  Gaia Data Release 2 includes observational data for 14,099 pre-selected
asteroids. From the sparsely sampled G band photometry, we derive lower-limit
lightcurve amplitudes for 11,665 main belt asteroids in order to provide
constraints on the distribution of shapes in the asteroid main belt. Assuming a
triaxial shape model for each asteroid, defined through the axial aspect ratios
a > b and b=c, we find an average b/a=0.80+-0.04 for the ensemble, which is in
agreement with previous results. By combining the Gaia data with asteroid
properties from the literature, we investigate possible correlations of the
aspect ratio with size, semi-major axis, geometric albedo, and intrinsic color.
Based on our model simulations, we find that main belt asteroids greater than
50 km in diameter on average have higher b/a aspect ratios (are rounder) than
smaller asteroids. We furthermore find significant differences in the shape
distribution of main belt asteroids as a function of the other properties that
do not affect the average aspect ratios. We conclude that a more detailed
investigation of shape distribution correlations requires a larger data sample
than is provided in Gaia Data Release 2.
