| Abstract |
<p>At a final stage of planet formation, planetary embryos grow through collisions with planetesimals. Gravitational scattering by larger embryos induces destructive collisions between planetesimals. Fragments produced by the collisions get smaller and smaller by successive collisions until the smallest fragments are removed by the gas drag (in protoplanetary disks) or by radiation pressure (in debris disks). As a result, the final planetary mass is determined by the equilibrium between the growth of the embryos and the depletion of planetesimals by collisional fragmentation.</p> <p>Fragmenting collisions are divided into two types, catastrophic disruption and cratering. Although some studies neglected the effect of cratering, it is unclear which of the two collision types makes a dominant contribution to the collision cascades. We construct a simple outcome model describing both catastrophic disruption and cratering, with the total ejecta mass, the mass of the largest fragment, and the power-law exponent of the size distribution of fragments as parameters. Using this model, we examine the mass depletion time in collision cascades. We find the cratering collisions to be much more efficient than disruptive ones over a wide range of the model parameters. It is also found that the mass depletion time in collision cascades is mainly governed by the total ejecta mass and is almost insensitive to the mass of the largest fragment and the size distribution of fragments for a realistic parameter region. The total ejecta mass is usually determined by the ratio of the impact energy per unit target mass $Q$ to its threshold value $Q_{
m D}^star$ for catastrophic disruption. We derive a mass depletion time in collision cascades, which is determined by $Q_{
m D}^star$ of the high-mass end of collision cascades.</p> <p>Using the mass depletion time, we estimate the final masses of embryos to be about Mars mass. Although the final mass becomes larger farther out from the star, the formation timescale of embryos in the outer region is longer. Thus, embryos become the largest at intermediate distances. They may grow further by another effect, which is an enhancement of the collisional cross section by a gaseous planetary ``atmosphere' (Inaba et al. 2003, Icarus 166, 46--62), until the embryo becomes massive enough to enable gas accretion and ultimately a gas giant formation. Therefore, we show a possibility for gas giants to form at intermediate distances from a central star.</p> |
