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From Planetesimals to Planets Pre-Galactic Black Holes and ALMA

From Planetesimals to Planets Pre-Galactic Black Holes and ALMA . Gravitational collapse cloud core. Disk formation. Planetesimal formation, 1 m → 1 km tough. Agglomeration of planetesimals. Solar system.

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From Planetesimals to Planets Pre-Galactic Black Holes and ALMA

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  1. From Planetesimals to PlanetsPre-Galactic Black Holes and ALMA

  2. Gravitational collapse cloud core Disk formation Planetesimal formation, 1 m → 1 km tough Agglomeration of planetesimals Solar system

  3. Growth of dust in disk; sticking through van der Waals forcesand/or (unstable) gravity

  4. Kernel Kij = <σv>ij = mi+mj Equal mass/log. bin Equal particles/log. bin Many particles problem • Many particles needed to sample distribution! • Very difficult to treat every collision separately

  5. With grouping Kernels and growth Linear kernel, No grouping Kij = mi + mj

  6. Particles m~1 dominate mass of system Particles in tail will start runaway Run-away kernels Large grouping (low resolution)‏ High-m particles require more focus than low-m particles Mass density Low/no grouping (high resolution)‏ mass

  7. Runaway time tR Run-away kernels Kij = mi mj, N=1020 Kij ~ (mass)β, β>1 particles i and j • E.g., product kernel; gravitational focussing: Kij=π(Ri+Rj)2 x[vij+2G(mi+mj)/(Ri+Rj)vij] • Vesc=[2G(mi+mj)/(Ri+Rj)]1/2 • At t=tR=1 the runaway particle separates from the distribution → Kuiper Belt [Wetherill (1990); Inaba et al. (1999); Malyshkin & Goodman (2001); Ormel & Spaans (2008); Ormel, Dullemond & Spaans, 2010]

  8. Run-away to oligargic growth: roughly when MΣ_M~mΣ_m; from planetesimal self-stirring to proto-planet determining random velocities km km

  9. Dynamics in Solar System • Hill radius: RH=a(M/M*)1/3, VH=ΩRH • Hill radius is distance over which 3-body effects become important • In general, one has physical collisions, dynamical friction: 2-body momentum exchange that preserves random energy, and viscous stirring: energy extracted from or added to the Keplerian potential through 3-body effects • Dispersion-dominated: ~VH< W < Vesc (common) • Shear-dominated: W < ~VH

  10. More Dynamics • Dynamical friction: Σ_M < Σ_m, planetesimal swarm dominates by mass and the orbit of the proto-planet is circularized by kinematically heating up the planetesimals (no physical collisions, only gravitational interactions, random energy preserved) • Viscous stirring: exchange of momentum can also be achieved by extracting from /adding to the Keplerian potential (random energy not preserved, three-body effect)

  11. Growth/Time (yr) Brief period of run-away growth (dM/dt ~ M^4/3); interplay between vescape and vHillof massive and satellite particles to oligarchic growth (dM/dt~M^2/3)

  12. Gas drag effects, 1 AU

  13. Fragmentation effects, 35 AU

  14. Summary • Gravitational focussing important above 1 km; run-away → oligarchic • Gravitational stirring causes low-mass bodies to fragment, W > Vesc → in the oligarchic phase (re-)accretion of fragments is important • Sweep-up of dynamically cold fragments in the shear-dominated regime (fast growth), but in gas-rich systems particles suffer orbital decay • Gas planets form by accretion on rocky (~10 M_earth) cores • Proto-planets clear out their surroundings (gap formation) • Gravitational collapse of unstable disk still alternative

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