Oligarchic growth in a fully interacting system

Abstract

Context. 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 planet formation can be defined by the mass ratio between formed protoplanets and the initial mass of the embryo-planetesimal belt. Aims. 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 by modeling the planet formation efficiency in a belt of embryos with self-interacting or non-self-interacting planetesimals. Methods. We used our own graphics processing unit-based direct N-body integrator for the simulations. We compared 2D models using different initial embryo numbers, different initial planetesimal numbers, and different total initial belt masses. For a limited number of cases, we compared the 2D and 3D simulations. Results. 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 the non-self-interacting and self-interacting models qualitatively give the same results above 200 embryos. Our findings show that the higher the initial mass of the embryo-planetesimal belt, the higher the discrepancy between models that use self-interacting or non-self-interacting planetesimals is. The study of 3D models showed quantitatively the same results as the 2D models for low average inclination. We conclude that it is important to include planetesimal self-interaction in both 2D and 3D models in cases where the initial embryo number is less than 200.