Evolution of Planetesimal Velocities Based on Three-Body Orbital Integrations and Growth of Protoplanets |
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| Authors: | Keiji OhtsukiGlen R Stewart Shigeru Ida |
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| Institution: | a Laboratory for Atmospheric and Space Physics, University of Colorado, 392 UCB, Boulder, Colorado, 80309-0392, f1ohtsuki@lasp.colorado.eduf1b Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo, 152-8551, Japan |
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| Abstract: | We obtain the viscous stirring and dynamical friction rates of planetesimals with a Rayleigh distribution of eccentricities and inclinations, using three-body orbital integration and the procedure described by Ohtsuki (1999, Icarus137, 152), who evaluated these rates for ring particles. We find that these rates based on orbital integrations agree quite well with the analytic results of Stewart and Ida (2000, Icarus 143, 28) in high-velocity cases. In low-velocity cases where Kepler shear dominates the relative velocity, however, the three-body calculations show significant deviation from the formulas of Stewart and Ida, who did not investigate the rates for low velocities in detail but just presented a simple interpolation formula between their high-velocity formula and the numerical results for circular orbits. We calculate evolution of root mean square eccentricities and inclinations using the above stirring rates based on orbital integrations, and find excellent agreement with N-body simulations for both one- and two-component systems, even in the low-velocity cases. We derive semi-analytic formulas for the stirring and dynamical friction rates based on our numerical results, and confirm that they reproduce the results of N-body simulations with sufficient accuracy. Using these formulas, we calculate equilibrium velocities of planetesimals with given size distributions. At a stage before the onset of runaway growth of large bodies, the velocity distribution calculated by our new formulas are found to agree quite well with those obtained by using the formulas of Stewart and Ida or Wetherill and Stewart (1993, Icarus106, 190). However, at later stages, we find that the inclinations of small collisional fragments calculated by our new formulas can be much smaller than those calculated by the previously obtained formulas, so that they are more easily accreted by larger bodies in our case. The results essentially support the previous results such as runaway growth of protoplanets, but they could enhance their growth rate by 10-30% after early runaway growth, where those fragments with low random velocities can significantly contribute to rapid growth of runaway bodies. |
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| Keywords: | celestial mechanics |
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