Planet Formation with Different Gas Depletion Timescales: Comparing with Observations Huigen Liu, Ji-lin Zhou, Su Wang Dept. of Astronomy Nanjing University Nanjing , China

Previous works: Core accretion scenario, Monte Carlo Method: Peering works: Ida & Lin 2004a,2004b ， 2005 ， 2008 Albert et al. 2005a ， 2005b Recent work: Mordasini et al Only a-M diagram. Lack of gravitation between planets. No information of eccentricity Adding N-body interaction, focus on the influence of

Outline:  1.Model  disk model  Core accretion scenario  initial conditions  2.Corelations with gas depletion timescale  Eccentricity of planets  hot or not hot  Mass of planets  3.Comparing with observations  Statistics of a, e, M  deserts and peaks  4.Conclusion and discussion

Model:  Modified MMNM: 2D, -disk Choose an index -1 (K.R.Bell et al. 1997).  MRI effect: (Gammie 1996) Accumulation of small planets outside  The snow line: (Kennedy & Kenyon 2008) Gravitational instability:

Gas accretion scenario: similar with Ida & Lin 2004 Critical mass (onset of gas accretion): Gas accretion rate: (considering the replenishment of materials) Asymptotic Mass:

Migrations: Type I: (Cresswell & Nelson 2006) Scaling factor: C 1 =0.3 Outward if Type II :( Albert et al. 2005) a braking phase, inward only Critical mass for gap-opening: (Armitage & Rice 2005) Tidal damp of gas disk : Low mass: Cresswell & Nelson 2006 Others: Lee & Peale 2002

Initial conditions: 40 embryos >0.1M Earth Location: 0.5~13AU (Zhou et al. 2007) Uniform: Haischi et al. 2001: Other parameters: gas disk: AU: remove planets: a 100AU 20 runs for each 220 runs totally Stop time: 10Myr

Corelations with Correlation between and

Eccentricity of planets:  Damped before gas disk depletion Smaller  gas depleted fast  larger e  Excited via N-body interaction scattering, resonance. Hill instability:, Due to different type I migration rates: Hill instability: (Sensitive to C 1 ) Corresponding with the minimum e. Correlations: and : possibility of collisions and : on average

Correlation between and Hot or not hot? Hot: period=1~20 day Hot Earth: Come out: Proportion: Ascending (Type I migration) Decreasing (scattered) Hot Jupiter: Come out: Proportion: Ascending (sufficient type II migration)

Correlation between and Growth timescale: For small : gas depleted before Insufficient gas accretion is evaluated by gas accretion rate

Comparing with observations: M-e diagram: Assuming V r < 3m/s: undetectable RV limited Maximum e: Observations: ~0.9 (single) ~0.67(multiple) Simulations: ~0.88 Moderate mass: Larger M  larger dispersion of e Larger dispersion for small planets: scattering

a-e diagram: For outer planets, Larger a  larger M  larger dispersion of e Few a~10AU and e>0.4: a desert? Scattering: Large e when a>10AU Materials of Neptune and Uranus

a-M diagram RV limit ： <3m/s 21.7%, <1m/s 15.5% Smaller mass in simulations: No distribution of f g (0.25~5) Comparing with Mordasini et al. 2009

Peaks: 1: inner boundary 2: MRI effectMRI effect 3: Type II migrationType II migration 4: insufficient gas accretioninsufficient gas accretion collision growth 5: Asymptotic Mass Deserts: i, ii: peak 1, 2 iii: onset of gas accretion iv: runaway gas accretion i ii i iii iv iiiiv iii Peaks and deserts

Cumulative distribution function (CDF): Observations: e=0 (unkown) More massive Scaling factor f g Few planets with a>6AU

Conclusions:  Reproduce the distribution of eccentricity  The influence of (a, e, M)  Proportion of Hot-Earth and Hot-Jupiter  Deserts and peaks of a, M  Indicate the of our solar systems for different Type I migration rates consistent with the result from geochemistry

Discussion:  Excluded effects: Gravitation of gas disk. tidal damp of host star Dynamical friction of small planetesimals Damp of e, difficulty: time costing ， uncertain model  Comparing with observations: Distribution of  Uncertainty of initial conditions: a, M of embryos.

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 Peaks around 0.2AU due to MRI effect inward migration of with different Halting round ~0.2AU ： small planets (Type I migration) Larger unconspicuous Not found in observations Back

 Peak around 5 AU: Type II migration of giants Braking phase, Less massive planets with larger  inner position The final position of giants: 1~10AU duo to different Back

Gas accretion growth for small Gas depleted too fast, limited by replenishment of materials Collision growth for large Migrate to inner range, limited by small asymptotic mass Example for  Peak at Example for