Understanding how planets become massive. I. Description and validation of a new toy model

Abstract

The formation of giant planets requires accumulation of ~10 Earth mass in solids; but how do protoplanets acquire their mass? There are many, often competing processes that regulate the accretion rate of protoplanets. To assess their effects we present a new, publicly-available toy model. The rationale behind the toy model is that it encompasses as many physically-relevant processes as possible, but at the same time does not compromise its simplicity, speed, and physical insight. The toy model follows a modular structure, where key features -- e.g. planetesimal fragmentation, radial orbital decay, nebula turbulence -- can be switched on or off. Our model assumes three discrete components (fragments, planetesimals, and embryos) and is zero dimensional in space. We have tested the outcomes of the toy model against literature results and generally find satisfactory agreement. We include, for the first time, model features that capture the three-way interactions among small particles, gas, and protoplanets. Collisions among planetesimals will result in fragmentation, transferring a substantial amount of the solid mass to small particles, which couple strongly to the gas. Our results indicate that the efficiency of the accretion process then becomes very sensitive to the gas properties -- especially to the turbulent state and the magnitude of the disk headwind (the decrease of the orbital velocity of the gas with respect to Keplerian) -- as well as to the characteristic fragment size.