Orbital eccentricity growth through disc-companion tidal interaction

We investigate the driving of orbital eccentricity of giant protoplanets an d brown dwarfs through disc-companion tidal interactions by means of two di mensional numerical simulations. We consider disc models that are thought t o be typical of protostellar discs during the planet forming epoch, with ch aracteristic surface densities similar to standard minimum mass solar nebul a models. We consider companions, ranging in mass between 1 and 30 Jupiter masses M-J, that are initially embedded within the discs on circular orbits about a central solar mass. We find that a transition in orbital behaviour occurs at a mass in the range 10-20 M-J. For low mass planetary companions , we find that the orbit remains essentially circular. However, for compani on masses greater than or similar to 20 M-J, we find that non steady behavi our of the orbit occurs, characterised by a growth in eccentricity to value s of 0.1 less than or similar to e less than or similar to 0.25. Analysis o f the disc response to the presence of a perturbing companion indicates tha t for the higher masses, the inner parts of the disc that lie exterior to t he companion orbit become eccentric through an instability driven by the co upling of an initially small disc eccentricity to the companion's tidal pot ential. This coupling leads to the excitation of an m = 2 spiral wave at th e 1:3 outer eccentric Lindblad resonance, which transports angular momentum outwards, leading to a growth of the disc eccentricity. The interaction of the companion with this eccentric disc, and the driving produced by direct resonant wave excitation at the 1:3 resonance, can lead to the growth of o rbital eccentricity, with the driving provided by the eccentric dis being t he stronger. Eccentricity growth occurs when the tidally induced gap width is such that eccentricity damping caused by corotating Lindblad resonances is inoperative. These simulations indicate that for standard disc models, g aps become wide enough for the 1:3 resonance to dominate, such that the tra nsition from circular orbits can occur, only for masses in the brown dwarf range. However. the transition mass might be reduced into the range for ext rasolar planets if the disc viscosity is significantly lower enabling wider gaps to occur for these masses. Another possibility is that an eccentric d isc is produced by an alternative mechanism, such as viscous overstability resulting in a slowly precessing non axisymmetric mass distribution. A larg e eccentricity in a planet orbit contained within an inner cavity might the n be produced.