Connecting Clump Sizes in Turbulent Disk Galaxies to Instability Theory

In this letter we study the mean sizes of Ha clumps in turbulent disk galaxies relative to kinematics, gas fractions, and Toomre Q. We use similar to 100. pc resolution HST images, IFU kinematics, and gas fractions of a sample of rare, nearby turbulent disks with properties closely matched to z similar to 1.5-2 main-sequence galaxies (the DYNAMO sample). We find linear correlations of normalized mean clump sizes with both the gas fraction and the velocity dispersion-to-rotation velocity ratio of the host galaxy. We show that these correlations are consistent with predictions derived from a model of instabilities in a self-gravitating disk (the so-called violent disk instability model). We also observe, using a two-fluid model for Q, a correlation between the size of clumps and self-gravity-driven unstable regions. These results are most consistent with the hypothesis that massive star-forming clumps in turbulent disks are the result of instabilities in self-gravitating gas-rich disks, and therefore provide a direct connection between resolved clump sizes and this in situ mechanism.