Simulations of planet migration driven by planetesimal scattering

Abstract Evidence has mounted for some time that planet migration is an important part of the formation of planetary systems, both in the Solar System [Malhotra, R., 1993. Nature 365, 819–821] and in extrasolar systems [Mayor, M., Queloz, D., 1995. Nature 378, 355–359; Lin, D.N.C., Bodenheimer, P., Richardson, D.C., 1996. Nature 380, 606–607]. One mechanism that produces migration (the change in a planet's semi-major axis a over time) is the scattering of comet- and asteroid-size bodies called planetesimals [Fernandez, J.A., Ip, W.-H., 1984. Icarus 58, 109–120]. Significant angular momentum exchange can occur between the planets and the planetesimals during local scattering, enough to cause a rapid, self-sustained migration of the planet [Ida, S., Bryden, G., Lin, D.N.C., Tanaka, H., 2000. Astrophys. J. 534, 428–445]. This migration has been studied for the particular case of the four outer planets of the Solar System (as in Gomes et al. [Gomes, R.S., Morbidelli, A., Levison, H.F., 2004. Icarus 170, 492–507]), but is not well understood in general. We have used the Miranda [McNeil, D., Duncan, M., Levison, H.F., 2005. Astron. J. 130, 2884–2899] computer simulation code to perform a broad parameter-space survey of the physical variables that determine the migration of a single planet in a planetesimal disk. Migration is found to be predominantly inwards, and the migration rate is found to be independent of planet mass for low-mass planets in relatively high-mass disks. Indeed, a simple scaling relation from Ida et al. [Ida, S., Bryden, G., Lin, D.N.C., Tanaka, H., 2000. Astrophys. J. 534, 428–445] matches well with the dependencies of the migration rate: (1) | d a d t | = a T 4 π Σ a 2 M Sun with T the orbital period of the planet and Σ the surface density of the planetesimal disk. When the planet's mass exceeds that of the planetesimals within a few Hill radii (the unit of the planet's gravitational reach), the migration rate decreases strongly with planet mass. Other trends are identified with the root-mean-squared eccentricity of the planetesimal disk, the mass of the particles dragged by the planet in the corotation region, and the index of the surface density power law. The trends are discussed in the context of an analysis of the scattering process itself, which was performed using a large simulation of massless planetesimals. The scattering process alters semi-major axes, eccentricities and timescales of interaction for the planetesimals. In particular, a bias in scattering timescales on either side of the planet's orbit leads to a very strong tendency for the planet to migrate inwards , towards the star, instead of outwards. The detection of this tendency relies on a level of resolution that may not have been achieved in past studies. The results of this work show that planet migration driven by planetesimal scattering should be a widespread phenomenon, especially for low-mass planets such as still-forming protoplanets.