Planetesimal formation by the gravitational instability of dust ring structures

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 planetesimal formation 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 the fragmentation by the ring GI as a function of the width of the ring. The inner-most radius for the ring GI is smaller for the 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 10^28 g at its birth after the fragmentation. It can be as low as about 10^25 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 formulas 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.