3) (close-in super-earths) ~ 26% These theoretical predictions are almost independent of type-I migration speed Mass vs. semimajor axis [super-earths]

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e a [AU] t [yr] Formation of non-resonant, multiple, close-in super-Earths Ida & Lin (2010, ApJ) type-I migration (Tanaka x 0.1) 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) high abundance

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M vs. a : parameter dependences close-in Super-Earths Jupiters 22%22% 25%26%33%16% 8%46% 16%39% 11%35% c

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Disks forming super-Earths and Jupiters >100M rocky, 1-20M icy, 1-20M massive disks: form massive multiple jupiters destroy SEs medium-mass disks: retain Super-Earths - SE + J systems: only 9% Disk mass [MMSN]

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Summary What observational data can core accretion model explain? What can not? using population synthesis model Distributions of Jupiters e-M, e-a -- well explained - refinement of scattering model is still needed. [talks by E. Ford, S. Chatterjee] M-a -- some problems remain - calculations with Paardekoopers type-I mig are needed [talk by W. Kley] distant Jupiters with small e -- possible Distributions of super-Earths look consistent but more obs. data are needed

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Modeling of dynamical interactions among gas giants Nagasawa & Ida 2010 a - high eccentricities of jupiters - distant (>30AU) jupiters [direct imaging] - explained by scattering? e

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3/18 If more than 3 giant planets form on circular orbits Orbit crossing starts on t cross One is ejected. The others remain in stable eccentric orbits. Δa [rH]Δa [rH] Marzari & Weidenschilling (2002) t cross t cross [yr] Origin of eccentric planets: jumping jupiter Weidenschilling & Marzari (1996), Lin & Ida(1997),... Solar system: 2 giants stable RV

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Zhou et al. (2007)

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t cross 3/18 Origin of eccentric planets: jumping jupiter Weidenschilling & Marzari (1996), Lin & Ida(1997),... a 0 = 5, 7.25, 9.5AU M = M J a Nagasawa et al. (2008) N-body simulations: 100 runs with different initial angular locations The system is chaotic, but shows a well determined distribution modeling (Monte Carlo) e

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N-body: Nagasawa et al. (2008) ~ an hour/run on a PC Modeling + Monte Carlo ~ 0.02sec/1000runs on a PC tidal cicularization M=M J, a 0 = 5.0, 7.25, 9.0 AU ( Comparison between N-body and Modeling -- Scattering of 3 giant planets -- Scattering of 3 giant planets ee a[AU] no tide

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N-body: Nagasawa et al. (2008) ~ an hour/run on a PC Modeling + Monte Carlo ~ 0.02sec/1000runs on a PC tidal cicularization M=M J, a 0 = 5.0, 7.25, 9.0 AU (

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3/18 Semi-analytical modeling Ida & Lin (in prep.) select an ejected planet (mass-weighted random chaos) select an inwardly scattered planet (random) excited e of scattered planets: ev K ~ (2GM dom /R dom ) 1/2 ( mean value – deterministic dispersion – random(Rayleigh) ) a of outer planet q = a(1- e) with appropriate q ( initial as; calibrated by N-body) (deterministic + random) a of inner planet by conservation of E (that of L : useless) (deterministic)

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Modeling of dynamical interactions among rocky planetary embryos eccentricity e semimajor axis a [AU] 0.5 1.0 1.5 2.0 oligarchic growth Kokubo & Ida (2002) Post-oligarchic giant impacts Kokubo et al. (2006) M ~ 0.1-0.2M isolation mass (deteministic) M ~1M MMSN case no ejection collisions after many scatterings

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a [AU] t [yr] Monte Carlo : Ida & Lin (2010, ApJ) deterministic celestial dynamics + (reasonable) chaotic features < 0.1sec/run on a PC Modeling of giant impacts - stochastic process - t [yr] 3x10 7 10 7 2x10 7 10 8 1 22 1 0 2x10 7 6x10 7 N-body : Kokubo et al. (2006) ~ a few days/run on a PC 0.5 1.5 0.5 1.5 0 0

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eccentricity M [M ] MMSN 10xMMSN 0.1xMMSN final largest bodies20 runs each Monte Carlo N-body Kokubo et al. (2006) semimajor axis [AU] Modeling of giant impacts of rocky planets - stochastic process - Ida & Lin (2010, ApJ)

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Modeling reveal intrinsic physics meta-stable t cross ~ t system stable t cros s >>t system e ~ ev K ~ 0.3 e < 0.1

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Implication: formation of multiple, non-resonant, close-in super-Earths Ida & Lin (2010, ApJ) Recent radial velocity surveys Large fraction (10-40%; why so common?) of solar-type stars have super-Earths (why didnt accrete gas?) at ~0.1AU (why > a hot jup ?) without signs of gas giants in the same systems Most of the super-Earth systems are non-resonant, multiple systems (why?)

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e a [AU] t [yr] Formation of non-resonant, multiple, close-in super-Earths Ida & Lin (2010, ApJ) type-I migration (conventional) 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) high abundance

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Ubiquity of short-P rocky planets M [M ] a [AU] 10.1 M [M ] 10 slow type I mig moderate type I mig

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Solar system vs. Super-Earth systems corotation radius channel flow strong magnetic coupling Inner Cavity weak magnetic coupling No Cavity spin period [day] number of stars 101550 Herbst & Mundt (2005) Observation of spin periods of young stars Spitzer: positive Corot: negative

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Diversity of short-P rocky planets M [M ] a [AU] 10.1 1 a [AU] M [M ] no cavitycavity Solar system Saturnian satellite system? Short-P super-Earths Jovian satellite system? 10 Sasaki, Steawrt & Ida (2010, ApJ) slow type I mig moderate type I mig

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Different a between hot super-Earths and jupiters Super-Eaths systems Ogihara, Duncan & Ida (2101, ApJ) type I migration of resonantly trapped embryos type II migration of gas giants a HSE > a HJ

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