Shear-dominated Protoplanetary Dynamics

Astronomy and Astrophysics – Astronomy

Scientific paper

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Scientific paper

We study the velocity dispersion, or eccentricity distribution, of protoplanetary bodies whose eccentricities are lower than their Hill eccentricity. We use a Boltzmann equation to calculate the effects of dynamical friction and viscous stirring on the distribution function. Dynamical friction, if present, balances the mutual excitations of the bodies to maintain an equilibrium distribution. If there is no dynamical friction, the typical eccentricity of bodies in the disk increases with time. We derive analytically the eccentricity distribution function with and without dynamical friction; we find it to be identical in both cases, and very different from the previously assumed Rayleigh distribution function. The peak of the distribution lies much lower than the rms value, indicating that a small subset of the population with the highest eccentricities contain most of the thermal energy at any given time. In addition, we measure the eccentricity distribution of both scenarios with N-body simulations and find remarkable agreement with the analytic result.

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