How much does turbulence change the pebble isolation mass for planet formation?

TL;DR

This study investigates how disk turbulence influences the pebble isolation mass in planet formation, revealing that turbulence can significantly increase the mass needed to trap pebbles, affecting planetary growth models.

Contribution

The paper provides a new semi-analytical model quantifying the dependence of pebble isolation mass on turbulence, gas disk properties, and particle Stokes number, supported by hydrodynamical simulations.

Findings

Turbulence can increase the pebble isolation mass by nearly an order of magnitude.

The semi-analytical model explicitly relates PIM to disk aspect ratio, viscosity, and particle Stokes number.

Turbulent diffusion reduces the efficiency of pebble trapping at the pressure maximum.

Abstract

When a planet becomes massive enough, it gradually carves a partial gap around its orbit in the protoplanetary disk. A pressure maximum can be formed outside the gap where solids that are loosely coupled to the gas, typically in the pebble size range, can be trapped. The minimum planet mass for building such a trap, which is called the pebble isolation mass (PIM), is important for two reasons: it marks the end of planetary growth by pebble accretion, and the trapped dust forms a ring that may be observed with millimetre observations. We study the effect of disk turbulence on the pebble isolation mass and find its dependence on the gas turbulent viscosity, aspect ratio, and particles Stokes number. By means of 2D gas hydrodynamical simulations, we found the minimum planet mass to form a radial pressure maximum beyond the orbit of the planet, which is the necessary condition to trap pebbles. We then carried out 2D gas plus dust hydrodynamical simulations to examine how dust turbulent diffusion impacts particles trapping at the pressure maximum. We finally provide a semi-analytical calculation of the PIM based on comparing the radial drift velocity of solids and the root mean square turbulent velocity fluctuations around the pressure maximum. From our results of gas simulations, we provide an expression for the PIM versus disk aspect ratio and turbulent viscosity. Our gas plus dust simulations show that the effective PIM can be nearly an order of magnitude larger in high-viscosity disks because turbulence diffuse particles out of the pressure maximum. This is quantified by our semi-analytical calculation, which gives an explicit dependence of the PIM with Stokes number of particles. We conclude than disk turbulence can significantly alter the PIM, depending on the level of turbulence in regions of planet formation.