Planetesimal Formation by the Gravitational Instability of Dust Ring Structures

Abstract

Abstract We investigate the gravitational instability (GI) of dust ring structures and the formation of planetesimals by their gravitational collapse. The normalized dispersion relation of a self-gravitating ring structure includes two parameters that are related to its width and line mass (the mass per unit length). We survey these parameters and calculate the growth rate and wavenumber. Additionally, we investigate the formation of planetesimals by growth of the GI of the ring that is formed by the growth of the secular GI of the protoplanetary disk. We adopt a massive, dust-rich disk as a disk model. We find the range of radii for fragmentation by the ring GI as a function of the width of the ring. The innermost radius for the ring GI is smaller for a smaller ring width. We also determine the range of the initial planetesimal mass resulting from the fragmentation of the ring GI. Our results indicate that the planetesimal mass can be as large as 1028 g at its birth after the fragmentation. It can be as low as about 1025 g if the ring width is 0.1% of the ring radius, and the lower limit increases with the ring width. Furthermore, we obtain approximate formulae for the upper and lower limits of the planetesimal mass. We predict that the planetesimals formed by the ring GI have prograde rotations because of the Coriolis force acting on the contracting dust. This is consistent with the fact that many trans-Neptunian binaries exhibit prograde rotation.