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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

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Planetesimal accretion in binary systems

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)


Planetesimal accretion in binary systems

Extrasolar planets in Binary systems

(Udry et al., 2004)

(Konaki, 2005)

HD 188753 12.6 0.04 1.14 0.0


Planetesimal accretion in binary systems

~40 planets in binaries (jan.2007)

(Desidera & Barbieri, 2007)


Planetesimal accretion in binary systems

Extrasolar planets in Binary systems

Gliese 86

HD 41004A

γ Cephei

(Raghavan et al., 2006)


Planetesimal accretion in binary systems

The-Cephei system

Companion star

M : 0,25 Mprimary,a=18,5 AU.

e=0,36

Planet

M mini. : 1,7 MJupiter, a=2,13AU

e=0,2


Planetesimal accretion in binary systems

Extrasolar planets in Binary systems

~23% of detected extrasolar planets in multiple systems

But...

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

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


Planetesimal accretion in binary systems

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


Planetesimal accretion in binary systems

Long-term stability analysis

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

A:

(Holman&Wiegert, 1999)


Planetesimal accretion in binary systems

Long-term stability analysis

Estimating the ejection timescale

(David et al., 2003)


Planetesimal accretion in binary systems

Long-term stability analysis

Role of mutual inclinations

(Fatuzzo et al., 2006)


Planetesimal accretion in binary systems

Long-term stability analysis

Physical mechansim for orbital ejection:

overlapping resonances

(Mudryk & Wu., 2006)


Planetesimal accretion in binary systems

Stability regions, a few examples…

μ=1

eb=0

μ=0.5

eb=0

μ=0.1

eb=0.7

μ=0.5

eb=0.3


Planetesimal accretion in binary systems

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)


Planetesimal accretion in binary systems

Stability analysis for γ Cephei

(Dvorak et al. 2003)


Planetesimal accretion in binary systems

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

x

3-formation of planetesimals

x

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,…)


Planetesimal accretion in binary systems

Cloud collapse & disc formation


Planetesimal accretion in binary systems

Tidal truncation of a circumstellar disc

(1994)


Planetesimal accretion in binary systems

(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


Planetesimal accretion in binary systems

A protoplanetary disc

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

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


Planetesimal accretion in binary systems

From grains to planetesimals…a miracle occurs


Planetesimal accretion in binary systems

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


Planetesimal accretion in binary systems

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…


Planetesimal accretion in binary systems

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 in binary systems

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


Planetesimal accretion in binary systems

Oligarchic growth

(Kokubo, 2004)


Planetesimal accretion in binary systems

CRUCIAL PARAMETER:

ENCOUNTER VELOCITY DISTRIBUTION

  • dV < Vesc => runaway accretion

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

  • Verosion < dV => erosion/no-accretion


Planetesimal accretion in binary systems

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


Planetesimal accretion in binary systems

Dynamical effect of a close-in stellar companion

Large e-oscillations

High dV??


Planetesimal accretion in binary systems

M2=0.5M1 e2=0.3 a2=20AU

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


Planetesimal accretion in binary systems

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 !!!


Planetesimal accretion in binary systems

A typical example


Planetesimal accretion in binary systems

  • eccentricity oscillations (e0=0)

  • oscillation frequency

revising the Secular Theory approximation


Planetesimal accretion in binary systems

  • Orbital crossing occurs when phasing gradient becomes too strong within one wave

analytical derivation of ac


Planetesimal accretion in binary systems

Accuracy of the analytical expression

eb=0.1

eb=0.3

eb=0.5


Planetesimal accretion in binary systems

Results

e2=0.5

M2=0.5M1


Planetesimal accretion in binary systems

Time dependancy


Planetesimal accretion in binary systems

Reaching a general empirical expression


Planetesimal accretion in binary systems

Effect of gas drag

With Gas

No Gas


Planetesimal accretion in binary systems

Effect of gas drag

  • Modelisation

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

  • Planetesimal sizes

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

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

N~104 particles


Planetesimal accretion in binary systems

dV increase!

typical gas drag run

5km planetesimals

1km planetesimals

Differential orbital alignement between objects of different sizes


Planetesimal accretion in binary systems

typical gas drag run

Orbital crossing occurrence in gas free case

Encounter velocity evolution between different

Target-Projectile pairs R1/R2


Planetesimal accretion in binary systems

Typical highly perturbed configuration:

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


Planetesimal accretion in binary systems

Critical Fragmentation Energy

Contradicting esimates

Benz&Asphaug, 1999


Planetesimal accretion in binary systems

Typical moderately perturbed configuration:

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


Planetesimal accretion in binary systems

M2=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


Planetesimal accretion in binary systems

Unperturbed runaway

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


Planetesimal accretion in binary systems

so what?

  • 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


Planetesimal accretion in binary systems

is all of this too 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?


Planetesimal accretion in binary systems

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

<e0> = eforced

100% orbital dephasing

<e0> = 0


Planetesimal accretion in binary systems

Gas streamlines in a binary system: Spiral waves!

Ciecielag (2005-?)


Planetesimal accretion in binary systems

Coupled dust-gas model


Planetesimal accretion in binary systems

Effect of mutual collisions (« bouncing balls » model}


Planetesimal accretion in binary systems

forced and proper eccentricities


Planetesimal accretion in binary systems

Detection of debris discs in binaries

Trilling et al. (2007)


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