We present an H-band image of the light scattered from circumstellar dust around the nearby (10 pc) young M star AU Microscopii (AU Mic, GJ 803, HD 197481), obtained with the Keck adaptive optics system. We resolve the disk both vertically and radially, tracing it over 17-60 AU from the star. Our AU Mic observations thus offer the possibility to probe at high spatial resolution (0.04 or 0.4 AU per resolution element) for morphological signatures of the debris disk on Solar-System scales. Various sub-structures (dust clumps and gaps) in the AU Mic disk may point to the existence of orbiting planets. No planets are seen in our H-band image down to a limiting mass of 1 M_Jup at >20 AU, although the existence of smaller planets can not be excluded from the current data. Modeling of the disk surface brightness distribution at H-band and R-band, in conjunction with the optical to sub-millimeter spectral energy distribution, allows us to constrain the disk geometry and the dust grain properties. We confirm the nearly edge-on orientation of the disk inferred from previous observations, and deduce an inner clearing radius <=10 AU. We find evidence for a lack of small grains in the inner (<60 AU) disk, either as a result of primordial disk evolution, or because of destruction by Poynting-Robertson and/or corpuscular drag. A change in the power-law index of the surface brightness profile is observed near 33 AU, similar to a feature known in the profile of the beta Pic circumstellar debris disk. By comparing the time scales for inter-particle collisions and Poynting-Robertson drag between the two systems, we argue that the breaks are linked to one of these two processes.
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