Will the Large Synoptic Survey Telescope detect extra-solar planetesimals entering the solar system?

Planetesimal formation is a common by-product of the star formation process. Taking the dynamical history of the Solar system as a guideline -- in which the planetesimal belts were heavily depleted due to graviational perburbation with the giant planets -- and assuming similar processes have take place in other planetary systems, one would expect the interestellar space to be filled with extra-solar planetesimals. However, not a single one of these objects has been detected so far entering the Solar system, even though it would clearly be distinguishable from a Solar system comet due to its highly hyperbolic orbit. The Large Synoptic Survey Telescope (LSST) will provide wide coverage maps of the sky to a very high sensitivity, ideal to detect moving objects like comets, both active and inactive. In anticipation of these observations, we estimate how many inactive "interstellar comets" might be detected during the duration of the survey. The calculation takes into account estimates (from observations and models) of the number density of stars, the amount of solids available to form planetesimals, the frequency of planet and planetesimal formation, the efficiency of planetesimal ejection, and the possible size distribution of these small bodies.