The accretion of Uranus and Neptune by collisions among planetary embryos in the vicinity of Jupiter and Saturn^⋆

¹ Astronomical Institute, Slovak Academy of Science, 05960 Tatranská Lomnica, Slovakia
e-mail: mjakubik@ta3.sk; ne@ta3.sk
² Département Cassiopée, University of Nice – Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, Nice, France
³ Institute for Astronomy and Astrophysics, Academia Sinica, PO Box 23-141, Taipei 106, Taiwan
e-mail: morby@oca.eu; brasser_astro@yahoo.com

Received: 12 July 2011
Accepted: 9 February 2012

Abstract

Context. Modeling the formation of the ice giants Uranus and Neptune has been a challenging problem in planetary science for a long time. Owing to gas-drag, collisional damping, and resonant shepherding, the planetary embryos repel the planetesimals from their reach and that is why they stop growing. This problem persists independently of whether the accretion took place at the current locations of the ice giants or closer to the Sun.

Aims. Instead of trying to push the runaway/oligarchic growth of planetary embryos up to 10−15 Earth masses, we envision the possibility that the planetesimal disk could generate a system of planetary embryos of only 1−3 Earth masses. Then we investigate whether these embryos could have collided with each other and grown enough to reach the masses of current Uranus and Neptune.

Methods. We performed several series of numerical simulations. The dynamics of a considered set of embryos is influenced by the presence of Jupiter and Saturn, assumed to be fully formed on non-migrating orbits in 2:3 resonance, and also by gravitational interactions with the gas disk.

Results. Our results point to two major problems. First, there is typically a large difference in mass between the first- and the second-most massive core formed and retained beyond Saturn. Second, in many simulations the final planetary system has more than two objects beyond Saturn. The growth of a major planet from a system of embryos requires strong damping of eccentricities and inclinations from the gas disk. But strong damping also enables embryos and cores to find a stable resonant configuration, so that systems with more than two surviving objects are found. In addition to these problems, it is necessary to assume that the surface density of the gas was several times higher than that of the minimum-mass solar nebula to achieve substantial accretion among embryos. However, this contradicts the common idea that Uranus and Neptune formed in a gas-starving disk, which is suggested by the relatively small amount of hydrogen and helium contained in the atmospheres of these planets.

Conclusions. Only one of our simulations serendipitously reproduced the structure of the outer solar system successfully. However, we point out that models of formation of Uranus and Neptune have non-trivial problems, which cannot be ignored and have to be addressed in future work.