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
other 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 cmsized pebbles in virial equilibrium?
•
•
•
Inelastic collisions would dissipate away energy
Negative heat capacity
Collision rates increases
system ‘heats’ up
runaway collapse
Simple scenario
•
•
Bouncing collisions dissipate energy
•
For Pluto mass cloud at Pluto’s distance from the
Sun: tcrit ~ 0.73 yrs
Analytically solvable with very short collapse time
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
Large projectile or similar sized particle: f ≥ 0.1
Large target: f < 0.1
0.1
B
0.001
B
vstick
0.001
vstick
C
C
F
C
F
1e-05
1e-06
1e-05
0.0001
0.01
Collision speed, ∆v, (m/s)
1
100
1e-06
0.0001
0.01
1
100
Collision speed, ∆v, (m/s)
(Güttler et al. 2010)
•
Outcome depends on particle size, collision speed
and relative size
Projectile radius (m)
Projectile radius (m)
0.1
Collapse of pebble cloud
Collapse parameter η as function of time.
Simulated η
Simulated ηeq
Free-fall collapse
1
η (R/R0)
0.8
0.6
0.4
0.2
0
0
10
20
30
Time (yrs)
40
50
Collapse time
Collapse time as a function of solid radius of the planetesimal.
10000
Simulations
Power-law fit 1
Power-law fit 2
Free-fall time of initial particle cloud
Collapse time (yrs)
1000
Bouncing
only
100
Fragmenting
collisions
10
1
0.1
1
10
100
Solid radius (km)
1000
10000
100000
Conclusions
•
Collapse times are
short
•
Prediction for KBOs:
-
High mass: Sand spheres
Low mass: Pebble piles
Thank you for your attention!