A multifluid approach for polydisperse pebble accretion: From particles to fluids, establishing the multifluid framework

TL;DR

This paper develops a multifluid simulation framework to model polydisperse pebble accretion in protoplanetary discs, validating it against previous results and exploring effects of disc evolution and size distribution on accretion efficiency.

Contribution

The authors introduce a validated multifluid approach for simulating polydisperse pebble accretion, enabling more accurate modeling of planet formation processes.

Findings

The framework accurately reproduces previous pebble accretion efficiencies for static discs.

Gas disc evolution affects accretion efficiency, lowering it for high Stokes numbers.

Polydisperse accretion rates are higher than previous estimates, especially with MRN size distribution.

Abstract

Pebble accretion offers an efficient pathway to form planets, driven by a constant supply of inward drifting mass and an accretion efficiency enhanced by gas drag. While most studies assume a single pebble size (monodisperse), real discs contain a range of sizes (polydisperse), that drift, interact, and accrete at different rates. We aim to model polydisperse pebble accretion with a fluid approach, validating the method and exploring how gas disc evolution, solid-to-gas back-reaction, and a polydisperse size distribution affect growth. We use FARGO3D, modified to allow pebble accretion, to run 2D hydrodynamic simulations in a global disc with multiple dust/pebble species representing an underlying continuous pebble size distribution. With our framework of a multifluid approach, we have found values for pebble accretion efficiency consistent with earlier studies for a static gas disc. This confirms that our approach gives an accurate representation of pebble accretion. Evolving the gas disc we find lower efficiencies compared to an unperturbed gas disc for high Stokes number ($\gtrsim 0.3$) and higher efficiency for smaller St ($\lesssim0.3$). This effect is increased for higher planet masses. The accretion rate is mostly dominated by the highest Stokes numbers in our parameter study ($\mathrm{St}\in[10^{-2},10^0]$). The ratio we find between polydisperse and monodisperse pebble accretion rate is higher than previous estimations. We have constructed a multifluid model framework capable of accurately simulating polydisperse pebble accretion consistent with previous studies. This framework has advantages for simulating higher planet masses, as well as modelling multiple pebble species which are coupled to the gas. We find the perturbation of the protoplanet on the gas-disc lowering accretion rate when assuming a MRN-distribution of solids.