Evolution of dusty vortices

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Evolution of dusty vortices

• P. Barge and S. Inaba
• LAM Marseille - Waseda University

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An hypothesis to help planetary formation

• Protop. disks could
• host long-lived vortices
• ? Plausible hypothesis
• ? Anticyclones capture solid particles very
  efficiently
• (Large amounts in a short time
• 10 MEarth in less than 104 yrs)
• - Coriolis gt Centrifugal
• - Capture is optimum for particles with Tstop gt
  Torb (boulders)

Barge Sommeria, 1995
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Consequences for planet building

• Vortices are good places for planet growth
• Avoid boulders to drift into the Sun
• Confine solid material into the core
• High densities of solid particles
• Low relative velocities
• Nearly keplerian motions (no press. gradients)
• Could make easier planetesimal formation
• Cores of Giant planet could form in much less
• than gas lifetime and with a MMS Nebula.

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An hypothesis based on analogies

• Well known property of 2D turbulence
• Vorticity concentrates into some long-lived
  structures
• Inverse cascade of energy from small scales to
  large scales

• Observed in rotating shear flows
• In nature
• In laboratory experiments
• In computer simulations (Marcus, ..
• Specific instabilities in PPN ?

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Do they form in Keplerian flows ?
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Relics of a primordial disc turbulence

• After the collapse phase
• concentration of random vorticity

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Maintained by disk turbulence
MHD turbulence powered by Rot. Instability
(Balbus Hawley, 1987) ? Turbulent
vorticity organizes into
long-lived structures
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Powered by an instability
Rossby Wave Instability Non axisymmetric
pertubations can be unstable
Baroclinic Instability Vorticity generation in
a Barotropic disk
Surface density after 104 yrs (Klahr
Bodenheimer, 2003)
Li et al (2000, 2001)
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Birth in the  dead zone  !
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At the edge of the dead zone

• 1AU lt r lt 5AU no transport , ?turb 0
• Outside regular transport by MHD turbulence

• Self-consistent formation of a density bump
• Triggering of the RWI
• Formation of long-lived vortices and spiral modes
• ? Accretion is possible
• inside the dead-zone

100yrs
200yrs
300yrs
Varnière Tagger, 2005
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Evolution with a two-phase code

• Eulerian code with annular grid (2D)
• Two phases approach
• One phase for the gas component
• The other for diluted solid particles (no
  pressure)
• The two phases are fully coupled by aerodyamical
  friction forces

• Initial conditions
• Annular bump at 7.5 AU
• as obtained by Varniere
• Tagger (2005).
• Standard density and
• temperature distributions
• (power laws and MMSN)

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Evolution of the gas (no particles)
0
10
50
100
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Evolution of the gas
Gas density contours after 100 rotations
The vortex is clockwise (anticyclonic) and
strectched in the azimutal direction
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Fully coupled evolution

• Centimeter particles
• Solid/gas 0.01 (initially)
• After
• 10, 50 and 90 rotations.
• - The formation of the final
• vortical structure take a
• longer time than for gas only
• The density of particles
• becomes 20 times higher
• than the initial density.

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Density and velocity field

• - Evolution after
• 50 and 100 rotations
• Rotation is clockwise
• (anticyclone)
• Particles concentrate
• The gaseous vortex
• becomes weaker

50
100
- Trapped mass in the vortex center 0.5
MEarth
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Evolution of the maximum density
0 --gt 1000 yrs gas density increases as
the vortex forms and
the particles are captured 1000 --gt 2000 yrs
particles are captured but the vortex weakens,
then particles begin
to disperse
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Vorticity, energy and enstrophy
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Evolution with 3cm particles
gas
solid
After 15 rots.
After 35 rots.
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Evolution with 10cm particles
After 10 rotations
gas
solid
Large particles are more weakly coupled to the
gas the evolution is more rapid
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Conclusions from our 2D approach

• Discs containing a dead zone can form long-lived
  vortices due to the Rossby Wave Instability (RWI)
• Gaseous vortices are stable over hundreds of
  rotations
• Solid particles are trapped very efficiently and
  their density increases by more than an order of
  magnitude in the center
• Big particles are captured and confined more
  rapidly than small ones
• The motion of the gas is affected by the
  particles
• A dusty vortex keeps its shape on a shorter time
  than a gaseous vortex
• The lifetime depends on the size and initial
  density of the particles

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Continuations

• Gravity could help to gather the particles and to
  maintain longer the vortex structure
• Collisional growth may change significantly the
  evolution
• Vortex formation and could be a reccurent
  mechanism
• Need for 3D simulations
• Do rotation and stratification strong enough to
  two-dimensionalize the flow ?
• (Barranco Marcus, 2005, )