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

TL;DR

This study combines analytic theory and simulations to explore how initial planetesimal mass influences the onset of oligarchic growth and the resulting size distribution of remnant planetesimals, shedding light on dwarf planet origins.

Contribution

It provides a new analytic framework linking initial planetesimal mass to oligarchic growth mass and remnant size distribution, explaining dwarf planet formation and asteroid belt features.

Findings

Oligarchic growth begins when velocity dispersion is minimal.

For small initial masses, oligarchic mass is independent of initial mass.

Remnant mass distribution slopes match observed asteroid and Kuiper belt features.

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 $M_{\rm oli}$ 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, $M_{\rm oli}$ is independent of $m_0$. If $m_0$ is large, on the other hand, oligarchic growth commences directly after runaway growth, and $M_{\rm oli} \propto m_0^{3/7}$. The planetary mass $M_{\rm oli}$ 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, $q \simeq -2.7$, and the bump at $10^{21}$ 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 $m_0 \sim 10^{13}$ g or less are favored to explain the slope of large asteroids, $q \simeq -2.0$, while the bump at $10^{21}$ g can be reproduced by introducing a small number of asteroid seeds each with mass of $10^{19} $ g.