Forming planetesimals via gravitational instability in maximally-settled protoplanetary disks

While investigating whether planetesimals might form via gravitational instability of a thin layer of solids at the midplane of a gas-dominated protoplanetary disk, Sekiya (1998) performed the first analytic investigation into Kelvin-Helmholtz stable density profiles of well-coupled dust in such a disk. He found that for given gas disk parameters, marginally stable profiles exist only up to a maximum dust surface density ∑_d,crit. We derive a natural extension of his profile solutions to larger dust surface densities. In these new profiles, additional dust mass above ∑_d,crit accumulates at the midplane, where orbital velocities are already Keplerian and where the dust’s effect on the vertical velocity profile is least destabilizing: the fraction of the dust at the midplane increases and the total height of the dust layer decreases as the dust surface density increases.

The new profiles suggest that for disks enriched by a factor of several over typical ISM metallicities -- for example disks whose gas has begun to dissipate as they approach the ends of their lifetimes -- solids at the midplane may concentrate enough to undergo gravitational instability before Kelvin-Helmholtz disruption of the dust density profile. Using physical parameters typical of observed disks, we characterize planetesimal populations that might form in this way.