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Planetesimal Accretion in Binary SystemsPowerPoint Presentation

Planetesimal Accretion in Binary Systems

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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)

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

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)

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

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

A:

(Holman&Wiegert, 1999)

Physical mechansim for orbital ejection:

overlapping resonances

(Mudryk & Wu., 2006)

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

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,…)

√

(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

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/(Gd)<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

Runaway growth:astrophysical Darwinism

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

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

(Kokubo, 2004)

ENCOUNTER VELOCITY DISTRIBUTION

- dV < Vesc => runaway accretion
- Vesc< dV < Verosion => accretion (non-runaway)
- Verosion < dV => erosion/no-accretion

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

M2=0.5M1 e2=0.3 a2=20AU

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

- 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 !!!

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

analytical derivation of ac

Time dependancy strong within one wave

Reaching a general empirical expression strong within one wave

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

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

Gas streamlines in a binary system: Spiral waves! time?

Ciecielag (2005-?)

Coupled time?dust-gas model

Detection of debris discs in binaries time?

Trilling et al. (2007)

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