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

Abstract

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. We explore how the simultaneous growth of two embryos at the present locations of Jupiter and Saturn affects the outcome of planetary formation. 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 $\Sigma$ 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. 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 $\Sigma$: if $\Sigma \propto r^{-3/2}$ and the protoplanetary disk is rather massive, Jupiter's formation inhibits the growth of Saturn. If $\Sigma \propto r^{-1}$ isolated and simultaneous formation lead to very similar outcomes; in the the case of $\Sigma \propto r^{-1/2}$ Saturn grows faster and induces a density wave that later acclerates the formation of Jupiter. Our results indicate that the simultaneous growth of several embryos impacts the final outcome and should be taken into account by planet formation models.