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Planetesimal Accretion in Binary Systems. Philippe Thébault Stockholm/Paris Observatory(ies). Marzari, Scholl,2000, ApJ Thébault, Marzari, Scholl, 2002, A&A Thébault, Marzari, Scholl,Turrini, Barbieri, 2004, A&A Thébault, Marzari, Scholl, 2006, Icarus

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Planetesimal Accretion in

Binary Systems

Philippe Thébault

Stockholm/Paris Observatory(ies)

  • Marzari, Scholl,2000, ApJ

  • Thébault, Marzari, Scholl, 2002, A&A

  • Thébault, Marzari, Scholl,Turrini, Barbieri, 2004, A&A

  • Thébault, Marzari, Scholl, 2006, Icarus

  • Marzari, Thebault, Kortenkamp, Scholl, 2007 (« planets in binaries » book chapter)

  • Scholl, Thébault, Marzari, 2007, Icarus (to be submitted)

Extrasolar planets in Binary systems

(Udry et al., 2004)

(Konaki, 2005)

HD 188753 12.6 0.04 1.14 0.0

~40 planets in binaries (jan.2007)

(Desidera & Barbieri, 2007)

Extrasolar planets in Binary systems

Gliese 86

HD 41004A

γ Cephei

(Raghavan et al., 2006)

The-Cephei system

Companion star

M : 0,25 Mprimary,a=18,5 AU.



M mini. : 1,7 MJupiter, a=2,13AU


Extrasolar planets in Binary systems

~23% of detected extrasolar planets in multiple systems


~2-3% (3-4 systems) in binaries with ab<30AU

(Raghavan et al., 2006, Desidera&Barbieri, 2007)

Statistical analysis

Are planets-in-binaries different?

Only correlation (?): more massive planets on short-period orbits around close-in (<75AU) binaries

long period planets

short period planets

  • Zucker & Mazeh, 2002

  • Eggenberger et al., 2004

  • Desidera&Barbieri, 2007

all planets

Long-term stability analysis

Q: In which regions of a given (ab, eb, mb) binary system can a (Earth-like) planet survive for ~109years ?


(Holman&Wiegert, 1999)

Long-term stability analysis

Estimating the ejection timescale

(David et al., 2003)

Long-term stability analysis

Role of mutual inclinations

(Fatuzzo et al., 2006)

Long-term stability analysis

Physical mechansim for orbital ejection:

overlapping resonances

(Mudryk & Wu., 2006)

Stability regions, a few examples…









Statistical distribution of binary systems

a0 ~30 AU

~50% binaries wide enough for stable Earths on S-type orbits

~10% close enough for stable Earths on P-type orbits

(Duquennoy&Mayor, 1991)

Stability analysis for γ Cephei

(Dvorak et al. 2003)

The « standard » model of planetary formation

to what extent is it affected by binarity?

  • Step by Step scenario:

1-protoplanetary disc formation (Artymowicz&Lubow 1994, Pichardo et al.2005)

2-Grain condensation


3-formation of planetesimals


4-Planetesimal accretion

5-Embryo accretion (Quintana 2004, Lissauer et al.2004, Quintana&Lissauer, 2006,…)


6-Later evolution, resonances, migration: (Wu&Murray 2003, Takeda&Rasio 2006,…)

(Jensen et al., 1996)

(Andrews & Williams, 2005)

model fit with Rdisc<0.4ab

model fit with Rdisc<0.2ab

Protoplanetary discs in binaries

Depletion of mm-flux for binaries with 1<a<50AU

A protoplanetary disc

Fondamental limit 1 : T ~ 1350°K condensation of silicates

Fondamental limit 2: T ~ 160°K condensation of water-ice

Formation of planetesimals from dust…

  • In a « quiet » disc: gravitational instabilities

Formation of a dense dust mid-plane: instability occurs when Toomre parameter

Q = kcd/(Gd)<1

  • In a turbulent disc:mutual sticking

  • Crucial parameter: Δv, imposed by particle/gas interactions.2 components:

  • - Δv differential vertical/radial drift

  • Δv due to turbulence

  • Small grains (μm-cm) are coupled to turbulent eddies of all sizes: Δv~0.1-1cm/s

  • Big grains (cm-m) decouple from the gas and turbulence, and Δvmax~10-50m/s for 1m bodies

In any case: formation of~ 1 km objects

Concurent scenarios: pros and cons

  • gravitational instability

- Requires extremely low turbulence and/or abundance enhancement of solids

  • Turbulence-induced sticking

- Particles with 1mm<R<10m might be broken up by dV>10-50m/s impacts

fierce debate going on…

Mutual planetesimal accretion: a tricky situation

Accretion criterion: dV<C.Vesc.

high-e orbits: high encounter rate but fragmentation instead of accretion

low-e orbits: low encounter rate but always accretion

Planetesimal accretion

Runaway growth:astrophysical Darwinism

gravitational focusing factor: (vesc(R)/v)2

If v~ vesc(r) then things get out of hand…=> Runaway growth

Oligarchic growth

(Kokubo, 2004)



  • dV < Vesc => runaway accretion

  • Vesc< dV < Verosion => accretion (non-runaway)

  • Verosion < dV => erosion/no-accretion

e ~ 0.006 (!!)

e ~ 0.03 (!)

Vesc(R=100km) ~ 150 m.s-1

Vesc(R=500km) ~ 750 m.s-1

Some figures to keep in mind

Accretion if V < k. Vescape

IF isotropic distribution : V ~ C.(e2 + i2)1/2 Vkeplerian

For a body at 1AU of a solar-type star

e ~ 0.0003 (!!!)

Vesc(R=5km) ~ 7 m.s-1

It doesn’t take much to stop planetesimal accretion

Dynamical effect of a close-in stellar companion

Large e-oscillations

High dV??

M2=0.5M1 e2=0.3 a2=20AU

Orbital phasing => V  C.(e2 + i2)1/2 VKep

Our numerical approach

  • Gravitational problem: analytical derivation

    orbital crossing acas a function of M2,e2,a2,tcross

  • Gas drag influence: numerical runs

    simplified gas friction modelisation

    differential orbital phasing effects

    dV(R1,R2) as a function of a2,e2

    interpret dV(R1,R2) in terms of accretion/erosion

    => Collision Outcome Prescriptions

    (Davis et al., Housen&Holsapple, Benz et al.)

!!! Time Scales & Initial Conditions !!!

  • oscillation frequency

revising the Secular Theory approximation

analytical derivation of ac

Accuracy of the analytical expression strong within one wave




Results strong within one wave



Time dependancy strong within one wave

Effect of gas drag strong within one wave

With Gas

No Gas

Effect of gas drag strong within one wave

  • Modelisation

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

  • Planetesimal sizes

- « small planetesimals » run: 1<R<10km

- « big planetesimals » run: 10<R<50km

N~104 particles

dV increase! strong within one wave

typical gas drag run

5km planetesimals

1km planetesimals

Differential orbital alignement between objects of different sizes

typical gas drag run strong within one wave

Orbital crossing occurrence in gas free case

Encounter velocity evolution between different

Target-Projectile pairs R1/R2

Typical highly perturbed configuration: strong within one wave

Mb=0.5 / ab=10AU / eb=0.3

Average dV for 0<t<2.104yrs

« Small » planetesimals

Average dV for 0<t<2.104yrs

« Big » planetesimals

Critical Fragmentation Energy strong within one wave

Contradicting esimates

Benz&Asphaug, 1999

Typical moderately perturbed configuration: strong within one wave

Mb=0.5 / ab=20AU / eb=0.4

Average dV for 0<t<2.104yrs

« Small » planetesimals

Average dV for 0<t<2.104yrs

« Big » planetesimals

M strong within one wave2=0.5 M1

Unperturbed runaway

No accretion

Type II runaway (?)

limit accretion/erosion

Average dV(R1,R2) for 0<t<2.104yrs

« Small » Planetesimals: R1=2.5 km & R2=5 km

Unperturbed runaway strong within one wave

No Accretion

Type II runaway (?)

M2=0.5 M1

M2=0.5 M1

Orbital crossing

limit accretion/erosion

Average dV(R1,R2) for 0<t<2.104yrs

« Big » Planetesimals: R1=15 km & R2=50 km

so what? strong within one wave

  • Gas drag increases dV for R1≠R2 pairs

  • => Friction works against accretion in « real » systems

  • For <10 km planetesimals: accretion inhibition for large fraction of the (a2,e2) space, type II runaway otherwise (?)

  • For 10<R<50 km planetesimals: type II runaway (?) for most of the cases

is all of this strong within one wavetoo simple?

  • Assume e=0 initially for all planetesimals

  •  bodies begin to « feel » perurbations at the same time

  • tpl.form < trunaway & tpl.form < tsecular

  • how do planetesimals form??

  • Progressive sticking or Gravitational instabiliies?

  • Time scale for Runaway/Oligarchic growth?

  • Phony gas drag modelisation?

  • Migration of the planet? Can only make things worse

  • Different initial configuration for the binary?

What if all planetesimals do not « appear » at the same time?

<e0> = eforced

100% orbital dephasing

<e0> = 0

Coupled time?dust-gas model

Detection of debris discs in binaries time?

Trilling et al. (2007)