Consequences of the simultaneous formation of giant planets by the core accretion mechanism

Abstract

Context. The core accretion mechanism is presently the most widely accepted cause of the formation of giant planets. For simplicity, most models presently assume that the growth of planetary embryos occurs in isolation. Aims. We explore how the simultaneous growth of two embryos at the present locations of Jupiter and Saturn affects the outcome of planetary formation. Methods. We model planet formation on the basis of the core accretion scenario and include several key physical ingredients. We consider a protoplanetary gas disk that exponentially decays with time. For planetesimals, we allow for a distribution of sizes from 100 m to 100 km with most of the mass in the smaller objects. We include planetesimal migration as well as different profiles for the surface density Σ of the disk. The core growth is computed in the framework of the oligarchic growth regime and includes the viscous enhancement of the planetesimal capture cross-section. Planet migration is ignored. Results. By comparing calculations assuming formation of embryos in isolation to calculations with simultaneous embryo growth, we find that the growth of one embryo generally significantly affects the other. This occurs in spite of the feeding zones of each planet never overlapping. The results may be classified as a function of the gas surface density profile Σ: if Σ ∝ r −3/2 and the protoplanetary disk is rather massive, Jupiter's formation inhibits the growth of Saturn. If Σ ∝ r −1 isolated and simultaneous formation lead to very similar outcomes; in the the case of Σ ∝ r −1/2 Saturn grows faster and induces a density wave that later accelerates the formation of Jupiter. Conclusions. Our results indicate that the simultaneous growth of several embryos impacts the final outcome and should be taken into account by planet formation models.

Planet formation models: the interplay with the planetesimal disc

“…For the purpose of the collision rate, the capture radius of the protoplanet should depend upon the mass of the protoplanet, upon the planetesimals' velocity with respect to the protoplanet, upon the density profile of the envelope, ρ(r), and upon the size of the accreted planetesimals (smaller planetesimals are more affected by the gas drag of the envelope and therefore are easier to capture). As in Guilera et al (2010), here we adopt the prescription of Inaba & Ikoma (2003) where the capture radius R can be obtained by solving the following equation…”

“…farther away planetesimals are less excited. Here we follow the approach of Guilera et al (2010) and consider that the effective stirring is given by…”

“…However, formation could be accelerated if most of the accreted mass is bound in small planetesimals (less than 0.1 km). Guilera et al (2010Guilera et al ( , 2011, also considering in situ models, studied the simultaneous formation of several planets where planetesimal drifting is included. These authors considered different density profiles for the disc and found that only for massive discs the formation of the giant planets as in the solar system is possible only if planetesimal radii are smaller than 1 km.…”

Simultaneous formation of Jupiter and Saturn

“…In our work Guilera et al (2010), we developed a numerical code to compute the simultaneous formation of giant planets immersed in a protoplanetary disk that evolves with time. We used this code to calculate the in situ simultaneous formation of the gaseous giant planets of the solar system.…”

“…This excitation causes an increment in the migration velocity of planetesimals at the Saturn's neighborhood when both planets are formed simultaneously. The increment in the migration velocity of planetesimals causes the solid accretion timescale to become longer than planetesimal migration timescales, and the solid accretion rate of Saturn (when it is formed simultaneously with Jupiter) becomes less efficient than for the isolated Saturn formation (see Guilera et al 2010). The most important result is that the rapid formation of Jupiter inhibits -or largely increases-the timescale of Saturn's formation when they grow simultaneously.…”