On the oligarchic growth in a fully interacting system

In the oligarchic growth model, protoplanets develop in the final stage of planet formation via collisions between planetesimals and planetary embryos. The majority of planetesimals are accreted by the embryos, while the remnant planetesimals acquire dynamically excited orbits. The efficiency of the planet formation can be defined by the mass ratio between formed protoplanets and the initial mass of the embryo-planetesimal belt.In numerical simulations of the oligarchic growth, the gravitational interactions between planetesimals are usually neglected due to computational difficulties. In this way, computations require fewer resources. We investigated the effect of this simplification via modeling the planet formation efficiency in a belt of embryos and self-interacting or non-self-interacting planetesimals.We used our own developed GPU-based direct N-body integrator for the simulations. We compared 2D models using different initial embryo number, initial planetesimal number, and total initial belt mass. For limited cases, we compared 2D to 3D simulations.We found that planet formation efficiency is higher if the planetesimal self-interaction is taken into account in models that contain the commonly used 100 embryos. The observed effect can be explained by the damping of planetesimal eccentricities by their self-gravity. The final numbers of protoplanets are independent of planetesimal self-gravity, while the average mass of the formed protoplanets is larger in the self-interacting models. We also found that above 200 embryos, the non-self-interacting and self-interacting models give qualitatively the same results. Our findings show that the higher is the initial mass of the embryo-planetesimal belt, the higher is the discrepancy between models that use self-interacting or non-self-interacting planetesimals. The study of 3D models showed quantitatively same result as 2D models for low average inclination. We conclude that planetesimal self-interaction must be included either in 2D and 3D models below 200 initial embryo number.