Rapid inward migration of planets formed by gravitational instability

The observation of massive exoplanets at large separation (greater than or similar to 10 au) from their host star, like in the HR 8799 system, challenges theories of planet formation. A possible formation mechanism involves the fragmentation of massive self-gravitating discs into clumps. While the conditions for fragmentation have been extensively studied, little is known of the subsequent evolution of these giant planet embryos, in particular their expected orbital migration. Assuming a single planet has formed by fragmentation, we investigate its interaction with the gravitoturbulent disc it is embedded in. 2D hydrodynamical simulations are used with a simple prescription for the disc cooling. A steady gravitoturbulent disc is first set up, after which simulations are restarted including a planet with a range of masses approximately equal to the clump's initial mass expected in fragmenting discs. Planets rapidly migrate inwards, despite the stochastic kicks due to the turbulent density fluctuations. We show that the migration time-scale is essentially that of type I migration, with the planets having no time to open a gap. In discs with aspect ratio similar to 0.1 at their forming location, planets with a mass comparable to or larger than Jupiter's can migrate in as short as 10(4) years, that is about 10 orbits at 100 au. Massive planets formed at large separation from their star by gravitational instability are thus unlikely to stay in place, and should rapidly migrate towards the inner parts of protoplanetary discs, regardless of the planet mass.