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Planetesimal Accretion in alpha Centauri

• Philippe Thébault (Stockholm/Paris
  Observatories)
• Francesco Marzari (Padua)
• Hans Scholl (Nice)

(Thébault, Marzari Scholl, Icarus,
2006) Thébault, Marzari Scholl, MNRAS, 2008
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the a Centauri system
a Cen B K1V MB 0.93 M?
a 23.4 AU e 0.52
a Cen A G2V MA 1.1 M?
No gt 2.5MJup planet around any of the stars (Endl
et al.2001)
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long term orbital stability
Holman Wiegert (1997)
the alt2.5AU region is safe in the coplanar case
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embryos-to-planets phase
possible in the alt2.5AU region
Quintana et al.(2002) (Barbieri et al.2002,
Guedes et al.,2008)
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planetesimals-to-embryos phase
MarzariScholl (2000)
possible in the alt2 AU region
BUT assuming single-size planetesimals !
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Planetesimal accretion dynamically quiet stage
Runaway growth
gravitational focusing factor (vesc(R)/?v)2 If
?v vesc(r) then things get out of handgt
Runaway growth
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CRUCIAL PARAMETER
ENCOUNTER VELOCITY DISTRIBUTION
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our numerical approach

• ltdVgt evolution among planetesimals of different
  sizes, under the influence of
• companion stars gravitational perturbations
• gaseous friction
• Derive ltdVgt  maps  for all impactor/target
  pairs (R1,R2)
• Use collision outcome prescriptions to Interpret
  ltdVgt(R1,R2) in terms of
• unperturbed accretion
• perturbed accretion
• erosion

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gas drag

• Modelling

• Gas density profile axisymmetric disc (??!!)

• Explored parameters

-r0 -a 
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Set-up
nominal set-up (parameters with ? are explored in
the runs)
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(e,a) evolution gas free case
secular oscillations with phased orbits
no ltdVgt increase untill orbit crossing occurs
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(e,a) evolution with gas
1kmltRlt10km
tfinal104yrs
differential orbital phasing according to size
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ltdV(R1,R2)gt distribution
high ltdVgt as soon as R1?R2
at 1AU from the primary and at t104yrs
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Critical fragmentation Energy (Q) conflicting
estimates
BenzAsphaug, 1999
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Accretion/Erosion behaviour
Vero2ltdV erosion
Vero1ltdVltVero2 unsure
VescltdVltVero1 perturbed accretion
VescltdVltVero1 normal accretion
at 1AU from the primary and at t104yrs
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Initial planetesimal size-distribution

• what is a  population of km-sized
  planetesimals ?
• depends on planetesimal formation process
• progressive sticking?
• gravitational instabilities?
• Our nominal distribution Maxwellian with ltRgt5km
• explore other distributions (Gaussian,
  power-laws, etc)
• explore different size ranges (0.1-1km
  5-50km)

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nominal case
the agt0.5AU region is hostile to planetesimal
accretion
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Alternative size distributions
accretion-friendly only for extremely peaked
distributions
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Alternative gas disc profiles
accretion friendly only for gas free cases (for
alt1.3AU)
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small planetesimals population
at 1AU from the primary and at t104yrs
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big planetesimals population
at 1AU from the primary and at t104yrs
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a Centauri B
erosion
perturbed accretion
unsure
normal accretion
nominal case
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simplifications

• Static axisymmetric gas disc

• Initial eplanetesimals0

• Time scale?

• i 0

can only make things worse
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a first go at coupled hydro/N-body simulations
Crucial role of the numerical wave damping
procedure
but ltdVgt always higher than in the axisymmetric
gas disc case!
(Paardekooper, Thebault, Mellema, 2008)
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initial conditions/time scale
lte0gt eforced 100 orbital dephasing
lte0gt 0
quick relaxation (few 103yrs) of the initial
conditions
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possible solutions to our problems(?)

• large (gt25km) initial planetesimals?

• outward migration of planets?

• Different initial binary configuration?

• Re-phasing after/during gas disc dissipation?

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large initial planetesimals?
at 1AU, mutual collisions result preferentially
in accretion for planetesimals gt25km...but

• how realistic is a large  initial 
  planetesimals population?
• -gtmaybe possible if quick formation by
  instabilities
• but how do grav.inst. proceed in the dynamically
  perturbed environment of a binary?
• -gtmore difficult if progressive sticking
• always have to pass through a km-sized phase

• in any case, it cannot be  normal  (runaway)
  accretion
• -gt   type II  runaway? (Kortenkamp, 2001)

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planet migration?

• gas disc induced migration (I,II or III)
• mostly inward (?)migration, makes things even
  worse
• later, planetesimal-scattering induced migration
  (gas-free disc)
•  Nice model  scenario
• BUT, so far, tested for giant planets beyond 5AU
• Realistic for terrestrial bodies within 1AU?

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different initial binary configuration?

• most stars born in clusters
• early encounters and binary compaction/exchanges
  are possible

Initial and final (e,a) for binaries in a typical
cluster (Malmberg et al., 2007)
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accretion after/during gas dispersion?

• gas is removed after 107yrs
• -But, differential ltdVgt acquired with gas cannot
  be easily erased
• -In addition pure gravitational effect alone
  trigger high ltdVgt within a few 105yrs.
• rephasing during gas dispersal (Xie Zhou,
  2008)
• - low ltdVgt after ?tdispers. (105yrs?)
• - But, not low enough for lt5km planetesimals
• - But, long accretion-hostile period
  (tlt?tdisper.)
• gt fragmentation of planetesimals into
  ever smaller debris
• gt fast removal by gas-drag induced
  inward drift?

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test run with sudden gas removal
1kmltRlt10km

• gas suddenly disappears at t104yrs

• tfinal 105yrs

ltdVgt stay at a high level
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test run with progressive gas dispersal
1kmltRlt10km

• dispersion starts at t104yrs

• tdisp. 105yrs

• tfinal 2x105yrs

progressive re-phasing BUT radial drift of small
bodies
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Conclusions

• agt0.5AU (0.75AU) region hostile to km-sized
  planetesimals accretion

• robust with respect to size-distribution and gas
  disc profile

• planetesimals-gtembryo phase more sensitive to
  binarity than embryo-gtplanets

in-situ planet formation in the habitable zone is
difficult with the present binary configuration