A multi-fluid approach for polydisperse pebble accretion. From particles to fluids, establishing the multi-fluid framework

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 used FARGO3D, modified to allow pebble accretion, to run 2D hydrodynamic simulations in a global disc with multiple pebble species representing an underlying continuous pebble size distribution. With our multi-fluid approach, we find 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 numbers (≳ 0.3) and higher efficiencies for smaller Stokes numbers (łesssim0.3). This effect increases for higher planet masses. The accretion rate is mostly dominated by the highest Stokes numbers in our parameter study (mathrm St ∈ 10^ ,10^0 -2 ). The ratio we find between the polydisperse and monodisperse pebble accretion rates is higher than previous estimations. We constructed a multi-fluid model framework capable of accurately simulating polydisperse pebble accretion consistent with previous studies. This framework offers advantages for simulating higher planet masses and for modelling multiple pebble species coupled to the gas. We find that the protoplanet's perturbation of the gas-disc lowers the accretion rate when assuming an MRN-distribution of solids.