Abstract
The origin and wide distribution of eccentricities in planetary systems remains to be explained, in particular in the context of planet-disc interactions. Here we present a set of linear equations that describe the behavior of small eccentricities in a protoplanetary system consisting of a gaseous disc and a planet. Eccentricity propagates through the disc by means of pressure, and is exchanged with the planet via secular interactions. Excitation and damping of eccentricity can occur through Lindblad and corotation resonances, as well as viscosity. Three-dimensional effects allow for an eccentric mode to be trapped in the inner parts of the disc. This eccentric mode can easily grow within the disc's lifetime. An eccentric mode dominated by the planet can also grow, although less rapidly. Application to a hot Jupiter surrounded by a gaseous disc suggests that the eccentricity of the planet can grow. Finally, the linear theory is compared to hydrodynamical simulations, and a very good agreement is found.
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