On Runaway Growth of Planetesimals

Abstract

We have performed 3-DN-body simulations of planetary accretion. The growth mode of planetesimals is investigated with 3000 equal-mass planetesimals under perfect and gas-free accretion. We present conclusive evidence of runaway growth, which was first found through the statistical studies of the coagulation equation with the particle-in-a-box kinetic theory (e.g., Wetherill, G. W., and G. R. Stewart 1989.Icarus77,330–367). The statistical approach is based on the averaged quantities and thus would not be suitable for describing runaway growth. Our approach can describe runaway growth naturally. The number of bodies in our simulations is large enough to derive the statistical properties of the system. We find that the mass distribution immediately relaxes into the continuous power-law mass distribution withdNc/dm∝m−2.5±0.4, whereNcis the cumulative number of bodies. Then the largest body of the continuous mass distribution becomes detached from the continuous mass distribution and shows runaway growth in mass. The velocity dispersion (eccentricity and inclination) is almost inversely proportional to the square-root of mass except for the top and tail parts of the mass distribution. These results agree with the results by the statistical kinetic theory approach.