The European Space Agencys Rosetta spacecraft passed by the main belt asteroid (21) Lutetia the 10th July 2010. With its ~100km size, Lutetia is one of the largest asteroids ever imaged by a spacecraft. During the flyby, the on-board OSIRIS imaging system acquired spectacular images of Lutetias northern hemisphere revealing a complex surface scarred by numerous impact craters, reaching the maximum dimension of about 55km. In this paper, we assess the cratering history of the asteroid. For this purpose, we apply current models describing the formation and evolution of main belt asteroids, that provide the rate and velocity distributions of impactors. These models, coupled with appropriate crater scaling laws, allow us to interpret the observed crater size-frequency distribution (SFD) and constrain the cratering history. Thanks to this approach, we derive the crater retention age of several regions on Lutetia, namely the time lapsed since their formation or global surface reset. We also investigate the influence of various factors -like Lutetias bulk structure and crater obliteration- on the observed crater SFDs and the estimated surface ages. From our analysis, it emerges that Lutetia underwent a complex collisional evolution, involving major local resurfacing events till recent times. The difference in crater density between the youngest and oldest recognized units implies a difference in age of more than a factor of 10. The youngest unit (Beatica) has an estimated age of tens to hundreds of Myr, while the oldest one (Achaia) formed during a period when the bombardment of asteroids was more intense than the current one, presumably around 3.6Gyr ago or older.
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