The Eccentricity Distribution of Extrasolar Planets

In the past decade we have witnessed the discoveries of over 200 extrasolar planets, and the measurements of their unexpected dynamical properties. Specifically, the eccentricities of currently known extrasolar planets exhibit a distribution unlike that of the solar system, with moderately and highly eccentric planets being the rule rather than the exception. In this paper we explore a possible dynamical origin of the observed eccentricity distribution through numerical integrations of ensembles of randomly constructed planetary systems in the $10^8$ yr after planet formation. We find that the eccentricity distributions of dynamically active systems relax towards an equilibrium eccentricity distribution, well described by an empirical fitting formula of the form $n(e)dn \propto e\exp(e^2 / (2 \cdot 0.3^2))dn$, irrespective of the details of the initial conditions. This distribution agrees well with the one observed in extrasolar planets, excluding the tidally circularized hot Jupiters. For this mechanism to be responsible for the observed distribution of eccentricities, a period of large-scale dynamical instability would be required in newly formed planetary systems, lasting 1--2 orders of magnitude longer than the $\sim 1$ Myr interval in which gas-giant planets are assembled