Planetesimal Accretion inBinary 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)

HD 188753 12.6 0.04 1.14 0.0 (Konaki, 2005)

~40 planets in binaries (jan.2007)

(Desidera & Barbieri, 2007)

(Raghavan et al., 2006)

Extrasolar planets in Binary systems

Gliese 86

HD 41004A

γ Cephei

Companion star

Planet M mini. : 1,7 MJupiter, a=2,13AU e=0,2

M : 0,25 Mprimary, a=18,5 AU.e=0,36

The -Cephei system

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)

Statistical analysis

Are planets-in-binaries different?

short period planets

long period planets

all planets•Zucker & Mazeh, 2002•Eggenberger et al., 2004•Desidera&Barbieri, 2007

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

Long-term stability analysis

22 20.015.059.063.038.046.0 bbbbb

crit eeeea

a

(Holman&Wiegert, 1999)

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

A:

(David et al., 2003)

Long-term stability analysis

Estimating the ejection timescale

Long-term stability analysis

(Fatuzzo et al., 2006)

Role of mutual inclinations

Long-term stability analysis

(Mudryk & Wu., 2006)

Physical mechansim for orbital ejection:

overlapping resonances

μ=1

eb=0

μ=0.5

eb=0

μ=0.5

eb=0.3

μ=0.1

eb=0.7

Stability regions, a few examples…

Statistical distribution of binary systems

(Duquennoy&Mayor, 1991)

a0 ~30 AU ~50% binaries wide enough for stable Earths on S-type orbits

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

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:

2-Grain condensation

3-formation of planetesimals

4-Planetesimal accretion

5-Embryo accretion (Quintana 2004, Lissauer et al.2004,

Quintana&Lissauer, 2006,…)

1-protoplanetary disc formation (Artymowicz&Lubow 1994, Pichardo et

al.2005)

√

√

√√√

x

x

6-Later evolution, resonances, migration: (Wu&Murray 2003,

Takeda&Rasio 2006,…)

√

Cloud collapse & disc formation

Tidal truncation of a circumstellar disc

(1994)

Protoplanetary discs in binaries

Depletion of mm-flux for binaries with 1<a<50AU(Jensen et al., 1996)

model fit with Rdisc<0.4ab

model fit with Rdisc<0.2ab

(Andrews & Williams, 2005)

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

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

A protoplanetary disc

From grains to planetesimals…a miracle occurs

In a « quiet » disc: gravitational instabilities

In a turbulent disc: mutual sticking

In any case: formation of~ 1 km objects

Formation of a dense dust mid-plane: instability occurs when Toomre parameter Q = kcd/(Gd)<1

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

Formation of planetesimals from dust…

gravitational instability

Concurent scenarios: pros and cons

- 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

high-e orbits: high encounter rate but

fragmentation instead of accretion

low-e orbits: low encounter rate but always accretion

Accretion criterion: dV<C.Vesc.

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

2

)2,1(22

21 12

vv

RR RResc

Oligarchic growth

(Kokubo, 2004)

CRUCIAL PARAMETER:

ENCOUNTER VELOCITY DISTRIBUTION

•dV < Vesc => runaway accretion

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

•Verosion < dV => erosion/no-accretion

Some figures to keep in mind

Accretion if V < k. Vescape

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

Vesc(R=5km) ~ 7 m.s-1 e ~ 0.0003 (!!!)

Vesc(R=100km) ~ 150 m.s-1 e ~ 0.006 (!!)

Vesc(R=500km) ~ 750 m.s-1 e ~ 0.03 (!)

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

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 ac as 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 !!!

A typical example

revising the Secular Theory approximation

10% within accurate 2

sin - 12

5

2

2

2

tu

ee

aa

e

• eccentricity oscillations (e0=0)

y)discrepenc 70% to (up unaccutare 1

1

23

32

2/3

2/322

2 a

a

eMu

• oscillation frequency

2

232

2

232

2/3

2/322

21

32 1 1

1 23

aa

eM

aa

eMu

analytical derivation of ac

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

taaC

aaaC 1

4

22

2

2

2/11

322

22

222/52

2

21

13224

1

13245

withe

MC

aM

e

eC

Accuracy of the analytical expression

eb=0.1

eb=0.3

eb=0.5

Results

M2=0.5M1 e2=0.5

Time dependancy

yrs

AUa

AUa

Mm

ee

tcr

7.23.4

2

1.1

*

2

2

75.2222

1111

104.3

Reaching a general empirical expression

AU

yrt

AUa

Mm

e

eacr

36.053.1

2

39.0

*

236.0

2

07.122

1111

30.0

Effect of gas drag

No Gas With Gas

Effect of gas drag

relreldgaz

g vvRCF

83 -

•Modelisation

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

390

75.2

0g

.x104.1

1 :81)Hayashi(19 M.M.S.N

AU

cmg

a

•Planetesimal sizes

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

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

N~104 particles

5km planetesimals1km planetesimals

Differential orbital alignement between objects of different sizes

typical gas drag run

dV increase!

Encounter velocity evolution between different

Target-Projectile pairs R1/R2

typical gas drag run

Orbital crossing occurrence in gas free case

Average dV for 0<t<2.104yrs

« Small » planetesimals

Average dV for 0<t<2.104yrs

« Big » planetesimals

Typical highly perturbed configuration:

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

Benz&Asphaug, 1999

Critical Fragmentation EnergyContradicting esimates

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

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

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

limit accretion/erosion

Unperturbed runaway

Type II runaway (?)

M2=0.5 M1

No accretion

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

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

limit accretion/erosionOrbital crossing

M2=0.5 M1

Unperturbed runaway

Type II runaway (?)

M2=0.5 M1

No Accretion

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

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?

<e0> = 0

<e0> = eforced

100% orbital dephasing

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

Ciecielag (2005-?)

Gas streamlines in a binary system: Spiral waves!

Coupled dust-gas model

Effect of mutual collisions (« bouncing balls » model}

forced and proper eccentricities

Detection of debris discs in binaries

Trilling et al. (2007)