Planetary accumulation with a continuous supply of planetesimals

Previous calculations of the accumulation of small (~10 km) planetesimals at ~ 1 AU to form Mars-sized bodies assumed that the initial assemblage of planetesimals were all present at the outset. This is an obviously reasonable assumption in systems in which the time scale for growth time of ~10²⁶ g planetary bodies is long compared to estimates of the evolutionary time scale of a protosolar disk, as was the case in the pioneering work of Safronov (1969). It is now found that as a result of the preplanetary assemblage being unstable with respect to the runaway growth of the largest bodies, this is unlikely to be the case. The more realistic alternative of adding the initial planetesimals on a ~10⁵ year time scale is considered here, as well as the consequences of the initial planetesimals being considerably smaller than those assumed previously. It is found that although the time scale for runaway growth is now actually controlled by the availability of planetesimals, for planetesimal production time scales of ~10⁵ yrs, the final consequences are very similar. These calculations do show, however, that as a consequence of continuous infall during the runaway growth process, the late initial planetesimals are likely to be catastrophically disrupted by mutual collisions. For this reason, a more detailed treatment of the growth of planetesimals into planetary embryos will require a better understanding of the difficult problem of formation of the initial planetesimals themselves.