SIMULTANEOUS FORMATION OF GIANT PLANETS ANDREA FORTIER O. GUILERA, O.G. BENVENUTO, A. BRUNINI RINGBERG, 30 NOVEMBER 2010 PHYSIKALISCHES INSTITUT, UNIVERSITY OF BERN, SWITZERLAND FCAGLP, UNIVERSIDAD DE LA PLATA, ARGENTINA
THE BASICS The formation of the giant planets must be completed before the protoplanetary disk dissipates, then apple form < 10 7 years. The final solid content in the planet s interior has to be in good agreement with current estimations.
THE MODEL (Benvenuto & Brunini 2005; Fortier et al. 2007, 2009; Benvenuto et al. 2009) numerical resolution of the stellar differential structure equations Henyey technique ( self consistent calculation of the growth and gas internal structure of the protoplanet) the solid s accretion rate is time dependent and corresponds to the oligarchic growth ( it is coupled to the structure equations) interaction between the accreted planetesimals and the gas envelope of the protoplanet ( energy exchange) size distribution for the accreted planetesimals circular orbit, no migration final stages of accretion are not calculated isolated formation with no disk evolution
THE NICE MODEL The Nice model (Tsiganis et al. 2005): in the beginning, the exterior planets of the Solar System formed a more compact system. After they were completely formed, they migrated to their current positions (Jupiter a little bit towards the Sun and the others away from it). In this process, Jupiter and Saturn cross their mean motion resonances 1:2. Orbital radii: a J = 5.5 AU a S = 8.3 AU a U = 14 AU a N = 11 AU In 50% of their simulations, Tsiganis et al. (2005) found that Uranus and Neptune exchange places during their outward migration.
SURFACE DENSITY PROFILE Desch (2007) calculated the nebular density profile compatible with the Nice model and he obtained: We will consider that Σ 0 = 10 g cm -2 in a J = 5.5 AU for the solid density of the disk.
INCLUDING A SIZE DISTRIBUTION FOR THE ACCRETED PLANETESIMALS Kokubo & Ida (2000) found that planetesimals that populate the disk follow a mass distribution that is well approximated by a power law: Depending on the value of α we can distinguish three different cases: α > -2 larger planetesimals dominate the distribution α = -2 all species are equally abundant α < -2 smaller planetesimals dominate the distribution In principle we will consider that there are 9 species, equally spaced in the logarithm of the radius where r min = 0.03 km and r max = 100 km.
RESULTS FORMATION TIME-SCALES
IMPROVING THE MODEL Guilera et al. (2010) improved the model in order to consider the simultaneous formation of giant planets, keeping the hypothesis of in situ formation. The model for simultaneous formation includes: the migration of planetesimals in the disk due to gas drag; an exponential decay for the gaseous component of the disk with a characteristic timescale of τ = 6 My; planetesimals random velocities out of equilibrium. In their work they studied the simultaneous formation of two planets and they found that it can proceed qualitatively different when compared to the case of isolated formation. They found cases where the presence of a second planet delays the formation and in other cases it can be accelerated.
With the numerical code developed by Guilera et al. (2010), we then studied the in situ, SIMULTANEOUS planetary formation of the four giant planets. We considered different surface density profiles for the disk, Σ a p (p = 2, 1.5, 1 and 0.5). We adopted α = -2.5 for the size distribution of planetesimals (in agreement with Ormel et al. (2010)), but now: the minimum radius of the planetesimal population, r min, is considered as a free parameter; the maximum radius is fixed in 100 km.
SIMULTANEOUS FORMATION: DESCH NEBULA (apple a -2, apple 0 (5.5 AU)= 11 g cm -2 ) COMPUTING SIMULTANEOUS FORMATION (JUST IN CASE) ISOLATED FORMATION: LOOKING FOR A COMMON r min WITH A MORE DETAILED MODEL FOR THE FORMATION OF GIANT PLANETS WE FOUND THAT DESCH NEBULA DOESN T FAVOUR THEIR FORMATION
apple a -1.5, apple 0 (5.5 AU)= 11 g cm -2 ISOLATED FORMATION SIMULTANEOUS FORMATION
apple a -1, apple 0 (5.5 AU)= 11 g cm -2 SIMULTANEOUS FORMATION
apple a -0.5, apple 0 (5.5 AU)= 11 g cm -2 SIMULTANEOUS FORMATION
CONSIDERING LOWER apple apple a -1, apple 0 (5.5 AU)= 11 g cm -2 JUPITER SATURN NEPTUNE URANUS apple 2 28.53 2.25 25.50 2.27 15.01 3.47 12.64 6.26 3 30.55 2.20 26.91 2.10 15.49 2.68 13.13 3.94 apple 3 28.34 2.76 20.10 3.11 14.15 6.59 11.70 12.06
SUMMARY Desch nebula does noavour the simultaneous formation For smoother density profiles the simultaneous formation of the four giant planets is possible in less than 10 Myr provided that most of the solid mass accreted by the planets is in small planetesimals (< 1 km) Our best results correspond to the density profile apple a -1 and dissipation timescales for the gas component of the disk of order 2 to 3 My We found some cases where the formation times of the four planets was approximately the same