Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006dps....38.6606c&link_type=abstract
American Astronomical Society, DPS meeting #38, #66.06; Bulletin of the American Astronomical Society, Vol. 38, p.617
Astronomy and Astrophysics
Astronomy
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.
Collins Benjamin
Sari Re'em
Schlichting Hilke
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