Two-Component Secular Gravitational Instability in a Protoplanetary Disk: A Possible Mechanism for Creating Ring-Like Structures

Abstract

The instability in protoplanetary disks due to gas-dust friction and self-gravity of gas and dust is investigated by linear analysis. In the case where the dust to gas ratio is enhanced and turbulence is week, the instability grows, even in gravitationally stable disks, on a timescale of order $10^{4- 5}$yr at a radius of order 100AU. If we ignore the dynamical feedback from dust grains in the gas equation of motion, the instability reduces to the so-called "secular gravitational instability", which was investigated previously as an instability of dust in a fixed background gas flow. In this work, we solve the equations of motion for both gas and dust consistently and find that long-wavelength perturbations are stable, in contrast to the secular gravitational instability in the simplified treatment. This may indicate that we should not neglect small terms in equation of motion if the growth rate is small. The instability is expected to form ring structures in protoplanetary disks. The width of the ring formed at a radius of 100 AU is a few tens of AU. Therefore, the instability is a candidate for the formation mechanism of observed ring-like structures in disks. Another aspect of the instability is the accumulation of dust grains, and hence the instability may play an important role in the formation of planetesimals, rocky protoplanets, and cores of gas giants located at radii $\sim$100 AU. If these objects survive the dispersal of the gaseous component of the disk, they may be the origin of debris disks.