Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants

Abstract

The growth of a planetary core by pebble accretion stops at the so-called pebble isolation mass, when the core generates a pressure bump that traps drifting pebbles outside its orbit. The value of the pebble isolation mass is crucial in determining the final planet mass. If the isolation mass is very low, gas accretion is protracted and the planet remains at a few Earth masses with a mainly solid composition. For higher values of the pebble isolation mass, the planet might be able to accrete gas from the protoplanetary disc and grow into a gas giant. Previous works have determined a scaling of the pebble isolation mass with cube of the disc aspect ratio. Here, we expand on previous measurements and explore the dependency of the pebble isolation mass on all relevant parameters of the protoplanetary disc. We use 3D hydrodynamical simulations to measure the pebble isolation mass and derive a simple scaling law that captures the dependence on the local disc structure and the turbulent viscosity parameter α. We find that small pebbles, coupled to the gas, with Stokes number τ f < 0.005 can drift through the partial gap at pebble isolation mass. However, as the planetary mass increases, particles must be decreasingly smaller to penetrate the pressure bump. Turbulent diffusion of particles, however, can lead to an increase of the pebble isolation mass by a factor of two, depending on the strength of the background viscosity and on the pebble size. We finally explore the implications of the new scaling law of the pebble isolation mass on the formation of planetary systems by numerically integrating the growth and migration pathways of planets in evolving protoplanetary discs. Compared to models neglecting the dependence of the pebble isolation mass on the α-viscosity, our models including this effect result in higher core masses for giant planets. These higher core masses are more similar to the core masses of the giant planets in the solar system.

Solid accretion onto planetary cores in radiative disks

“…2). This effect has been predicted by Bitsch et al (2018), who found that the pebble isolation mass scales strongly with the disk aspect ratio for a locally isothermal disk…”

“…A growing planet is able to open a partial gap in the surrounding gaseous disk by generating a pressure maximum, which effectively halts the inward drift of solids in the disk, in particular the pebble component. The mass at which the pebble flux is halted has been defined as the pebble isolation mass , and it varies based on the local physical properties of the disk (Bitsch et al 2018;Ataiee et al 2018;Picogna et al 2018).…”

Are the observed gaps in protoplanetary discs caused by growing planets?

“…However, even low mass planets can perturb the disc large enough to E-mail: nndugu@must.ac.ug generate a small pressure bump exterior to their orbits. This pressure bump results in reversing the gas-drag such that small dust grains and pebbles are halted in their inward drift (Whipple 1972;Paardekooper & Mellema 2006;Pinilla et al 2012a;Morbidelli & Nesvorny 2012;Bitsch et al 2018b). This results in an accumulation of particles exterior to the planet which can explain the formation of rings and gaps in the disc observations (Dullemond et al 2018).…”

“…The planet has thus reached pebble isolation mass and can start to accrete gas (e.g. Morbidelli & Nesvorny 2012;Bitsch et al 2018b). As the pebbles pile up exterior to the planet in rings, a planet that causes such a change in the disc structure must thus be located in a gap of the dust distribution.…”

Influence of migration models and thermal torque on planetary growth in the pebble accretion scenario

“…During core growth, the planet accretes 90% in solids and 10% in gas, building a gaseous envelope alongside the core. When the planet reaches pebble isolation mass Bitsch et al 2018a;Ataiee et al 2018), core growth is halted and the gaseous envelope is accreted onto the planet. Following Bitsch et al (2018b), the pebble isolation mass is calculated via:…”