Planetesimal Accretion in Binary Systems

1. 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)

2. Extrasolar planets in Binary systems (Udry et al., 2004) (Konaki, 2005) HD 188753 12.6 0.04 1.14 0.0

3. ~40 planets in binaries (jan.2007) (Desidera & Barbieri, 2007)

4. Extrasolar planets in Binary systems Gliese 86 HD 41004A γ Cephei (Raghavan et al., 2006)

5. 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

6. 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)

7. 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

8. 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)

9. Long-term stability analysis Estimating the ejection timescale (David et al., 2003)

10. Long-term stability analysis Role of mutual inclinations (Fatuzzo et al., 2006)

11. Long-term stability analysis Physical mechansim for orbital ejection: overlapping resonances (Mudryk & Wu., 2006)

12. 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

13. 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)

14. Stability analysis for γ Cephei (Dvorak et al. 2003)

15. 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,…) √

16. Cloud collapse & disc formation

17. Tidal truncation of a circumstellar disc (1994)

18. (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

19. A protoplanetary disc Fondamental limit 1 : T ~ 1350°K condensation of silicates Fondamental limit 2: T ~ 160°K condensation of water-ice

20. From grains to planetesimals…a miracle occurs

21. 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

22. 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…

23. 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

24. 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

25. Oligarchic growth (Kokubo, 2004)

26. CRUCIAL PARAMETER: ENCOUNTER VELOCITY DISTRIBUTION • dV < Vesc => runaway accretion • Vesc< dV < Verosion => accretion (non-runaway) • Verosion < dV => erosion/no-accretion

27. 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

28. Dynamical effect of a close-in stellar companion Large e-oscillations High dV??

29. M2=0.5M1 e2=0.3 a2=20AU Orbital phasing => V  C.(e2 + i2)1/2 VKep

30. 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 !!!

31. A typical example

33. eccentricity oscillations (e0=0) • oscillation frequency revising the Secular Theory approximation

34. Orbital crossing occurs when phasing gradient becomes too strong within one wave analytical derivation of ac

35. Accuracy of the analytical expression eb=0.1 eb=0.3 eb=0.5

36. Results e2=0.5 M2=0.5M1

37. Time dependancy

38. Reaching a general empirical expression

39. Effect of gas drag With Gas No Gas

40. 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

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

42. typical gas drag run Orbital crossing occurrence in gas free case Encounter velocity evolution between different Target-Projectile pairs R1/R2

43. 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

44. Critical Fragmentation Energy Contradicting esimates Benz&Asphaug, 1999

45. 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

46. 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

48. 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

49. 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

50. 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?