Onset of oligarchic growth and implication for accretion histories of dwarf planets

Ryuji Morishima

doi:10.1016/j.icarus.2016.07.019

paper

Onset of oligarchic growth and implication for accretion histories of dwarf planets

arXiv:1608.00043 · doi:10.1016/j.icarus.2016.07.019

Abstract

We investigate planetary accretion that starts from equal-mass planetesimals using an analytic theory and numerical simulations. We particularly focus on how the planetary mass $M_{oli}$ at the onset of oligarchic growth depends on the initial mass $m_{0}$ of a planetesimal. Oligarchic growth commences when the velocity dispersion relative to the Hill velocity of the protoplanet takes its minimum. We find that if $m_{0}$ is small enough, this normalized velocity dispersion becomes as low as unity during the intermediate stage between the runaway and oligarchic growth stages. In this case, $M_{oli}$ is independent of $m_{0}$ . If $m_{0}$ is large, on the other hand, oligarchic growth commences directly after runaway growth, and $M_{oli} \propto m_{0}^{3/7}$ . The planetary mass $M_{oli}$ for the solid surface density of the Minimum Mass Solar Nebula is close to the masses of the dwarf planets in a reasonable range of $m_{0}$ . This indicates that they are likely to be the largest remnant planetesimals that failed to become planets. The power-law exponent $q$ of the differential mass distribution of remnant planetesimals is typically $- 2.0$ and $- 2.7$ to $- 2.5$ for small and large $m_{0}$ . The slope, $q ≃ - 2.7$ , and the bump at $1 0^{21}$ g (or 50 km in radius) for the mass distribution of hot Kuiper belt objects are reproduced if $m_{0}$ is the bump mass. On the other hand, small initial planetesimals with $m_{0} \sim 1 0^{13}$ g or less are favored to explain the slope of large asteroids, $q ≃ - 2.0$ , while the bump at $1 0^{21}$ g can be reproduced by introducing a small number of asteroid seeds each with mass of $1 0^{19}$ g.

arXiv comment34 pages, 10 figures, accepted for publication in Icarus

Onset of oligarchic growth and implication for accretion histories of dwarf planets

Abstract

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