Protoplanet collisions: New scaling laws from smooth particle hydrodynamics simulations

One common approach for solving collisions between protoplanets in simulations of planet formation is to employ analytical scaling laws. The most widely used one was developed by Leinhardt & Stewart (2012, ApJ, 745, 79) from a catalog of ~180 N-body simulations of rubble-pile collisions. In this work, we use a new catalogue of more than 20 000 SPH simulations to test the validity and the prediction capability of Leinhardt & Stewart (2012, ApJ, 745, 79) scaling laws. We find that these laws overestimate the fragmentation efficiency in the merging regime and they are not able to properly reproduce the collision outcomes in the super-catastrophic regime. In the merging regime, we also notice a significant dependence between the collision outcome, in terms of the largest remnant mass, and the relative mass of the colliding protoplanets. Here, we present a new set of scaling laws that are able to better predict the collision outcome in all regimes and it is also able to reproduce the observed dependence on the mass ratio. We compare our new scaling laws against a machine learning approach and obtain similar prediction efficiency.