Collision Rates in the Present-day Kuiper Belt and Centaur Regions: Applications to Surface Activation and Modiication on Comets, Kuiper Belt Objects, Centaurs, and Pluto-charon Proposed Running Header: Collisions in the Edgeworth-kuiper Belt Address Editorial Correspondence To

We present results from our model of collision rates in the present-day Edgeworth-Kuiper Belt and Centaur region. We have updated previous results to allow for new estimates of the total disk population, in order to examine surface activation and modi cation time scales due to cratering impacts. We extend previous results showing that the surfaces of EdgeworthKuiper Belt objects are not primordial and have been moderately to heavily reworked by collisions. Objects smaller than about r = 2:5 km have collisional disruption lifetimes less than 3.5 Gyr in the present-day collisional environment and have probably been heavily damaged in their interiors by large collisions. In the 30{50 AU region, impacts of 1 km radius comets onto individual 100 km radius objects occur on 7 107{4 108 yr time scales, cratering the surfaces of the larger objects with 8{54 craters 6 km in diameter over a 3.5 Gyr period. Collision time scales for impacts of 4 meter radius projectiles onto 1 km radius comets range from 3{5 107 yr. The cumulative fraction of the surface area of 1 and 100 km radius objects cratered by projectiles with radii larger than 4 m ranges from a few to a few tens percent over 3.5 Gyr. The ux of Edgeworth-Kuiper Belt projectiles onto Pluto and Charon is also calculated and is found to be 3{5 times that of previous estimates. Our impact model is also applied to Centaur objects in the 5{30 AU region. We nd that during their dynamical lifetimes within the Centaur region, objects undergo very little collisional evolution. Therefore, the collisional/cratering histories of Centaurs are dominated by the time spent in the Edgeworth-Kuiper Belt rather than the time spent on planet-crossing orbits. Further, we nd that the predominant surface activity of Centaur objects like Chiron is most likely not impact-induced.