Formation of planetesimals in collapsing particle clouds Karl - - PowerPoint PPT Presentation

Formation of planetesimals in collapsing particle clouds

Karl Wahlberg Jansson Supervisor: Anders Johansen Department of Astronomy and Theoretical Physics Lund University

Stages of planet formation

Credit: Daniel Carrera

Stages of planet formation

• Formation of planetesimals, the

building blocks of planets

• E.g. Pluto and Kuiper belt objects

Credit: Daniel Carrera

New Horizons: A mission to the outer Solar System

• NASA fly-by mission

to Pluto

• Launched in January

2006

• Arrives in 2015
• Will fly by Pluto, its

moons and some

• ther KBOs once and

never be seen again

Problems

• Larger particles (mm/cm) don’t stick very well
• High relative velocity reduce the sticking capacity
• Other outcomes:
• Bouncing
• Fragmentation

Formation of a self-gravitating cloud

• Gravitationally bound clouds of pebbles can form

through the streaming instability

• Unresolved in hydrodynamical simulations

Solution to the problem?

• What happens to a self-gravitating cloud of cm-

sized pebbles in virial equilibrium?

• Inelastic collisions would dissipate away energy
• Negative heat capacity ⇒ system ‘heats’ up
• Collision rates increases ⇒ runaway collapse

Simple scenario

• Bouncing collisions dissipate energy
• Analytically solvable with very short collapse time
• For Pluto mass cloud at Pluto’s distance from the

Sun: tcrit ~ 0.73 yrs

More realistic model

• One Pluto split into cm-sized pebbles results in

~1024 pebbles

• Use a statistical approach: Monte Carlo scheme of

Zsom & Dullemond, 2008, A&A

• Look at a smaller number of representative

particles/swarms of identical particles

Representative particle approach

Collision between swarm i and swarm k (1000 representative particles)

Numerical implementation

• Calculate collision rates of particles from number

density, size and relative velocity of particles

• From total collision rate find time until next

collision

• Outcome of collision from particle properties:
• Coagulation, fragmentation or bouncing
• Energy dissipated
• New particle properties: size, velocity, etc.

Colisional outcomes

1e-05 0.001 0.1 1e-06 0.0001 0.01 1 100 Projectile radius (m) Collision speed, ∆v, (m/s) Large projectile or similar sized particle: f ≥ 0.1 1e-05 0.001 0.1 1e-06 0.0001 0.01 1 100 Projectile radius (m) Collision speed, ∆v, (m/s) Large projectile or similar sized particle: f ≥ 0.1 vstick C B F vstick C B F 1e-06 0.0001 0.01 1 100 1e-05 0.001 0.1 Projectile radius (m) Collision speed, ∆v, (m/s) Large target: f < 0.1 1e-06 0.0001 0.01 1 100 1e-05 0.001 0.1 Projectile radius (m) Collision speed, ∆v, (m/s) Large target: f < 0.1 vstick C B F C vstick C B F C

• Outcome depends on particle size, collision speed

and relative size

(Güttler et al. 2010)

Collapse of pebble cloud

0.2 0.4 0.6 0.8 1 10 20 30 40 50 η (R/R0) Time (yrs) Collapse parameter η as function of time. Simulated η Simulated ηeq Free-fall collapse

Collapse time

1 10 100 1000 10000 0.1 1 10 100 1000 10000 100000 Collapse time (yrs) Solid radius (km) Collapse time as a function of solid radius of the planetesimal. Simulations Power-law fit 1 Power-law fit 2 Free-fall time of initial particle cloud

Bouncing

• nly

Fragmenting collisions

Conclusions

• Collapse times are

short

• Prediction for KBOs:
• High mass: Sand spheres
• Low mass: Pebble piles

Thank you for your attention!