N-Body Simulation of Planetesimal Formation through Gravitational Instability and Coagulation. II. Accretion Model

The gravitational instability of a dust layer is one of the scenarios for planetesimal formation. If the density of a dust layer becomes sufficiently high as a result of the sedimentation of dust grains toward the midplane of a protoplanetary disk, the layer becomes gravitationally unstable and spontaneously fragments into planetesimals. Using a shearing box method, we performed local $N$-body simulations of gravitational instability of a dust layer and subsequent coagulation without gas and investigated the basic formation process of planetesimals. In this paper, we adopted the accretion model as a collision model. A gravitationally bound pair of particles is replaced by a single particle with the total mass of the pair. This accretion model enables us to perform long-term and large-scale calculations. We confirmed that the formation process of planetesimals is the same as that in the previous paper with the rubble pile models. The formation process is divided into three stages: the formation of non-axisymmetric structures, the creation of planetesimal seeds, and their collisional growth. We investigated the dependence of the planetesimal mass on the simulation domain size. We found that the mean mass of planetesimals formed in simulations is proportional to $L_y^{3/2}$, where $L_y$ is the size of the computational domain in the direction of rotation. However, the mean mass of planetesimals is independent of $L_x$, where $L_x$ is the size of the computational domain in the radial direction if $L_x$ is sufficiently large. We presented the estimation formula of the planetesimal mass taking into account the simulation domain size.