Keck Pencil-Beam Survey for Faint Kuiper Belt Objects

We present the results of a pencil-beam survey of the Kuiper Belt using theKeck 10-m telescope. A single 0.01 square degree field is imaged 29 times for atotal integration time of 4.8 hr. Combining exposures in software allows thedetection of Kuiper Belt Objects (KBOs) having visual magnitude V < 27.9. Twonew KBOs are discovered. One object having V = 25.5 lies at a probableheliocentric distance d = 33 AU. The second object at V = 27.2 is located at d= 44 AU. Both KBOs have diameters of about 50 km, assuming comet-like albedosof 4%. Data from all surveys are pooled to construct the luminosity function fromred magnitude R = 20 to 27. The cumulative number of objects per square degree,N (< R), is fitted to a power law of the form log_(10) N = 0.52 (R - 23.5).Differences between power laws reported in the literature are due mainly towhich survey data are incorporated, and not to the method of fitting. Theluminosity function is consistent with a power-law size distribution forobjects having diameters s = 50 to 500 km; dn ~ s^(-q) ds, where thedifferential size index q = 3.6 +/- 0.1. The distribution is such that thesmallest objects possess most of the surface area, but the largest bodiescontain the bulk of the mass. Though our inferred size index nearly matchesthat derived by Dohnanyi (1969), it is unknown whether catastrophic collisionsare responsible for shaping the size distribution. Implications of the absenceof detections of classical KBOs beyond 50 AU are discussed.Comment: Accepted to AJ. Final proof-edited version: references added, discussion of G98 revised in sections 4.3 and 5.