1. 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)

2. 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

3. 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)

4. 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

5. 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

6. 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

7. 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

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

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

10. 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

11. Eccentricity Distributions

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

13. 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

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

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

16. 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

17. e vs. a : weak parameter dependences

18. Distant Jupiters (>100AU) by scattering

19. 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

20. Mass – Semimajor axis Distribution

21. 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]

22. 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

23. Formation of close-in super-Earths

24. 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]

25. 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

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

27. 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]

28. 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

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

31. 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

32. Zhou et al. (2007)

33. 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

34. 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

35. 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 (

36. 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)

37. 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

38. 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

39. 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)

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

42. 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?)

43. 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

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

45. 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

46. 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

47. 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