Orbital eccentricity growth through disc-companion tidal interaction

Abstract

We investigate the driving of orbital eccentricity of giant protoplanets and brown dwarfs through disc-companion tidal interactions by means of two dimensional numerical simulations. We consider disc models that are thought to be typical of protostellar discs during the planet forming epoch, with characteristic surface densities similar to standard minimum mass solar nebula models. We consider companions, ranging in mass between 1 and 30 Jupiter masses $M_{\rm J},$ 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_{\rm J}.$ For low mass planetary companions, we find that the orbit remains essentially circular. However, for companion masses $\gtrsim 20 M_{\rm J},$ we find that non steady behaviour of the orbit occurs, characterised by a growth in eccentricity to values of $0.1 \lesssim e \lesssim 0.25$. Analysis of the disc response to the presence of a perturbing companion indicates that for the higher masses, the inner parts of the disc that lie exterior to the companion orbit become eccentric through an instability driven by the coupling of an initially small disc eccentricity to the companion's tidal potential. This coupling leads to the excitation of an $m=2$ spiral wave at the 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 orbital eccentricity, with the driving provided by the eccentric disc being the 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, gaps become wide enough for the 1:3 resonance to dominate, such that the transition from circular orbits can occur, only for masses in the brown dwarf range. However, the transition mass might be reduced into the range for extrasolar planets if the disc viscosity is significantly lower enabling wider gaps to occur for these masses. Another possibility is that an eccentric disc is produced by an alternative mechanism, such as viscous overstability resulting in a slowly precessing non axisymmetric mass distribution. A large eccentricity in a planet orbit contained within an inner cavity might then be produced.