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) HD (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 M Jupiter, a=2,13AU e=0,2 M : 0,25 M primary, 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 a b <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 (Holman&Wiegert, 1999) Q: In which regions of a given (a b, e b, m b ) binary system can a (Earth-like) planet survive for ~10 9 years ? 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 e b =0 μ=0.5 e b =0 μ=0.5 e b =0.3 μ=0.1 e b =0.7 Stability regions, a few examples…

Statistical distribution of binary systems (Duquennoy&Mayor, 1991) a 0 ~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 R disc <0.4a b model fit with R disc <0.2a b (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 =  kc d /(  G  d )<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 Δv max ~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 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. V esc.

Planetesimal accretion Runaway growth :astrophysical Darwinism gravitational focusing factor: (v esc(R) /  v) 2 If  v~ v esc(r) then things get out of hand…=> Runaway growth

Oligarchic growth (Kokubo, 2004)

CRUCIAL PARAMETER: ENCOUNTER VELOCITY DISTRIBUTION dV runaway accretion V esc accretion (non-runaway) V erosion erosion/no-accretion

Some figures to keep in mind Accretion if  V < k. V escape IF isotropic distribution :  V ~ C.(e 2 + i 2 ) 1/2 V keplerian V esc (R=5km) ~ 7 m.s -1 e ~ (!!!) V esc (R=100km) ~ 150 m.s -1 e ~ (!!) V esc (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??

M 2 =0.5M 1 e 2 =0.3 a 2 =20AU Orbital phasing =>  V  C.(e 2 + i 2 ) 1/2 V Kep

Our numerical approach  Gravitational problem: analytical derivation orbital crossing a c as a function of M 2,e 2,a 2, t cross  Gas drag influence: numerical runs simplified gas friction modelisation differential orbital phasing effects dV (R1,R2) as a function of a 2,e 2 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 eccentricity oscillations (e 0 =0) oscillation frequency

analytical derivation of a c Orbital crossing occurs when phasing gradient becomes too strong within one wave

Accuracy of the analytical expression e b= 0.1 e b= 0.3 e b= 0.5

Results M 2 =0.5M 1 e 2 =0.5

Time dependancy

Reaching a general empirical expression

Effect of gas drag No Gas With Gas

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~10 4 particles

5km planetesimals 1km planetesimals Differential orbital alignement between objects of different sizes typical gas drag run dV increase!

Encounter velocity evolution between different Target-Projectile pairs R 1 /R 2 typical gas drag run Orbital crossing occurrence in gas free case

Average dV for 0<t< yrs « Small » planetesimals Average dV for 0<t< yrs « Big » planetesimals Typical highly perturbed configuration: M b =0.5 / a b =10AU / e b =0.3

Benz&Asphaug, 1999 Critical Fragmentation Energy Contradicting esimates

Typical moderately perturbed configuration: M b =0.5 / a b =20AU / e b =0.4 Average dV for 0<t< yrs « Small » planetesimals Average dV for 0<t< yrs « Big » planetesimals

Average dV (R1,R2) for 0<t< yrs « Small » Planetesimals: R 1 =2.5 km & R 2 =5 km limit accretion/erosion Unperturbed runaway Type II runaway (?) M 2 =0.5 M 1 No accretion

Average dV (R1,R2) for 0<t< yrs « Big » Planetesimals: R 1 =15 km & R 2 =50 km limit accretion/erosion Orbital crossing M 2 =0.5 M 1 Unperturbed runaway Type II runaway (?) M 2 =0.5 M 1 No Accretion

so what? Gas drag increases dV for R 1 ≠R 2 pairs => Friction works against accretion in « real » systems For <10 km planetesimals: accretion inhibition for large fraction of the (a 2,e 2 ) 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   t pl.form < t runaway &  t pl.form < t secular 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?

= 0 = e forced 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)