Keck Pencil-Beam Survey for Faint Kuiper Belt Objects

We present the results of a pencil-beam survey of the Kuiper Belt using the Keck 10-m telescope. A single 0.01 square degree field is imaged 29 times for a total integration time of 4.8 hr. Combining exposures in software allows the detection of Kuiper Belt Objects (KBOs) having visual magnitude V < 27.9. Two new KBOs are discovered. One object having V = 25.5 lies at a probable heliocentric 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 albedos of 4%. Data from all surveys are pooled to construct the luminosity function from red 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 to which survey data are incorporated, and not to the method of fitting. The luminosity function is consistent with a power-law size distribution for objects having diameters s = 50 to 500 km; dn ~ s^(-q) ds, where the differential size index q = 3.6 +/- 0.1. The distribution is such that the smallest objects possess most of the surface area, but the largest bodies contain the bulk of the mass. Though our inferred size index nearly matches that derived by Dohnanyi (1969), it is unknown whether catastrophic collisions are responsible for shaping the size distribution. Implications of the absence of detections of classical KBOs beyond 50 AU are discussed