Long range outward migration of giant planets, with application to Fomalhaut b

Recent observations of exoplanets by direct imaging, reveal that giant planets orbit at a few dozens to more than a hundred of AU from their central star. The question of the origin of these planets challenges the standard theories of planet formation. We propose a new way of obtaining such far planets, by outward migration of a pair of planets formed in the 10 AU region. Two giant planets in mean motion resonance in a common gap in the protoplanetary disk migrate outwards, if the inner one is significantly more massive than the outer one. Using hydrodynamical simulations, we show that their semi major axes can increase by almost one order of magnitude. In a flared disk, the pair of planets should reach an asymptotic radius. This mechanism could account for the presence of Fomalhaut b ; then, a second, more massive planet, should be orbiting Fomalhaut at about 75 AU.

The dynamical role of the circumplanetary disc in planetary migration

Numerical simulations of planets embedded in protoplanetary gaseous discs are a precious tool for studying the planetary migration ; however, some approximations have to be made. Most often, the selfgravity of the gas is neglected. In that case, it is not clear in the literature how the material inside the Roche lobe of the planet should be taken into account. Here, we want to address this issue by studying the influence of various methods so far used by different authors on the migration rate. We performed high-resolution numerical simulations of giant planets embedded in discs. We compared the migration rates with and without gas selfgravity, testing various ways of taking the circum-planetary disc (CPD) into account. Different methods lead to significantly different migration rates. Adding the mass of the CPD to the perturbing mass of the planet accelerates the migration. Excluding a part of the Hill sphere is a very touchy parameter that may lead to an artificial suppression of the type III, runaway migration. In fact, the CPD is smaller than the Hill sphere. We recommend excluding no more than a 0.6 Hill radius and using a smooth filter. Alternatively, the CPD can be given the acceleration felt by the planet from the rest of the protoplanetary disc. The gas inside the Roche lobe of the planet should be very carefully taken into account in numerical simulations without any selfgravity of the gas. The entire Hill sphere should not be excluded. The method used should be explicitly given. However, no method is equivalent to computing the full selfgravity of the gas.