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 mV ∼< 27.9. Two new KBOs are discovered. One object having mV = 25.5 lies at a probable heliocentric distance R ≈ 33AU. The second object at mV = 27.2 is located at R ≈ 44AU. 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 mR = 20 to 27. The cumulative number of objects per square degree, Σ(< mR), is fitted to a power law of the form log10 Σ = α(mR − 23.5), where the slope α = 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 consistent with a power-law size distribution for objects having diameters s = 50–500 km; dN ∝ s 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. We estimate to order-of-magnitude that 0.2M⊕ and 1× 10 comet progenitors lie between 30 and 50 AU. 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. Impact strengths may increase strongly with size from 50 to 500 km, whereas the derivation by Dohnanyi (1969) assumes impact strength to be independent of size. In the present-day Belt, collisional lifetimes of KBOs having diameters 50–500 km exceed the age of the Solar System by at least 2 orders of magnitude, assuming bodies consist of solid, cohesive rock. Implications of the absence of detections of classical KBOs beyond 50 AU are discussed. Alfred P. Sloan Research Fellow