Collisional evolution and reddening of asteroid surfaces I. The problem of conflicting timescales and the role of sizedependent effects

Space weathering is the generic term used for processes that modify the optical properties of surfaces of atmosphereless rocky bodies under exposure to the space environment. The general agreement about the relevance of the effects of space weathering on the spectral properties of S-complex asteroids fails when some basic quantitative estimates are attempted. In particular, there is severe disagreement regarding the typical time-scales for significant spectral reddening to occur, ranging from 1 Myr to 1 Gyr. Generally speaking, the spectral reddening of an individual object can be considered as the sum of three terms, one (which is relevant for statistical analyses) depending on the exposure of the object to space weathering during its lifetime, a second one due to the original surface composition, and a third one (a noise term) due to the combination of poorly constrained effects (e.g. structure and texture of the surface). The surface of an asteroid is usually covered by regolith, and its presence and properties presumably play a critical role in the weathering processes. In this paper, we discuss the role played by collisional evolution in affecting the spectral properties of asteroids and refreshing the surfaces due to the formation of ejecta, and the necessity of a simultaneous modelling of collisions and weathering processes. We introduce a new idea, based on the possibility of a sort of saturation of the refreshing process whenever a massive re-accumulation of the impact ejecta takes place. In this case, a dependence of the overall reddening on the asteroid size should naturally come out. We show that this conclusion is indeed supported by available main belt asteroid spectroscopic data.