Acceleration of Runaway Growth Due to Collisional Disruption

Mathematics – Probability

Scientific paper

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Scientific paper

We investigated the effect of collisional disruption of planetesimals on the growth of a protoplanet. Fragments created by collisional disruption collide with a protoplanet at fairly high probability because of their small inclination. Thus, the growth of a protoplanet is accelerated due to the collisional disruption. Wetherill and Stewart(1993, Icarus 106, 190-209) performed numerical simulations of planetary accretion, taking into account the disruption of planetesimals. Their results showed that the effect of the disruption enhances the growth rate of protoplanets by the factor 3. However, in their simulation, it is not clear how general the enhance factor is. In the present study, we adopted a simple mass distribution of fragments obtained under the assumption of the steady state, and analytically calculated the enhance factor of the growth rate. Then we obtained the dependence of factor on various parameters. Our result almost reproduced that of Wetherill and Stewart(1993), which justifies our simple model. In our simulation, we also took into account the distribution of inclination of fragments, which is neglected in Wetherill and Stewart(1993). This further enhanced the collisional probability of fragments.

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