Gas-Assisted Growth of Protoplanets in a Turbulent Medium

TL;DR

This paper presents a model showing that turbulence in protoplanetary disks affects pebble accretion efficiency but does not prevent rapid growth of planetary cores, especially in the high-mass regime, within disk lifetimes.

Contribution

The study introduces an order of magnitude model quantifying turbulence effects on pebble accretion, including impact on velocity, capture radius, and particle scale height, highlighting conditions for rapid core growth.

Findings

Turbulence does not hinder rapid growth of planetary cores above 10 Earth masses.

Growth timescales are sensitive to disk properties but generally allow large core formation within disk lifetime.

A 'Flow Isolation Mass' emerges, indicating where binary capture ceases, with dependence on orbital separation.

Abstract

Pebble accretion is a promising process for decreasing growth timescales of planetary cores, allowing gas giants to form at wide orbital separations. However, nebular turbulence can reduce the efficiency of this gas-assisted growth. We present an order of magnitude model of pebble accretion, which calculates the impact of turbulence on the average velocity of small bodies, the radius for binary capture, and the sizes of the small bodies that can be accreted. We also include the effect of turbulence on the particle scale height, which has been studied in previous works. We find that turbulence does not prevent rapid growth in the high-mass regime: the last doubling time to the critical mass to trigger runaway gas accretion ($M \sim 10 \, M_\oplus$) is well within the disk lifetime even for strong ($\alpha \gtrsim 10^{-2}$) turbulence. We find that while the growth timescale is quite sensitive to the local properties of the protoplanetary disk, over large regimes of parameter space large cores grow in less than the disk lifetime if appropriately-sized small bodies are present. Instead, the effects of turbulence are most pronounced for low planetary masses. For strong turbulence the growth timescale is longer than the gas disk lifetime until the core reaches masses $\gtrsim 10^{-2}-10^{-1} M_\oplus$. A "Flow Isolation Mass", at which binary capture ceases, emerges naturally from our model framework. We comment that the dependence of this mass on orbital separation is similar to the semi-major axis distribution of solar-system cores.