Anders Johansen (Max-Planck-Institut für Astronomie) From Stars to Planets Gainesville, April 2007

Transcription

1 in in (Max-Planck-Institut für Astronomie) From Stars to Planets Gainesville, April 2007 Collaborators: Hubert Klahr, Thomas Henning, Andrew Youdin, Jeff Oishi, Mordecai-Mark Mac Low

2 in 1. Problems with forming planetesimals through collisions: Macroscopic bodies do not stick (Chokshi, Tielens, & Hollenbach 1993; Benz 2000) Radial drift of rocks and boulders in a few 10 rotation periods imposes severe time-scale constraint (Weidenschilling 1977) 2. Problems with forming planetesimals by gravitational instability: Need to increase solids-to-gas ratio by about factor 10 4 Turbulence prevents sedimentation of solids (Goldreich & Ward 1973, Weidenschilling 1980, Weidenschilling & Cuzzi 1993)

3 in 1. Problems with forming planetesimals through collisions: Macroscopic bodies do not stick (Chokshi, Tielens, & Hollenbach 1993; Benz 2000) Radial drift of rocks and boulders in a few 10 rotation periods imposes severe time-scale constraint (Weidenschilling 1977) 2. Problems with forming planetesimals by gravitational instability: Need to increase solids-to-gas ratio by about factor 10 4 Turbulence prevents sedimentation of solids (Goldreich & Ward 1973, Weidenschilling 1980, Weidenschilling & Cuzzi 1993) is a major unsolved problem of modern astrophysics.

4 in 1. Problems with forming planetesimals through collisions: Macroscopic bodies do not stick (Chokshi, Tielens, & Hollenbach 1993; Benz 2000) Radial drift of rocks and boulders in a few 10 rotation periods imposes severe time-scale constraint (Weidenschilling 1977) 2. Problems with forming planetesimals by gravitational instability: Need to increase solids-to-gas ratio by about factor 10 4 Turbulence prevents sedimentation of solids (Goldreich & Ward 1973, Weidenschilling 1980, Weidenschilling & Cuzzi 1993) is a major unsolved problem of modern astrophysics. We propose that planetesimals form as regions of transient overdensity of solids collapse under their own gravity.

5 Magnetorotational turbulence in Robust and reliable source of turbulence in protoplanetary discs with a sufficient degree of ionization. Simulation box Disc Shearing box, no vertical gravity on the gas. Code: The Pencil Code [MHD code, finite differences, 6th order in space, 3rd order in time, Brandenburg (2003)]

6 Concentration in transient gas high pressures in y/(c s Ω 0 1 ) Σ/Σ x/(c s Ω 0 1 ) Σ d /(ε 0 Σ 0 ) x/(c s Ω 0 1 ) y/(c s Ω 0 1 ) Strong correlation between high gas density and high particle density Solid particles are caught in transient gas high pressures of magnetorotational turbulence Gravo of planetesimals (, Klahr, & Henning 2006)

7 Concentration in transient gas high pressures in 100 <Σ> y /Σ <Σ d > y /(ε 0 Σ 0 ) t/(2πω 0 1 ) t/(2πω 0 1 ) x/(c s Ω 0 1 ) x/(c s Ω 0 1 ) Strong correlation between high gas density and high particle density Solid particles are caught in transient gas high pressures of magnetorotational turbulence Gravo of planetesimals (, Klahr, & Henning 2006)

8 Pressure gradient trapping in Outer edge: Gas sub-keplerian. Particles forced by gas drag to move inwards. Inner edge: Gas super-keplerian. Particles forced by gas drag to move outwards. (Klahr & Lin 2001, Haghighipour & Boss 2003; see also poster by Nader Haghighipour and talk by Ken Rice)

9 Streaming instability (Youdin & Goodman 2005) in Bulk density of cm-sized pebbles in mid-plane of non-magnetic disc (, Henning, & Klahr 2006): The traffic jam view of the streaming instability: Regions with slightly more solids have less radial drift Lower density material piles up from upstream, increasing the local solids-to-gas ratio (see also Youdin & 2007, & Youdin 2007)

10 High pressure trapping vs. streaming in Without back reaction 10 0 b) ρ p (z)/ρ gas ρ p (z)/ρ gas With back reaction max(ρ p /ρ gas ) c) t/t orb x/h Σ p (x,t)/σ g t/t orb d) z/h a) x z/h y z x/h Σ p (x,t)/σ g t/t orb t/t orb max(ρ p /ρ gas ) Ω K τ f =0.2 Ω K τ f =0.5 Ω K τ f =1.0

11 in New term in equation of motion of the particles: dv i dt =... Φ self The gravitational potential of the particles Φ self is found by solving the Poisson equation 2 Φ self = 4πGρ par We have developed a fully parallel shearing sheet Poisson equation solver. Technical details: Solids are treated as particles Gravity potential is solved on the mesh using FFT method Triangular Shaped Cloud assignment/interpolation scheme (Hockney & Eastwood 1981) Much faster than direct summation, but resolution limited by mesh Collaboration with Jeff Oishi and Mordecai Mac Low at the American Museum of Natural History in New York.

12 The kitchen sink simulation in Combine known effects (but never before studied together): Magnetorotational turbulence (256 3 grid points) Sedimentation of boulders (8,000,000 superparticles) Concentrations in transient gas high pressures Streaming instability () with some new physics: of boulders Several particle sizes Radii from 15 cm to 60 cm Differential radial drift of different particle sizes potentially disrupts gravitational collapse (Weidenschilling 1995) Collisional cooling Collisions between boulders dynamically important for solids-to-gas ratio Collisions are highly inelastic local rms speed of particles damped on collisional time-scale

13 Clump condensation in t=0.0 T orb t=1.0 T orb t=2.0 T orb t=3.0 T orb log 10(Σ p/<σ p>) Ω Kτ f = 0.25 Ω Kτ f = Σ p (i) /<Σp (i) > Σ p /<Σ p > 20.0 t=4.0 T orb Ω Kτ f = 0.75 Ω Kτ f = y/h x/h t=7.0 T orb t=6.5 T orb t=6.0 T orb t=5.0 T orb

14 Clump condensation in t=0.0 T orb t=1.0 T orb t=2.0 T orb t=3.0 T orb log 10(Σ p/<σ p>) 2 MMSN Ω Kτ f = 0.25 Ω Kτ f = Σ p (i) /<Σp (i) > Σ p /<Σ p > 20.0 t=4.0 T orb M clump M Ceres Ω Kτ f = 0.75 Ω Kτ f = y/h x/h t=7.0 T orb t=6.5 T orb t=6.0 T orb t=5.0 T orb

15 in Turbulent concentrations and streaming instability interact constructively and produce overdensities of several 100 in the mid-plane layer Gravitationally bound clumps condense out even in discs comparable to minimum mass solar nebula. Differential radial drift of different particle sizes does not disrupt the collapse (Weidenschilling 1995). Clumps have masses similar to dwarf planets and continue to accrete. max(ρ p /ρ g ), Oishi, Mac Low, Klahr, Henning, & Youdin (submitted) Ω K τ f = M Hill/M Ceres > t Sedimentation Self gravity t/t orb Growth from boulders to planetesimals does not rely on sticking efficiency. Collapse happens much faster than the radial drift time-scale Image: NASA, ESA, J. Parker (SRI)