Self-consistent $N$-body simulation of Planetesimal-Driven Migration I. The trajectories of single planets in the uniform background

Abstract: Recent exoplanet observations have revealed a diversity of exoplanetary systems, which suggests the ubiquity of radial planetary migration. One powerful known mechanism of planetary migration is planetesimal-driven migration (PDM), which can let planets undergo significant migration through gravitational scattering with planetesimals. In this series of papers, we present the results of our high-resolution self-consistent $N$-body simulations of PDM, in which gravitational interactions among planetesimals, the gas drag, and Type-I migration are all taken into account. In this first paper (Paper I), we investigate the migration of a single planet through PDM within the framework of the classical standard disk model (the Minimum-Mass Solar Nebula model). Paper I aims to improve our understanding of planetary migration through PDM, addressing previously unexplored aspects of both the gravitational interactions among planetesimals and the interactions with disk gas. Our results show that even small protoplanets can actively migrate through PDM. Such active migration can act as a rapid radial diffusion mechanism for protoplanets and significantly influence the early stages of planetary formation (i.e., during the runaway growth phase). Moreover, a fair fraction of planets migrate outward. This outward migration may offer a potential solution for the ``planet migration problem" caused by Type-I migration and gives a natural mechanism for outward migration assumed in many recent scenarios for the formation of outer planets.