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

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

Introduction: context and motivation JupiterSaturnUranusNeptune M [M  ] a [UA] Internal structure: The basics “solid” core gaseous envelope The giant planets of the solar system

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

The nucleated instability model (Mizuno 1980)  Formation of planetesimals  Formation of the embryos  Accretion of gas and solids  Cross-over mass (M c =M env )  Runaway accretion of gas  Gap opening and termination of the process (Armitage 2007)

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

But before that … Keep in mind that: o The formation of the giant planets must be completed before the protoplanetary disk dissipates, then  form < 10 7 years. o The final masses of the cores have to be in good agreement with current estimations. 0 < M c [M  ]< 18 9 < M c [M  ]< 14 9 < M c [M  ]< < M c [M  ]< 16

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

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

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? The external boundary condition gives the accretion rate … how???

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

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

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

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

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

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

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

SOLID COMPONENT: The effective cross-section                                                   The growing embryo “heats” the planetesimal disk. V rel increases, 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: Runaway-oligarchic growth transition  Roughly speaking, a body of the mass of the Moon (~10 -2 M  ) is already an oligarch.  Timescales: Runaway growth: T grow  M -1/3 (order of magnitude ~ yrs) Oligarchic growth: T grow  M 1/3 (order of magnitude ~ 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)

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

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.

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

SOLID COMPONENT: The feeding zone   a ~ 4 R H  aM P 1/3

SOLID COMPONENT: The feeding zone   a ~ 4 R H  aM P 1/3 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 M P 1/3 M P  4  a  a   M iso  (a 2  ) 3/2 Isolation mass

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

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

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

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

What else matters?  Planetesimal size:  0 (5.2AU) = 15 g cm -2 (~ 5 MMSN) 21 M  25 M  29 M  Time [10 6 yrs.] Mass [M  ] (Fortier et al. 2007, 2009)

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

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.

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

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 ~ M P ~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) M p << local M disk : the planet is coupled to the viscous evolution of the disk and migrates with the gas viscous timescale. M P ~ local M disk : the disk is not capable to give the planet the angular momentum it needs to migrate with the gas. Migration eventually stops.

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

What else matters? Simultaneous formation  In situ, simultaneous formation considering planetesimal migration 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. Planets don’t see each other Steep  profile: Formation of P1 is delayed by P2 P2 forms first Formation of P1 is accelerated P1 forms first Formation of P2 is delayed density wave P1P2 (Guilera et al. 2010, Guilera et al. sumbitted)

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

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

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

Thank you !!!