Considerations on the accretion of Uranus and Neptune by mutual collisions of planetary embryos in the vicinity of Jupiter and Saturn

Modeling the formation of the ice giants Uranus and Neptune is a long-lasting problem in planetary science. Due to gas-drag, collisional damping, and resonant shepherding, the planetary embryos repel the planetesimals away from their reach and thus they stop growing (Levison et al. 2010). This problem persists independently of whether the accretion took place at the current locations of the ice giants or closer to the Sun. 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. 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 disk of gas. But strong damping also favors 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, in order to have substantial mutual accretion among embryos, it is necessary to assume that the surface density of the gas was several times higher than that of the minimum-mass solar nebula. However this contrasts with 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. Only one of our simulations "by chance" successfully reproduced the structure of the outer Solar System.