Introducing the Gaussian shape hypothesis for asteroids and comets

A hypothesis is presented that the irregular shapes of asteroids and cometary nuclei can be modeled by using lognormal statistics (Gaussian random sphere). The Gaussian sphere is fully described by the mean and covariance function of the radius. A suitable covariance function is devised here for the generation of sample Gaussian spheres that closely resemble the shapes observed for asteroids. To collect more evidence for the Gaussian hypothesis, assuming simple Lommel-Seeliger and Lambert scattering laws, lightcurves are computed for rotating Gaussian spheres. The results show striking similarities to asteroid lightcurves. For example, the observed increase of lightcurve amplitude with increasing solar phase angle appears to be at least partly explained by the numerical simulations. Making further use of the Gaussian random sphere, a statistical model is developed for albedo variegations on asteroids, and for characterizing active regions on cometary nuclei.