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We have developed a model to predict the post-collision brightness increaseof sub-catastrophic collisions between asteroids and to evaluate the likelihoodof a survey detecting these events. It is based on the cratering scaling lawsof Holsapple and Housen (2007) and models the ejecta expansion following animpact as occurring in discrete shells each with their own velocity. Weestimate the magnitude change between a series of target/impactor pairs,assuming it is given by the increase in reflecting surface area within aphotometric aperture due to the resulting ejecta. As expected the photometricsignal increases with impactor size, but we find also that the photometricsignature decreases rapidly as the target asteroid diameter increases, due togravitational fallback. We have used the model results to make an estimate ofthe impactor diameter for the (596) Scheila collision of D=49-65m depending onthe impactor taxonomy, which is broadly consistent with previous estimates. Wevaried both the strength regime (highly porous and sand/cohesive soil) and thetaxonomic type (S-, C- and D-type) to examine the effect on the magnitudechange, finding that it is significant at early stages but has only a smalleffect on the overall lifetime of the photometric signal. Combining the resultsof this model with the collision frequency estimates of Bottke et al. (2005),we find that low-cadence surveys of approximately one visit per lunation willbe insensitive to impacts on asteroids with D<20km if relying on photometricdetections.

Modelling the brightness increase signature due to asteroid collisions