Things that matter during the first stages of formation of giant planets

1. Things that matter during the first stages of formation of giant planets Andrea Fortier Physikalisches Institut – UniBe 02/03/2011

2. Some of the important things Things that matter during the first stages of formation of giant planets Andrea Fortier Physikalisches Institut – UniBe 02/03/2011

3. “solid” core Internal structure: The basics gaseous envelope Introduction: context and motivation The giant planets of the solar system

4. Internal structure of the giant planets of the Solar System Solid content: Jupiter:0 < Mc < 11 M 1 < Mz < 39 M Saturn:9 < Mc < 22 M 1 < Mz < 8 M Uranus: 9 < Mc < 14 M Neptune: 12 < Mc < 16 M (EOS: SCVH 1995) Introduction: context and motivation (Guillot 1999)

5. (Armitage 2007) The nucleated instability model (Mizuno 1980) • Formation of planetesimals • Formation of the embryos • Accretion of gas and solids • Cross-over mass (Mc=Menv) • Runaway accretion of gas • Gap opening and termination of the process

6. MASS Xcross-over mass TIME FIRST STAGE Example On what depends the cross-over mass and the time of cross-over?

7. 9 < Mc [M]< 14 0 < Mc [M]< 18 9 < Mc [M]< 22 12 < Mc [M]< 16 But before that … Keep in mind that: • The formation of the giant planets must be completed before the protoplanetary disk dissipates, then form< 107 years. • The final masses of the cores have to be in good agreement with current estimations.

8. MODEL FOR THE GAS COMPONENT MODEL FOR THE SOLID COMPONENT PROTOPLANETARY DISK Recipe to make a planet TO FORM A GIANT PLANET

9. GAS COMPONENT:Internal structure and growth of the envelope + Internal and external boundary conditions + Equation Of State (EOS) + Opacity () tables

10. The external boundary condition gives the accretion rate … how??? GAS COMPONENT:The growth of the envelope How do planets grow? • By accreting solids (details later): the embryo increases its gravitational field. • By accreting gas: The embryo is immersed in a gaseous disk so … where does it ends?

11. grows because of solid accretion The condition RP=min(Ra, RH) must be fulfilled at any time, so the contraction of the envelope implies accretion of gas from the disk GAS COMPONENT:The growth of the envelope How does gas accretion proceed? Hydrostatic equilibrium should be satisfied:

12. and (Hubickyj et al. 2005) The lower the opacity, the faster the formation GAS COMPONENT:Opacity matters

13. The cutoff speeds up the formation (Hubickyj et al. 2005) The cutoff delays the formation GAS COMPONENT:Solids accretion matters • Sudden cutoff of the solids accretion: ×

14. THE MASS OF THE CORE CONTRIBUTES TO THE TOTAL MASS PLANETESIMALS ARE THE MAIN LUMINOSITY SOURCE SUMMARY GAS COMPONENT  SOLID COMPONENT • And also: • ablation of planetesimals  energy deposition, EOS,  • the core is not inert • …

15. GROWTH OF PLANETESIMALS THROUGH MUTUAL COLLISIONS N-BODY CALCS. GROWTH OF SOLID PLANETARY EMBRYOS SOLID COMPONENT ???? FORMATION OF PLANETESIMALS

16. v vt Relative velocity of the approaching planetesimals Effective cross-section Density of solids SOLID COMPONENT:The growth of the core STATISTICAL APPROXIMATION: Particle-in-a-box approximation (Safronov 1969)           Accretion rate of solids

17. GRAVITATIONAL FOCUSING ENLARGES THE CROSS-SECTION Enhancement factor SOLID COMPONENT:The effective cross-section Gravitational focusing favors the growth of the biggest planetesimals: vesc increases faster than vrel runaway growth

18.                                 Vrelincreases, gravitational focusing decreases The growth of the big body becomes self-regulated: the stirring rate of the small planetesimals is determined by the one that accretes them. oligarchic growth (e.g. Ida & Makino 1993, Kokubo & Ida 1996, 1998, 2000, 2002) SOLID COMPONENT:The effective cross-section                     The growing embryo “heats” the planetesimal disk.

19. SOLID COMPONENT:Runaway-oligarchic growth transition • Roughly speaking, a body of the mass of the Moon (~10-2 M ) is already an oligarch. • Timescales: Runaway growth: Tgrow M-1/3 (order of magnitude ~104 - 105 yrs) Oligarchic growth: Tgrow M1/3 (order of magnitude ~106 - 107 yrs) • IN PRACTICE, THE FORMATION OF A 10 M EMBRYO IS GOVERNED BY THE OLIGARCHIC GROWTH. THIS INTRODUCES A SERIOUS PROBLEM IN PLANETARY FORMATION: SOLID EMBRYOS FORM TOO SLOW. • Example: After 10 Myrs, at 5 AU only a 1 M embryo is formed(Thommes et al. 2003)

20. GAS COMPONENT  SOLID COMPONENTThe effective cross-section But protoplanets have a gaseous envelope that enlarge the cross-section more than the gravitational focusing alone: Gas drag of the envelope matters!! Moreover, there is a strong dependence on the planetesimal size.

21. The protoplanetary disk The Minimum Mass Solar Nebula (MMSN) (Hayashi 1981) … but in general the MMSN does not work (i.e. can not form the giant planets of the Solar System in reasonable timescales). Then, usually people consider disks more massive than the MMSN (some factor×MMSN), other indexes for the power law (a-p) or more complex models for the protoplanetary disk and its evolution.

22. The surface solids density at the is very important in determining the accretion rate: Where? In the feeding zone of the planet: (a-a, a+a) with a=3-5 RHill SOLID COMPONENT: Dependence on the solids disk density But  evolves with time. Simplest case: in situ formation (a fixed),  decreasing due to the accretion

23.  a ~ 4 RH  aMP1/3 SOLID COMPONENT: The feeding zone

24. a ~ 4 RH  aMP1/3 Isolation mass SOLID COMPONENT: The feeding zone  Examples At a=5.2 AU we have: 1 M  0.4 AU 10 M  0.9 AU 100 M  1.9 AU Jupiter  2.8 AU What’s the limiting mass? a a MP1/3 MP 4aa  Miso (a2)3/2

25. SOLID COMPONENT: Dependence on the solids’ surface density (A.F. PhD Thesis)

26. SOLID COMPONENT: Dependence on the solids’ surface density (A.F. PhD Thesis)

27. SOLID COMPONENT: Dependence on the solids’ surface density (A.F. PhD Thesis)

28. The importance of the oligarchic growth in giant planet calculations Oligarchic growth for the core Runaway growth for the core Parameters: a=6 AU 0= 16 g cm-2 Rpsimal= 100 km

29. 29 M Mass [M] 25 M 21 M Time [106 yrs.] What else matters? • Planetesimal size: 0(5.2AU) = 15 g cm-2 (~ 5 MMSN) (Fortier et al. 2007, 2009)

30. What else matters? • Giant planet formation adopting a size distribution for the accreted planetesimals the mass of solids is in big planetesimals the mass of solids is in small planetesimals rmin=30 m rmax=100 km all planetesimal sizes are equally abundant (Benvenuto et al, submitted)

31. What else matters? • Planetesimal size: How big were planetesimals born? This problem is under debate. Recent models claim that planetesimals were born big (> or >> 100 km, e.g. Johansen et al. 2007) What was the original size distribution? We don’t know. How did this distribution evolve? By mutual collisions that lead to both accretion and fragmentation.

32. What else matters?Planetesimal migration 0 = 10 MMSN     (Thommes et al. 2003)

33. What else matters?Planet migration

34. What else matters?Planet migration • Interaction between planets and the gaseous protoplanetary disk. Orbital migration is a consequence of angular momentum exchange between the planet and the gas disk. The type of migration depends on the planet’s mass. Type I: (low mass planets) In the “classical version” migration rates ~ MP ~0.1 Myr for planet core Must be slower in reality Local thermal effects reduce the migration rate • Type II: (the planet is massive enough to open a gap) • Mp << local Mdisk : the planet is coupled to the viscous evolution of the disk and migrates with the gas viscous timescale. • MP ~ local Mdisk : the disk is not capable to give the planet the angular momentum it needs to migrate with the gas. Migration eventually stops.

35. What else matters?Planet migration In situ formation Formation with migration Parameters: a=6 AU 0= 16 g cm-2 Rpsimal= 100 km

36. P1 P2 (Guilera et al. 2010, Guilera et al. sumbitted) What else matters?Simultaneous formation • In situ, simultaneous formation considering planetesimal migration Planets don’t see each other • The different cases correspond to different density profiles and planetesimal size distribution. • Planets do not migrate in any of these cases. • (a,t) is affected by planetesimal migration due to the gas drag of the disk, planet accretion and the presence of another growing embryo. Steep  profile: Formation of P1 is delayed by P2 P2 forms first Formation of P1 is accelerated density wave P1 forms first Formation of P2 is delayed

37. (Preliminary results) What else matters?Simultaneous formation with planet migration

38. MODEL FOR THE GAS COMPONENT MODEL FOR THE SOLID COMPONENT PROTOPLANETARY DISK Recipe to make a planet TO FORM A GIANT PLANET

39. MODEL FOR THE GAS COMPONENT MODEL FOR THE SOLID COMPONENT PROTOPLANETARY DISK MODEL FOR THE GAS COMPONENT MODEL FOR THE SOLID COMPONENT Recipe to make a planet GIANT PLANET MORE THAN ONE PLANET? INTERACTIONS!!

40. Thank you !!!