A method to search for large-scale concavities in asteroid shape models

Light curve inversion is proven to produce an unique model solution only under the
hypothesis that the asteroid is convex. However, it was suggested that the resulting
shape model, for the case of non-convex asteroid, is the convex-hull of the true asteroid
non-convex shape. While a convex shape is already useful to provide the overall aspect
of the target, much information about real shapes is missed, as we know that asteroids
are very irregular. It is a commonly accepted evidence that large flat areas sometimes
appearing on shapes derived from light curves correspond to concave areas, but this
information has not been further explored and exploited so far. We present in this
paper a method that allows to predict the presence of concavities from such flat regions.
This method analyzes the distribution of the local normals to the facets composing
shape models to predict the presence of abnormally large flat surfaces. In order to test
our approach, we consider here its application to a large family of synthetic asteroid
shapes, and to real asteroids with large scale concavities, whose detailed shape is known
by other kinds of observations (radar and spacecraft encounters). The method that
we propose is proven to be reliable and capable of providing a qualitative indication
of the relevance of concavities on well-constrained asteroid shapes derived from purely
photometric data sets.