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 deg(2) field is imaged 29 times for a t otal integration time of 4.8 hr. Combining exposures in software allows the detection of Kuiper Belt objects (KBOs) having visual magnitude m(V) less than or similar to 27.9. Two new KBOs are discovered. One object having m(V ) = 25.5 lies at a probable heliocentric distance R approximate to 33 AU. T he second object at m(V) = 27.2 is located at R approximate to 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 m(R) = 20 to 27. The cumulative number of objects per square degree, Sigma(<m(R )), is fitted to a power law of the form log(10) Sigma = a(m(R) - 23.5), wh ere the slope alpha = 0.52 +/- 0.02. Differences between slopes reported in the literature are due mainly to which survey data are incorporated in the fit and not to the method of analysis. The luminosity function is consiste nt with a power-law size distribution for objects having diameters s = 50-5 00 km within 50 AU; dN proportional to s-(q) ds, where the differential siz e index q = 3.6 +/- 0.1. We estimate to order of magnitude that 0.2 M+ and 1 x 10(10) comet progenitors lie between 30 and 50 AU. Though our inferred size index nearly matches that derived by Dohnanyi, it is unknown whether c atastrophic collisions are responsible for shaping the size distribution. I mpact strengths may increase strongly with size from 50 to 500 km, whereas the derivation by Dohnanyi assumes impact strength to be independent of siz e. Collisional lifetimes of KBOs having diameters 50-500 km exceed the age of the solar system by at least 2 orders of magnitude in the present-day Be lt, assuming bodies consist of solid, cohesive rock. Implications of the ab sence of detections of classical KBOs beyond 50 AU are discussed.