Catching drifting pebbles II. A stochastic equation of motions for pebbles

TL;DR

This paper develops a stochastic equation of motion to quantify how turbulence affects pebble accretion efficiency in protoplanetary disks, revealing that turbulence suppresses accretion especially in outer disk regions.

Contribution

It introduces a new stochastic equation of motion for pebbles in stratified disks and provides a comprehensive parameter study of pebble accretion efficiency under turbulence.

Findings

Turbulence suppresses pebble accretion via turbulent diffusion.

Large turbulent motions can inhibit the settling mechanism.

Outer disk regions are more affected by turbulence than inner regions.

Abstract

Turbulence plays a key role in the transport of pebble-sized particles. It also affects the ability of pebbles to be accreted by protoplanets, because it stirs pebbles out of the disk midplane. In addition, turbulence can suppress pebble accretion once the relative velocities become too large for the settling mechanism to be viable. Following Paper I, we aim to quantify these effects by calculating the pebble accretion efficiency $\varepsilon$ using three-body simulations. To model the effect of turbulence on the pebbles, we derive a stochastic equation of motion (SEOM) applicable to stratified disk configurations. In the strong coupling limit (ignoring particle inertia) the limiting form of this equation agrees with previous works. We conduct a parameter study and calculate $\varepsilon$ in 3D, varying pebble and gas (turbulence) properties and accounting for the planet inclination. We find that strong turbulence suppresses pebble accretion through turbulent diffusion, agreeing within factors of order unity with previous works. Another reduction of $\varepsilon$ occurs when the turbulent rms motions are large and the settling mechanism fails. Efficiency-wise, the outer disk regions are more affected by turbulence than the inner regions. At the location of the H$_2$O iceline, planets around low-mass stars achieve much higher efficiencies. Including the results from Paper I, we present a framework to obtain $\varepsilon$ under general circumstances.