Investigation of gravitational stability of protoplanetary disks based on statistical analysis of their masses

Abstract

We compiled a sample of $1155$ protoplanetary disks, combining data from ten surveys of star-forming regions. Based on the sample, we constructed a power-law approximation of the disk mass distribution: $dN/dM \propto M^{-\beta}$, $\beta = 1.36 \pm 0.14$. We used the sample for a statistical analysis of the gravitational stability of protoplanetary disks. To analyze the stability of the disks, we calculated the Toomre parameter ($Q$) for each of them. In the calculations, it was assumed that the radial density distribution in the disks is described by a power-law profile. The calculations of the Toomre parameter show that only $1.2$ % of the disks in the sample are formally unstable ($Q < 1$), while $1.7$ % are in a state of marginal stability ($1 \leq Q \leq 2$). The low observed abundance of unstable disks contradicts theoretical expectations and may be explained by a systematic underestimation of disk masses due to limitations of observational methods. Considering the effects of optical depth, CO depletion, as well as uncertainty in the gas-to-dust ratio, we conclude that the actual fraction of the gravitationally unstable systems may be significantly higher.